ANSYS Fluid Dynamics Verification Manual
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Table of Contents I. Verification Test Case Descriptions ..................................................... 1 1. Introduction ................................................................... 3 1.1. Expected Results ............................................................ 3 1.2. References ................................................................. 4 1.3. Using the Verification Manual and Test Cases ........................................ 4 1.4. Quality Assurance Services ..................................................... 5 1.5. Index of ANSYS Fluid Dynamics Test cases ......................................... 5 VMFL001: Flow Between Rotating and Stationary Concentric Cylinders .......................... 9 VMFL002: Laminar Flow Through a Pipe with Uniform Heat Flux ............................... 11 VMFL003: Pressure Drop in Turbulent Flow through a Pipe ................................... 13 VMFL004: Plain Couette Flow with Pressure Gradient ....................................... 15 VMFL005: Poiseuille Flow in a Pipe ..................................................... 19 VMFL006: Multicomponent Species Transport in Pipe Flow .................................. 21 VMFL007: Non-Newtonian Flow in a Pipe ................................................ 23 VMFL008: Flow Inside a Rotating Cavity ................................................. 25 VMFL009: Natural Convection in a Concentric Annulus ..................................... 31 VMFL010: Laminar Flow in a 90° Tee-Junction. ............................................ 35 VMFL011: Laminar flow in a Triangular Cavity ............................................ 39 VMFL012: Turbulent Flow in a Wavy Channel ............................................. 43 VMFL013: Turbulent Flow with Heat Transfer in a Backward-Facing Step ......................... 49 VMFL014: Species Mixing in Co-axial Turbulent Jets ........................................ 51 VMFL015: Flow Through an Engine Inlet Valve ............................................ 55 VMFL016: Turbulent Flow in a Transition Duct ............................................ 59 VMFL017: Transonic Flow over an RAE 2822 Airfoil ......................................... 63 VMFL018: Shock Reflection in Supersonic Flow ........................................... 65 VMFL019: Transient Flow near a Wall Set in Motion ........................................ 71 VMFL020: Adiabatic Compression of Air in Cylinder by a Reciprocating Piston .................... 75 VMFL021: Cavitation over a Sharp-Edged Orifice Case A: High Inlet Pressure ...................... 79 VMFL022: Cavitation over a Sharp-Edged Orifice Case B: Low Inlet Pressure ...................... 83 VMFL023: Oscillating Laminar Flow Around a Circular Cylinder ................................ 87 VMFL024: Interface of Two Immiscible Liquids in a Rotating Cylinder ........................... 89 VMFL025: Turbulent Non-Premixed Methane Combustion with Swirling Air ...................... 91 VMFL026: Supersonic Flow with Real Gas Effects inside a Shock Tube ........................... 99 VMFL027: Turbulent Flow over a Backward-Facing Step .................................... 105 VMFL028: Turbulent Heat Transfer in a Pipe Expansion ..................................... 109 VMFL029: Anisotropic Conduction Heat Transfer ......................................... 111 VMFL030: Turbulent Flow in a 90° Pipe-Bend ............................................ 113 VMFL031: Turbulent Flow Behind an Open-Slit V Gutter .................................... 117 VMFL032: Turbulent Flow with Separation Along an Axisymmetric Afterbody .................... 121 VMFL033: Viscous Heating in an Annulus ............................................... 125 VMFL034: Particle Aggregation inside a Turbulent Stirred Tank ............................... 129 VMFL035: 3-Dimensional Single-Stage Axial Compressor ................................... 131 VMFL036: Turbulent Round Jet ...................................................... 133 VMFL037: Turbulent Flow over a Forward Facing Step ..................................... 137 VMFL038: Falling Film over an Inclined Plane ............................................ 141 VMFL039: Boiling in a Pipe with Heated Wall ............................................ 143 VMFL040: Separated Turbulent Flow in Diffuser .......................................... 145 VMFL041: Transonic Flow Over an Airfoil ............................................... 149 VMFL042: Turbulent Mixing of Two Streams with Different Density ............................ 153 VMFL043: Laminar to Turbulent Transition of Boundary Layer over a Flat Plate ................... 157 Release 14.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.
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ANSYS Fluid Dynamics Verification Manual VMFL044: Supersonic Nozzle Flow .................................................... 161 VMFL045: Oblique Shock over an Inclined Ramp ......................................... 165 VMFL046: Supersonic Flow with Normal Shock in a Converging Diverging Nozzle ................. 167 VMFL047: Turbulent Flow with Separation in an Asymmetric Diffuser .......................... 171 VMFL048: Turbulent flow in a 180° Pipe Bend ........................................... 173 VMFL049: Combustion in an Axisymmetric Natural Gas Furnace .............................. 177 VMFL050: Transient Heat Conduction in a Semi-Infinite Slab ................................ 181 VMFL051: Isentropic Expansion of Supersonic Flow over a Convex Corner ...................... 183 VMFL052: Turbulent Natural Convection inside a Tall Cavity ................................. 185 VMFL053: Compressible Turbulent Mixing Layer ......................................... 189 VMFL054: Laminar flow in a Trapezoidal Cavity .......................................... 191 VMFL055: Transitional Recirculatory Flow inside a Ventilation Enclosure ........................ 195 VMFL056: Combined Conduction and Radiation in a Square Cavity ........................... 197 VMFL057: Radiation and Conduction in Composite Solid Layers .............................. 199 VMFL058: Turbulent Flow in an Axisymmetric Diffuser ..................................... 201 VMFL059: Conduction in a Composite Solid Block ........................................ 203 VMFL060: Transitional Supersonic Flow over a Rearward Facing Step .......................... 205 VMFL061: Surface to Surface Radiative Heat Transfer between Two Concentric Cylinders ........... 209 VMFL062: Fully Developed Turbulent Flow Over a “Hill” .................................... 213 VMFL063: Separated Laminar Flow over a Blunt Plate ...................................... 215 VMFL064: Low Reynolds Number Flow in a Channel with Sudden Asymmetric Expansion ........... 217 VMFL065: Swirling Turbulent Flow Inside a Diffuser ....................................... 219 VMFL066: Radiative Heat Transfer in a Rectangular Enclosure with Participating Medium ........... 221
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Verification Test Case Descriptions
Chapter 1: Introduction The Verification Manual presents a collection of test cases that demonstrate a representative set of the capabilities of the ANSYS Fluid Dynamics product suite. The primary purpose of this manual is to demonstrate a wide range of capabilities in straightforward problems which have 'classical' or readilyobtainable theoretical solutions and in some cases have experimental data for comparison. The close agreement of the ANSYS solutions to the theoretical or experimental results in this manual is intended to provide user confidence in the ANSYS solutions. These problems may then serve as the basis for additional validation and qualification of ANSYS capabilities by the user for specific applications that may be of interest. The ANSYS software suite is continuously being verified by the developers (ANSYS, Inc.) as new capabilities are added to the programs. Verification of ANSYS products is conducted in accordance with written procedures that form a part of an overall Quality Assurance program at ANSYS, Inc. This manual represents a small subset of the Quality Assurance test case library which is used in full when testing new versions of ANSYS FLUENT and ANSYS CFX. This test library and the test cases in this manual represent comparisons of ANSYS solutions with known theoretical solutions, experimental results, or other independently calculated solutions. Since ANSYS FLUENT and ANSYS CFXare programs capable of solving very complicated practical engineering problems having no closed-form theoretical solutions, the relatively simple problems solved in this manual do not illustrate the full capability of these ANSYS programs. In order to solve some test cases will require different product licenses; ANSYS CFD, ANSYS FLUENT or ANSYS CFX. If you do not have the appropriate licenses, you may not be able to reproduce the results.
1.1. Expected Results The test cases in this manual have been modeled to give reasonably accurate comparisons with a low number of elements and iterations. In some cases, even fewer elements and/or iterations will still yield an acceptable accuracy. The test cases employ a balance between accuracy and solution time. An attempt has been made to present a test case and results that are grid independent. If test results are not grid independent, it is due to the need to limit the run time for the test to be in the manual. Improved results can be obtained in some cases by refining the mesh but requires longer solution times. The ANSYS solutions in this manual are compared with solutions or experimental data from textbooks or technical publications. In some cases, the target (theoretical) answers reported in this manual may differ from those shown in the reference. In several fluid flow simulation problems where experimental results are available in the form of plots of the relevant parameters, the simulation results are also presented as plots so that the corresponding values can be compared on the same graph. Many of the fluid dynamics simulation methods have to make use of data available from experimental measurements for their verification primarily because closed form theoretical solutions are not available for modeling the related phenomena. In this manual several test cases for ANSYS FLUENT and ANSYS CFX make use of experimental data published in reputed journals or conference proceedings for verification of the computational results. The experimental measurements for fluid flow systems are often presented in the form of plots of the relevant parameters. Hence the published experimental data for
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Chapter 1: Introduction those cases and the corresponding simulation results are presented in graphical format to facilitate comparison. Experimental data represent the “real world” physics reproduced in a controlled manner and provides more complex details of the flow field than theoretical solutions. The test cases in this manual have been modeled to give reasonably accurate comparisons with experimental data wherever applicable, with a low number of elements and iterations. Different computers and operating systems may yield slightly different results for some of the test cases in this manual due to numerical precision variation from machine to machine. Solutions that are nonlinear, iterative, or have convergence options activated are among the most likely to exhibit machinedependent numerical differences. Because of this, an effort has been made to report an appropriate and consistent number of significant digits in both the target and the ANSYS solution. If you run these test cases on your own computer hardware, be advised that an ANSYS result reported in this manual as 0.01234 may very well show up in your printout as 0.012335271.
1.2. References The goal for the test cases contained in this manual was to have results accuracy within 3% of the target solution. The solutions for the test cases have been verified, however, certain differences may exist with regard to the references. These differences have been examined and are considered acceptable. It should be noted that only those items corresponding to the given theoretical solution values are reported for each problem. In most cases the same solution also contains a considerable amount of other useful numerical solution data. Different computers and different operating systems may yield slightly different results for some of the test cases in this manual, since numerical precision varies from machine to machine. Because of this, an effort has been made to report an appropriate and consistent number of significant digits in both the target and the ANSYS solution. These results reported in this manual are from runs on an Intel Xeon processor using Microsoft Windows XP Professional. Slightly different results may be obtained when different processor types or operating systems are used.
1.3. Using the Verification Manual and Test Cases You are encouraged to use these tests as starting points when exploring features in these products. Geometries, material properties, loads, and output results can easily be changed and the solution repeated. As a result, the tests offer a quick introduction to new features with which you may be unfamiliar. The test cases in this manual are primarily intended for verification of the ANSYS programs. An attempt has been made to include most significant analysis capabilities of the ANSYS products in this manual. Although they are valuable as demonstration problems, the test cases are not presented as step-bystep examples with lengthy data input instructions and printouts. The reader should refer to the online help for complete input data instructions. Users desiring more detailed instructions for solving problems or in-depth treatment of specific topics should refer to the suite of to the ANSYS FLUENT Documentation. ANSYS FLUENT Tutorials and ANSYS CFX Tutorials are also available for various specific topics. These publications focus on particular features or program areas, supplementing other ANSYS reference documents with theory, procedures, guidelines, examples, and references.
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Index of ANSYS Fluid Dynamics Test cases
1.4. Quality Assurance Services For customers who may have further need for formal verification of the ANSYS, Inc. products on their computers, ANSYS, Inc. offers the Quality Assurance Testing Agreement. The user is provided with input data, output data, comparator software, and software tools for automating the testing and reporting process. If you are interested in contracting for such services, contact the ANSYS, Inc. Quality Assurance Group.
1.5. Index of ANSYS Fluid Dynamics Test cases Dimensionality Column Key: 2 -- 2-D 3 -- 3-D A -- 2-D Axisymmetric
VMFL001
2
VMFL002
A
VMFL003
A
VMFL004
2
VMFL005
A
VMFL006
A
VMFL007
A
VMFL008
A
VMFL009
2
VMFL010
2
VMFL011
2
VMFL012
2
X
VMFL013
2
X
VMFL014
A
X
VMFL015
3
X
VMFL016
3
X
VMFL017
2
X
X
X
VMFL018
2
X
X
X
VMFL019
2
X
VMFL020
2
X
VMFL021
A
X
X
X
VMFL022
A
X
X
X
X X
X X X
X
X X
X
X
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Chapter 1: Introduction
VMFL023
2
X
VMFL024
A
X
VMFL025
A
VMFL026
3
VMFL027
2
X
VMFL028
A
X
VMFL029
2
VMFL030
3
X
VMFL031
2
X
VMFL032
A
X
VMFL033
2
VMFL034
2
X
VMFL035
3
X
VMFL036
A
X
VMFL037
2
X
VMFL038
2
VMFL039
A
X
VMFL040
A
X
VMFL041
2
X
VMFL042
2
X
VMFL043
2
X
VMFL044
A
X
VMFL045
2
VMFL046
2
VMFL047
2
X
VMFL048
3
X
VMFL049
A
X
VMFL050
2
VMFL051
2
VMFL052
2
X
VMFL053
2
X
VMFL054
2
VMFL055
2
VMFL056
2
6
X X
X
X
X
X
X
X
X
X X
X
X
X X X
X
X
X
X X X
X
X
X
X X
X
X
X
X
X
X
X
X
X
X
X
X
X
X X
X
X
X X
X
X
X
X X
X
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Index of ANSYS Fluid Dynamics Test cases
VMFL057
2
VMFL058
A
VMFL059
2
VMFL060
2
VMFL061
2
VMFL062
2
VMFL063
2
VMFL064
2
VMFL065
A
VMFL066
2
X
X
X X X
X
X
X X
X
X
X
X
X
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VMFL001: Flow Between Rotating and Stationary Concentric Cylinders
Overview Reference
F. M. White.“Viscous Fluid Flow”. Section 3-2.3. McGraw-Hill Book Co., Inc. New York, NY. 1991.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Laminar flow, rotating wall
Input Files
rot_conc_cyl.cas for ANSYS FLUENT rotating_cylinder.def for ANSYS CFX
Test Case Steady laminar flow between two concentric cylinders is modeled. The flow is induced by rotation of the inner cylinder with a constant angular velocity, while the outer cylinder is held stationary. Due to periodicity only a section of the domain needs to be modeled. In the present simulation a 180° segment (half of the domain shown in Figure 1 (p. 9)) is modeled. The sketch is not to scale.
Figure 1 Flow Domain
y Outer Cylinder r2 x
r1 Inner Cylinder
Material Properties Density = 1 kg/m3 Viscosity = 0.002 kg/m-s
Geometry Radius of the Inner Cylinder = 17.8 mm
Boundary Conditions Angular velocity of the inner wall = 1 rad/s
Radius of the outer Cylinder = 46.8 mm
Analysis Assumptions and Modeling Notes The flow is steady. The tangential velocity at various sections can be calculated using analytical equations for laminar flow. These values are used for comparison with simulation results.
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VMFL001
Results Comparison for ANSYS FLUENT Table 1 Comparison of Tangential Velocity in the Annulus at Various Radial Locations Tangential Velocity at
Target Calculation, m/s
ANSYS FLUENT, m/s
Ratio
r = 20 mm
0.0151
0.0151
0.999
r = 25 mm
0.0105
0.0105
0.996
r = 30 mm
0.0072
0.0072
0.990
r = 35 mm
0.0046
0.0045
0.979
Results Comparison for ANSYS CFX Table 2 Comparison of Tangential Velocity in the Annulus at Various Radial Locations Location
Target Calculation, m/s
ANSYS CFX, m/s
Ratio
r = 20 mm
0.0151
0.0150
0.991
r = 25 mm
0.0105
0.0105
0.998
r = 30 mm
0.0072
0.0071
0.988
r = 35 mm
0.0046
0.0045
0.976
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VMFL002: Laminar Flow Through a Pipe with Uniform Heat Flux
Overview Reference
F. M. White. “Fluid Mechanics ”. 3rd Edition. McGraw-Hill Book Co. New York, NY. 1994. F. P. Incropera and D. P. DeWitt. “Fundamentals of Heat Transfer”. John Wiley & Sons. 1981.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Laminar flow with heat transfer
Input File
laminar-pipe-hotflow.cas for ANSYS FLUENT VMFL002B_VV002CFX.def for ANSYS CFX
Test Case Laminar flow of Mercury through a circular pipe is modeled, with uniform heat flux across the wall. A fully developed laminar velocity profile is prescribed at the inlet. The resulting pressure drop and exit temperature are compared with analytical calculations for Laminar flow. Only half of the 2–D domain is modeled due to symmetry.
