Leishman-Beddoes model definition

@LEISHMAN_BEDDOES_MODEL_DEFINITION {
@LEISHMAN_BEDDOES_MODEL_NAME {LsbModlName} {
@ATTACHED_FLOW_DATA {
@RECOVERY_COEFFICIENT {η}
@TABLE_OF_INDICIAL_RESPONSE_COEFFICIENT {
@MACH_NUMBER {Machi}
@INDICIAL_RESPONSE_COEFFICIENTS {A1, A2, A3, A4, A5}
...
}
@TABLE_OF_INDICIAL_RESPONSE_EXPONENTS {
@MACH_NUMBER {Machi}
@INDICIAL_RESPONSE_EXPONENTS {b1, b2, b3, b4, b5}
...
}
@TABLE_OF_TIME_CONSTANT_MULTIPLIERS {
@MACH_NUMBER {Machi}
@TIME_CONSTANT_MULTIPLIERS {k1, k2, k3, k4}
...
}
@TABLE_OF_CM_CN_RATIO {
@MACH_NUMBER {Machi}
@CM_CN_RATIOS {k0, k1, k2, m}
...
}
@AERODYNAMIC_CENTER_OFFSET {k0}
@SEPARATED_FLOW_MODEL {YES/NO}
@T.E_SEPARATION_POINT_DATA {α1, S1, S2}
@SEPARATED_FLOW_MOMENT_DATA {k1, k2}
@SEPARATED_FLOW_TIME_CONSTANTS {tp, tf}
@VORTEX_EFFECT {YES/NO}
@CRITICAL_NORMAL_FORCE_COEFFICIENT {CN1}
@VORTEX_TIME_CONSTANTS {tv, tvl}
@CHORD_FORCE_DECAY_CONSTANT {Df}
@COMMENTS {CommentText}
}
}
}

NOTES

  1. The data required for the Leishman-Beddoes unsteady aerodynamic model is defined in this section.
  2. It is possible to attach comments to the definition of the object; these comments have no effect on its definition.
  • η is the recovery factor for viscosity effect, see section~\ref{Unsteady attached flow}.
  • Ai, i = 1, 5, are the coefficients of circulatory indicial response functions, see section~\ref{Unsteady attached flow}, default values are listed in the line “Consolidated Data” of table~\ref{LBM: coefficients Ai}.
  • bi, i = 1, 5, are the exponents or poles of indicial response functions, see section~\ref{Unsteady attached flow}, default values are listed in the line “Consolidated Data” of table~\ref{LBM: coefficients bi}.
  • kNα, kNq, kMα and kMq are the non-circulatory time constant multiplier, see section~\ref{Unsteady attached flow}, default values are kNα ≈ 0.75, kNq ≈ 0.75, kMα ≈ 0.8 and kMq ≈ 0.8.
  • k0 = (0.25 - xac) is aerodynamic center offset from the quarter chord xac.
  • If flag @SEPARATED_FLOW_MODEL = YES, the Leishman-Beddoes separated flow model is activated.
  • If flag @SEPARATED_FLOW_MODEL = YES the following data must be added.

    1. If flag @VORTEX_EFFECT = YES, Leishman-Beddoes vortex dynamic stall model is activated (if and only if @SEPARATED_FLOW_MODEL = YES).
    2. α1, S1, S2, which are three empirical parameters which may be fitted to the test data for the T.E. separation point versus the angle of attack. α1 is closely correspond to the static stall angle of attack for most airfoil sections. They are input to the model in degrees.
    3. k1 k2 where k1 represents the direct effect on the center of pressure due to the growth of the separated flow region, and k2 helps describe the shape of the moment break at stall.
    4. tp and tf which are Mach number dependent time constants.

    If flag @VORTEX_EFFECT = YES the following data must be added.

    1. The critical normal force coefficient CN1, and can be obtained from the value of CN(static) that corresponds to either the break in pitching moment or the chord force at stall.
    2. The vortex decay constant, tv, and the center of pressure travel time constant tvl.
    3. Df which is a constant that models empirically the increased rate at which the chord force is lost after the onset of the gross separation of flow in dynamic stall.