Estimation of the Accuracy Obtained from CFD for industrial
applications
Prepared by
Imama Zaidi
Sources of Uncertainty
• Computational Grid– Grid Spacing– Grid Topology
• Numerical Approximation• User Errors• Post Processing• Turbulence Modelling• Flow complexity (multi-phase flow, combustion…
etc)
Problem Definition
• Rayleigh Number
Ra=
• Reference Velocity
V0=
k
THCg P
32
THg
Part I
Laminar Flow
Flow inside Cavity
Types of Grids testedSquare grid
Polyhedral
SkewedButterfly type
_ . _h Control Vol N cells
Numerical Schemes tested
Convection schemes:
• Second Order Upwind• First Order Upwind• Central Differencing Scheme
Note: Runs are carried out in steady state mode
Richardson Extrapolation• Grid independent
solution
• Order of convergence
• Exact solution
• Targets: Nu
and Mass flow across ½ section =>
)ln(
)ln(
2
1
32
21
hhXXXX
n
1)(3
2
233
nt
hh
XXXX
Second Order UpwindSquare grid
First Order UpwindSquare grid
Central Differencing Scheme
n=2.33
Ra=103
Effect of Order of ConvergenceRich. Extrap. Using 102, 20, 40
Rich. Extrap. Using 202, 402, 802
Effect of Order of Convergence
n=1.72
n=1.96
Richardson Extrapolation at Hot Wall
Post Processing Error
20X2040X40
Example for user input Error
THgV 0Reference velocity is defined as:
Effect of Changing Reference Velocity
Effect of Numerical Scheme
Square Grid
Polyhedral Grid
Skewed Grid
Butterfly Type Grid
Why does error not always decrease?
• For square grid– Dx.Dt error > Dx2 ? But this is steady state– Residual normalisation? But increasing nb of
iteration => no change
• For skewed grid– Error = constant, whatever h.– Need to test other “gradient reconstruction”
methods for non-orthogonality
Part II
Turbulent Flow
Flow inside Cavity
Type of Mesh
Low Reynolds Number Model
• Standard Low Reynolds Number Model (Lein et all)
• Abe Nagano Kondoh (ANK)Low Reynolds Model (Abe et all)
• V2f Model(Durbin et all)• Model(Mentor)• Spalart Allamaras (SA) Model (Baldwin et all)
sstk
k
k
Y+ from 40*40 Grid
Y+ from 80*80 Grid
Y+ from 160*160 Grid
Error From Different Turbulence Models For Nu
Kω-sst model
Spalart Allmaras
V2f Model
K-sst Model
Near Wall Grid Dependence Kw-sst Model
Grid 80X80 and changing near-wall cell x
Near Wall Grid Dependence V2f Model
Conclusions
• For distorted grids (Skewed Mesh), the refinement does not guarantee the accuracy
• The higher the order of scheme is, the higher will be the accuracy.
• Richardson extrapolation theory tested for laminar flow, seems to be in good agreement with the results for order of convergence nearly equals to 2
Conclusions
• K SST model compared to the other models tested, seems more dependent on the grid refinement near the wall and grid independence is not reached even with 160x160 grid.
