9 Appendix 1 - Turbulence Mechanics/CFD Research Group Website

School of Mechanical Aerospace and Civil Engineering
University of Manchester













First Year Transfer Report





Application of CFD to Industrial Safety Studies
(with Prediction Accuracy and Error estimations)

Imama Zaidi


Supervised by

Prof. Dominique Laurence









2009


Table of Contents
1 Abstract 7
2 Introduction 8
3 Literature Review: 9
3.1 Numerical Errors: 10
3.1.1 Round off Error: 10
3.1.2 Iterative Convergence Error: 11
3.1.3 Discretisation Error 11
3.2 User errors 12
3.3 Turbulence 12
3.4 Physical Model Uncertainty: 13
3.5 Verification and Validation 14
3.6 Best Practice Guidelines (BPG): 15
3.6.1 Defining the objective: 16
3.6.2 Selection of Equations Describing the Flow Pattern: 16
3.6.3 Computational Domain 16
3.6.4 Computational Grid 16
4 Governing Equations of Fluid Dynamics 20
4.1.1 Mass Conservation in Three Dimensions: 20
4.1.2 Momentum Conservation: 20
5 STAR CCM 22
5.1 Automated Engineering 22
5.2 Numerical Scheme 23
5.2.1 Transient Term: 23
5.2.2 Source Term: 23
5.2.3 Diffusion Term: 23
5.2.4 Convection Term: 24
5.3 Turbulence Modeling 25
5.3.1 Standard Spalart-Allmaras (SSA) Model 25
5.3.2 Standard Low Reynolds Number [pic]model 26
5.3.3 V2f Model 26
5.3.4 Abe Kondo Nagano (AKN) Low Reynolds Number [pic] Model 27
5.3.5 [pic]SST [pic] Model 27
5.4 Convergence Criteria. 28
6 The Square Cavity Test Case: 30
6.1 Part I 31
6.1.1 Results: 31
6.2 Part II - turbulent flow cases 35
6.2.1 Results 36
7 Conclusion 68
8 Future Work 69
8.1 Experimental Setup 69
9 Appendix 1 72
10 Appendix 2 74
11 Appendix 3 76
12 References: 89