Figure 1 Flow Domain
τw
r=R
τ (r)
r Pi
Po Vx (r) Material Properties
Geometry
Fluid: Mercury
Length of the pipe = 0.1 m
Density = 13529
Radius of the pipe = 0.0025 m
kg/m
3
Boundary Conditions Fully developed velocity profile at inlet. Inlet temperature = 300 K Heat Flux across wall = 5000 W/m2
Viscosity = 0.001523 kg/m-s Specific Heat = 139.3 J/kg-K Thermal Conductivity = 8.54 W/m-K
Analysis Assumptions and Modeling Notes The flow is steady and incompressible. Pressure drop can be calculated from the theoretical expression for laminar flow given in Ref. 1. Correlations for temperature calculations are given in Ref. 2.
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VMFL002
Results Comparison for ANSYS FLUENT Table 1 Comparison of Pressure Drop and Outlet Temperature Target Calculation
ANSYS FLUENT
Ratio
Pressure Drop
1.000 Pa
0.999 Pa
0.999
Centerline Temperature at the Outlet
341.00 K
340.50 K
0.999
Results Comparison for ANSYS CFX Table 2 Comparison of Pressure Drop and Outlet Temperature Target Calculation
ANSYS CFX
Ratio
Pressure Drop
1.000 Pa
1.019 Pa
1.019
Centerline Temperature at the Outlet
341.00 K
340.8 K
0.9994
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VMFL003: Pressure Drop in Turbulent Flow through a Pipe
Overview Reference
F. M. White.“Fluid Mechanics”. 3rd Edition. McGraw-Hill Co. New York, NY. 1994.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Turbulent flow, standard k-ε Model
Input File
turb_pipe_flow.cas for ANSYS FLUENT VMFL003B_VV003CFX.def for ANSYS CFX
Test Case Air flows through a horizontal pipe with smooth walls. The flow Reynolds number is 1.37 X 104. Only half of the axisymmetrical domain is modeled.
Figure 1 Flow Domain P1
P2
v Inlet
Outlet ℓ
The figure is not to scale. Material Properties
Geometry Length of the pipe = 2m
Density = 1.225 kg/m3
Boundary Conditions Inlet velocity = 50 m/s Outlet pressure = 0 Pa
Viscosity = 0.001523 kg/m-s
Radius of the pipe = 0.002 m
Analysis Assumptions and Modeling Notes The flow is steady. Pressure drop can be calculated from analytical formula using friction factor f which can be determined for the given Reynolds number from Moody chart. The calculated pressure drop is compared with the simulation results (pressure difference between inlet and outlet).
Results Comparison for ANSYS FLUENT Table 1 Comparison of Pressure Drop in the Pipe
Pressure Drop
Target Calculation
ANSYS FLUENT
Ratio
21789 Pa
21480 Pa
0.988
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VMFL003
Results Comparison for ANSYS CFX Table 2 Comparison of Pressure Drop in the Pipe
Pressure Drop
14
Target Calculation
ANSYS CFX
Ratio
21789 Pa
21740 Pa
0.9975
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VMFL004: Plain Couette Flow with Pressure Gradient
Overview Reference
Munon,Young, Okiishi.“Fundamentals of Fluid Mechanics”. 5th Edition.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Laminar flow, moving wall, periodic boundaries
Input Files
couette_flow.cas for ANSYS FLUENT Couette_Flow.def for ANSYS CFX
Test Case Viscous flow between two parallel plates is modeled. The top plate moves with a uniform velocity while the lower plate is fixed. A pressure gradient is imposed in a direction parallel to the plates.
Figure 1 Flow Domain Moving Wall Periodic Boundaries
Stationary Wall
Material Properties Density = 1 kg/m
3
Viscosity = 1 kg/m-s
Geometry
Boundary Conditions
Length of the domain = 1.5 m
Velocity of the moving wall = 3 m/s in X-direction
Width of the domain = 1 m
For ANSYS FLUENT, pressure gradient across periodic boundaries = -12 Pa/m For ANSYS CFX, pressure gradient across periodic boundaries = -12 Pa/m (pressure change = –18 Pa)
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VMFL004
Analysis Assumptions and Modeling Notes The flow is steady and laminar. Periodic conditions with specified pressure drop are applied across the flux boundaries.
Results Comparison for ANSYS FLUENT Figure 2 Comparison of X-Velocity (m/s) at a Section Where X = 0.75 m
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VMFL004
Results Comparison for ANSYS CFX Figure 3 Comparison of X-Velocity (m/s) at a Section Where X = 0.75 m
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VMFL005: Poiseuille Flow in a Pipe
Overview Reference
F. M. White.“Fluid Mechanics”. 3rd Edition. McGraw-Hill Book Co. New York, NY. 1994.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Steady laminar flow
Input File
poiseuille-flow.cas for ANSYS FLUENT VMFL005B_VV005CFX.def for ANSYS CFX
Test Case Fully developed laminar flow in a circular tube is modeled. Reynolds number based on the tube diameter is 500. Only half of the axisymmetric domain is modeled.
Figure 1 Flow Domain
Inlet
Pipe Wall
Axis
Outlet
Material Properties
Geometry Length of the pipe = 0.1 m
Density = 1 kg/m3 Viscosity = 1e-5 kg/m-s
Boundary Conditions Fully developed laminar velocity profile at inlet with an average velocity of 2.00 m/s
Radius of the pipe = 0.00125 m
Analysis Assumptions and Modeling Notes The flow is steady. A fully developed laminar velocity profile is prescribed at the inlet. Hagen-Poiseuille equation is used to determine the pressure drop analytically.
Results Comparison for ANSYS FLUENT Table 1 Comparison of Pressure Drop in the Pipe
Pressure Drop
Target Calculation
ANSYS FLUENT
Ratio
10. 24 Pa
10.22 Pa
0.998
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VMFL005
Results Comparison for ANSYS CFX Table 2 Comparison of Pressure Drop in the Pipe
Pressure Drop
20
Target Calculation
ANSYS CFX
Ratio
10. 24 Pa
10.49 Pa
1.024
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VMFL006: Multicomponent Species Transport in Pipe Flow
Overview Reference
W. M. Kays and M. E. Crawford.“Convective Heat and Mass Transfer”. 3rd Edition. McGraw-Hill Book Co., Inc. New York, NY. 126-134. 1993.
Solver
ANSYS FLUENT (ANSYS CFX simulation is not available for this case)
Physics/Models
Steady laminar flow, species transport
Input File
Species-diffusion.cas
Test Case Fully developed laminar flow in a circular tube, with two species is modeled. Species A enters at the inlet and species B enters from the wall. Uniform and dissimilar mass fractions are specified at the pipe inlet and wall. Fluid properties are assumed to be the same for both species, so that computed results can be compared with analytical solution.
Figure 1 Flow Domain Inlet
Axis
Pipe Wall Outlet
Material Properties Species A
Length of the pipe = 0.1 m
Density = 1 kg/m3 -5
Viscosity = 1.0 x 10 Pa-s Diffusivity
BA
= 1.43 x 10–5
m2/s
Radius of the pipe = 0.0025 m
Boundary Conditions Fully developed laminar velocity profile at inlet with an average velocity of 1 m/s Mass fraction of species A at pipe inlet = 1.0 Mass fraction of species B at pipe inlet = 0.0 Mass fraction of species A at pipe wall = 0.0
Species B Density = 1 kg/m3 Viscosity = 1.0 x 10-5 Pa-s Diffusivity
Geometry
AB
Mass fraction of species B at pipe wall = 1.0
= 1.43 x 10-5
m2/s
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VMFL006
Analysis Assumptions and Modeling Notes The flow is steady. A fully developed laminar velocity profile is prescribed at the inlet. Species transport model is used.
Results Comparison Table 1 Comparison of Mass Fraction of Species A Along the Axis Axial location (m)
Target Calculation
ANSYS FLUENT
Ratio
0.01
0.8225
0.8223
1.000
0.02
0.7308
0.7307
1.000
0.03
0.6593
0.6592
1.000
0.04
0.5992
0.5991
1.000
0.05
0.5469
0.5469
1.000
0.06
0.5006
0.5006
1.000
0.07
0.4589
0.4591
1.000
0.08
0.4212
0.4214
1.000
0.09
0.3869
0.3871
1.001
0.10
0.3555
0.3558
1.001
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VMFL007: Non-Newtonian Flow in a Pipe
Overview Reference
W. F. Hughes and J. A. Brighton.“Schaum's Outline of Theory and Problems of Fluid Dynamics.” McGraw-Hill Book Co., Inc. New York, NY. 1991.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Steady laminar flow, power law for viscosity
Input File
powerlaw-visc.cas for ANSYS FLUENT VMFL007B_vv007CFX.def for ANSYS CFX
Test Case Flow of a non-Newtonian fluid in a circular pipe is modeled. Viscosity is specified by power law equation.
Figure 1 Flow Domain Inlet
Pipe Wall
Axis
Outlet
Material Properties
Geometry
Boundary Conditions
Density = 1000 kg/m3
Pipe length = 0.1 m
Viscosity: Power law
Pipe diameter = 0.0025 m
Fully developed velocity profile at inlet with an average velocity of 2 m/s
Parameters: k = 10 n = 0.4
Analysis Assumptions and Modeling Notes The flow is steady. Viscosity is specified using non-Newtonian power law equation.
Results Comparison for ANSYS FLUENT Table 1 Comparison of Pressure Drop in the Pipe
Pressure Drop
Target Calculation
ANSYS FLUENT
Ratio
60.52 kPa
60.37 kPa
0.998
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VMFL007
Results Comparison for ANSYS CFX Table 2 Comparison of Pressure Drop in the Pipe
Pressure Drop
24
Target Calculation
ANSYS CFX
Ratio
60.52 kPa
61.52 kPa
1.0165
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VMFL008: Flow Inside a Rotating Cavity
Overview Reference
J. A. Michelsen.“Modeling of Laminar Incompressible Rotating Fluid Flow”. AFM 86-05., Ph.D. thesis. Department of Fluid Mechanics, Technical University of Denmark. 1986.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Laminar flow, Rotating reference frame
Input File
rotcv_RRF.cas for ANSYS FLUENT VMFL008B_rot_cyl.def for ANSYS CFX
Test Case Flow in a cylindrical cavity enclosed with a lid that spins at Ω = 1.0 rad/s. The flow field is 2–D axisymmetric, so only the region bounded by the dashed lines in Figure 1 (p. 25)needs to be modeled. The Reynolds number of the flow based on the cavity radius R and the tip-speed of the disk is 1800.
Figure 1 Flow Domain Rotating Cover
Ω L = 1.0 m R = 1.0 m Ω= 1.0 rad/s
Region to be modeled
L
x y R
Material Properties
Geometry
Density = 1 kg/m3
Height of the cavity = 1m
Viscosity: 0.000556 kg/ms
Radius of cavity = 1m
Boundary Conditions Speed of rotation of the moving wall = 1rad/s Rotational velocity for cell zone = -1rad/s
Analysis Assumptions and Modeling Notes The flow is laminar. The problem is solved using rotating reference frame.
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VMFL008
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Distribution of Radial Velocity Along a Section at X= 0.6 m
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VMFL008
Figure 3 Comparison of Distribution of Swirl Velocity Along a Section at X= 0.6 m
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VMFL008
Results Comparison for ANSYS CFX Figure 4 Comparison of Distribution of Radial Velocity Along a Section at X= 0.6 m
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VMFL008
Figure 5 Comparison of Distribution of Swirl Velocity Along a Section at X= 0.6 m
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VMFL009: Natural Convection in a Concentric Annulus
Overview Reference
Kuehn, T.H. and Goldstein, R.J., An Experimental Study of Natural Convection Heat Transfer in Concentric and Eccentric Horizontal Cylindrical Annuli, Journal of Heat Transfer, 100:635-640, 1978.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Heat transfer, natural convection, laminar flow
Input Files
concn.cas for ANSYS FLUENT ecc_cfx.def for ANSYS CFX
Test Case Natural convection inside a concentric annular domain. The inner wall is maintained at a higher temperature than the outer wall, thereby causing buoyancy induced circulation.
Figure 1 Flow Domain
Top Plane of Symmetry Bottom Plane of Symmetry
Only half of the domain is modeled due to symmetry. Material Properties Density: Incompressible ideal gas
Geometry Radius of outer cylinder = 46.25 mm
Boundary Conditions Inner wall temperature = 373 K Outer wall temperature = 327 K
Viscosity: 2.081 X 10 kg/m-s
Radius of inner cylinder = 17.8 mm
-5
Specific Heat: 1008 J/kg-K
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VMFL009 Material Properties
Geometry
Boundary Conditions
Thermal Conductivity: 0.02967 W/m-K
Analysis Assumptions and Modeling Notes The flow is symmetric and only half of the domain is modeled. Density is calculated based on incompressible ideal gas assumption. The flow is laminar.
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Static Temperature Distribution on the Bottom Wall of Symmetry
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VMFL009
Figure 3 Comparison of Static Temperature Distribution on the Top Wall of Symmetry
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VMFL009
Results Comparison for ANSYS CFX Figure 4 Comparison of Static Temperature Distribution on the Bottom Wall of Symmetry
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VMFL010: Laminar Flow in a 90° Tee-Junction.
Overview Reference
R.E. Hayes, K. Nandkumar, and H. Nasr-El-Din.“Steady Laminar Flow in a 90 Degree Planar Branch”. Computers and Fluids, 17(4). 537-553. 1989.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Laminar flow
Input File
plarb_r4.cas for ANSYS FLUENT VMFL010B_plarb.def for ANSYS CFX
Test Case The purpose of this test is to compare prediction of the fractional flow in a dividing tee-junction with experimental results. The fluid enters through the bottom branch and divides into the two channels whose exit planes are held at the same static pressure.
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VMFL010
Figure 1 Flow Domain Ps= 0
L
L Ps= 0
w
2/3 L
w
v
Table 1 Comparison of Flow Split from Tee Material Properties Fluid: Air
Geometry L=3.0 m
Density : 1 kg/m3 Viscosity: 0.003333 kg/m-s
W=1.0 m
Boundary Conditions Fully developed inlet velocity profile for:
=
000100040002 = 0003
where 00050006 is the inlet centerline velocity. 0007 =
Analysis Assumptions and Modeling Notes The flow is steady and incompressible. Pressure based solver is used. It is seen that with increasing flow rate in the main channel, less fluid escapes through the secondary (right) branch. For analysis of results, we calculate and compare the fractional flow in the upper branch.
Results Comparison for ANSYS FLUENT Table 2 Comparison of Flow Split from Tee
Flow split
36
Target
ANSYS FLUENT
Ratio
0.887
0.884
0.997
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VMFL010
Results Comparison for ANSYS CFX Table 3 Comparison of Flow Split from Tee
Flow split
Target
ANSYS CFX
Ratio
0.887
0.8837
0.9962
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VMFL011: Laminar flow in a Triangular Cavity
Overview Reference
R. Jyotsna and S.P. Vanka.“Multigrid Calculation of Steady, Viscous Flow in a Triangular Cavity”. J. Comp. Phys., 122. 107-117. 1995.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Viscous flow, driven by a moving wall
Input Files
driv.cas for FLUENT driven_cavity.def for ANSYS CFX
Test Case Laminar flow induced by the motion of the top wall of a triangular cavity (Figure 1 (p. 39)). The side walls are stationary.
Figure 1 Flow Domain 2m
U wall = 2 m/s
h=4m
Material Properties
Geometry
Boundary Conditions
Density = 1 kg/m3
Height of the triangular cavity = 4m
Velocity of the top (base) wall = 2 m/s
Viscosity = 0.01 kg/m-s
Width of the base = 2 m
Other walls are stationary
Analysis Assumptions and Modeling Notes The flow is steady. Pressure based solver is used. A hybrid mesh with triangular and quadrilateral cells is used to discretize the domain.
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VMFL011
Results Comparison for FLUENT Figure 2 Comparison of Distribution of Normalized X-Velocity Along a Vertical Line that Bisects the Base of the Cavity
In this figure, X-velocity is normalized by the velocity of the moving wall.
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VMFL011
Results Comparison for ANSYS CFX Figure 3 Comparison of Distribution of Normalized X-Velocity Along a Vertical Line that Bisects the Base of the Cavity
In this figure also the X-velocity is normalized by the velocity of the moving wall.
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VMFL012: Turbulent Flow in a Wavy Channel
Overview Reference
J.D. Kuzan.“Velocity Measurements for Turbulent Separated and Near-Separated Flows Over Solid Waves”. Ph.D. thesis. Dept. Chem. Eng., Univ. Illinois. Urbana, IL. 1986.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Turbulent internal flow with separation and recirculation, periodic boundaries
Input File
wavy.cas for ANSYS FLUENT VMFL012B_VV012.def for ANSYS CFX
Test Case A periodic flow domain bounded on one side by a sinusoidal wavy wall and with a straight wall on the other side. Due to periodicity only a part of the channel needs to modeled. Figure 1 (p. 43) depicts the channel geometry. Flow direction is from left to right.
