Bow Shock Spurious Mach-Waves

[julius]

Hi Everyone,

I’m currently trying do an implicit LES of a supersonic turbine with inlet Ma=1.8. I’m using the newest version of PyFR (3.1) with entropy-filter as shock capturing, rk4, and a 2D structured mesh. Parts of my .ini can be found below.

[solver]
system = navier-stokes
order = 4
viscosity-correction = sutherland
shock-capturing = entropy-filter

[solver-entropy-filter]
d-min = 1e-6
p-min = 1e-6
e-tol = 1e-6
formulation = nonlinear
niters = 2 ; (I also tested niters=100, didn’t change)

[solver-interfaces]
riemann-solver = hllc
hllc-wave-speed-estimate = toro
ldg-beta = 0.5
ldg-tau = 0.1

[solver-elements-quad]
soln-pts = gauss-legendre-lobatto
flux-pts = gauss-legendre-lobatto

[solver-interfaces-line]
flux-pts = gauss-legendre-lobatto

[soln-bcs-outlet]
type = sup-out-fn

[soln-bcs-inlet] ; those values are specified in the constants
type = sup-in-fa
u = u1
v = 0
rho = rho1
p = p1

[soln-bcs-airfoil]
type = no-slp-adia-wall

My issue is, that at the LE bow shock, spurious mach waves form that are then also reflected from the surface of the blade (see figures below).

Density field, snapshot:

dRho / dx, snapshot:

All those features also appear when time-averaging. So far, changing

• time-step

• mesh resolution (I also tried an unstructured mesh, did not change it)

• etol to 1e-3 (planning to test further values)

did not resolve the issue.

Does anyone have an idea what to change/ test in order to get rid of those?

Best regards,

Julius

[kaschau]

Hi Julius

I cant see your images for some reasons, but have some suggestions. Your ini files looks fine in terms of shock capturing.

I would try a few changes, though:

Use gauss-legendre points everywhere and see what that does.

Second, I cant see your mesh, but the more you can align your grid to a bow shock the better in my experience. I even go so far as to overlay initial runs back into my CAD files to create geometries that I can use to align my mesh.

[julius]

Hi Kyle,

thanks for your answer, and sorry for the figures, I hope you can see the ones attached here.

The mesh above is just an example, I’ve tried many more meshes, all with similar phenomena.

I’ve tried using Gauss-Legendre points, however, it seemed that the simulation became much less stable, I will test it more, maybe by changing the initial conditions (instead of restarting result files with GLL points).

I definitely agree that a better mesh alignment would help, since the origin of those features seems to depend on the shock position relative to the mesh, but my aim is to simulate unsteady shocks, where mesh alignment would then be impossible.

Nonetheless, thank you very much for your answer!