from dimensional analysis, one could conclude that the the pitching moment coefficients of the models (numerical and experimental) have the same value, when the other relevant dimensionless numbers have the same value, i.e Re_M=Re_E and in compressible flow Ma_M=Ma_E. The moment coefficient could be defined by
cm=M(Pitching Torque) / (rho*U_infty^2/2 * Area * chord-length) and thus
cm_M=cm_E
=>
M_E=M_M*/ (rho*U_infty^2/2 * Area * chord-length)_M * (rho*U_infty^2/2 * Area * chord-length)_E
However, you stated that Re and u_infty have the same value at the same time for the model and the experiments. Did you scale the viscosity too?
It is a part of developing a methodology for scaling.
The Mach number, AOA and Re was kept constant. So I believe the CL and CD should be same as long as the shape is same as it is a function of Re, AOA and M alone, which are dimensionless.
Where as in case of CM it is dependent of Chord length also ... So i believe we cant directly compare the CM..
As stated by Bastian, you don't have to worry about scaling dimensions if the flow conditions are the same. That's why non-dimensional coefficients do exist. Of course, you have to take the same reference point of the experimental model.
Did you find different results between the models?