Verification and Validation in CFD and Heat Transfer: ANSYS Practice and the New ASME Standard Dimitri P. Tselepidakis & Lewis Collins ASME 2012 Verification and Validation Symposium May 3 rd, 2012 1
Outline Code Verification Solution Verification Validation Discussion Conclusions 2
I. Code Verification 3
Code Verification: Couette Flow Navier-Stokes Equations Laminar Couette flow b Input Parameter Moving plate velocity Distance between plates Length of domain Pressure drop Value 3 m/s 1 m 1.5 m -12 Pa/m Fluid density 1 kg/m 3 Fluid viscosity 1 kg/m-s 4
) Couette Flow: Meshes Loc-2 Loc-1 Mesh 4: 21 x 9 Mesh 3: 35 x 15 Mesh 2: 59 x 25 Mesh 1: 99 x 41 5
) Couette Flow: Velocity Profiles Loc-2 Loc-1 6
Couette Flow: Code Verification Solution Total Number of Cells Code Verification Results Cells Along x-direction Cells Along y-direction Velocity at Loc-1 (m/s) Velocity at Loc-2 (m/s) Mass Flow Rate (kg/s) Mesh 4 189 21 9 3.0185 3.3889 2.5247 Mesh 3 525 35 15 3.0067 3.3800 2.5089 Mesh 2 1475 59 25 3.0024 3.3768 2.5032 Mesh 1 4059 99 41 3.0009 3.3757 2.5012 Analytical - - - 3.0000 3.3750 2.5000 Mesh Error (E h ) in the Code Simulation during Mesh Refinement Characteristic Mesh Size, h i (m) Refinement Factor, h i+1 /h i Velocity Error at Loc-1 (m/s) Velocity Error at Loc-2 (m/s) Integrated Mass Flow Rate Error (kg/s) 4 0.0891-0.0185 0.0139 0.0247 3 0.0535 1.67 0.0067 0.0050 0.0089 2 0.0319 1.68 0.0024 0.0018 0.0032 1 0.0192 1.66 0.0009 0.0007 0.0012 7
Couette Flow: Order of Convergence Error Mesh size, h Observed Order of Convergence from Mesh Refinement Meshes Velocity at Loc-1 Velocity at Loc-2 Mass Flow Rate 3 and 4 1.99 2.00 2.00 2 and 3 1.99 1.98 1.98 1 and 2 1.94 1.87 1.94 All (1 to 4) 1.97 1.95 1.97 8
II. Solution Verification 9
Solution Verification: Pipe Expansion with Heat Flux Axisymmetric computational domain Double precision Second-order discretization SST k-ω turbulence model with low-reynolds-number corrections 3 meshes 10
) Pipe Expansion with Heat Flux: Problem Parameters and Detail of Mesh #3 Input Parameter Value Pipe diameter before expansion 0.0381 m Pipe diameter after expansion Heat flux Mass flow 0.09525 m 10.0 W/m 2 0.0513 kg/s Density 1.225 kg/m 3 Viscosity 1.683e-5 kg/m-s Specific heat 1006.43 J/kg-K Thermal conductivity 0.0242 W/m-K Mesh #3 Variables in the evaluation of uncertainties Reattachment length, L/H Nusselt number at the heated wall 11
) Pipe Expansion with Heat Flux: Uncertainty Analysis L/H N 1 620,800 620,800 N 2 155,200 155,200 N 3 38,800 38,800 r 21 2 2 r 32 2 2 11.290 2.284 11.280 2.269 11.250 2.230 p 1.58 1.38 11.295 2.293 0.09% 0.7% 0.04% 0.4% 0.06% 0.6% 0.17% 1.3% 12
III. Validation 13
ASME V&V 20 Procedure Estimate the modeling error of a given mathematical model in relation to a given set of experimental data Validation uncertainty Validation comparison error If E >> u val the comparison error is probably dominated by the modeling error, which indicates that the model must be improved For E < u val, modeling error is likely within the noise level imposed by the numerical, experimental and input uncertainties 14
Nusselt Number along the Heated Wall x/h 5.00 Nu(x)/Nu DB 4.50 4.00 3.50 Baughn et al exp. data Simulation 3.00 2.50 2.00 1.50 1.00 0.50 0.00 0.00 10.00 20.00 30.00 40.00 50.00 60.00 x/h 15
Comparison of Validation Uncertainty with the Comparison Error 0.8 0.7 0.6 0.5 0.4 0.3 uval E 0.2 0.1 16 0 0.00 10.00 20.00 30.00 40.00 50.00 60.00 x/h
IV. Discussion 17
V&V in CFD ASME Standard involves a partitioning of non-numerical simulation error sources into modeling assumptions ( model ) and input parameters ( input ) input errors are combined with experimental and numerical error sources Alternative established definitions of verification and validation DoD: the process of determining that a model implementation and its associated data accurately represent the developer's conceptual description and specifications. IEEE: providing objective evidence that the software and its associated products conform to requirements ANSYS typically adopts the strong form definition of the model so that, for example, BC uncertainties can be treated more explicitly 18
ANSYS V&V Practices ANSYS uses ASME Standard and additional practices as appropriate to each situation MMS monitoring of conserved quantities multi-level integration testing recourse to experimental results benchmark code-to-code comparisons Due to breadth of ANSYS CFD features and models, V&V is a continuous and joint endeavor between code developer and end-user ANSYS performs verification on the basic features of the code ANSYS performs validation on a more-limited set of carefully selected problems ANSYS customers extend this foundation as needed for application-specific V&V ANSYS offers an array of software features* and services to assist *(e.g. adjoint solver, design-of-experiments, latin hypercube sampling, etc.) 19
Next Steps in CFD V&V A more general V&V approach is required, and further work is needed to establish robust factors of safety for the application of RE and GCI, or otherwise extend these methods, to more complex cases unstructured grids of widely varying sizes particle-based methods (typically associated with multiphase flows) moving-boundary problems transient fluid/thermal problems large-eddy simulations (LES) 20
V. Conclusions 21
Conclusions We presented an example of each of the three procedures: code verification, solution verification and validation. The study was performed with the FLUENT solver Code verification was exercised on the Navier-Stokes and heat transfer equations, and solution verification and validation was achieved using the GCI method on a non-isothermal, turbulent flow with well-documented experimental data In general, FLUENT is well verified and validated for this class of CFD and CHT problems The ASME V&V procedures represent a significant step of progress and clarity compared to commonly-adopted methods of comparison of simulation predictions with experiments ANSYS V&V practices are generally compliant with ASME V&V 20-2009 subject to the issues discussed in the paper, which suggest promising topics for further research 22