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TURBOSPEC - MIT actuator duct (block)

TURBOSPEC
ZONE izoneFILE filename[BLADEOUT bladewidth]ZONE izone ...ENDTURBOSPEC |

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.

Information defining the characteristics of the turbomachinery being
modeled is read from a set of
turbomachinery data files.
The files contain tables specifying the leading and trailing edge blade
angles, and force coefficients defining the local blade forces.
The input value *filename* specifies the name of the file
containing blade data for zone *izone*.
A separate file is required for each blade row, and currently each blade
row must be in a separate zone.
Multiple pairs of `ZONE` and `FILE` keywords may be used
to model multiple blade rows.
The optional `BLADEOUT` keyword indicates that the row has a
missing blade of width *bladewidth* degrees.

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

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

where *V* is the fluid velocity, and *K _{v}* is the
parallel (i.e., viscous) force coefficient.
The subscript

The normal forces are represented in Wind-US as

where the total normal force *F _{n}* is modeled as

and *K _{n}* 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

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

In the above, *p* is the pitch between blades,

where *N _{B}* is the number of blades,

Last updated 1 Apr 2016