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amphy404 February 25, 2013 21:48

Rotating reference frame
 
Hi,

I have a question about the rotating reference frame source code for the space centered schemes in numerics_convective.cpp.

For instance, in numerics_convective.cpp: L3198-3208.

Code:

    /*--- Adjustment for a rotating frame ---*/
    if (rotating_frame) {
        ProjVelocity = Rot_Flux;
        for (iVar = 0; iVar < nVar; iVar++) {
            val_resconv[iVar] -= ProjVelocity * 0.5*(U_i[iVar]+U_j[iVar]);
            if (implicit) {
                val_Jacobian_i[iVar][iVar] -= 0.5*ProjVelocity;
                val_Jacobian_j[iVar][iVar] -= 0.5*ProjVelocity;
            }
        }
    }

From this code, it looks like the rotation is accounted for by subtracting the rotational velocity (Rot_Flux) from the projected flux (val_resconv). This makes sense for the continuity and momentum equations. Perhaps it is just my misunderstanding, but for the energy equation shouldn't it be subtracting the enthalpy, rather than the internal energy?

That is,
Code:

val_resconv[nVar-1] -= ProjVelocity * MeanDensity * MeanEnthalpy;
Thanks,
KW

economon February 26, 2013 07:10

Hi,

Thanks for the question. In SU2, we are using a version of the equations expressed in a non-interial frame while still solving for the absolute velocities as part of the conserved variables (an 'absolute velocity' formulation). The transformation of the equations to this form results in not only an adjustment of the convective fluxes to take into account the rotational velocity of the mesh faces, but also changes in the momentum and energy equations. More specifically, the momentum equations gain a source term, and the energy flux is slightly modified to become density*enthalpy*(velocity - rotational_velocity) + rotational_velocity*pressure, which could also be written as density*enthalpy*velocity - rotational_velocity*density*energy after substituting the definition of enthalpy. The latter expression is implemented in SU2.

If you are interested in more details on the formulation, there is a nice description in "A Three-Dimensional Euler Solver for Turbomachinery Blade Rows" by D. G. Holmes & S. S. Tong, or please see the following paper using the formulation within SU2: http://adl.stanford.edu/papers/AIAA-2012-3018.pdf.

Hope this helps!
Tom


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