Hello, I have been kicking around the net (also in this forum) for quite a while now. And I have browsed some literature, too. However, I haven't found a satisfying answer to these questions:

The situation is the following: I would like to prescribe a velocty profile at an inflow boundary. The velocity profile was measured in an experiment. The flow is turbulent but statistically steady. I am using a compressible Navier-Stokes solver (Jameson scheme plus local preconditioning for low Mach-number flows) to compute this flow.

What boundary treatment is recommeded at the inflow boundary in order to match/prescribe the velocity profile of the experiment?

It seems like "everyone" prescribes total pressure, total tempereture and flow angle in such cases. However, in my case total pressure is not constant since it is a boundary layer profile. How do I compute total temperature and total pressure profiles from a given velocity profile? Couldn't I just set constant density and use the exp. vel. profile to set (rho*u) at the inflow while extrapolating static pressure from the interior??

I appreciate any comments, hints and references. (In particular regarding any theory about why it is common practice to use total conditions as inflow bcs)

Thanks in advance, Alan

as far as I know,the specification of boundary conditions for flow equations is usually determined according the characteristics of the flow along the boundaries.For subsonic inflow,there are three characteristics running inward and one running outward(in 2D),so three boundary conditions need to be specified. For supersonic inflow,all 4 characteristics run inwards and need specifying. I think you can also specify velocity profile with other two boundry conditions.

In principle, what dingxiwang said is correct, but I have to add something. Not only the directions of the characteristics are important, but also the type of quantities (characteristic variables) that are transported along the charateristic lines. It's good to know that three quantities enter the domain from outside, and one should leave the domain (subsonic, 2D, inlet) but you cannot just choose any quantity. Some choices will work better than others, some won't work at all, and the correct choice (characteristic variables) should work best. Often we cannot take the best choice, though, because it's just not available.

You are already familiar with the choice of total pressure, total temperature and flow angle, so why don't you go that way? Given the velocity profile, you might assume a uniform static pressure and density profile at the inlet and obtain a corresponding total pressure profile. You may further assume a uniform total temperature profile. Directly enforcing the velocity profile has been done before, but these boundary conditions usually don't behave that well. The problem is not well posed that way.

dingxiwang, Mani, thank you very much for your replies - it's good to discuss with you.

I am aware of the fact that setting characterstic variables corresponding to the direction of characteristics is the proper way to go - at least for Euler equations. And I understand that often we don't know them and, hence, we set other variables.

I have read the chapters about setting boundary conditions in Hirsch "Numerical Computation of Internal and External Flows" and in Poinsot "Theoretical and Numerical Combustion". However, I couldn't find any hints why it is advantagous to set ptot, Ttot and flow angle?

Mani: Can you give me any reference on why it is good to use total conditions? (A reference containing some equations that show how one comes to this conclusion.)

Also: I don't see the link between setting total pressure and prescribing the velocity profile. I could go the way you suggested: assuming a constant static pressure and temp. With this and the given vel. profile I could obtain a ptot-profile that I set in the computations. But then, do I need to extrapolate the velocities from the interior in order to get the numerical BCs for the momentum equations? Also, doesn't BL theory tell us that T (and Ttot) is not constant in the BL?

I addition, my impression is that all the chracteristic variables theory is assuming isentropic flow. This is not the case in the boundary layer....??

I am sorry to bug you with those beginner's questions. It's just that I am stuck with my own investigations.

Thanks in advance for your comments, Alan

>Can you give me any reference on why it is good to use total conditions? (A reference containing some equations that show how one comes to this conclusion.)

I am not aware of any reference that specifically discusses this problem, although you might find some hints in any discussion of inlet conditions. I guess the major reason for using total quantities and flow direction are that it seems natural. These are the conditions that are actually applied in experiments, and that are usually measured and provided. Maybe that's all there is to it. Another (equivalent) set of inlet variables is total enthalpy, entropy, and flow angles.

Yes, there are some open questions about the inlet profile (it's not uniquely defined just by velocity, that's for sure). The total temperature may or may not have a uniform profile. If it's uniform despite a velocity profile, you basically assume that the static temperature is not uniform (it's hotter near the wall, not entirely unrealistic). In essence, you'll have to make some assumption, and see which one works best for you.

You would probably extrapolate entropy, not velocity.

>addition, my impression is that all the chracteristic variables theory is assuming isentropic flow. This is not the case in the boundary layer....??

correct. However, if the boundary layer is not too thick, it is dominated by the inviscid isentropic core. Also, even with fully developed flow, applying the quasi-1D boundary conditions along streamlines should still be ok, even if not exact.

Thanks for your comments. I will try it out...

You can certainly try specifying the following at your inlet:

3 velocity components, static temperature

where i am assuming a 3D flow solving 5 transport equations (mass, 3 momentum, energy). This may not be as accurate as using characteristic bcs, but may be better suited to your problem, assuming you have a decent guess for static temperature (uniform or profile). I have run the above inlet boundary conditions for many viscous cases using a finite volume code with low-Mach number preconditioning.

Thanks for your comments! I am glad to hear that someone else has (or had) the same problem before...

Hm, static temperature is not uniform in a boundary layer - although I believe variations of Tstat are small in my case since the Mach number is small (0.1). I'd prefer to set a uniform pressure. Have you tried this out?

Also: if I went the way you suggested (assuming a good guess for Tstat) then I would extrapolate static pressure from the interior. Is this correct?

Thanks, Alan

For the compressible flow inlet bc i suggested,

3 velocity components, static temperature

yes, you want to define static pressure at the inlet faces using values from within the computational domain, and then calculate inlet density from the prescribed temperature and extrapolated pressure value.

I would NOT recommend trying a combination such as

3 velocity components, static pressure

or

3 velocity components, static density

Thanks for your help.

What is the difference between static temperature and Total temperature?