Figure 1 Flow Domain 1m
Periodic Boundaries D=1m
h = 0.9 m
H = 1.1 m
0.25 m 0.75 m Material Properties
Geometry Amplitude of the sinusoidal wave = 0. 1m
Density = 1 kg/m3 Viscosity = 0.0001 kg/m-s
Boundary Conditions Periodic Conditions: Mass flow rate = 0.816 kg/S
Wave length = 1 m Length of the periodic segment = 1 m
Pressure Gradient = 0.01687141 Pa/m
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VMFL012
Analysis Assumptions and Modeling Notes The flow is steady. Pressure based solver is used. Periodic boundaries are used. For analysis of results, velocity in the x –direction is normalized by the mean mainstream velocity, U = 0.816 m/s, at mean channel height.
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Distribution of Normalized X-Velocity along Transverse Direction at the Wave Crest
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VMFL012
Figure 3 Comparison of Predicted Normalized X-Velocity along Transverse Direction at the Wave Trough
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VMFL012
Results Comparison for ANSYS CFX Figure 4 Comparison of Distribution of Normalized X-Velocity along Transverse Direction at the Wave Crest
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VMFL012
Figure 5 Comparison of Predicted Normalized X-Velocity along Transverse Direction at the Wave Trough
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VMFL013: Turbulent Flow with Heat Transfer in a Backward-Facing Step
Overview Reference
J.C.Vogel and J.K. Eaton.“Combined Heat Transfer and Fluid Dynamic Measurements Downstream of a Backward-Facing Step”. J. Heat Transfer. Vol. 107. 922-929. 1985.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Incompressible, turbulent flow with heat convection and reattachment.
Input File
step_ve.cas for ANSYS FLUENT VMFL013B_vv013.def for ANSYS CFX
Test Case The fluid flow and convective heat transfer over a 2–D backward-facing step is modeled. A constant heat-flux surface behind the sudden expansion leads to a separated and reattaching boundary layer that disturbs local heat transfer. Measured values of the distribution of the local Nusselt number along the heated wall are used to validate the CFD simulation.
Figure 1 Flow Domain
adiabatic walls
4H
.
Q (heated wall) H
3.8 H
30 H
Material Properties for Dry Air
Geometry H=1m
Density = 1 kg/m3
Boundary Conditions Velocity profile at inlet corresponding to ReH = 28,000
Viscosity = 0.0001 kg/m-s Wall heat transfer, Q ˙= 1,000 Conductivity = 1.408 W/m-K
W/m2
Specific Heat = 10,000 J/kgK
Analysis Assumptions and Modeling Notes A Cartesian non-uniform 121 x 61 mesh is used. The flow is steady and incompressible. Fluid properties are considered constant. Pressure based solver is used. The inlet boundary conditions are specified using the fully-developed profiles for the U-velocity, k, and epsilon. The incoming boundary layer thickness is 1.1 H. Under the given pressure conditions, the Reynolds number, ReH is about 28,000 The RNG k-ε model with standard wall functions is used for accounting turbulence.
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VMFL013
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Predicted Local Nusselt Number Distribution Along the Heated Wall with Experimental Data
Results Comparison for ANSYS CFX Figure 3 Comparison of Predicted Local Nusselt Number Distribution Along the Heated Wall with Experimental Data
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VMFL014: Species Mixing in Co-axial Turbulent Jets
Overview Reference
R.W. Schefer and R.W. Dibble. “Simultaneous Measurements of Velocity and Density in a Turbulent Non-premixed Flame”. AIAA Journal, 23. 1070-1078. 1985. R.W. Schefer. “Data Base for a Turbulent, Nonpremixed, Nonreacting PropaneJet Flow”. http://www.sandia.gov/TNF/DataArch/ProJet.html
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Multi-Species flow, turbulent , jet mixing
Input File
san_jet.cas for ANSYS FLUENT VMFL014B_san_jet.def for ANSYS CFX
Test Case A propane jet issues into a co-axial stream of air. There is turbulent mixing between the species in the axisymmetric tunnel. Only half of the domain is considered due to axial symmetry.
Figure 1 Flow Domain D = 0.3 m
L=2m
C3 H8 air
air d o = 11 mm d i = 5.2 mm
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VMFL014 Material Properties Density: Incompressible ideal gas law Viscosity: 1.72X10
–5
kg/m-s
Geometry
Boundary Conditions
Tunnel length = 2 m
Inlet velocity of air = 9.2 m/s
Tunnel diameter = 0.3 m
Inlet velocity of Propane – Specified as fully developed profile
Propane jet tube: Inner diameter = 5.2 mm Outer diameter = 11 mm
Inlet temperature (both streams) = 300 K Temperature at the wall = 300 K
Analysis Assumptions and Modeling Notes The flow is steady. Species mixing is modeled with the three species; propane, oxygen, and nitrogen. There is no reaction.
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Distribution of Propane Along Axis of the Jets
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VMFL014
Figure 3 Comparison of Distribution of X-Velocity Along Axis of the Jets
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VMFL014
Results Comparison for ANSYS CFX Figure 4 Comparison of Distribution of Propane Along Axis of the Jets
Figure 5 Comparison of Distribution of X-Velocity Along Axis of the Jets
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VMFL015: Flow Through an Engine Inlet Valve
Overview Reference
A. Chen, K.C. Lee, M.Yianneskis, and G. Ganti.“Velocity Characteristics of Steady Flow Through a Straight Generic Inlet Port”. International Journal for Numerical Methods in Fluids, 21. 571-590. 1995.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
3–D turbulent flow
Input File
valve10.cas for ANSYS FLUENT VMFL017B_VV017.def for ANSYS CFX
Test Case Flow in an idealized engine cylinder with a straight inlet port and a valve lift of 10 mm (the distance from the top of the cylinder to the bottom of the valve). The configuration of the inlet port, valve, and cylinder is shown in Figure 1 (p. 55).
Figure 1 Flow Domain flow inlet 1.379 kg/s
46
.0
Z
φ
40
o
φ 39.5
y
10 43.0
562
φ 93.65 flow exit
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55
VMFL015 Material Properties Density : 894 kg/m3
Geometry All dimensions shown in Figure 1 (p. 55) are in mm.
Boundary Conditions Inlet velocity = 0.9282 m/s Inlet turbulent intensity = 10%
Viscosity: 0.001529 kg/m-s
Inlet turbulent length scale = 0.046m Outlet gauge pressure = 0 Pa
Analysis Assumptions and Modeling Notes The flow is steady, isothermal and incompressible. The standard k-ε model with standard wall functions is used. The length of the cylinder is chosen to be large enough that it will not affect the flow in the cylinder.
Results Comparison for ANSYS FLUENT Figure 2 (p. 56) and Figure 3 (p. 57) compare ANSYS FLUENT's results with the experimental data (zcomponent of velocity at different heights).
Figure 2 Z-Velocity Component at Z= -5mm
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VMFL015
Figure 3 Z-Velocity Component at Z = +10mm
Results Comparison for ANSYS CFX Figure 4 Z-Velocity Component at Z= -5mm
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VMFL015
Figure 5 Z-Velocity Component at Z = +10mm
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VMFL016: Turbulent Flow in a Transition Duct
Overview Reference
D.O. Davis and F.B. Gessner.“Experimental Investigation of Turbulent Flow Through a Circular-to-Rectangular Transition Duct”. AIAA Journal, 30(2). 367-375. 1992.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
3–D Turbulent flow with separation, Reynolds stress model
Input Files
tranduct-rsm-1.cas for ANSYS FLUENT transition_duct.def for ANSYS CFX
Test Case Turbulent flow through a circular-to-rectangular transition duct having the same inlet and outlet crosssectional areas is modeled. The curvature of the duct walls induces a strong pressure-driven cross-flow that develops into a counter-rotating vortex pair near the short side walls of the duct. Due to symmetry of the flow field, only one fourth of the duct is modeled (as shown in Figure 1 (p. 59)). Station 5 is located 23 m downstream of the inlet.
Figure 1 Flow Domain Station 5
Outlet
Inlet
Material Properties
Geometry
Density: 1 kg/m3
Inlet radius = 1 m
Viscosity: 5.13X10–6 kg/m-s
Length of duct = 35 m
Boundary Conditions Inlet velocity: 1 m/s
Analysis Assumptions and Modeling Notes The flow is steady. Reynolds Stress Model (RSM) is used to model turbulence.
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VMFL016
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Pressure Coefficient at Station 5
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VMFL016
Figure 3 Comparison of Pressure Coefficient Along Centerline of the Duct
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VMFL016
Results Comparison for ANSYS CFX Figure 4 Comparison of Pressure Coefficient Along Centerline of the Duct
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VMFL017: Transonic Flow over an RAE 2822 Airfoil
Overview Reference
P.H. Cook, M.A. McDonald, and M.C.P. Firmin.“AEROFOIL RAE 2822 Pressure Distribution and Boundary Layer and Wake Measurements”. AGARD Advisory Report. No. 138. 1979.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Compressible, turbulent flow
Input File
r2822.cas for ANSYS FLUENT VMFL017B_VV017.def for ANSYS CFX
Test Case Flow over an RAE 2822 airfoil at a free-stream Mach number of 0.73. The angle of attack is 2.79°. The flow field is 2D, compressible (transonic), and turbulent. The geometry of the RAE 2822 airfoil is shown in Figure 1 (p. 63). It is a thick airfoil with a chord length, c, of 1.00 m and a maximum thickness, d, of 0.121 m. The domain extends 55c from the airfoil, so that the presence of the airfoil is not felt at the outer boundary.
Figure 1 Geometry of the RAE 2822 Airfoil x
0.121 m
1.00 m Mach Number = 0.73 Re = 6.5 x 10^6 Angle of Attack = 2.79 degrees Static Pressure = 43765 Inlet Temperature = 300 K Turbulent Intensity =0.05% Turbulent Viscosity Ratio = 10
Material Properties
Geometry
Boundary Conditions
Fluid: Air
Chord length = 1 m
The inlet conditions are:
Maximum thickness = 0.121 m
Mach number = 0.73
•
Density: Ideal Gas -5
•
Viscosity: 1.983x10 kg/m-s
•
Thermal conductivity: 0.0242 W/m-K
•
Molecular Weight: 28.966
•
Specific Heat: 1006.43 J/kg-K
Re = 6.5 x 106 Static pressure = 43765 Pa Inlet temperature = 300 K
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VMFL017 Material Properties
Geometry
Boundary Conditions Turbulent intensity = 0.05 % Turbulent viscosity ratio = 10
Analysis Assumptions and Modeling Notes The implicit formulation of the density-based solver is used. The SST k-ω turbulence model is used to account for turbulence effects. The problem is solved in steady state mode.
Results Comparison for ANSYS FLUENT Table 1 Comparison of Coefficients Coefficients
Target
ANSYS FLUENT
Ratio
Drag
0.0168
0.0165
0.982
Lift
0.803
0.783
0.975
Results Comparison for ANSYS CFX Table 2 Comparison of Coefficients Coefficients
Target
ANSYS CFX
Ratio
Drag
0.0168
0.0165
0.982
Lift
0.803
0.7825
0.974
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VMFL018: Shock Reflection in Supersonic Flow
Overview Reference
H. B. Hopkins, W. Konopka, and J. Leng. Validation of scramjet exhaust simulation technique at Mach 6. NASA Contractor Report 3003. 1979.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Reflecting shocks in supersonic flow; Compressible turbulent flow
Input File
scram-nozzle-flow.cas for ANSYS FLUENT VMFL018B_VV018.def for ANSYS CFX
Test Case Supersonic flow from a nozzle that represents the exhaust nozzle of a supersonic combustion ramjet (SCRAMJET) is modeled. Jet from the nozzle is issued into a domain which is bounded on one side by an afterbody wall which is parallel to the centerline of the nozzle. Shocks propagating from the nozzle exit reflect from the afterbody. Measured values of (i) the distribution of wall pressure and (ii) heat transfer rate along the afterbody are used to validate the CFD simulation.
Figure 1 Flow Domain
cowl wall
D=1.524 cm
M=1.66 P=Pe To=477.8 K
afterbody
Tw=328 K Material Properties
Geometry
Density: Ideal Gas
D = 1.524 cm
Molecular Weight: 113.2
Length of cowl = 3.5 D
-5
Viscosity: 1.7894 X 10 kg/m-s Thermal Conductivity: 0.0242 w/m-K Specific Heat: Temperature Dependent
Boundary Conditions Inlet Total Pressure (gauge) = 551600 Pa Inlet Static Pressure (gauge) = 127100 Pa Inlet Total Temperature = 477.8 K Inlet Turbulent Intensity = 2 % Wall temperature = 328 K Outlet Pressure (gauge) = 2780 Pa
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VMFL018
Analysis Assumptions and Modeling Notes The flow is steady. Specific heat is defined as a linear function of temperature. Density based solver is used. Under the given pressure conditions, the inlet Mach number is about 1.66.
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Predicted Static Pressure Distribution on the Afterbody with Experimental Data
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VMFL018
Figure 3 Comparison of Predicted Total Heat Flux Along the Afterbody with Experimental Data
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VMFL018
Results Comparison for ANSYS CFX Figure 4 Comparison of Predicted Static Pressure Distribution on the Afterbody with Experimental Data
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VMFL018
Figure 5 Comparison of Predicted Total Heat Flux Along the Afterbody with Experimental Data
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VMFL019: Transient Flow near a Wall Set in Motion
Overview Reference
Boundary Layer Theory, H. Schlichting & K. Gersten, 8th Edition, 1999; Page 126-127.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Unsteady flow, moving wall
Input File
VMFL019_FLUENT.cas for ANSYS FLUENT VMFL019_CFX.def for ANSYS CFX
Test Case Flow near a wall suddenly set into motion is modeled. The start up flow is modeled as a transient problem with a constant wall-velocity at t (time) > 0. The flow is highly viscous and the velocity is 0 at t= 0.
Figure 1 Flow Domain
Fixed Wall
Inlet
Outlet
Moving Wall
Material Properties Density = 1000 kg/m3
Geometry Dimensions of the domain: 0.75 m X 0.3 m
Viscosity = 1 kg/m-s
Boundary Conditions Velocity of the moving wall = 0.02 m/s Gauge Pressure at Inlet = 0 N/m2 Gauge Pressure at Outlet = 0 N/m2
Analysis Assumptions and Modeling Notes The density based solver is used in ANSYS FLUENT. Pressure boundaries are specified to model the driving head in the direction of flow. The fluid is at rest initially (t = 0). The similarity parameter is defined as: η(
)=
(
ν
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VMFL019 Where ν is the kinematic viscosity.
Results Comparison using ANSYS FLUENT Figure 2 Comparison of Velocity Profile Near the Wall at Outlet
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VMFL019
Results Comparison using ANSYS CFX Figure 3 Comparison of Velocity Profile Near the Wall at Outlet
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VMFL020: Adiabatic Compression of Air in Cylinder by a Reciprocating Piston
Overview Reference
L. D. Russell and G. A. Adebiyi.“Classical Thermodynamics”. Saunders College Publishing. Philadelphia, PA (Now Oxford University Press). 1993.
Solver
ANSYS FLUENT (ANSYS CFX simulation is not available for this case)
Physics/Models
Dynamic Mesh, Transient flow with ideal gas effects
Input File
box2d_remesh.cas
Test Case Air undergoes adiabatic compression due to the movement of a piston inside a rectangular box, representing a cylinder geometry in 2–D as shown in Figure 1 (p. 75). The Top Dead Center (TDC) corresponds to a crank angle of 360°. The piston moves back after reaching TDC.
Figure 1 In-Cylinder Piston Description
ϑ crank angle
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VMFL020
Figure 2 Flow Domain 8m
TDC
10 m
8m
BDC
PISTON Material Properties Ideal gas law for density Viscosity = 1.7894 X 10–5 kg/m-s
Geometry Length of the block = 10 m
Boundary Conditions Movement of the piston modeled using deforming mesh
Width of the block = 8 m
Analysis Assumptions and Modeling Notes The compression within the cylinder is assumed to be adiabatic. The Spring-based smoothing method with local remeshing is used for modeling the dynamic mesh motion.
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VMFL020
Results Comparison Figure 3 Comparison of Static Temperature Variation with Time
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VMFL020
Figure 4 Comparison of Static Pressure Variation with Time
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VMFL021: Cavitation over a Sharp-Edged Orifice Case A: High Inlet Pressure
Overview Reference
W.H. Nurick.“Orifice Cavitation and Its Effects on Spray Mixing”. Journal of Fluids Eng. Vol.98. 681-687. 1976.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Turbulent multiphase flow with cavitation and phase change
Input File
cav_orifice_HP.cas for ANSYS FLUENT VMFL021B_VV021.def for ANSYS CFX
Test Case A steady, axisymmetric, multiphase (water/steam) flow, with phase change taking place. Due to sudden contraction a low pressure region occurs near the sharp edge which results in cavitation. Figure 1 (p. 79)depicts the orifice geometry. Flow direction is from left to right.