List of Figures
Figure 5-1: Comparison of results obtained with residual tolerance of 10-4
for X-momentum for different grids 20
Figure 5-2: Comparison of results obtained after monitoring temperature
asymptotic value of 1E-4 at center and near boundaries of the cavity
20
Figure 6-1: Geometry of the problem 20
Figure 6-2: Mesh Types 20
Figure 6-3: Mesh Types for Turbulent Flow 20
Figure 6-4: Temperature Profile inside Cavity at Ra=103 20
Figure 6-5: Error in temperature for different mesh numbers 20
Figure 6-6: u-Velocity Profile in side cavity at Ra=103 20
Figure 6-7: Error in u-Velocity for different mesh numbers 20
Figure 6-8: v-Velocity Profile in cavity at Ra=103 20
Figure 6-9: Error in v-Velocity for different mesh numbers 20
Figure 6-10: Results for Square mesh 20
Figure 6-11: Results for Polyhedral Mesh 20
Figure 6-12: Results for Skewed Mesh 20
Figure 6-13: Comparison of order of accuracy for three meshes. 20
Figure 6-14: Effect of change of design parameters at Ra=103 20
Figure 6-15: Richardson Extrapolation for results obtained using Second
order Upwind Scheme at Ra=103 20
Figure 6-16: Richardson Extrapolation for results obtained using Second
order Upwind Scheme at Ra=104 20
Figure 6-17: Richardson Extrapolation for results obtained using Second
order Upwind Scheme at Ra=105 20
Figure 6-18: Richardson Extrapolation for results obtained using First
order Upwind Scheme at Ra=103 20
Figure 6-19: Richardson Extrapolation for results obtained using First
order Upwind Scheme at Ra=104 20
Figure 6-20: Richardson Extrapolation for results obtained using Central
Differencing Scheme at Ra=103 20
Figure 6-21: Richardson Extrapolation for Nu at hot wall using Second Order
Upwind Scheme Ra=103 20
Figure 6-22: Comparison of Nu number profile obtained from second order
approximation and Star CCM for 20*20 grid at Ra=103 20
Figure 6-23: Comparison of Nu number profile obtained from second order
approximation and Star CCM for 40*40 grid at Ra=103 20
Figure 6-24: Comparison of Nu number profile obtained from second order
approximation and Star CCM for 20*20 grid at Ra=104 20
Figure 6-25: Comparison of Nu number profile obtained from second order
approximation and Star CCM for 40*40 grid at Ra=104 20
Figure 6-26: Comparison of Convergence of Nusslet Number with grid spacing
obtained from Second order Approximation and From Star CCM 20
Figure 6-27: Variation of Temperature at Center of Cavity for Polyhedral
Mesh 20
Figure 6-28: Variation of Temperature at Center of Cavity for Skewed Mesh
20
Figure 6-29: Variation of Temperature at Center of Cavity for Square Mesh
20
Figure 6-30: Variation of Error in Temperature along X axis of grid for
Polyhedral Mesh 20
Figure 6-31: Variation of Error in Velocity along X axis of grid for
Polyhedral Mesh 20
Figure 6-32: Variation of Error in Temperature along X axis of grid for
Skewed Mesh 20
Figure 6-33: Variation of Error in Velocity along X axis of grid for Skewed
Mesh 20
Figure 6-34: Variation of Error in Temperature along X axis of grid for
Square Mesh 20
Figure 6-35: Variation of Error in Velocity along X axis of grid for Square
Mesh 20
Figure 6-36: Effect of grid refinement for square grid while using Second
Order Upwind Scheme 20
Figure 6-37: Effect of grid refinement for square grid while using First
Order Upwind Scheme 20
Figure 6-38: Effect of grid refinement for square grid while using Implicit
Unsteady Solver 20
Figure 6-39: Effect of refinement for square grid using Central
Differencing Scheme 20
Figure 6-40: Effect of Different Schemes on Error Convergence for Square
Grid 20
Figure 6-41: Effect of grid refinement for polyhedral grid using Second
Order Upwind Scheme 20
Figure 6-42: Effect of grid refinement for polyhedral grid while using
First Order Upwind Scheme 20
Figure 6-43: Effect of grid refinement for polyhedral grid while using
Central Differencing Scheme 20
Figure 6-44: Effect of grid refinement for polyhedral grid while using
Implicit Unsteady Solver 20
Figure 6-45: Effect of Different Schemes on Error Convergence for
Polyhedral Grid 20
Figure 6-46: Effect of grid refinement for Skewed Mesh while using Second
Order Upwind Scheme 20
Figure 6-47: Effect of grid refinement for Skewed Mesh while using First
Order Upwind Scheme 20
Figure 6-48: Effect of grid refinement for Skewed Mesh while using Implicit
Unsteady Solver 20
Figure 6-49: Effect of grid refinement for Skewed Mesh while using Central
Differencing Scheme 20
Figure 6-50: Effect of Different Schemes on Error Convergence for Skewed
Mesh 20
Figure 6-51: Effect of grid refinement for Butterfly Mesh while using
Second Order Upwind Scheme 20
Figure 6-52: Effect of grid refinement for Butterfly Mesh while using First
Order Upwind Scheme 20
Figure 6-53: Effect of grid refinement for Butterfly Mesh while using
Implicit Unsteady Solver 20
Figure 6-54: Effect of grid refinement for Butterfly Mesh while using
Central Differencing Scheme 20
Figure 6-55: Effect of Different Schemes on Error Convergence for Butterfly
Mesh 20
Figure 6-56: Effect of Mesh topology on the solution 20
Figure 6-57: Error Convergence for Second Order Upwind Scheme 20
Figure 6-58: Error Convergence for First Order Upwind Scheme 20
Figure 6-59: Error Convergence for Central Differencing Scheme 20
Figure 6-60: Nu profile along the hot wall using 40x40 Grid 20
Figure 6-61: Nu profile along the hot wall using 80x80 Grid 20
Figure 6-62: Nu profile along the hot wall using 160x160 Grid 20
Figure 6-63: Error in Nu along the hot wall using 40x40 Grid 20
Figure 6-64: Error in Nu along the hot wall using 80x80 Grid 20
Figure 6-65: Error in Nu along the hot wall using 160x160 Grid 20
Figure 6-66: Effect of grid convergence using [pic] model on the Nu profile
along the hot wall 20
Figure 6-67: Effect of grid convergence using v2f model on the Nu profile
along the hot wall 20
Figure 6-68: Effect of grid convergence using [pic] model on the Error in
Nu profile along the hot wall 20
Figure 6-69: Effect of grid convergence using Spalart Allmaras model on the
Error in Nu profile along the hot wall 20
Figure 6-70: Effect of grid convergence using v2f model on the Error in Nu
profile along the hot wall 20
Figure 6-71: Effect of grid convergence using [pic] model on the velocity
profile near the wall 20
Figure 6-72: Effect of grid convergence using Spalart Allamaras model on
the velocity profile near the wall 20
Figure 6-73: Effect of grid convergence using v2f model on the velocity
profile near the wall 20
Figure 6-74: Kinetic Energy at mid height of the Cavity 20
Figure 6-75: Kinetic Energy at mid height of the Cavity near the Cold Wall
20
Figure 6-76: Kinetic Energy at mid height of the Cavity near the Hot Wall
20
Figure 6-77: Effect of first cell spacing for [pic] model 20
Figure 6-78: Effect of first cell spacing for v2f model 20
Figure 8-1: Experimental Setup [46] 20
Figure 8-2: A schematic diagram of experimental Setup [46] 20


Abstract

There are certain factors which contribute to enhance the accuracy of
CFD results including computational grid, numerical approximation, user
experience, post processing and turbulence modeling etc. One can obtain the
desired accuracy if expected outputs are known. But in case of design
applications sometimes there is no data available for comparison. In that
situation reliability of the CFD output becomes a question mark. There are
certain Best Practice Guidelines (BPGs) available in the literature to
obtain the accurate results. Basic intention of this thesis is to test and
verify these BPGs.
A square cavity with differentially heated walls has been taken as th