[liliana]

I am simulating a convergent-divergent nozzle benchmark (Arina's nozzle).

I am trying to reproduce the paper "Numerical simulation of near-critical fluids" (Renzo Arina, 2004). The authors provided results from a theoretical studies with the conditions: P at inlet = 1 bar; P at outlet = 0.83 bar; T at inlet = 288 K; T at outlet = 300 K. Also, the authors cited the Mach number at inlet, with is 0.24. The fluid is air, they used EOS Redlich-Kwong and simulated inviscid flow.

So, I was trying to reproduce the results in Star CCM+ commercial software. I am using: axisymmetric model, inviscid flow, EOS Redlich-Kwong and coupled solver.

The problem was when I was setting the BC. According to Star CCM+ manuals, the "FreeStream" BC is used for external flow, when we need to specify the Mach number at upstream. For internal flows, we should use Stagnation Inlet, since we know the pressure at the inlet. I tried both.

For FreeStream, I used the following values:

Mach number = 0.24

Static pressure = 1 bar

Static temperature = 288 K.

For Stagnation inlet, I used the following values:

Supersonic static pressure = 0 (according to manuals, if the flow at inlet is subsonic, this value makes no difference)

Total pressure: 1 bar;

Total temperature: 288 K.

In both cases, I have used Pressure Outlet BC, with pressure 0.83 bar and static temperature 300 K.

The results were quite surprising when I compare the density profile at the center of model (see picture below). By using the FreeStream (blue dots), I've got the same results as the authors (yellow dots). But when I use Stagnation Inlet (red dots), which I supposed to be the right choice, the results were quite difference.

I have 2 questions here:

1) should the results be the same?
2) if the answer for 1) is not, why the "correct BC" (Stagnation Inlet) is giving the wrong results?

Moreover, I observed one more thing when I plotted the pressure profile at the centerline of the model (see picture below). When using FreeStream, the pressure at the inlet is 1 bar (like we set). But when using Stagnation Inlet, the pressure at inlet is a little smaller than 1 bar. Why?

Thanks!

Picture: https://drive.google.com/file/d/1E_o...ew?usp=sharing

[Voluped]

Should the results be the same?

The results might not be exactly the same because the boundary conditions for FreeStream and Stagnation Inlet are fundamentally different. FreeStream conditions are more suitable for external flows and might not capture internal flow characteristics accurately, while Stagnation Inlet is designed for internal flows where total pressure and temperature are known far upstream.

Why is the "correct BC" (Stagnation Inlet) giving different results?
The Stagnation Inlet boundary condition specifies the total pressure and temperature, which are the conditions at an imaginary plenum where the flow is at rest. In your case, the discrepancy might be due to the way STAR-CCM+ handles the conversion from total to static quantities at the inlet. The flow conditions might not be perfectly capturing the inlet pressure profile as intended, especially if there are numerical inaccuracies or differences in how STAR-CCM+ interprets the boundary conditions compared to the theoretical study.

Observation about the Pressure Profile:
When using FreeStream, the static pressure at the inlet is set directly, which is why you see 1 bar as expected.
When using Stagnation Inlet, the total pressure is set, and the static pressure is derived from it. If there are any numerical errors or if the flow is not perfectly subsonic at the inlet, the static pressure might not be exactly 1 bar.

[liliana]

Yes, I found the problem.
I was using the static pressure instead of total pressure in stagnation inlet. Now, the results are the same.
Thanks.