acoustics and low mach number
Hello! I am writing a finite volume code in 3D for unsteady turbulent low speed flow.The density depends on both the pressure and the temperature.When I use the standard pressure correction for compressible flow (as described in Peric book) I see that the density depends only on pressure.And when I compute density fron the equation of state,I think some acoustic phenomena happen and the resulting flow field is very strange.I also have read that for low speed the density should be computed from the equation of state, using the mean pressure that is spatially constant and depends only on time.But also using this method, I have almost the same results. Does anyone have the same problem?Any thoughts? Thank you for reading.

Re: acoustics and low mach number
What is causing your variation in density at low Mach numbers?
> When I use the standard pressure correction for compressible flow (as : described in Peric book) I see that the density depends only on pressure. This is not correct. In compressible flow with a pressure correction method, the density will depend on pressure and the variable used in the energyrelated equation (e.g. energy, enthalpy, entropy, temperature or whatever). Using a constant in space background pressure for the equation of state is a means of killing acoustic waves at low Mach numbers. However, given the above I am not sure this is where your problem lies. You are solving an energyrelated equation? 
Re: acoustics and low mach number
Yes,actually I am solving for temperature.And the variation of density is due to pressure and temperature variations. But I do not know the correct way to compute density because of the T variation.When I use the equation of state (rho=P/R/T) the results are very strange (also there is no convergence).When I compute density: rho=rho+P(correction)/R/T , as in Peric book, the density depends only from pressure. And when I differentiate the equation of state and I find the d(rho) and I use : rho=rho+d(rho) , I have the same results as the first method. Also in the SIMPLE algorithm I have changed the coefficients, so that rho(correction) will be a function of both P and T. One important thing is that when I have constant temperature (not solving for Tequation) and I compute density from the equation of state, everything is just fine.
As you can see, I am quite confused. Thank you for reading my problem 
Re: acoustics and low mach number
What is your test problem (i.e. how do you get temperature variations) and what is your Mach number?
Why have you opted to solve for temperature rather than, say, enthalpy? If you do not get convergence then you have no results. What you have is a stability problem. At low Mach numbers this is to be expected unless you use a background pressure. If you set up and solve your constant temperature problem without solving the temperature equation and then, starting from the converged answer, continue iterating but with the temperature switched on. Are the residuals zero on the first iteration? Does the solution slowly diverge, quickly diverge or remain stable? 
Re: acoustics and low mach number
I am trying to simulate the flow in a cylinder in an internal combustion engine. The mach number is qiute low, around 0.1 up to 0.35. I chose to solve for temperature,because the temperature variation is quite small (normally around 30 K) and I assume the specific heat under constant pressure (Cp) to be constant.Also the boundary conditions were more directly implemented. The background pressure that you refer is a constant spatial pressure, depending only on time?

Re: acoustics and low mach number
I did what you proposed and with constant T and computind density as: rho=P/287/P the solution was converging. Then at the next time step,I solved also for T,the solution was again converging (!!!), but the results were quite strange (as the strange ones,but this time there was convergence)

Re: acoustics and low mach number
I also did what you said and I continue iterating with the temperature switched on.The residual was zero at the first iterate, it remained stable with all the normalised residuals around 0.002 and the solution was again strange. One more thing that I should mention is that in the pressure correction equation for rho(correction) I use the dependence on both pressure and temperature and the coefficients (Ap,An,As,Su,Sp, etc) contain terms concerning the contribution of Tvariation to density. I am really confused,because this specific problem troubles me from March (I am in the middle of my PhD) and I would like to continue...

Re: acoustics and low mach number
What is strange about the solution?
Is a residual of 0.002 large or small? What is the roundoff residual? When you start from a converged solution and iterate (solving all the equations) what happens to the residuals? Do they oscillate around or does the solution diverge? If you have started from a converged solution all the equations are in balance. On the first iteration something has changed the residual from zero to 0.002. Assuming 0.002 is not roundoff then some term somewhere on the grid has moved the value of the solution variables from "correct" to "correct + a bit which should not have been added". Find where the largest change occurs and add print statements to find out what caused the change and why. 
Re: acoustics and low mach number
If you are wanting to isolate all possible extraneous effects from your simulation, then set all parameters like density etc to constant. Add in a !healthy dose! of additional viscosity  & see if your solution converges.
If it does converge, then begin relieving the constraints onebyone in order to make sure the problem does not lie in your code. I suggest leaving the 'additional viscosity' until the end. Once you are confident that all the parameters are 'playing nicely together', then begin lowering the 'artificial viscosity'. You may very well have 'acoustic effects' but these most likely come from the way in which you relax your pressure term, or your boundaryconditions. diaw... 
Re: acoustics and low mach number
I think that 0.002 is a large residual (it is the sum of every cell).When I started iterating from a converged solution,then the sum of the residuals for every equation was about 0.002.I think the problem should be on the boundary conditions,but I am not exactly sure. Another strategy that I follow is to use the pressure correction method and to correct density,assuming that rho depends only on pressure (rho=rho+P(correction)/287/T ) and when all the equations are solved,before a new iteration, to update again the density,assuming that the pressure is constant (rho=rho(old)*T(old)/T ).But this method fails once again and the results are the usual strange.

