Airtable definition

@AIRTABLE_DEFINITION {
@AIRTABLE_NAME {AirTableName} {
@TABLE_OF_LIFT_COEFFICIENTS {
}
@TABLE_OF_DRAG_COEFFICIENTS {
}
@TABLE_OF_MOME_COEFFICIENTS {
}
@TABLE_OF_HMOM_COEFFICIENTS {
}
@TABLE_OF_STALL_ANGLES {
}
@DYNAMIC_STALL_MODEL_NAME {OdsModlName}
@LEISHMAN_BEDDOES_MODEL_NAME {LsbModlName}
}
}

Introduction

Airfoils can be characterized experimentally by wind tunnel tests or numerically using computational fluids dynamics. In both cases, tables of airfoil properties are constructed that consist of lift, drag, and pitching moment coefficient tabulated as functions of angle of attack and Mach number. A typical test configuration is depicted in fig. 1. The airfoil is at an angle α with respect to the far field flow of velocity, V, and wind tunnel measurements are made of the lift, Lwt, drag, Dwt, and moment about the quarter chord, Mqcwt. The corresponding non-dimensional quantities are the lift, drag, and moment coefficients, defined as c = Lwt/(qc), cd = Dwt/(qc), and cm = Mqcwt/(qc2), respectively, where the dynamic pressure, q = ρV2/2 and ρ is the air density. The arrows shown in fig. 1 define the positive sign convention for the various quantities.

Figure 1. Testing an airfoil in the wind tunnel.                                 Figure 2. Testing an airfoil with a trailing edge flap.

In some cases, the airfoil features a trailing edge flap, as illustrated in fig. 2. The flap angular deflection is denoted δ. An additional measurement is made in the wind tunnel: the flap hinge moment, denoted Mhwt. The corresponding non-dimensional quantity is the hinge moment coefficient, defined as ch = Mhwt/(qc2). The arrow shown in fig. 2 indicates the positive sign convention for the flap hinge moment.

NOTES

1. This section defines tables of airfoil properties. Each airfoil data set consists of tables of lift, drag, and pitching moment coefficients. Optionally, for airfoils with trailing edge flaps, a table of hinge moments can be provided. Each coefficient table defines the corresponding aerodynamic coefficients as a function of Mach number and angle of attack by means of a double entry table. Plots of the airtable lift, drag, moment and hinge moment coefficients will be generated, if requested by the plotting control parameters.
2. Each table of coefficients is a double entry table. The first independent variable is the angle of attack, measured in degrees, and the second independent variable is the Mach number. Coefficients are defined for Nα values of the angle of attack and Nm values of the Mach number. The first Nm numbers define the Mach number entries, M1 M2 ... MNm, of the second independent variable of the table. Next, Nα sets of data define the lines of the double entry table. The first number, α1, defines the angle of attack entry and the next Nm numbers, c1,1 ... c1,Nm, the corresponding coefficients for the various Mach number at that angle of attack. The last set of data defines the last angle of attack entry, αNα, followed by the Nm corresponding coefficients, cNα,1 ... cNα,Nm, at the various Mach numbers.
3. @TABLE_OF_LIFT_COEFFICIENTS {
@NUMBER_OF_ENTRIES {Nm, Nα}
M1 M2 ... MNm
α1         c1,1 ...         c1,Nm
...
αNα       cNα,1...       cNα,Nm
@XAXIS_RANGE {αlo, αhi}
@INTERPOLATION_RANGE {βlo, βhi}
@NUMBER_OF_CHEBYSHEV_COEFFICIENTS {Nc}
}
4. The tables of lift, drag, and pitching moment coefficients, denoted c, cd, and cm, respectively, are defined in the format defined above and introduced by the keywords @TABLE_OF_LIFT_COEFFICIENTS, @TABLE_OF_DRAG_COEFFICIENTS, and @TABLE_OF_MOME_COEFFICIENTS, respectively. Optionally, a table of hinge moment coefficients, denoted ch, can be defined and is introduced by keyword @TABLE_OF_HMOM_COEFFICIENTS.
5. If requested by the plotting control parameters, plots of the airtable lift, drag, and moment coefficients will be generated. The x-axis of these plot extends over the entire input range of angles of attack. For instance, if the airtables are defined for angles of attack from -180 to +180 degrees, the plot x-axis will extend from -180 to +180 degrees. It is possible to override this convention by specifying the x-axis range to extend from αlo to αhi degrees.
6. Some unsteady aerodynamic theories require the knowledge of linearized aerodynamic coefficients for small angles of attack. At a specific Mach number Mi, angles of attack 1, ... αNα) are associated with a column of coefficients, (c1,i, ... αNα,i). An analytical relationship is obtained using Chebyshev expansion,

c(α) = b0 T0(α) + b1 T1(α) + ... bNc TNc(α),

where Ti(α), i = 0, 1, 2, ..., Nc are the Chebyshev polynomials. A total of Nc polynomials are used in the approximation. Once the Chebyshev expansion is obtained, the derivative of the coefficient with respect to the angle of attack, c'(α) = dc/dα, can be obtained analytically. The Chebyshev expansion uses the tabulated data for angles of attack βlo ≤ α ≤ βhi, (Default values: βlo = -8 and βhi = 8 degrees, Nc = 4). The Chebyshev approximation is plotted together with the tabulated data.
• Lift Table. Unsteady aerodynamic theories typically require the slope of the lift curve, whose theoretical value is a0 = 2π. If tabulated data is available, a more accurate value, a0 = c'(α = 0), is obtained from the derivative of the Chebyshev expansion. When using the ONERA dynamic stall model, a linear approximation to the lift coefficient is required and is obtained as c(α) = b0 T0 + b1 T1, i.e., by using the first two coefficients of the Chebyshev expansion only. (Default value: 2 ≤ Nc ≤ 12)
• Drag Table. Unsteady aerodynamic theories typically require the skin friction coefficient, cd0, which is obtained as a function of Mach number by interpolating the drag table for a vanishing angle of attack. When using the ONERA dynamic stall model, a quadratic approximation to the drag coefficient is required and is obtained as cd(α) = b0 T0 + b1 T1 + b2 T2, i.e., by using the first three coefficients of the Chebyshev expansion only. (Default value: 3 ≤ Nc ≤ 12)
• Moment Table. When using the ONERA dynamic stall model, a linear approximation to the moment coefficient is required and is obtained as cm(α) = b0 T0 + b1 T1, i.e., by using the first two coefficients of the Chebyshev expansion only. (Default value: 2 ≤ Nc ≤ 12)
7. If the ONERA dynamic stall model OdsModlName is defined, this model will be associated with this airfoil. To activate this model for the airfoil, the use of this model must be called for in the Peters or Leishman-Beddoes unsteady aerodynamic models.
8. If the Leishman-Beddoes unsteady aerodynamic model is defined, this model will be associated with this airfoil. To activate this model for the airfoil, the use of this model must be called for in the Leishman-Beddoes unsteady aerodynamic model.
9. It is possible to attach comments to the definition of the object; these comments have no effect on its definition.