[BigJoe]

I'm simulating a cone at transonic flow. The detached bow shock is reflected from the top and bottom wall which moves upstream and change the inlet boundary condition. As a result, the inlet Mach number is not the one that I could get based on isentropic relation between inlet total pressure and outlet static pressure.The Mach is fluctuating and does not stabilize.

Does anybody have same issues?

[LuckyTran]

The Mach number at the inlet will depend on downstream conditions for sub-sonic inlets. Only when the inlet is supersonic is the Mach number unique. This is completely physical.

Isentropic relations are usually derived assuming purely one-dimensional flow and hence gives rise to this discrepancy. The isentropic relations themselves are not wrong, what is wrong is assuming the flow is one-dimensional and that there are no two-dimensional effects.

Analytically, what you need to do is solve the 2D/3D equation (using method of characteristics perhaps) and you will be able to resolve these discrepancies.

A notorious example to those skilled in the lost arts is the critical pressure ratio needed for flow in a nozzle to become choked. The 1D isentropic relations will tell you that ratio is around 1.8, but because of 2D effects the actual ratio may be as low as 1.2 depending on the particular nozzle contour. If you solve the 2D/3D equations, you do indeed get the correct answer.

[BigJoe]

Dude thanks so much. I originally set 0.75 at inlet and it will decrease, increase, and decrease. In the end it will keep fluctuating between 0.72 and 0.73 more or less....

So in fluent we could also use Method of Characteristics(MOC)?

[LuckyTran]

Fluctuations are fluctuations. These are generally present in all simulations as long as the shock isn't completely resolved.

Method of characteristics is an analytical technique. Fluent is a numerical solver and does not use it. Compare method of characteristics to separation of variables, eigenfunction expansions, etc.