Figure 1 Flow Domain L2
L1
P1
vapor liquid jet
P2 r2
r1
Material Properties Liquid: Water Density : 1000 kg/m3 Viscosity: 0.001 kg/ms Gas: Water-Vapor Density: 0.02558 kg/m3
Geometry
Boundary Conditions
L1 = 1.60 cm
P1 = 250,000,000 Pa
L2 = 3.20 cm
P2 = 95,000 Pa T = 300 K
r1 = 1.15 cm
Pvapor = 3,540 Pa
r2 = 0.40 cm
Viscosity: 1.26x10-6 kg/m-s
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VMFL021
Analysis Assumptions and Modeling Notes The flow is steady and incompressible. Pressure based solver is used. Standard k-ε model with standard wall functions is used for turbulence. The Zwart-Gerber-Belamri cavitation model is applied together with mixture multiphase model. For analysis of results, we calculate and compare the discharge coefficient with the experimental data. The coefficient of discharge, maximum mass flow rate:
0001, is the ratio of the mass flow rate through the nozzle to the theoretical
0004 00020003 = 0005 0006 0007 − 0007 In the above equation, 000e is the mass flow rate as calculated by the CFD solver.
Results Comparison for ANSYS FLUENT Table 1 Comparison of Discharge Coefficient
Coefficient of Discharge
Target
ANSYS FLUENT
Ratio
0.620
0.631
1.018
Figure 2 Contours of Liquid (Water) Volume Fraction
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VMFL021
Results Comparison for ANSYS CFX Table 2 Comparison of Discharge Coefficient
Coefficient of Discharge
Target
ANSYS CFX
Ratio
0.620
0.6429
1.037
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VMFL022: Cavitation over a Sharp-Edged Orifice Case B: Low Inlet Pressure
Overview Reference
W.H. Nurick.“Orifice Cavitation and Its Effects on Spray Mixing”. Journal of Fluids Eng. Vol.98. 681-687. 1976.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Turbulent multiphase flow with cavitation and phase change
Input File
cav_orifice_LP.cas for ANSYS FLUENT VMFL022B_VV022.def for ANSYS CFX
Test Case A steady, axisymmetric, multiphase (water/steam) flow, with phase change taking place. Due to sudden contraction a low pressure region occurs near the sharp edge which results in a weak cavitation. Figure 1 (p. 83) depicts the orifice geometry. Flow direction is from left to right.
Figure 1 Flow Domain L2
L1
vapor
P1
liquid jet
r2
r1
Material Properties Liquid: Water Density: 1000 kg/m3 Viscosity: 0.001 kg/ms Gas: Water-Vapor Density: 0.02558 kg/m3
P2
Geometry L1 = 1.60 cm
Boundary Conditions P1 = 250,000 Pa P2 = 95,000 Pa
L2 = 3.20 cm r1 = 1.15 cm
T = 300 K Pvapor = 3,540 Pa
r2 = 0.40 cm
Viscosity: 1.26x10-6 kg/m-s
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VMFL022
Analysis Assumptions and Modeling Notes The flow is steady and incompressible. Pressure based solver is used. Standard k-ε model with standard wall functions is used for turbulence. The Zwart-Gerber-Belamri cavitation model is applied together with mixture multiphase model. For analysis of results, we calculate and compare the discharge coefficient with the experimental data. The coefficient of discharge, maximum mass flow rate:
0001, is the ratio of the mass flow rate through the nozzle to the theoretical
0004 00020003 = 0005 0006 0007 − 0007 In the above equation, 000e is the mass flow rate as calculated by the CFD solver.
Results Comparison for ANSYS FLUENT Table 1 Comparison of Discharge Coefficient Target Coefficient of Discharge
0.780
ANSYS FLUENT 0.777
Figure 2 Contours of Liquid (Water) Volume Fraction
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Ratio 0.996
VMFL022
Results Comparison for ANSYS CFX Table 2 Comparison of Discharge Coefficient
Coefficient of Discharge
Target
ANSYS CFX
Ratio
0.780
0.8051
1.032
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VMFL023: Oscillating Laminar Flow Around a Circular Cylinder
Overview Reference
F. M. White. “Fluid Mechanics”. 3rd Edition. McGraw-Hill Book Co. New York, NY. 1994. S.J. Kim and C.M. Lee. “Numerical Investigation of Cross-Flow Around a Circular Cylinder at a Low-Reynolds Number Flow Under an Electromagnetic Force”. KSME International Journal. Vol 16. No. 3. 363-375. 2002.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Laminar, transient flow
Input File
cyl_2d.cas for ANSYS FLUENT VMFL023B_osc_cyl.def for ANSYS CFX
Test Case The purpose of this case is to validate the ability of ANSYS FLUENT and ANSYS CFX to predict the flow structure as well as the reattachment length and Strouhal number against experimental results. The present calculations are confined to the low-Reynolds-number regime (Re = 100), which encompasses unsteady asymmetric flow.
Figure 1 Flow Domain
D 10D
Flow U∞ = 1 m/s
y
20D
x
Table 1 Materials, Geometry, and Boundary Conditions Material Properties Density: 1 kg/m
3
Geometry Diameter of the cylinder = 2m
Boundary Conditions U
∞
= 1 m/s
Viscosity: 0.02 kg/m-s
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VMFL023
Analysis Assumptions and Modeling Notes The flow is laminar, and unsteady. An FFT analysis of the lift coefficient on the cylinder wall is presented to determine the frequency of oscillations. The Strouhal number corresponding to the maximum magnitude of oscillations is presented in the Table below.
Results Comparison for ANSYS FLUENT The formula for the Strouhal number is S = (N * D)/U∞, where N is the frequency, D is the diameter of the cylinder, and U∞ is the freestream velocity.
Table 2 Predicted Strouhal Number for Re = 100
Strouhal Number
Target
ANSYS FLUENT
Ratio
0.165
0.173
1.048
Target
ANSYS CFX
Ratio
0.165
0.172
1.040
Results Comparison for ANSYS CFX Table 3 Predicted Strouhal Number for Re = 100
Strouhal Number
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VMFL024: Interface of Two Immiscible Liquids in a Rotating Cylinder
Overview Reference
T. Sugimoto and M. Iguchi.“Behavior of Immiscible Two Liquid Layers Contained in Cylindrical Vessel Suddenly Set in Rotation”. ISIJ Int., 42. 338-343. 2002.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Multiphase (Volume of Fluid), transient flow, body force
Input File
rot-cyl_2liq_vof.cas for ANSYS FLUENT VMFL024B_rot_cyl.def for ANSYS CFX
Test Case Laminar interface between two immiscible liquids, water and silicon oil, inside a vertical cylinder which is set in rotation starting from a state of rest. The silicone oil layer rests on top of the water due to its lower density. The cylinder is sealed at the top. The vessel is set to rotate with a constant angular velocity.
Figure 1 Flow Domain ω
Hso
Silicone Oil
Hw
Water
120 mm
g
φ 46 mm
Table 1 Materials, Geometry, and Boundary Conditions Material Properties Water :
Geometry Diameter of the cylinder = 46mm
Boundary Conditions All walls are set up at rotational speed of 2.39577 rad/s
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VMFL024 Material Properties Density: 1030 kg/m3
Geometry
Boundary Conditions
Height of the cylinder = 120 mm
Viscosity: 0.0103 kg/m-s Silicon Oil: Density: 935 kg/m3 Viscosity: 0.00935 kg/m-s
Analysis Assumptions and Modeling Notes The flow is laminar, unsteady and axisymmetric. Non-dimensionalized swirl velocity, defined as Swirl velocity / (Rotational speed X Cylinder radius) is used to validate the results.
Results Comparison for ANSYS FLUENT Table 2 Comparison of the Non-Dimensional Swirl Velocity at Various Radial Locations (for a Given Axial Location, X = 20mm) at Time t = 80 s Radial locations (at x = 20 mm)
Target
ANSYS FLUENT
Ratio
4.83 mm
0.21
0.2093
0.997
9.43 mm
0.41
0.4109
1.002
14.26 mm
0.62
0.6221
1.003
Results Comparison for ANSYS CFX Table 3 Comparison of the Non-Dimensional Swirl Velocity at Various Radial Locations (for a Given Axial Location, X = 20mm) at Time t = 80 s Radial locations (at x = 20 mm)
Target
ANSYS CFX
Ratio
4.83 mm
0.21
0.2093
0.997
9.43 mm
0.41
0.4109
1.002
14.26 mm
0.62
0.6221
1.003
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VMFL025: Turbulent Non-Premixed Methane Combustion with Swirling Air
Overview Reference
P.A.M. Kalt, Y.M. Al-Abdeli, A.R. Masri, and R.S. Barlow . “Swirling turbulent nonpremixed flames of methane: Flow field and compositional structure”. Proc. Combust. Inst., 29. 1913-1919. 2002. Y.M. Al-Abdeli and A.R. Masri. “Stability Characteristics and Flow Fields of Turbulent Swirling Jet Flows”. Combust. Theory and Modeling, 7. 731-766. 2003.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Turbulent swirling flow with reaction, non-premixed combustion model, Radiation heat transfer, Discrete ordinates method
Input File
non-premix_17k-final.cas for ANSYS FLUENT VMFL025B_CFX for ANSYS CFX
Test Case Air and Methane enter as separate streams into an annular chamber. Air issues as a swirling jet and also as a separate co-flowing stream with axial velocity. Both the air streams are free of methane. Species mixing and combustion take place in the axisymmetric chamber. Radiative heat transfer is taken into account.
Figure 1 Flow Domain co-flowing air inlet
outlet
swirling air inlet
axis
methane inlet
Material Properties Species mixture properties specified through PDF file Viscosity: 1.72 x 10 kg/m-s
-05
Refractive Index = 1
Geometry
Boundary Conditions
The fuel (methane only) inlet has a diameter of 3.6 mm.
Methane inlet velocity: 32.7 m/s
The air inlet for the annular shroud has an inner diameter of 50mm and an outer diameter of 60 mm.
Axial velocity of swirling air: 38.2 m/s
Co-flowi ng air inlet has an outer diameter of 310 mm.
Co-flowing air velocity: 20 m/s
Swirl velocity of air: 19.1 m/s
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VMFL025 Material Properties
Geometry
Boundary Conditions Walls are adiabatic
Analysis Assumptions and Modeling Notes The flow is steady. Realizable k-ε is used to model turbulence. Discrete ordinates method used to model radiation. The walls are treated as adiabatic. Non-premixed combustion model is used to model reactions.
Results Comparison ANSYS FLUENT Figure 2 Comparison of Axial Velocity at X = 40mm
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VMFL025
Figure 3 Comparison of Swirl Velocity at X = 40mm
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VMFL025
Figure 4 Comparison of Temperature at X = 40mm
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VMFL025
Figure 5 Comparison of Mass Fraction of CO at X = 40mm
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VMFL025
Results Comparison for ANSYS CFX Figure 6 Comparison of Axial Velocity at X = 40mm
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VMFL025
Figure 7 Comparison of Swirl Velocity at X = 40mm
Figure 8 Comparison of Temperature at X = 40mm
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VMFL025
Figure 9 Comparison of Mass Fraction of CO at X = 40mm
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VMFL026: Supersonic Flow with Real Gas Effects inside a Shock Tube
Overview Reference
K. Mohamed and M. Paraschivoiu.“Real Gas Numerical Simulation of Hydrogen Flow”. 2nd International Energy Conversion Engineering Conference. Providence, Rhode Island. Aug. 16-19, 2004.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Transient Compressible flow, Real Gas effects, Shock
Input File
realgas_shock-tube.cas for ANSYS FLUENT VMFL026B_CFX.def for ANSYS CFX
Test Case Transient flow inside a hydrogen filled shock tube is modeled. A diaphragm separating regions of high and low pressures ruptures at t = 0 thereby creating a shock wave in the tube.
Figure 1 Flow Domain
L = 1.0 m 2 Area = 0.01 m
L
Table 1 Materials, Geometry, and Boundary Conditions Material Properties Density is specified using the Aungier-Redlich-Kwong real gas model
Geometry Length of the tube = 1 m
Boundary Conditions Cell zone conditions are specified with high pressure and low pressure properties of hydrogen
Area of cross section = 0.01 m2
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VMFL026
Analysis Assumptions and Modeling Notes The flow is compressible and unsteady by nature. Real gas effects are significant in the pressure range considered here.
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Static Temperature Along Centerline of the Tube
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VMFL026
Figure 3 Comparison of Static Pressure Along Centerline of the Tube
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VMFL026
Results Comparison for ANSYS CFX Figure 4 Comparison of Static Temperature Along Centerline of the Tube
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VMFL026
Figure 5 Comparison of Static Pressure Along Centerline of the Tube
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VMFL027: Turbulent Flow over a Backward-Facing Step
Overview Reference
D.M. Driver and H.L. Seegmiller. 'Features of a Reattaching Turbulent Shear Layer in Divergent Channel Flow'. AIAA Journal. Vol. 23, No. 2. 163-171. Feb. 1985.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
2-D turbulent flow with separation and reattachment, realizable k-ε model
Input File
drivseeg-rke-neqwf.cas for ANSYS FLUENT VMFL027B_step.def for ANSYS CFX
Test Case Turbulent flow over a backward facing step is modeled. The flow separates at the step and reattaches on the wall downstream, enclosing a region of recirculation. The inlet is at 4 H upstream and the outlet at 30 H downstream from the location of the step, where H is the step height. Reynolds number based on the step-height is about 28,000.
Figure 1 Flow Domain
Inlet
Outlet
Step
Table 1 Materials, Geometry, and Boundary Conditions Material Properties
Geometry
Density : 1 kg/m3
Step height = 1m
Viscosity: 0.0001 kg/m-s
Total length of the channel = 34 m
Boundary Conditions Inlet velocity specified as fully developed turbulent velocity profile
Height of the channel = 9 m
Analysis Assumptions and Modeling Notes The flow is steady. Realizable k-ε model was used to model turbulence.
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VMFL027
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Skin Friction Coefficient Along the Wall
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VMFL027
Results Comparison for ANSYS CFX Figure 3 Comparison of Skin Friction Coefficient Along the Wall
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VMFL028: Turbulent Heat Transfer in a Pipe Expansion
Overview Reference
Baughn et al.“Local Heat Transfer Downstream of an Abrupt Expansion in a Circular Channel With Constant Wall Heat Flux”. Journal of Heat Transfer, 106. 789-796. 1984.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Heat transfer, turbulent flow with recirculation and reattachment
Input File
bghnexp.cas for ANSYS FLUENT VMFL028B_pipe_expansion.def for ANSYS CFX
Test Case Fully developed turbulent flow through an axisymmetric pipe expansion is modeled. The flow reattaches to the pipe wall downstream of the expansion, enclosing a zone of recirculation. The pipe wall downstream of the expansion is heated at a constant rate. Inlet to the computational domain is placed at 1 step height upstream of the expansion and the outlet at 40 step-heights downstream.
Figure 1 Flow Domain q” = 0.3 W/m 2
q” = 0 W/m 2
H=1m
pressure outlet
R velocity inlet
r
axis
H
40 H x
Material Properties
Geometry Pipe radius before expansion = 0.667 m
Density: 1.225 kg/m3 Viscosity: 1.68318e-5kg/m-s Specific Heat: 1006.43 J/kg-K
Pipe radius after expansion = 1.6667 m
Thermal Conductivity: 0.0242 W/m-K
Boundary Conditions Inlet velocity: Specified by fully developed turbulent velocity profile Inlet temperature = 273 K Heat flux across the wall after expansion = 0.3 W/m2
Analysis Assumptions and Modeling Notes Steady flow in axisymmetric domain. The wall upstream of expansion is adiabatic.
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VMFL028
Results Comparison for ANSYS FLUENT Figure 2 Nusselts Number Variation along the Heat Wall
Results Comparison for ANSYS CFX Figure 3 Nusselts Number Variation along the Heat Wall
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VMFL029: Anisotropic Conduction Heat Transfer
Overview Reference Solver
ANSYS FLUENT (ANSYS CFX simulation is not available for this case)
Physics/Models
Heat conduction, anisotropic conductivity
Input File
aniso.cas
Test Case Heat conduction in a solid with anisotropic thermal conductivity is modeled. A square domain is considered. Two opposite walls are maintained at uniform temperatures. Conductivity of the solid material is specified using matrix components to account for the anisotropy. The simulation results are compared with analytical solution for temperature distribution.
