Equation 3-166 through Equation 3-168 must be solved using a Time Dependent study. This can be computationally expensive. The Rotating Machinery, Fluid Flow interfaces therefore support the so-called frozen rotor approach. The frozen rotor approach assumes that the flow in the rotating domain, expressed in the rotating coordinate system, is fully developed. Equation 3-164 then reduces to

and Equation 3-165 to

Frozen rotor is both a study type and an equation form. When solving a rotating machinery model using a Frozen Rotor study step, the Rotating Machinery, Fluid Flow interfaces effectively solve Equation 3-170 and Equation 3-170 in a “rotating” domain, but “rotating” domains do not rotate at all. Boundary conditions remain transformed as if the domains were rotating, but the domains remain fixed, or frozen, in position. As in the time-dependent case, the Rotating Machinery, Fluid Flow interfaces solve for the velocity vector in the stationary coordinate system, u, rather than for v.

To make Equation 3-166 and Equation 3-167 equivalent to Equation 3-169 and Equation 3-170, the Frozen Rotor study step defines a parameter TIME, which by default is set to zero (TIME appears in the Parameters node under Global Definitions). Equation 3-168 is replaced by

Since TIME is a parameter and x is a function of TIME, ∂x/∂T evaluates to its correct value. Finally, ∂ρ/∂T = 0 and the mesh time derivative of the velocity is replaced by

The frozen rotor approach can in special cases give the same solution as solving Equation 3-166 through Equation 3-168 to steady state. This is the case if, for example, the whole geometry is rotating, or if the model is invariant with respect to the position of the rotating domain relative to the nonrotating domain. The latter is the case for a fan placed in the middle of a straight, cylindrical duct.

In most cases, however, there is no steady-state solution to the rotating machinery problem. Only a pseudo-steady state where the solution varies periodically around some average solution. In those cases, the frozen rotor approach gives an approximate solution to the pseudo-steady state. The approximation depends on the position in which the rotor is frozen, and the method cannot capture transient effects (see Ref. 3 and Ref. 4). An estimate of the effect of the rotor position can be obtained by making a parametric sweep over TIME.

The frozen rotor approach is very useful for attaining initial values for time-dependent simulations. Starting from a frozen rotor solution, the pseudo-steady state can be reached within a few revolutions, while starting from u = 0 can require tens of revolutions. See, for example, Ref. 5.