Re: acoustics and low mach number
I have tried to keep constant some parameters,but nothing changes.The only parameter that I must not keep constant is density,because this troubles me and is the cause of all my problems...The code is working just fine.I have used one similar version that I have written for others problems (incompressible) and everything went OK. We will see....

Re: acoustics and low mach number
Remember this little hint... The NS equations are merely a 'disguised form' of an underlying wave equation... So, do not be surprised to see wave phenomena...
diaw... 
Re: acoustics and low mach number
Pressure perturbations may be the root cause of the observed wave effects in your solution. I would suggest using heavy underrelaxation on your pressure update & see what happens. Double the viscosity & see what effects this has.
diaw... 
Re: acoustics and low mach number
> I think that 0.002 is a large residual
Why don't you know? Residuals can be normalised in various ways and the only one who can tell the forum if this represents a roundoff residual (solution converged  possibly nonlinear instability needing a bit of patience to find) or an unconverged residual (big change from converged solution to unconverged solution in one iteration  easy to find cause) is you. Similarly for "strange results", unless you tell the forum what is strange about the results there is no chance of anyone providing anything except vague suggestions. > Another strategy... Since you have been stuck for months, making random changes to the solution procedure without fully understanding what is going on is daft. Engage in some research and find out what is going on and fix it. As a PhD student in the area of CFD this is what you are supposed to be learning how to do. If your immediate supervisor cannot help because he is not experienced in this area then ask him to point you at someone who is. This is what supervisors are for and most universities have experienced researchers in numerical methods somewhere. 
Re: acoustics and low mach number
About the strange results,the flow field has some shocks,but this cannot be happening,because the velocity is around 5 to 25 m/sec.

Re: acoustics and low mach number
Why can't you have shocks at 5 to 25 m/s?
What is your working fluid? diaw... 
further thoughts: acoustics and low mach number
diaw wrote: Why can't you have shocks at 5 to 25 m/s?
What is your working fluid?  George, Take a small tube (20mm long x 1mm x 1mm (if you're in 3d) filled with water, or your working fluid. Apply an inlet velocity of 1 m/s, with no convection stabilisation & tell us what happens. Depending on how you introduce your inlet velocity, you should end up with waterhammer & lots of shocks. Your solver needs to be 'soft in time' for you to see this. If your solver does not show the effect, then take out the artificial viscosity  or lower your working viscosity. Tell us what you observe. diaw... 
Re: further thoughts: acoustics and low mach numbe
My working fluid is air at temperature of 300 K, which is compressible fluid not like water. That is why I believe that no shocks can occur.Up to now I simulate the flow in a closedend duct.There are 3 solid walls and one inlet. I simulated the duct with the water that you proposed and I saw some shocklike results, but air is something different. Any other thoughts?

Re: further thoughts: acoustics and low mach numbe
George wrote: My working fluid is air at temperature of 300 K, which is compressible fluid not like water. That is why I believe that no shocks can occur.Up to now I simulate the flow in a closedend duct.There are 3 solid walls and one inlet. I simulated the duct with the water that you proposed and I saw some shocklike results, but air is something different. Any other thoughts?
 Think about why air should be different to water. Does your air have viscosity? If yes, then it is possible for you to observe acoustic effects  in my opinion. I would suggest that you look carefully into any scaling used in your model  this is vital. Again, I stress, look at how you are converging in on the model pressure. This is the key link to your acoustic effects  either perceived, or artificial. If they are real, then you will have some explaining to do. Good luck along that path, as it is a tough journey. diaw... 
Re: further thoughts: acoustics and low mach numbe
> Up to now I simulate the flow in a closedend duct.There are 3 solid walls and one inlet.
Outlet? What do you expect the predicted flowfield to look like? 
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