Figure 1 Domain
Material Properties Density of solid = 2719 kg/m3
Geometry Dimensions of the domain: 1m X 1 m
Specific heat = 871 J/kg-K Thermal conductivity: Anisotropic
Boundary Conditions Fixed wall temperatures = 100 K and 200K respectively User-defined profile for temperature distribution on the other two walls
Analysis Assumptions and Modeling Notes Steady state conduction. Anisotropic conductivity modeled by specified matrix components for the solid conductivity.
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VMFL029
Results Comparison Figure 2 Comparison of Temperature Distribution at X = 0.5 m
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VMFL030: Turbulent Flow in a 90° Pipe-Bend
Overview Reference
M. M. Enayet, M. M. Gibson, A. M. K. P. Taylor, and M. Yianneskis. “Laser-Doppler Measurements of Laminar and Turbulent Flow in a Pipe Bend”. Znt. J. Heat & Fluid Flow. Vol. 3. 213-219. 1982.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
3–D Turbulent flow with separation, RNG k-ε model with non-equilibrium wall functions
Input File
pipebnd-rng-noneq.cas for ANSYS FLUENT VMFL030B_vv030.def for ANSYS CFX
Test Case Turbulent flow through a 90° circular pipe bend is modeled. The flow separates and reattaches around the bend. Due to symmetry of the flow field only half of the domain is modeled. Velocity profile at an angle of 75° (as measured from the inlet) is used to validate the simulation.
Figure 1 Flow Domain plane at 75 deg symmetry plane outlet
inlet
Z
Y X
Material Properties Density: 1 kg/m
Geometry Radius of the pipe = 0.5 m
3
Viscosity: 2.3256 x 10-05 kg/m-s
Boundary Conditions Inlet velocity: Fully developed turbulent profile for z-velocity. Non components in other directions
Analysis Assumptions and Modeling Notes The flow is steady. RNG k- ε is used to model turbulence along with non-equilibrium wall functions.
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VMFL030
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Velocity Magnitude (m/s) at 75° Along the Bend
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VMFL030
Results Comparison for ANSYS CFX Figure 3 Comparison of Velocity Magnitude (m/s) at 75° Along the Bend
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VMFL031: Turbulent Flow Behind an Open-Slit V Gutter
Overview Reference
J.-T. Yang and G.-L. Tsai. “Near-wake flow of a v-gutter with slit bleed”. Journal of Fluid Engineering. Vol. 115. 13-20. March, 1993.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Turbulent flow
Input File
spltvee.cas for ANSYS FLUENT VMFL031B_veesplit.def for ANSYS CFX
Test Case The near-wake flow structure behind an open-slit V gutter at airflow speed of 20 m/s is modeled. The interaction between the flow penetrating through the open slit and the shear layer results in an asymmetric wake flow structure. The size of the entire recirculation zone shifts toward one of the two wings due to the Coand effect.
Figure 1 Flow Domain
a
φ
H
b
L
Material Properties
Geometry L = 40 cm
Density: 1 kg/m3 Viscosity: 1.8333 X 10-05 kg/m-s
H = 10 cm a=2 mm
Boundary Conditions uinlet = 20 m/s kinlet = 0.04335 m2/s2 εinlet = 0.2119 m2/s3
b = 22 mm ø= 45°
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VMFL031
Analysis Assumptions and Modeling Notes Steady, turbulent, incompressible flow. The standard k-ε model is used for turbulence.
Results Comparison for ANSYS FLUENT The x-velocity at x = 22 mm downstream of the split-V-gutter, is compared with experimental data.
Figure 2 X-Velocity at x = 22 mm Downstream of the V-Gutter
Figure 3 The Coand Effect
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VMFL031
Results Comparison for ANSYS CFX Figure 4 X-Velocity at x = 22 mm Downstream of the V-Gutter
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VMFL032: Turbulent Flow with Separation Along an Axisymmetric Afterbody
Overview Reference
T.T. Huang and N.C. Groves. “Propeller/stern boundary layer interaction on axisymmetric bodies: Theory and experiment”. David W. Taylor Naval Ship Research and Development Center Rep. 76-0113. 1976.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Turbulent flow
Input File
axiaft.cas for ANSYS FLUENT VMFL032B_afterbody.def for ANSYS CFX
Test Case Flow past an axisymmetric afterbody, representing the hull of ship. The flow separates on the rear face of the body.
Figure 1 Flow Domain
Inlet
Outlet
Axis Afterbody (wall) Material Properties Density: 1 kg/m3 Viscosity: 1 X 10–6 kg/m-s
Geometry
Boundary Conditions
Length of the afterbody = 1.0 m
Fully developed turbulent velocity profile on the inlet normal to axis
Maximum radius of the afterbody = 0.04556 m
Axial velocity = 5.9 m/s on the inlet parallel to axis
Analysis Assumptions and Modeling Notes The far-field boundary of the domain is set parallel to the axis and is modeled as velocity inlet. Fully developed profile is specified at the transverse velocity inlet.
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VMFL032
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Pressure Coefficient Along the Afterbody Wall
Figure 3 Comparison of Skin Friction Coefficient Along the Afterbody Wall
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VMFL032
Results Comparison for ANSYS CFX Figure 4 Comparison of Pressure Coefficient Along the Afterbody Wall
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VMFL032
Figure 5 Comparison of Skin Friction Coefficient Along the Afterbody Wall
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VMFL033: Viscous Heating in an Annulus
Overview Reference
R. B. Bird, W. E. Stewart, and E. N. Lightfoot.“Transport phenomena”. John Wiley and Sons. New York. 1960.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Viscous flow and heating driven by a moving wall
Input File
plate_polar.cas for ANSYS FLUENT VMFL033B_CFX.def for ANSYS CFX
Test Case In this problem, we model the viscous heating and mass flow in a 2-D annulus induced by the rotation of one of the two walls (Figure 1 (p. 125)). This problem can be solved analytically.
Figure 1 Geometry r1
r2
Ω1 Ω2
Material Properties Density: 1 kg/m3
Geometry
Boundary Conditions
r1= 1 m
Ω1 = 0.0 rad/s Ω2 = 0.5 rad/s
Specific heat: 1 J/kg-K Thermal conductivity: 1 W/m-K Viscosity: 300 kg/m-s
r2 = 2 m
T1 = 273 K T2 = 274 K
Analysis Assumptions and Modeling Notes The flow is laminar and steady. Pressure based solver is used. A 2–D mesh with quadrilateral cells is used to discretize the domain.
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VMFL033
Results Comparison for ANSYS FLUENT Normalized velocity and temperature profiles are compared with the analytical solution provided by Bird et al (1960).
Figure 2 Comparison of Velocity Profile
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VMFL033
Figure 3 Comparison of Temperature Profile
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VMFL033
Results Comparison for ANSYS CFX Figure 4 Comparison of Velocity Profile
Figure 5 Comparison of Temperature Profile
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VMFL034: Particle Aggregation inside a Turbulent Stirred Tank
Overview Reference
B. Wan, T.A. Ring, K. Dhanasekharan, and J. Sanyal.“Comparison of Analytical Solutions for CMSMPR Crystallizer with QMOM Population Balance Modeling in ANSYS FLUENT”. China Particuology. Vol. 3(4). 213-218. 2005.
Solver
ANSYS FLUENT (ANSYS CFX simulation is not available for this case)
Physics/Models
Multi-phase, Population balance model, turbulent flow
Input File
agglomeration.cas
Test Case A 2-D approximation of a stirred tank is simulated in order to verify the population balance model that operates in conjunction with its multiphase calculations to predict the particle size distribution within the flow field. The flow rate at the inlet is equal to that at the outlet, allowing the mean residence time to be calculated from the inlet flow rate (velocity x inlet area) and the “volume” (box area x unit depth) of the box. To simulate the agitation in the tank the top and bottom walls are assumed to move in the direction of the outlet. The flow is turbulent, steady, and incompressible. Multi-phase, with QMOM population balance model is used for particle aggregation. The standard k-ε model is used for turbulence.
Figure 1 Flow Domain
Material Properties
Geometry
Boundary Conditions
Density: 998.2 kg/m3
Square box side = 0.1 m
Top wall velocity: 101 m/s
Viscosity: 0.00103 kg/m-s
Inlet/Outlet openings = 0.02 m
Bottom wall velocity: 100 m/s Inlet velocity = 0.005 m/s Outlet gauge pressure = 0 Pa
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VMFL034
Analysis Assumptions and Modeling Notes The results of the ANSYS FLUENT simulation are compared to steady state analytical solution for the population balance in a stirred tank where aggregation takes place.
Results Comparison In this table, moment of PBE for ANSYS FLUENT turbulent simulations is compared with analytical solution for aggregation alone at the outlet of the tank.
Table 1 Comparison of Moment of PBE Moment
Target
ANSYS FLUENT
Ratio
m0
0.132
0.132
1.000
m1
0.225
0.226
1.004
m2
0.547
0.548
1.002
m3
1.910
1.910
1.000
m4
9.073
9.133
1.007
m5
53.797
53.816
1.000
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VMFL035: 3-Dimensional Single-Stage Axial Compressor
Overview Reference
Density-based solver (ANSYS FLUENT)
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Compressible (transonic), turbulent flow, moving reference frame
Input File
axial-compressor.cas
Test Case A 3-D model of a single-stage axial compressor is simulated. The flow through the rotor blades is computed in a rotating reference frame, while the flow in the stator blades in a stationary frame. The purpose of this case is to validate the performance of the pressure-based coupled solver for a compressible turbomachinery problem with a mixing plane. The flow is compressible, turbulent and steady.
Figure 1 Flow Domain
Material Properties (for Air) Density = Ideal – Gas
Geometry
Boundary Conditions
Geometry is as shown in in Figure 1 (p. 129)
Rotational speed = 37,500 rpm
Number of rotor blades = 16
For Inlet:
Molecular weight = 28.966 Specific heat = 1006.43 J/kg-K Viscosity, Thermal conductivity: Kinetic theory
Number of stator blades = 40
•
Ptotal = 1 atm
•
Ttotal = 288 K
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VMFL035
Analysis Assumptions and Modeling Notes Steady, turbulent, compressible flow. Ideal-gas law is used for density calculations and kinetic theory for fluid viscosity and thermal conductivity. The standard k-ε model is used for turbulence. Pressurebased coupled solver with a mixing plane at the rotor-outlet/stator-inlet interface.
Results Comparison for ANSYS FLUENT The results of the pressure-based ANSYS FLUENT simulation are compared to the steady state solution from the density-based solver.
Table 1 Comparison of Pressure and Mass Flow Rate Target
ANSYS FLUENT
Ratio
Pressure at Stator-Outlet (atm)
1.4725
1.4822
1.007
Mass-Flow Rate at Stator-Outlet (kg/s)
0.1049
0.1076
1.026
Results Comparison for ANSYS CFX Table 2 Comparison of Pressure and Mass Flow Rate Target
ANSYS CFX
Ratio
Pressure at Stator-Outlet (atm)
1.4725
1.4754
1.0020
Mass-Flow Rate at Stator-Outlet (kg/s)
0.1049
0.1078
1.0276
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VMFL036: Turbulent Round Jet
Overview Reference
D. C. Wilcox. 'Turbulence Modeling for CFD'. DCW Industries, Inc. 1993.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Turbulent flow
Target File
axjet.cas
Test Case A turbulent round jet is defined by a velocity inlet adjacent to a symmetry boundary, and exhausts into a rectangular domain or plenum. The domain is chosen large enough and the boundary does not interfere with the jet. The flow is turbulent and steady. The purpose of this case is to validate the performance of the Reynolds Stress Model for turbulence.
Figure 1 Round Jet Geometry
um /2
U0
U0
Computational Domain
H
Shear Layer
Core D
um
y x
L
Material Properties Density = 1 kg/m3 Viscosity = 1e-05 kg/m-s
Geometry D=1 m L = 50 m H= 20 m
Boundary Conditions Inlet: U0 = 1 m/s Turbulent intensity = 1% Turbulent length scale = 1 m Outlet: pout = 1 atm
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VMFL036
Analysis Assumptions and Modeling Notes Steady, turbulent, incompressible flow. The Reynolds Stress Model (RSM) is used for turbulence.
Results Comparison for ANSYS FLUENT The jet’s spreading rate is compared to the Wilcox (1998) data for round jets. The scattering of the data is due to the coarse triangular grid that has been used in this study. A finer grid would have produced a much smoother computational curve.
Figure 2 Comparison of Results for ANSYS FLUENT
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VMFL036
Results Comparison for ANSYS CFX Figure 3 Comparison of Results for ANSYS CFX
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VMFL037: Turbulent Flow over a Forward Facing Step
Overview Reference
S. Baker.“Regions of Recirculating Flow Associated with Two-Dimensional Steps”. Ph.D. thesis. Department of Civil Engineering, University of Surrey. UK. 1977.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
SST model, turbulent flow with separation and reattachment
Input File
VMFL037_ffstep.cas for ANSYS FLUENT ffstep.def for ANSYS CFX
Test Case Turbulent flow over a forward facing step is modeled. The flow undergoes separation and reattachment.
Figure 1 Flow Domain Free Slip Wall
Pref
U ref
7.3H
10H
INLET y
5.9H
0
x
No Slip Wall
H 14H
19H
Material Properties Density = 1.02 kg/m3 Viscosity = 1.5 X 10-5 kg/m-s
Geometry Step height H = 0.0758 m
Boundary Conditions Inlet Velocity = 9.7 m/s Outer boundary (in transverse direction) is modeled as slip wall
Analysis Assumptions and Modeling Notes The flow is steady. Pressure coefficient, Cp on the wall is calculated with reference to the pressure at point upstream of the step at coordinates as indicated in Figure 1 (p. 137).
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VMFL037
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Pressure Coefficient Along the Wall
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VMFL037
Results Comparison for ANSYS CFX Figure 3 Comparison of Pressure Coefficient Along the Wall
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VMFL038: Falling Film over an Inclined Plane
Overview Reference
RB Bird.“Transport Phenomena”. WE Stewart and EN Lightfoot. Pg. 45. 2005
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Laminar Flow, Coupled solver
Input File
VMFL038_FLUENT.cas for ANSYS FLUENT VMFL038_CFX.def for ANSYS CFX
Test Case Laminar flow of a fluid over an inclined plane, driven by the pressure difference due to gravity head is modeled. The flow channel is inclined at an angle β = 30° with the horizontal direction.
Figure 1 Flow Domain
X Sym m
etr
y
Wa ll
Y
Material Properties Density = 800 kg/m3 Viscosity = 1 kg/m-s
Geometry Dimensions of the domain: 1 m X 18 m Angle with X-axis = 30°
Boundary Conditions Gauge Pressure at Inlet = 0 N/m2 Gauge Pressure at Outlet = -706.32 N/m2
Analysis Assumptions and Modeling Notes The density based solver is used in ANSYS FLUENT. Pressure boundaries are specified to model the driving head in the direction of flow.
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VMFL038
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Velocity Profile at Outlet
Results Comparison for ANSYS CFX Figure 3 Comparison of Velocity Profile at Outlet
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VMFL039: Boiling in a Pipe with Heated Wall
Overview Reference
G.G. Bartolomej, V.G. Brantov,Y.S. Molochnikov,Y.V. Kharitonov, V.A. Solodkii, G.N. Batashova, V.N. Mikhailov.“An experimental investigation of the true volumetric vapour content with subcooled boiling tubes”. Thermal Engineering. Vol. 29, No. 3. 20-22. 1982.
Solver
ANSYS CFX (ANSYS FLUENT simulation is not available for this case)
Physics/Models
Multiphase flow, phase change, RPI Wall boiling Model
Input File
wall-boiling.def
Test Case Bubble formation and boiling near the heated wall of a vertical pipe are modeled. Outer wall of the pipe is heated with a constant heat flux.
Figure 1 Flow Domain
Z
q
Mass Flow
Material Properties Steam-Water 2-phase Flow: •
Water: continuous phase
Geometry
Boundary Conditions
Radius of the pipe = 7.7 mm
Mass flux at inlet = 900
Height of the pipe =2m
Inlet pressure = 4.5 X 106 N/m2
kg/m2/s
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VMFL039 Material Properties •
Geometry
Water Steam: dispersed bubbles
Bubble diameter dependent on fluid temperature
Boundary Conditions Heat transfer at the wall = 570000 W/m2
Analysis Assumptions and Modeling Notes The flow is steady. SST model is used for turbulence. RPI model for wall boiling is used with a value of 0.8 for the wall area fraction affected by vapor.
Results Comparison Figure 2 Comparison of Temperature Along the Pipe Wall
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VMFL040: Separated Turbulent Flow in Diffuser
Overview Reference
D.M. Driver.“Reynolds shear stress measurements in a separated boundary layer flow”. AIAA-91-1787. 1991.
