Cp at stagnation point too high
 

Hello,

I am calculating an incompressible air flow (V,free=36 m/sec at T=0°C) for a blunt body. Using SST-turbulence model and SBF=1 (i.e. kinda maximum accuracy) I am getting a maximum pressure coefficient of Cp=1.06 and a range of 1.07>Cp>-1.6.

Theory however predicts that the maximum stagnation pressure surplus in incompressible flow cannot exceed the dynamic pressure, i.e. CPmax=1. Has anyone made the same observations and knows maybe what to do in order to fix that?

Secondly my concrete issue is now that I have to setup the sensors for the experiments. The question is if the CP-scale is shifted in general that is the minimum CP is more like -1.7 or is only the maximum value affected and the suction zones are predicted correctly?

Thanks Andy

Re: Cp at stagnation point too high
 

Hi Andy,

This is not unusual and there are a few papers on the topic (can't remember exacly which ones off hand). There is in fact a physical phenomenon that can lead to this occurrence. If you follow an element of fluid along a streamline to your stagnation point, the shear stresses one either side will be pointing in the same direction, transferring additional momentum to this fluid. This leads to a total pressure around the stagnation point which is higher than the upstream total pressure.

The region of Cp>1 shrinks rapidly as Reynolds number increases. However, in a CFD code there are other factors such as grid resolution and turbulence models which can lead to it's appearance in high Reynolds number flows. The turbulence model increases the effective viscosity, which decreases the effective Reynolds number.

Furthermore, two equation models will incorrectly increase the production of turbulent kinetic energy in regions of decelerating flow (because production ~ strain rate, which is a scalar value and does not distinguish between shear strain and strain due to acceleration). There are limiters to these models which will minimize this. In CFX, only the SST model has the production limiter, so switching to SST may reduce your Cp. The equivalent k-e limiter has been added for version 11.

Finally, if you grid is too coarse approaching the stagnation point, numerical diffusion will also amplify the effect.

All of that said, the effect is local and momentum and energy are still conserved globally, so other than having an unexpectedly high Cp at your stagnation point, the results are probably not greatly affected. Switching your turbulence model and refining your grid is still a good idea, however, as it will give you an idea of the quality of your solution.

Regards,,br> Robin

Re: Cp at stagnation point too high
 

Thanks again!

Re: Cp at stagnation point too high
 

Hi Andy,

there is a paper by Issa of Imperial College which addresses this point exactly. I do not have the publication info handy but remember it was short and to the point.

Regards,

Bak_Flow