I got a question about the operating pressure in a CVD or any other chamber. For example, if you say the operating pressure is 100 Torr, does it mean the pressure is uniformly 100 Torr inside the chamber? If so, the gradient P will be zero, the pressure-correction is not necessary. If not? what does the operating pressure mean.

Thank you

Leo

If your flow is assumed incompressible, the pressure you obtain from the numercal simulation is not the thermodynamic pressure. When solve the flow numerically, the pressure correction is required to obtain a flow field of the SOLENOIDAL (divergence u = 0) one. When compressible one is of interset, the case are not same as the incompressible flow but I think you may concern an incompressible flow.

BDO

Hi, BDO,

Thanks for your reply. you are right, I am interested in incompressible flow in a chamber. Could you please tell me what is the relation between the calculated pressure filed and the thermodynamic pressure used in the publications? And which pressure is used for \rho=PM/RT in obtaining the density of ideal gas?

Thanks

Leo

Let's start with the incompressible NS equation. Take divergence on the NS equation and then we have,

p_{ii} = - divergence{convection term}. --(*)

Therefore, the pressure field in the incompressible flow strictly depend on the velocity field. All pressure-correction methods are to solve (*) with an approximation. Like the book written by G.K. Batchelor, the pressure from (*) is called mechanical pressure. Therefore there's no relation with the thermodynamic pressure and neither with the equation of state like the ideal gas law. And it is direct consequence that the density cannot be alterred by the flow under the assumption of the incompressibel flow.

It is of interest to note that the calculated pressure in the pressure correction method may have an error larger than the order of the error introdeced in discretization. When you have an interest on the pressure field, we should take care or confirm the accuracy of the pressure field.

And for the last question, the variables in the ideal gas law are thermodynamic variable defined in the (thermodynamically) equalibrium state. I think thermodynamic varible should be used.

BDO