Solver
ANSYS CFX, ANSYS FLUENT
Physics/Models
SST model, Adverse pressure gradient, flow separation
Input Files
diffuser-sep.def for ANSYS CFX VMFL040A_diffuser-sep.cas for ANSYS FLUENT
Test Case The test case geometry is shown in Figure 1 (p. 145). It consists of an axisymmetric diffuser with an internally mounted cylinder along the centre line. The curvature of the diffuser wall results in an adverse pressure gradient. A relatively short separation region was detected in the experiment.
Figure 1 Sketch of Flow Domain
Diffuser Streamline
y x
0 mm Separation 250 mm 140 mm cylinder
This figure is not to scale. Material Properties Density: 1 kg/m3 Viscosity: 1.5 X 10-5 kg/m-s
Geometry
Boundary Conditions
Diameter of the cylinder = 140 mm
Velocity profile at inlet with average velocity = 29 m/s
Length of the domain = 1100 mm
Outer wall modeled as a slip (inviscid) wall
Analysis Assumptions and Modeling Notes The flow is steady. SST model is used for turbulence.
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VMFL040
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Skin Friction Coefficient on the Cylinder Wall
146
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VMFL040
Results Comparison for ANSYS CFX Figure 3 Comparison of Skin Friction Coefficient on the Cylinder Wall
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VMFL041: Transonic Flow Over an Airfoil
Overview Reference
P.H. Cook, M.A. McDonald, and M.C.P. Firmin.“AEROFOIL RAE 2822 - PRESSURE DISTRIBUTIONS, AND BOUNDARY LAYER AND WAKE MEASUREMENTS.” AGARD Advisory Report No. 138.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Transonic flow, shock, SST model
Input File
VMFL041_transonic.cas for ANSYS FLUENT air_foil.def for ANSYS CFX
Test Case Transoinc flow over air foil RAE 2822 is modeled for an angle of attack of 3.19°. The flow domain spans over 100 Chord lengths in both stream-wise and transverse directions.
Figure 1 Flow Domain
Material Properties Density: Ideal gas law for Air
Geometry Chord length of the airfoil = 1 m
Boundary Conditions Velocity profile at inlet with an average velocity of 218 m/s
Viscosity: 1.831 X 10-5 kg/m-s
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VMFL041
Analysis Assumptions and Modeling Notes The flow is steady. The inlet flow Mach number is close to transonic range. Walls are assumed to be adiabatic.
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Pressure Coefficient on the Airfoil
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VMFL041
Results Comparison for ANSYS CFX Figure 3 Comparison of Pressure Coefficient on the Airfoil
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152
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VMFL042: Turbulent Mixing of Two Streams with Different Density
Overview Reference
R.E. Uittenbogaard. “Stably Stratified Mixing Layer”. Data Report for the 14th meeting of the IAHR Working Group on Refined Flow Modeling. 1989. R.E. Uittenbogaard. “The Importance of Internal Waves for Mixing in a Stratified Estaurine Tidal Flow”. 1995.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
SST model, mixing layer, density difference, buoyancy
Input File
VMFL042_mixing.cas for ANSYS FLUENT saline-mixing_layer.def for ANSYS CFX
Test Case Mixing of two turbulent streams of fresh water and saline water is modeled. The two streams are parallel at the inlet and mixing proceeds downstream.
Figure 1 Flow Domain
Fresh water y x
0.56 m
Saline 0.323 m 40 m
Material Properties Density of fresh water: 1015 kg/m3
Geometry Length of the mixing duct = 40 m
Density of saline water: 1030 kg/m3 Mixture kinematic diffusivity: 1 X 10-9
Boundary Conditions Fresh water inlet velocity = 0.52 m/s Salt water inlet velocity = 0.32 m/s
m2/s
Analysis Assumptions and Modeling Notes The flow is steady. SST model is used. Buoyancy turbulence production option is used.
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VMFL042
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Mass Fraction of Salt Water Across the Mixing Layer at x = 10m
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VMFL042
Results Comparison for ANSYS CFX Figure 3 Comparison of Mass Fraction of Salt Water Across the Mixing Layer at x = 10m
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VMFL043: Laminar to Turbulent Transition of Boundary Layer over a Flat Plate
Overview Reference
A. M. Savill. “Some recent progress in the turbulence modeling of bypass transition”. Near-Wall Turbulent Flows (eds. R. M. C. So, C. G. Speziale & B. E. Launder). Elsevier Science Publishers. 829-848. 1993. P.E. Roach, and D.H. Brierley. “The influence of a turbulent free stream on zero pressure gradient transitional boundary layer development. Part I: Test Cases T3A and T3B”. Numerical Simulation of Unsteady and Transition to Turbulence (eds. Pironneau, Rodi, Ryhming, Savill, and Truong). Cambridge University Press. Cambridge. 319-347. 1992.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
SST model, transitional flow
Input File
VMFL043_transition.cas for ANSYS FLUENT bl-transition.def for ANSYS CFX
Test Case Laminar to turbulent transition of a boundary layer over a flat plate is modeled. The free stream turbulence intensity is 3.3%.
Figure 1 Flow Domain
Leading edge
Material Properties Density: 1.2 kg/m3
Geometry Length of the flat plate = 2m
Boundary Conditions Inlet Velocity = 5.3 m/s Inlet eddy viscosity ratio = 9.7
Viscosity: 1.831 X 10-5 kg/m-s
Analysis Assumptions and Modeling Notes The flow is steady. SST model with Gamma Theta model for transitional turbulence is used. Langry Menter correlation was used for transition onset.
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VMFL043
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Skin Friction Coefficient on the Plate
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VMFL043
Results Comparison for ANSYS CFX Figure 3 Comparison of Skin Friction Coefficient on the Plate
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160
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VMFL044: Supersonic Nozzle Flow
Overview Reference
L.H. Back, P.F. Massier, and H.L. Gier.“Convective Heat Transfer in a Convergent-Divergent Nozzle”. Int. J. Heat Mass Transfer. Vol. 7. 549-568. 1964.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Compressible flow in supersonic regime, SST Model
Input File
VMFL044_nozzleflow.cas for ANSYS FLUENT supersonic-nozzle.def for ANSYS CFX
Test Case Supersonic flow in a convergent-divergent nozzle is modeled. The flow is supersonic in the entire divergent section of the nozzle.
Figure 1 Flow Domain Outlet Cooled wall Constant wall temperature (~0.5 x Tt )
Nozzle
Cooled-approach section
Material Properties Density: Ideal Gas Viscosity: 1.831 X 10 kg/m-s
Geometry
Boundary Conditions
Length of the nozzle = 0.1594 m
Inlet Relative Pressure = 1 X
Exit-to-throat area ratio = 2.68
Inlet Total Temperature = 825 K
Half angle of divergence = 15°
Wall temperature = 413 K
-5
106 Pa
Analysis Assumptions and Modeling Notes The flow is steady. The walls are assumed to be at constant temperature. Only a 3° sector of the domain is modeled due to symmetry.
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VMFL044
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Pressure Ratio Along the Nozzle Wall with Experimental Data
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VMFL044
Results Comparison for ANSYS CFX Figure 3 Comparison of Pressure Ratio Along the Nozzle Wall with Experimental Data
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VMFL045: Oblique Shock over an Inclined Ramp
Overview Reference
F. M. White.“Fluid Mechanics”. 3rd Edition. McGraw-Hill Book Co. New York, NY. 560567. 1994.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Compressible flow in supersonic regime, Oblique shock
Input File
VMFL045_obliqueshock.cas for ANSYS FLUENT ramp_supersonic_tet.def for ANSYS CFX
Test Case Supersonic flow over a 15° ramp is modeled. The ramp leads to the formation of an oblique shock. Inlet Mach number is about 2.5. The flow is laminar. The ANSYS CFX values are taken at a Point 1 (x=0.38 m, y=0.14 m)
Figure 1 Flow Domain
Outlet
Supersonic Inlet
Ramp
Material Properties
Geometry
Density: Ideal Gas
Angle of the ramp = 15°
Viscosity: 1 X 10-8 kg/m-s
Width of the domain (in transverse direction) = 0.3048 m
Boundary Conditions Inlet velocity = 852.68 m/s Inlet Temperature = 289 K Wall: Adiabatic
Analysis Assumptions and Modeling Notes The flow is steady and laminar. The walls are assumed to be adiabatic.
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VMFL045
Results Comparison for ANSYS FLUENT Table 1 Comparison of Properties Downstream of the Oblique Shock Target
ANSYS FLUENT
Ratio
Mach Number
1.87
1.9
1.01
Temperature
382 K
Density
2.279 kg/m
377.6 K 3
2.233 kg/m
0.99 3
0.98
Results Comparison for ANSYS CFX Table 2 Comparison of Properties Downstream of the Oblique Shock Target
ANSYS CFX
Ratio
Mach Number
1.87
1.88
1.00
Temperature
382 K
Density
166
2.279 kg/m
381.6 K 3
2.30 kg/m
0.999 3
1.01
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VMFL046: Supersonic Flow with Normal Shock in a Converging Diverging Nozzle
Overview Reference
F. M. White.“Fluid Mechanics”. 3rd Edition. McGraw-Hill Book Co. New York, NY. 518531. 1994.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Compressible flow in supersonic regime, Normal shock
Input File
VMFL046_supersonic.cas for ANSYS FLUENT Supersonic2x.def for ANSYS CFX
Test Case Supersonic flow in a CD nozzle is modeled. The maximum Mach number is 2.2. A normal shock is formed in the divergent section. Mach number distribution in the nozzle is compared with analytical solution for nozzle flow.
Figure 1 Flow domain
Material Properties Density: Ideal Gas Viscosity: 1.831 X 10-5 kg/m-s
Geometry Length of the nozzle = 2m
Boundary Conditions Inlet Relative Pressure 200 kPa Inlet Total Temperature = 500 K
Exit-to-throat area ratio =3
Wall temperature = 328 K Outlet Relative Pressure (gauge) = 75 kPa
Analysis Assumptions and Modeling Notes The flow is steady. The walls are assumed to be adiabatic. The flow is modeled as laminar.
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167
VMFL046
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Mach Number Along Center Line of the Nozzle With Analytical Solution
168
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VMFL046
Results Comparison for ANSYS CFX Figure 3 Comparison of Mach Number Along Center Line of the Nozzle With Analytical Solution
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169
170
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VMFL047: Turbulent Flow with Separation in an Asymmetric Diffuser
Overview Reference
C. U. Buice and J. K. Eaton. “Experimental Investigation of Flow Through an Asymmetric Plane Diffuser”. J. Fluids Engineering. Volume 122 (June 2000): 433435.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Turbulent separation, standard k-ω model in ANSYS FLUENT, and SST model in ANSYS CFX.
Input File
VMFL047_FLUENT.cas for ANSYS FLUENT VMFL047_CFX.def for ANSYS CFX
Test Case Turbulent flow with gradual separation and reattachment is modeled in an asymmetric 2-D diffuser. The lower wall of the diffuser is divergent with an angle of 10° and expands to about 4.7 times the inlet height.
Figure 1 Flow Domain
Flow Direction Inlet
Material Properties Density: 1 kg/m
3
Viscosity: 0.0001 kg/m-s
Geometry Inlet height H = 2 M Outlet height = 4.7 H
Boundary Conditions Fully developed turbulent profile for velocity at inlet with an average velocity = 0.7041 m/s
Angle of the divergent section = 10° Length of the straight section after divergence = 21 H
Analysis Assumptions and Modeling Notes Steady turbulent flow.
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VMFL047
Results Comparison for ANSYS FLUENT Figure 2 Comparison of X-Velocity at X = 24.4 m
Results Comparison for ANSYS CFX Figure 3 Comparison of X-Velocity at X = 24.4 m
172
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VMFL048: Turbulent flow in a 180° Pipe Bend
Overview Reference
T.Takamasa and A.Tomiyama.“Three-dimensional gas-liquid two-phase bubbly flow in a C-shaped tube”. NURETH-9. San Francisco, USA. 1-17. 1999.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
SST model, turbulent flow with separation and reattachment
Input File
VMFL048_pipebend.cas for ANSYS FLUENT 180deg_pipe_bend.def for ANSYS CFX
Test Case Flow in a 3-D pipe bend as shown in Figure 1 (p. 173).
Figure 1 Flow Domain
Material Properties
Geometry
Density: 997 kg/m3
Radius of the pipe = 14 mm
Viscosity: 8.899 X 10-4 kg/m-s
Radius of the pipe bend = 125 mm
Boundary Conditions Velocity profile at inlet with an average velocity of 1.42 m/s
Analysis Assumptions and Modeling Notes The flow is steady. Symmetry condition is applied on one side of the pipe.
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VMFL048
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Velocity in the Axial Direction at a Section 1.555 m upstream of the Outlet (after the bend)
174
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VMFL048
Results Comparison for ANSYS CFX Figure 3 Comparison of Velocity in the Axial Direction at a Section 1.555 m upstream of the Outlet (after the bend)
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VMFL049: Combustion in an Axisymmetric Natural Gas Furnace
Overview Reference
Westbrook and Dryer (1981), Coffee (1985).
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Turbulent non-premixed combustion, Eddy dissipation model, k-ε model
Target File
VMFL049_combustion.cas for ANSYS FLUENT ENEL_Furnace.def for ANSYS CFX
Test Case Non-premixed combustion in a natural gas fired furnace is modeled. The axisymmetric flow field is modeled by a 3° cylindrical domain. Fuel jet consists of natural gas modeled as 93% Methane and 7% Nitrogen by mass.
Figure 1 Flow Domain
Air Natural Gas Air
Material Properties Properties for the mixture of reactants used
Geometry Inner diameter of air annulus = 60 mm
Boundary Conditions Air velocity at inlet = 34 m/s Fuel velocity at inlet = 4 m/s
Outer diameter of air annulus = 100 mm
Wall temperature = 120°C
Diameter of combustion chamber = 500 mm
CH4 Mass fraction at inlet = 0.93
Length of chamber = 1700 mm
Analysis Assumptions and Modeling Notes The flow is steady. Reactions modeled using Eddy Dissipation Model. The domain is axisymmetric.
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VMFL049
Results Comparison for ANSYS FLUENT Figure 2 Comparison of the Mole Fraction of CH4 Along the Axis
Figure 3 Comparison of Temperature Along the Axis
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VMFL049
Results Comparison for ANSYS CFX Figure 4 Comparison of the Mole Fraction of CH4 Along the Axis
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VMFL049
Figure 5 Comparison of Temperature Along the Axis
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VMFL050: Transient Heat Conduction in a Semi-Infinite Slab
Overview Reference
F.P. Incropera and D.P. Dewitt.“Fundamentals of Heat and Mass Transfer”. 5th Edition. Wiley & Sons, 2002; Page 289.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Transient heat transfer, Conduction
Input File
VMFL050_FLUENT.cas for ANSYS FLUENT VMFL050_CFX.def for ANSYS CFX
Test Case Unsteady heat conduction in a thick copper plate is modeled. Initially (at t = 0) the plate is at a uniform temperature of 293 K. It is suddenly exposed to a heat transfer at one surface with a constant heat flux of 3 X 105 W/m2. The temperature distribution after 2 minutes is considered for verification.
Figure 1 Flow Domain Heat Flux at T>0
Conduction
Material Properties Density = 8995.67 kg/m
3
Specific Heat = 391 J/kg-K
Geometry Dimensions of the slab: 750 mm X 300 mm
Boundary Conditions Heat Flux = 3 X 105 W/m2 on one wall. The opposite wall is adiabatic. Lateral boundaries are modeled as planes of symmetry.
Conductivity = 401 W/m-K
Analysis Assumptions and Modeling Notes The flow is steady transient. The dimensions considered her are adequate for the semi-infinite slab assumption. The domain is initialized with a uniform temperature of 293 K corresponding to the condition at time = 0 sec.
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VMFL050
Results Comparison for ANSYS FLUENT Table 1 Comparison of Temperature after 2 Minutes ANSYS FLUENT
Exact Solution
Ratio
Temperature of the all exposed to heat flux, at t=120 sec
392.95 K
393 K
0.9998
Temperature at a point 150 mm from the heat flux wall, at t=120 sec
318.41 K
318.4 K
1.0000
Results Comparison for ANSYS CFX Table 2 Comparison of Temperature after 2 Minutes ANSYS CFX
Exact Solution
Ratio
Temperature of the wall exposed to heat flux, at t=120 sec
393 K
393 K
1.0000
Temperature at a point 150 mm from the heat flux wall, at t=120 sec
318.4 K
318.4 K
1.0000
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VMFL051: Isentropic Expansion of Supersonic Flow over a Convex Corner
Overview Reference
John Anderson. “Modern Compressible Flow: With Historical Perspective”.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Compressible, inviscid flow
Input File
VMFL051_FLUENT.cas for ANSYS FLUENT VMFL051_CFX.def for ANSYS CFX
Test Case Centered expansion of inviscid supersonic flow around a corner is modeled. The expansion results in a change in direction of the flow, a drop in static pressure, and increase in Mach number. The approaching flow is supersonic, with a Mach number of 2.5. The expansion process is reversible and adiabatic.
