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Compressible vs. incompressible NS at high Temperatures

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Old   December 19, 1999, 08:38
Default Compressible vs. incompressible NS at high Temperatures
Jean Lacroix
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* which are the Stokes Terms of the Navier Stokes Equations (NS)?

* Considering a flow (air+ 20% Fuel) at Re=400-1700; a Temperature range of 400-1700 K at P=1 atm. which Form of the NS do we have to use? Schlichting suggests the use of the compressible form of the NS above 0.3Mach because in this case the arise of pressure influenses the density. We operate quite far from this Mach region, but because of Heating and the occurance of chemical reactions we get a density change. In this case the density changes is a result of heating (from 400 to 1700K) and chemical reactions; the pressure remains almost unchanged.

Can we use the incompressible Form of the NS while considering the density change? Which terms of the Energy Equation do we have to use? ( only convection, conduction and heat generation) or we have to consider some other Terms ( see Bird, Lightfoot) that deal with pressure and so on?

Any literature about this topic? I found almost nothing about this subject in books!

thanks in advance

Jean Lacroix
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Old   December 24, 1999, 06:21
Default Re: Compressible vs. incompressible NS at high Temperatures
Ioannis Dotsikas
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Basically itīs more secure to use the compressible Form of the Navier Stgokes Equations. Even if your System concerns an incompressible case, the compressible form gives you the right solution. The "incompressible Equations" is only a simplifacation of the compressible NS which you get if you assume that density and viscosity donīt change (kontinuity). With the compressible NS you are always on the right side, regardless whether you have a compressible or an incompressible Flow. Surelly the compressible form is not as easy to solve as the incompressible.

Specific about your Problem: I suppose that if you use the incompressible NS considering the density change \frac{\partial r u u}{\partial z}+ ... you should get the same results as the compressible NS. The spare Terms of the compresible Eq. shouldnīt change the results significally. The continuity in this case should make it. The arise of your temperature is not strong; even if your T-gradients are strong you shouldnīt get any problem

The other terms of the energy equation as you say deal with the pressure/temperature dependence. Try to neglect them.

What is the oppinion of J. Chien?

best regards

I. Dotsikas
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