Revolutionary methodology for solution of periodically repeating turbulent flows at cheaper cost
CFD applied to turbo-machinery has come a long way from the inviscid 2D blade-to-blade methods of the 1960’s and recent developments using the Harmonic Balance Method have ensured that numerical simulation now plays a major role in turbo-machinery design.
• The choice between steady-state and transient methods for turbo machinery applications depends on having the right balance between computational cost, accuracy and efficiency. The nonlinear harmonic balance method in STAR-CCM+ offers the best of both worlds specifically for periodic flows. Shown here is a rotor/stator mesh.

In general, turbo-machinery devices are multi-stage with unequal pitches for stators and rotors, and a majority of the flows are highly unsteady in nature.

The choice between steady-state and transient methods for these types of applications depends on having the right balance between computational cost, accuracy and efficiency.

The nonlinear Harmonic Balance Method in STAR-CCM+ is an entirely new computational approach, offering the best of both worlds specifically for periodic flows.

The Harmonic Balance Method in STAR-CCM+ is a full decomposition of the Navier-Stokes equations in the frequency domain where the unsteady, transient flow is represented in the frequency domain as a Fourier series in time.

All transport equations for momentum, energy and turbulence are decomposed into the frequency domain on the basis of fundamental driving modes, usually a blade-passing frequency or repeating wake modes. To obtain the Fourier Coefficients, the steady-state equations representing the unsteady solution at discrete time levels in a single unsteady period are solved.

The number of time levels required depends on the number of modes retained in the problem and the steady state solution in every time-level is implicitly coupled at the periodic boundaries by the physical time derivatives.

The linear system is then subjected to approximate factorization to achieve implicit coupling between time levels.

Applications

Axial flow turbo-machinery was one of the first devices that were modeled using the Harmonic Balance Method, although the method can be applied to centrifugal machines as well. The method can, in principle, be applied to a wide range of physical problems, provided the problem is periodic in time. Some examples include flutter, forced response, heat transfer, performance (efficiency) and acoustics.

Benefits

The main benefit of the Harmonic Balance Method is that you can solve unsteady flow problems using steady flow solver techniques. This means that the method is often faster and therefore much more cost-efficient than conventional time-accurate time-marching approaches.

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