Figure 1 Flow Domain
Incoming flow, M>1 Ø = 195º
Flow after expansion, M>>1
adiabatic wall
Material Properties Density: Ideal Gas law
Geometry Angle round the corner = 195°
Boundary Conditions Inlet: Pressure = 202636.9 Pa Mach number = 2.5, Static temperature = 300 K (In CFX, the corresponding velocity is specified).
Specific Heat = 1006.43 J/kg-K Molecular weight = 28.966
Wall is adiabatic.
Analysis Assumptions and Modeling Notes The flow is steady and compressible. Inviscid and incompressible. Analytic expressions for isentropic expansion can be used to calculate the Mach number downstream of the corner.
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VMFL051
Results Comparison for ANSYS FLUENT Table 1 Comparison of Mach Number Downstream of the Corner, after Expansion
Mach number after expansion
ANSYS FLUENT
Analytical Calculation
Ratio
3.2316
3.2370
0.9980
Results Comparison for ANSYS CFX Table 2 Comparison of Mach Number Downstream of the Corner, after Expansion
Mach number after expansion
184
ANSYS CFX
Analytical Calculation
Ratio
3.2340
3.2370
0.9990
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VMFL052: Turbulent Natural Convection inside a Tall Cavity
Overview Reference
P.L. Betts and I.H. Bokhari. 'Experiments on turbulent natural convection in an enclosed tall cavity'. International Journal of Heat and Fluid Flow, 21. 675-683. 2000.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Turbulent flow, buoyancy effects, Boussinesq approximation (FLUENT)/Ideal gas (CFX)
Input File
VMFL052_FLUENT.cas for ANSYS FLUENT VMFL052_CFX.def for ANSYS CFX
Test Case Natural convection in the turbulent flow field of an enclosed cavity with a length-to-width ratio of 28.6 is modeled. The Rayleigh number is in the turbulent range. The two vertical walls are kept at different temperatures, while the horizontal walls are adiabatic.
Figure 1 Flow Domain (not to scale)
Hot Wall
Cold Wall
g = 9.81m/sec 2
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VMFL052 Material Properties
Geometry
Boundary Conditions
Density : Boussinesq approximation (FLUENT), Ideal Gas law (CFX)
Length of the cavity = 2.18 m
Temperature of Cold wall = 288.25 K
Specific Heat = 1005 J/kg-K
Width of the cavity = 0.0762 m
Temperature of Hot wall = 307.85 K
Viscosity = 1.81X 10-5 kg/m-sec Molecular weight = 28.966
Top and bottom walls are adiabatic
Analysis Assumptions and Modeling Notes The flow is steady and is induced by natural convective heat transfer.
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Vertical Velocity at Y/h = 0.05
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VMFL052
Figure 3 Comparison of Temperature at Y/h = 0.05
Results Comparison for ANSYS CFX Figure 4 Comparison of Vertical Velocity at Y/h = 0.05
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VMFL052
Figure 5 Comparison of Temperature at Y/h = 0.05
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VMFL053: Compressible Turbulent Mixing Layer
Overview Reference
S.G. Goebel and J.C. Dutton. “Experimental Study of Compressible Turbulent Mixing Layers”. AIAA Journal, 29(4). 538-546. 1991.
Solver
ANSYS FLUENT
Physics/Models
Turbulence: RNG k-ε model, compressible, energy equation
Input File
VMFL053_FLUENT.cas for ANSYS FLUENT
Test Case Two streams of air are mixed in a rectangular tunnel. The length of the computational domain is chosen such that the local Reynolds number at the exit of the test section, which is based on the velocity difference between the streams and the mixing layer thickness, is greater than 100,000. This is the Reynolds number needed for the complete development of the mixing layer.
Figure 1 Flow Domain Inlet
Outlet
Symmetry
U_1 = 616 m/s 72 mm Outlet
U_2 = 100 m/s
Symmetry 300 mm
Material Properties Air:
Geometry Dimensions of the domain:
Density: Ideal Gas Specific Heat: 1006.43 J/kg-K Thermal Conductivity: 0.0242 W/m-K Viscosity: 1.4399e-05 kg/m-s
300mm X 72 mm
Boundary Conditions Primary Stream (1): Total Pressure = 487 kPa Static Pressure = 36 kPa Total Temperature = 360 K Mach Number = 2.35 Turbulent Kinetic Energy = 74 m2/s2 Turbulent Dissipation Rate = 62,300 m2/s3 Secondary Stream (2): Total Pressure = 38 kPa Static Pressure = 36 kPa Total Temperature = 290 K
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189
VMFL053 Material Properties
Geometry
Boundary Conditions Mach Number = 0.36 Turbulent Kinetic Energy = 226 m2/s2 Turbulent Dissipation Rate = 332,000 m2/s3
Analysis Assumptions and Modeling Notes The flow is steady, turbulent, and compressible. The RNG k-ε model is used for turbulence.
Results Comparison The velocity profiles as the mixing layer evolves are compared with the experimental data.
Figure 2 X Velocity Profiles at x = 50 mm
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VMFL054: Laminar flow in a Trapezoidal Cavity
Overview Reference
J.H. Darr and S.P. Vanka. “Separated Flow in a Driven Trapezoidal Cavity”. Phys. Fluids A, 3(3):385-392. March 1991.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Viscous flow, driven by a moving walls
Input File
VMFL054_FLUENT.cas for ANSYS FLUENT VMFL054_CFX.def for ANSYS CFX
Test Case Laminar flow induced by the motion of the top wall of a trapezoidal cavity. The top and bottom walls move but the side walls are stationary. The height of the cavity h is 1 m. The widths of the top and bottom walls are 1 m and 2 m, respectively (Figure 1 (p. 191)).
Figure 1 Flow Domain 1m U wall = 400 m/s
1m
U wall = 400 m/s 2 mm
Material Properties Density = 1 kg/m
Geometry Height of cavity = 1 m
3
Viscosity = 1 kg/m-s
Width of the bottom base = 2m
Boundary Conditions Velocity of the base walls = 400 m/s Other walls are stationary
Width of the top base = 1 m
Analysis Assumptions and Modeling Notes The flow is steady. A pressure based solver is used. A triangular mesh of 4016 cells is used to discretize the domain.
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VMFL054
Results Comparison for ANSYS FLUENT The u-velocity profile at the vertical centerline of the cavity and the ν-velocity profile at the horizontal centerline of the cavity are compared to Darr and Vanka results. Velocity is normalized by velocity of the moving wall.
Figure 2 Normalized u-Velocity at the Horizontal Centerline of the Cavity
Figure 3 Normalized v-Velocity at the Vertical Centerline of the Cavity
Results Comparison for ANSYS CFX The u-velocity profile at the vertical centerline of the cavity and the ν-velocity profile at the horizontal centerline of the cavity are compared to Darr and Vanka results. Velocity is normalized by velocity of the moving wall.
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VMFL054
Figure 4 Normalized u-Velocity at the Horizontal Centerline of the Cavity
Figure 5 Normalized v-Velocity at the Vertical Centerline of the Cavity
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194
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VMFL055: Transitional Recirculatory Flow inside a Ventilation Enclosure
Overview Reference
A. Restivo. Turbulent Flow in Ventilated Rooms. Ph.D. Thesis, University of London, U.K. 1979.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Transitional turbulence modeling (k-kl model for ANSYS FLUENT, BSL Gamma Model for ANSYS CFX)
Input File
VMFL055_FLUENT.cas for ANSYS FLUENT VMFL055_CFX-BSL-Gamma.def for ANSYS CFX
Test Case Flow inside an enclosure similar to a ventilated room is modeled. The flow field is transitional and dominated by recirculation. Reynolds number is based on the inlet dimension and is around 5000.
Figure 1 Flow Domain Inlet
H = 3m Outlet
Material Properties Density : 1.225 kg/m3 Viscosity = 1.81X 10-5 kg/m-sec
Geometry Height of the enclosure (H) = 3 m
Boundary Conditions Inlet velocity = 0.454 m/S
Length of the enclosure = 9 m (3 H) Inlet : 0.056 H Outlet : 0.16 H
Analysis Assumptions and Modeling Notes The flow is modeled using transitional turbulence models.
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VMFL055
Results Comparison for ANSYS FLUENT Figure 2 Comparison of X-Velocity Velocity at Y = 2.916 m
Results Comparison for ANSYS CFX Figure 3 Comparison of X-Velocity Velocity at Y = 2.916 m
196
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VMFL056: Combined Conduction and Radiation in a Square Cavity
Overview Reference
Daniel R. Rousse, Guillaume Gautier, and Jean-Francois Sacadura. “Numerical predictions of two-dimensional conduction, convection, and radiation heat transfer. II. Validation”. International Journal of Thermal Sciences. Volume 39, Issue 3 (March 2000). 332-353.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Radiation modeling; discrete ordinate model in ANSYS FLUENT
Input File
VMFL056_FLUENT.cas for ANSYS FLUENT VMFL056_CFX.def for ANSYS CFX
Test Case Coupled conduction and radiation is modeled in a square enclosure. The material properties are set to model a condition corresponding to the Conduction-Radiation parameter N = 1.0. Scattering coefficient of the medium is 0. Steady state heat transfer is modeled. One wall of the square cavity is kept at a higher temperature than the other 3 walls.
Figure 1 Flow Domain
Cold Walls
Hot Wall
Material Properties Thermal Conductivity = 1 W/m-K Absorption Coefficient = 0.228/m
Geometry Dimensions of the domain: 1 m X 1 m
Boundary Conditions Temperature of the hot wall = 100 K Temperature of the cold walls = 50 K
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VMFL056
Analysis Assumptions and Modeling Notes The material properties are set to model the desired conduction-radiation fraction. Radiative heat flux is only a small fraction of the total heat flux.
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Non-Dimensional Temperature at X = 0.5 m
Results Comparison for ANSYS CFX Figure 3 Comparison of Non-Dimensional Temperature at X = 0.5 m
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VMFL057: Radiation and Conduction in Composite Solid Layers
Overview Reference
C.M. Spuckler and R. Siegel. “Two-Flux and Diffusion Methods for Radiative Transfer in Composite Layers”. J. Heat Transfer, 118. 218-222. 1996.
Solver
ANSYS FLUENT
Physics/Models
Radiation modeling with DO model, participating medium with gray-band absorption
Input File
VMFL057_FLUENT.cas for ANSYS FLUENT
Test Case Heat transfer by conduction and radiation is modeled in a composite solid domain consisting of two layers. Both the layers participate in radiation. The two layers are separated by a semi-transparent wall. The upstream and downstream sides of the domain are subjected to convective as well as radiative heat transfer.
Figure 1 Flow Domain
Symmetry
Wall
lid
1
So
d2
Wall
li So
Symmetry
Material Properties Solid 1: Density = 2719 kg/m3 Specific Heat = 871 J/kg-k Thermal Conductivity = 5.67 W/m-K Absorption Coefficient: grayband Refractive Index = 1.5
Geometry Dimensions of the domain: 2 m X 1 m (the two solid zones are of equal length)
Boundary Conditions Left-most wall: Convective Heat Transfer Coefficient = 56.7 W/m2 K free stream temperature = 1000K Semi-transparent Right-most wall:
Solid 2: Convective
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VMFL057 Material Properties
Geometry
Density = 2719 kg/m3 Specific Heat = 871 J/kg-k Thermal Conductivity = 5.67 W/m-K Absorption Coefficient: grayband Refractive Index = 3
Boundary Conditions Heat Transfer Coefficient = 56.7 W/m2 K free stream temperature = 250K Semi-transparent
Analysis Assumptions and Modeling Notes Transverse boundaries of the domain are modeled as planes of symmetry.
Results Comparison for ANSYS FLUENT Figure 2 Comparison temperature distribution along Y = 0.5 m
200
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VMFL058: Turbulent Flow in an Axisymmetric Diffuser
Overview Reference
R. S. Azad and S. Z. Kassab. “Turbulent Flow in a Conical Diffuser: Overview and implications”. Phys. Fluids A 1, 564. 1989.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Turbulent flow with adverse pressure gradient
Input File
VMFL058_FLUENT.cas for ANSYS FLUENT VMFL058_CFX.def for ANSYS CFX
Test Case Fully developed turbulent flow is modeled in an axisymmetric diffuser. The flow is fully developed at the inlet to the diffuser.
Figure 1 Flow Domain Wall Axis
Material Properties
Geometry Included angle for the divergent
Density = 1 kg/m3
section = 8 Viscosity = 1.64 X 10-5 kg/m-s
0
Boundary Conditions Fully developed turbulent profile at inlet with an average velocity = 1 m/s
Length of Inlet section (straight) = 6m Inlet radius = 1m Outlet radius = 2m
Analysis Assumptions and Modeling Notes Steady turbulent flow.
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VMFL058
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Pressure Coefficient along the Divergent Diffuser Wall
Results Comparison for ANSYS CFX Figure 3 Comparison of Pressure Coefficient along the Divergent Diffuser Wall
202
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VMFL059: Conduction in a Composite Solid Block
Overview Reference
F.P. Incropera and D.P. Dewitt.“Fundamentals of Heat and Mass Transfer”. 5th Edition. Page 117. 2006.
Solver
ANSYS FLUENT
Physics/Models
Conduction with heat source
Input File
VMFL059_FLUENT.cas for ANSYS FLUENT
Test Case Heat conduction in a plane wall formed as composite of two materials is modeled. One of the materials has a uniform volumetric heat generation source while the other material has an outer surface exposed to convective cooling.
Figure 1 Flow Domain
i ter Ma
al 1
i ter Ma
al 2
Heat Source
Material Properties Material 1:
Geometry Dimensions of the domain:
Density = 2719 3
kg/m Specific Heat = 871 J/kg-k Thermal Conductivity = 75W/m-K
0.07 m X 0.08 m Thickness of slab 1 (material 1) = 0.05 m
Boundary Conditions Left-most wall: Adiabatic Right-most wall: Convective, with Heat Transfer Coefficient = 1000 W/m2 K and free stream temperature = 303 K Other boundaries are adiabatic walls.
Material 2:
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203
VMFL059 Material Properties
Geometry
Boundary Conditions
Density = 8978 kg/m3 Specific Heat = 381 J/kg-k Thermal Conductivity = 150 W/m-K
Analysis Assumptions and Modeling Notes Contact resistance between the slabs is neglected.
Results Comparison Table 1 Comparison Temperatures on the Side Walls ANSYS FLUENT
Analytical
Ratio
Temperature of the cooled wall
378.16 K
378 K
1.0004
Temperature of the adiabatic wall on extreme left side
413.12 K
413 K
1.0003
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VMFL060: Transitional Supersonic Flow over a Rearward Facing Step
Overview Reference
Howard E Smith. “The Flow Field and Heat Transfer downstream of a Rearward Facing Step in Supersonic Flow”. ARL 67-0056, Aerospace Research Laboratories. Ohio, USA.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Compressible Flow, Transitional turbulence modeling (Transition SST model for ANSYS FLUENT, SST Gamma-Theta Model for ANSYS CFX)
Input File
VMFL060_FLUENT.cas for ANSYS FLUENT VMFL060_CFX.def for ANSYS CFX
Test Case Supersonic flow with an inlet Mach number 2.5 past a backward facing step is modeled. Key features of the flow field include sudden expansion, free shear layer, recirculation zone, and oblique shock. Reynolds number of the flow (based on step height) is in the transitional range.
Figure 1 Flow Domain Traverse boundary Supersonic Flow (M = 2.5)
Step (h = 0.443”)
Material Properties Density: Ideal gas Viscosity = 1.81X 10-5 kg/m-sec
Geometry
Boundary Conditions
Step Height = 0.443 in
Total pressure at inlet = 227527 Pa
Inlet: 4 in upstream of the step
Static Pressure at Inlet = 13316.6 Total temperature at inlet = 344.44 K
Outlet: 12 in downstream of the step Transverse (top) boundary: 6.25 in above the step.
Transverse boundary modeled as farfield (ANSYS FLUENT)/ Supersonic outlet (ANSYS CFX) Walls are modeled as adiabatic
Analysis Assumptions and Modeling Notes The flow is modeled using transitional turbulence models.
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VMFL060
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Non-Dimensionalized Static Pressure along the Stepped Wall Downstream of the Corner
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VMFL060
Results Comparison for ANSYS CFX Figure 3 Comparison of Non-Dimensionalized Static Pressure along the Stepped Wall Downstream of the Corner
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208
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VMFL061: Surface to Surface Radiative Heat Transfer between Two Concentric Cylinders
Overview Reference
F.P. Incropera and D.P. Dewitt. “Fundamentals of Heat and Mass Transfer”. 4th Edition. New York City, New York: John Wiley & Sons, Inc. 1996.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Radiation Modeling (S2S Model in ANSYS FLUENT, Monte Carlo Method in ANSYS CFX)
Input File
VMFL061_FLUENT.cas for ANSYS FLUENT VMFL061_CFX.def for ANSYS CFX
Test Case Radiative heat transfer between two cylindrical surfaces forming a concentric annulus is modeled. There is no participating medium. Due to symmetry only the shaded portion of the domain in Figure 1 (p. 209) is modeled.
