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TURBOSPEC - MIT actuator duct (block)

Structured Grids

The TURBOSPEC keyword block specifies that an actuator duct model is to be used to model the effects of turbomachinery in a duct. Body force source terms are added to the energy and momentum equations, representing the effect of turbomachinery blades on the flow.

Note that the blade forces must be known a priori, either from experimental data or a separate CFD calculation of the flow past the actual blade geometry. Once the blade forces are known, the force coefficients to be specified in the data file can be computed using the equations presented below.

The x-axis of the Cartesian coordinate system is assumed to coincide with the axial direction in the cylindrical coordinate system used in the actuator duct model. It's also assumed that the i, j, and k computational indices correspond to the axial, radial, and circumferential directions, respectively. And, the zone extent must exactly match the blade; i.e., the leading and trailing edges of the blade must lie in the upstream and downstream zonal boundaries.

The model used is based on an MIT actuator duct model developed by Gong. [Gong, Y., "A Computational Model for Rotating Stall and Inlet Distortion in Multistage Compressors," Ph. D. Dissertation, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1999.] The force on the blade is expressed as the sum of forces parallel and normal to the blade section mean line, analogous to the drag and lift forces on an airfoil section. Assuming a right-handed cylindrical coordinate system, the forces in the axial, circumferential, and radial directions may be written as

Fx = Fp, x + Fn, x

Fθ = Fp, θ + Fn, θ

Fr = Fp, r

where the subscripts p and n represent the directions parallel and normal to the blade section mean line, and x, θ, and r represent the axial, circumferential, and radial coordinate directions.

The parallel forces are represented as

Fp, x = − (Kv / h ) Vrel Vx

Fp, θ = − (Kv / h ) Vrel Vθ, rel

Fp, r = − (Kv / h ) Vrel Vr

where V is the fluid velocity, and Kv is the parallel (i.e., viscous) force coefficient. The subscript rel represents a value relative to the blade.

The normal forces are represented in Wind-US as

Fn, x = Fn (Vθ, rel / Vrel ) e−σ

Fn, θ = − Fn (Vx / Vrel )

where the total normal force Fn is modeled as

Fn = (Kn / h ) (Vθ, rel cos βVx sin β ) (Vx cos β + Vθ, rel sin β ) + (2 / c ) sin (Δ β / 2) (Vx cos βVθ, rel sin β )2

and Kn is the normal force coefficient. It should be noted that the expressions used in Wind-US for the normal forces are different from those derived by Gong.

In the above expressions for the parallel and normal forces, h is the blade-to-blade gap staggered spacing, given by

h = s cos β

where β is the local blade mean line angle measured from the axial direction, and s is given by

s = p (1 − t ) σ1/2

In the above, p is the pitch between blades,

p = 2 π r / NB

where NB is the number of blades, σ = c / p is the blade solidity, c is the local blade chord length, and t is the blade thickness, which is assumed to be zero in Wind-US. Finally, Δ β is a measure of the blade camber, defined as the difference in leading and trailing edge blade angle,

Δ β = βLEβTE

Last updated 1 Apr 2016