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zeroGradient Boundary Condition

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Figure: The meaning of zeroGradient boundary condition

zeroGradient boundary condition simply extrapolates the quantity to the patch from the nearest cell value. The meaning is, the quantity is developed in space and its gradient is equal to zero in direction perpendicular to the patch (perpendicular to the boundary). See figure (crossref 3).

U, k, omega, epsilon, T:

 boundaryField
 {
 ".*_outlet"
    {
        type            zeroGradient;
    }
 }

Water Turbine Efficiency

The water turbine efficiency can be evaluated using following efficiency formula:

34(6.1)

where 36 denotes the efficiency, 37 is the torque, 40 is the angular velocity, 38 is the volume flow rate and 39 is the specific enthalpy which can be evaluated as follows:

41(6.2)

Subscript 42in means averaged quantities at the inlet, whereas subscript 42out denotes averaged quantities at the outlet. The evaluation of turbine efficiency for different patches is also possible.

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Frozen Rotor vs. Mixing Plane

At the interface between stator and rotor part, for each variable one can prescribe either Frozen Rotor boundary condition or Mixing Plane boundary condition. Frozen Rotor maps variable directly to the neighbour patch. Mixing Plane computes the variable average first and then maps just the average value to the neighbour patch. Both approaches can be combined (each variable can have its own option). Both approaches have benefits and drawbacks to each other. Authors of this methodology recommend to prefer Mixing Plane boundary condition.

Figure: Radial turbine. Example of Mixing Plane Averaging from stator region to rotor region.

frozenT

Figure: Radial turbine. Example of Frozen rotor interpolation from stator region to rotor region.