Figure 1 Flow Domain
Cold outer wall
Hot inner wall
Material Properties Material does not participate in the energy transfer.
Geometry
Boundary Conditions
Radius of inner wall = 0.04625 m
Temperature of inner wall = 700 K
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VMFL061 Material Properties
Geometry
Boundary Conditions
Radius of outer wall = 0.0178 m
Temperature of outer wall = 300 K
Analysis Assumptions and Modeling Notes Because there is no flow of mass, only the energy equation is solved. Radiation models are used for the simulation. Heat transfer is purely due to radiation between the two surfaces.
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Temperature Variation along Radius
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VMFL061
Results Comparison for ANSYS CFX Figure 3 Comparison of Temperature Variation along Radius
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212
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VMFL062: Fully Developed Turbulent Flow Over a “Hill”
Overview Reference
V. Baskaran, A. J. Smits, and P. N. Joubert. 'A turbulent flow over a curved hill Part 1. Growth of an internal boundary layer'. Journal of Fluid Mechanics, (1987), 182: 47-83.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Low Re k-e Model in ANSYS FLUENT, k-e Model in ANSYS CFX
Input File
VMFL062_FLUENT.cas for ANSYS FLUENT VMFL062_CFX.def for ANSYS CFX
Test Case Flow over a “hill” geometry with separation and reattachment is modeled. Fully developed turbulent profile is specified at the inlet.
Figure 1 Flow Domain
Flow Direction
Hill
Material Properties
Geometry Height of the hill = 20.5 mm
Density : 1 kg/m3 Viscosity = 7.5188e-07 kg/m-s
Boundary Conditions Fully developed profiles are specified at the inlet for (i) Velocity, (ii) Turbulent kinetic Energy, and (iii) Eddy dissipation rate. Average velocity at inlet = 1 m/s
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VMFL062
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Skin Friction along the Wall
Results Comparison for ANSYS CFX Figure 3 Comparison of Skin Friction along the Wall
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VMFL063: Separated Laminar Flow over a Blunt Plate
Overview Reference
J.C . Lane and R.I. Loehrke. “Leading Edge Separation from a Blunt Plate at Low Reynolds Number”. Transactions of ASME, Volume 102 (December 1980): 494496.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Laminar flow, high resolution numerical models
Input File
VMFL063_FLUENT.cas for ANSYS FLUENT VMFL063_CFX.def for ANSYS CFX
Test Case The flow separation over a blunt leading edge in laminar flow is modeled. The flow separates and reattaches along the plate. The reattachment length predicted by the solvers is validated against experimental results. Due to symmetry, only half of the domain shown in Figure 1 (p. 215) is modeled. The Reynolds number based on plate thickness is 227.
Figure 1 Flow Domain
Flow Direction
Reattachment Plane of Symmetry
Material Properties Density: 1 kg/m
Blunt plate
Geometry Thickness of the plate, 2t = 90 mm
3
Viscosity: 1.7894 X 10-5 kg/m-s
Boundary Conditions Velocity at inlet = 0.045133 m/s
Length of the plate = 1500 mm
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VMFL063
Results Comparison for ANSYS FLUENT Table 1 Comparison of Reattachment Length
Non-dimensionalized Reattachment length (LR/2t)
ANSYS FLUENT
Experiment
Ratio
3.8
4.0
0.95
Results Comparison for ANSYS CFX Table 2 Comparison of Reattachment Length
Non-dimensionalized Reattachment length (LR/2t)
216
ANSYS CFX
Experiment
Ratio
4.37
4.0
1.093
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VMFL064: Low Reynolds Number Flow in a Channel with Sudden Asymmetric Expansion
Overview Reference
1.
B. Armaly, F. Durst, J. Pereira, and B. Schönung. “Experimental and theoretical investigation of a backward-facing step”. J. Fluid Mech. 127 (1983): 473.
2.
C.J. Freitas. “Perspective: Selected Benchmarks from Commercial CFD Codes”. J. Fluids Eng. Volume 117, Issue 2 (June 1995): 208.
Solver
ANSYS FLUENT, ANSYS CFX
Physics/Models
Laminar flow, Separation, and Reattachment
Input File
VMFL064_FLUENT.cas for ANSYS FLUENT VMFL064_CFX.def for ANSYS CFX
Test Case Laminar flow in a channel with a backward facing step expansion is modeled. The channels section upstream of the expansion is long enough to ensure fully developed laminar profile. The reattachment length predicted by the solvers is validated against experimental results. Reynolds number based on D (equal to twice the channel height at inlet) is 200. The domain extends to about 40 times the stepheight upstream and over 20 times the step-height downstream.
Figure 1 Flow Domain
Flow Direction
Material Properties
Geometry
Density: 1 kg/m3
Step height, s = 4.9 mm
Viscosity: 1.5 X 10-5 kg/m-s
Channel height at inlet = 5.2 mm Length of inlet section = 200 mm
Boundary Conditions Velocity at inlet = 0.288462 m/s No-slip condition at the walls
Length downstream of the step = 100 mm
Analysis Assumptions and Modeling Notes The flow is fully developed before the step. Reattachment length is measured from the reversal of the sign of the wall shear along the flow direction.
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VMFL064
Results Comparison for ANSYS FLUENT Table 1 Comparison of Reattachment Length
Non-dimensionalized Reattachment length (LR/Step-height)
ANSYS FLUENT
Experiment
Ratio
4.93
5.0
0.986
Results Comparison for ANSYS CFX Table 2 Comparison of Reattachment Length
Non-dimensionalized Reattachment length (LR/Step-height)
218
ANSYS CFX
Experiment
Ratio
4.90
5.0
0.98
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VMFL065: Swirling Turbulent Flow Inside a Diffuser
Overview Reference
P.D. Clausen, S.G. Koh, and D.H. Wood.“Measurements of a Swirling Turbulent Boundary Layer Developing in a Conical Diffuser.”Experimental Thermal and Fluid Science.Volume 6, Issue 1 (January 1993): 39-48.
Solver
ANSYS FLUENT
Physics/Models
Turbulent flow, swirl velocity, Reynolds stress model for turbulence
Input File
VMFL065_FLUENT.cas for ANSYS FLUENT
Test Case Turbulent flow with a strong swirl component is modeled in an axisysmmetric diffuser. The swirl component of the velocity has a dominant effect on the flow field inside the diffuser.
Figure 1 Flow Domain
Flow
Material Properties Density: 1 kg/m3 Viscosity: 1.293 X 10-6 kg/m-s
Geometry Length of the straight inlet section = 25 mm Length of the diffuser (divergent section) = 510 mm
Boundary Conditions Fully developed turbulent profile for velocity, k and ε at inlet (with average axial inlet velocity = 1 m/s) No-slip condition at the walls
Inlet Diameter = 260 mm Outlet Diameter = 440 mm
Analysis Assumptions and Modeling Notes RS model is used for turbulence due to the strong swirl component.
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VMFL065
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Swirl Velocity at X = 0.175 m
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VMFL066: Radiative Heat Transfer in a Rectangular Enclosure with Participating Medium
Overview Reference
G.D Raithby and E.H. Chui. “A Finite Volume Method for Predicting a Radiant Heat Transfer in Enclosoures with Participating Media”. Journal of Heat Transfer. Volume 112 (May 1990): 415-423.
Solver
ANSYS FLUENT
Physics/Models
Radiation modeling, discrete Ordinate Model in ANSYS FLUENT
Input File
VMFL066_FLUENT.cas for ANSYS FLUENT
Test Case Two dimensional radiative heat transfer in an enclosure with one hot wall and three cold walls at equal temperature is modeled. The enclosure is a rectangular cavity with a length-to-width ratio of 5. For the problem being considered, σsLy = 1.0, where σs is the scattering coefficient and Ly is the normal distance between the hot wall and the cold wall opposite to it.
Figure 1 Flow Domain
Cold Walls
Hot Wall
Material Properties Scattering coefficient = 0.5/m
Geometry Dimensions of the domain: 10 m x 2 m
Boundary Conditions Temperature of the hot wall = 200 K Temperature of he cold walls = 100 K
Analysis Assumptions and Modeling Notes Isotropic scattering and radiative equilibrium are assumed.
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VMFL066
Results Comparison for ANSYS FLUENT Figure 2 Comparison of Non-Dimensional Heat Flux along the Hot Wall
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<p>17.6. Substructuring Analysis</p><p>Page 1 of 6</p><p>Theory Reference Chapter 17. Analysis Procedures </p><p>17.6. Substructuring Analysis</p><p>The substructure analysis (ANTYPE,SUBSTR) uses the technique of matrix reduction to reduce the system matrices to a smaller set of DOFs. Matrix reduction is also used by the reduced modal, reduced harmonic and reduced transient analyses. The following substructuring analysis topics are available: Assumptions and Restrictions (within Superelement) Description of Analysis Statics Transients Component Mode Synthesis (CMS)17.6.1. Assumptions and Restrictions (within Superelement)</p><p>1. Any degree of freedom (DOF) may be used. 2. The elements have constant stiffness, damping, and mass effects (e.g., material properties do not change with temperature). 3. Coupled-field elements using load-vector coupling and elements with Lagrange multipliers cannot be used.17.6.2. Description of Analysis</p><p>A superelement (substructure) may be used in any analysis type. It simply represents a collection of elements that are reduced to act as one element. This one (super) element may then be used in the actual analysis (use pass) or be used to generate more superelements (generation or use pass). To reconstruct the detailed solutions (e.g., displacements and stresses) within the superelement, an expansion pass may be done. See the Basic Analysis Guide for loads which are applicable to a substructure analysis.17.6.3. Statics</p><p>Consider the basic form of the static equations ((Equation 171)):(1791)</p><p>{F} includes nodal, pressure, and temperature effects. It does not include {Fnr} (see NewtonRaphson Procedure). The equations may be partitioned into two groups, the master (retained) DOFs, here denoted by the subscript m, and the slave (removed) DOFs, here denoted by the subscript s.</p><p>(1792)</p><p>or expanding:</p><p>mk:@MSITStore:C:Program%20Files%20(x86)ANSYS%20Incv110commonfiles.. 28.10.2010</p><p>17.6. Substructuring Analysis</p><p>Page 2 of 6</p><p>(1793) (1794)</p><p>The master DOFs should include all DOFs of all nodes on surfaces that connect to other parts of the structure. If accelerations are to be used in the use pass or if the use pass will be a transient analysis, master DOFs throughout the rest of the structure should also be used to characterize the distributed mass. The automatic selection of master DOFs is discussed in more detail in Automatic Master DOF Selection, and guidelines for their selection are given in Modal Analysis of the Structural Analysis Guide. Solving (Equation 1794) for {us},(1795)</p><p>Substituting {us} into (Equation 1793)(1796)</p><p>or,(1797)</p><p>where:(1798) (1799) (17100)</p><p>and</p><p>are the superelement coefficient (e.g., stiffness) matrix and load vector, respectively.</p><p>In the preceding development, the load vector for the superelement has been treated as a total load vector. The same derivation may be applied to any number of independent load vectors, which in turn may be individually scaled in the superelement use pass. For example, the analyst may wish to apply thermal, pressure, gravity, and other loading conditions in varying proportions. Expanding the right-hand sides of (Equation 1793) and (Equation 1794) one gets, respectively:</p><p>(17101)</p><p>(17102)</p><p>where:N = number of independent load vectors.</p><p>mk:@MSITStore:C:Program%20Files%20(x86)ANSYS%20Incv110commonfiles.. 28.10.2010</p><p>17.6. Substructuring Analysis</p><p>Page 3 of 6</p><p>Substituting into (Equation 1799):</p><p>(17103)</p><p>To have independently scaled load vectors in the use pass, expand the left-hand side of (Equation 17103)</p><p>(17104)</p><p>Substituting (Equation 17104) into (Equation 17103) :(17105)</p><p>If the load vectors are scaled in the use pass such that:</p><p>(17106)</p><p>where bi is the scaling factor (FACT on the LVSCALE command), then (Equation 1795) becomes:</p><p>(17107)</p><p>(Equation 17107) is used in the expansion pass to obtain the DOF values at the slave DOFs if the backsubstitution method is chosen (SEOPT command). If the resolve method is chosen for expansion pass, then the program will use (Equation 1792) to resolve for {us}. In doing so, the program makes {um} as the internally prescribed displacement boundary conditions since {um} are known in expansion pass. As the program treats DOFs associated with {um} as displacement boundary conditions, the reaction forces by resolve method will be different from that computed at those master DOFs by the backsubstitution method. However, they are all in self-equilibrium satisfying (Equation 1792). The above section Statics is equally applicable at an element level for elements with extra displacement shapes. The master DOFs become the nodal DOFs and the slave DOFs become the nodeless or extra DOFs.17.6.4. Transients</p><p>The general form of the equations for transients is (Equation 175) and (Equation 1729):(17108)</p><p>For substructuring, an equation of the form:</p><p>mk:@MSITStore:C:Program%20Files%20(x86)ANSYS%20Incv110commonfiles.. 28.10.2010</p><p>17.6. Substructuring Analysis</p><p>Page 4 of 6</p><p>(17109)</p><p>is needed. and are computed as they are for the static case ((Equation 1798) and (Equation 1799)). The computation of the reduced mass matrix is done by:</p><p>(17110)</p><p>This simplification was suggested by Guyan(14) because direct partitioning and condensation are not practical (the condensed matrices would be functions of the time derivatives of displacement and very awkward to implement). The damping matrix is handled similarly:</p><p>(17111)</p><p>(Equation 17107) is also used to expand the DOF values to the slave DOFs in the transient case if the backsubstitution method is chosen. If the resolve method is chosen, the program will use (Equation 1792) and make {um} as displacement boundary conditions the same way as the static expansion method does.17.6.5. Component Mode Synthesis (CMS)</p><p>Component mode synthesis is an option used in substructure analysis (accessed with the CMSOPT command). It reduces the system matrices to a smaller set of interface DOFs between substructures and truncated sets of normal mode generalized coordinates (see Craig(344)). For a undamped system, each CMS substructure is defined by a stiffness and a mass matrix. The matrix equation of the motion is:(17112)</p><p>Partitioning the matrix equation into interface and interior DOFs:</p><p>(17113)</p><p>where subscripts m and s refer to:m = master DOFs defined only on interface nodes s = all DOFs that are not master DOFs</p><p>The physical displacement vector, (u), may be represented in terms of component generalized coordinates (see Craig(344)) as in (Equation 17114).(17114)</p><p>mk:@MSITStore:C:Program%20Files%20(x86)ANSYS%20Incv110commonfiles.. 28.10.2010</p><p>17.6. Substructuring Analysis</p><p>Page 5 of 6</p><p>where:y = truncated set of generalized modal coordinates [T] = transformation matrix.</p><p>Fixed-Interface Method For the fixed-interface method (see Craig and Bampton(345)), the transformation matrix has the form:(17115)</p><p>where:[Gsm] = -[Kss]-1[Ksm] = redundant static constraint modes (see Craig and Bampton(345)) s = fixed-interface normal modes (eigenvectors obtained with interface nodes fixed) [I] = identity matrix</p><p>Free-Interface Method For the free-interface method, the transformation matrix has the form:</p><p>(17116)</p><p>where:[sr] = matrix of inertia relief modes</p><p>[m] = matrix of the master dof partition of the free-interface normal modes (eigenvectors obtained with interface dofs free). [s] = matrix of the slave dof partition of the free-interface normal modes.</p><p>Residual Flexibility Free Interface Method For the Residual Flexiblility Free interface (RFFB) method, the transformation matrix has the form:</p><p>(17117)</p><p>where:</p><p>mk:@MSITStore:C:Program%20Files%20(x86)ANSYS%20Incv110commonfiles.. 28.10.2010</p><p>17.6. Substructuring Analysis</p><p>Page 6 of 6</p><p>[Rmm], [Rsm] = submatrices of residual vectors [R]</p><p>(see Residual Vector Method)</p><p>After applying the transformation in (Equation 17114) into the matrix equation of motion (Equation 17112) , the equation of motion in the reduced space is obtained. The reduced stiffness and mass matrices of the CMS substructure will be:(17118) (17119)</p><p>In the reduced system, master DOFs will be used to couple the CMS superelement to other elements and/or CMS superelements.</p><p>Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.</p><p>mk:@MSITStore:C:Program%20Files%20(x86)ANSYS%20Incv110commonfiles.. 28.10.2010</p>