Aerodynamics

OpenConcept’s aerodynamics components provide an estimate of drag as a function of lift coefficient, flight conditions, and other parameters.

Simple drag polar: PolarDrag

PolarDrag is the most basic aerodynamic model and uses a parabolic drag polar. This component computes the drag force given the flight condition (dynamic pressure and lift coefficient) at each node along the mission profile. In run script, users should set the values for the following aircraft design parameters, or declare them as design variables.

Aircraft design variables for drag polar model

Variable name	Property
ac|geom|wing|S_ref	Reference wing area
ac|geom|wing|AR	Wing aspect ratio
e	Wing Oswald efficiency
CD0	Zero-lift drag coefficient

Drag buildups

A drag buildup can provide a first estimate of an aircraft’s drag coefficient. It uses empirical estimates for the drag of individual components, such as the fuselage and engine, and sums them to predict the total drag. Empirical interference factors included in the summation account for drag caused by the interaction of components.

In OpenConcept, the drag buildups return \(C_{D, 0}\), the zero-lift drag coefficient. Drag buildups for two configurations are included. For a conventional tube and wing configuration, use ParasiteDragCoefficient_JetTransport. For a blended wing body configuration, use ParasiteDragCoefficient_BWB (the BWB version requires the use of OpenAeroStruct to predict the wing and centerbody drag). This value can then be used either with the simple drag polar (PolarDrag) or one of the OpenAeroStruct-based drag models to add in the lift-induced component of drag. OpenAeroStruct already includes the zero-lift drag of the wing. To prevent double counting this drag, the ParasiteDragCoefficient_JetTransport has an option called include_wing, which should be set to False when using OpenAeroStruct for drag prediction.

The source code describes details of the implementation, including sources for the individual empirical equations and constants.

Using OpenAeroStruct

Instead of the simple drag polar model, you can use OpenAeroStruct to compute the drag. This enables a more detailed parameterization of the aircraft wing. OpenAeroStruct implements the vortex-lattice method (VLM) for aerodynamics and beam-based finite element method (FEM) for structures (in the case of the aerostructural drag polar). For more details, please check the documentation.

The aerodynamic-only model supports three types of mesh generation for planform and geometry flexibility. The aerostructural model is currently limited to simple planform geometries. Additionally, the wing does not include a horizontal tail to trim it.

OpenConcept uses a surrogate model trained by OpenAeroStruct analyses to reduce the computational cost. The data generation and surrogate training is automated; specifying the training grid manually may improve accuracy and decrease computational cost.

VLM-based aerodynamic model: VLMDragPolar

This model uses the vortex-lattice method (VLM) to compute the drag. The inputs to this model are the flight conditions (Mach number, altitude, dynamic pressure, lift coefficient) and aircraft design parameters.

The aerodynamic mesh can be defined in one of three ways:

1. Use simple planform variables to define a trapezoidal planform. These planform variables are wing area, aspect ratio, taper ratio, and quarter chord sweep angle.

2. Define multiple spanwise wing sections between which a mesh is linearly interpolated. Each section is defined by its streamwise offset, chord length, and spanwise position. The whole planform is then scaled uniformly to match the desired wing area.

3. Directly provide an OpenAeroStruct-compatible mesh.

More details on the inputs, outputs, and options are available in the source code documentation.

Aerostructural model: AerostructDragPolar

This model is similar to the VLM-based aerodynamic model, but it performs aerostructural analysis (that couples VLM and structural FEM) instead of aerodynamic analysis (just FEM). This means that we now consider the wing deformation due to aerodynamic loads, which is important for high aspect ratio wings. The structural model does not include point loads (e.g., for the engine) or distributed fuel loads.

The additional input variables users need to set in the run script are listed below. Like the num_twist option, you may need to set num_toverc, num_skin, and num_spar.

Additional design variables for aerostructural model

Variable name	Property	Type
ac|geom|wing|toverc	Spanwise distribution of thickness to chord ratio.	1D ndarray, lendth num_toverc
ac|geom|wing|skin_thickness	Spanwise distribution of skin thickness.	1D ndarray, lendth num_skin
ac|geom|wing|spar_thickness	Spanwise distribution of spar thickness.	1D ndarray, lendth num_spar

In addition to the drag, the aerostructural model also outputs the structural failure indicator (failure) and wing weight (ac|weights|W_wing). The failure variable must be negative (failure <= 0) to constrain wingbox stresses to be less than the yield stress.

Understanding the surrogate modeling

OpenConcept uses surrogate models based on OpenAeroStruct analyses to reduce the computational cost for mission analysis. The surrogate models are trained in the 3D input space of Mach number, angle of attack, and altitude. The outputs of the surrogate models are CL and CD (and failure for AerostructDragPolar).

For more details about the surrogate models, see our paper.

\(C_{L, \text{max}}\) estimates

Accurately predicting \(C_{L, \text{max}}\), the maximum lift coefficient, is a notoriously challenging task, but doing so is crucial for estimating stall speed and takeoff field length.

Empirical fits

In conceptual design, empirical estimates are often used. OpenConcept’s CleanCLmax uses a method from Raymer[1] to model the maximum lift coefficient of a clean wing (without high lift devices extended). The FlapCLmax component adds a delta to the clean \(C_{L, \text{max}}\) to account for flaps and slats, using fits of data from Roskam[2].

With OpenAeroStruct

An alternative way to predict \(C_{L, \text{max}}\) is to use the critical section method with a panel code. In this method, the wing angle of attack is increased until the wing’s sectional lift coefficient first hits the airfoil’s \(C_{l, \text{max}}\) at some point along the span. As with before, the sectional \(C_{l, \text{max}}\) is often predicted using empirical estimates.

OpenConcept includes a method to use OpenAeroStruct to carry out the critical section method. The first step is to perform an OpenAeroStruct analysis of the wing. Next, the difference between the spanwise sectional lift coefficient computed by OpenAeroStruct and the associated \(C_{l, \text{max}}\) is aggregated to smoothly compute the nearest point to stall. Finally, a solver varies OpenAeroStruct’s angle of attack to drive the aggregated \(\max(C_l - C_{l, \text{max}})\) to zero. A Newton solver is capable of this system, but it is very slow because it needs to invert the whole system’s Jacobian. A better method is to use OpenMDAO’s NonlinearSchurSolver. At the time of writing this, it is available on this OpenMDAO branch, but not in the main OpenMDAO repository.

Other models

The aerodynamics module also includes a couple components that may be useful:

• StallSpeed, which uses \(C_{L, \text{max}}\), aircraft weight, and wing area to compute the stall speed

• Lift, which computes lift force using lift coefficient, wing area, and dynamic pressure

[1]

Daniel P. Raymer. Aircraft design: a conceptual approach fourth edition. American Institute of Aeronautics and Astronautics, Reston, VA, 2006. ISBN 1563478293.

[2]

Jan Roskam. Airplane Design Part VI: Preliminary Calculation of Aerodynamic, Thrust, and Power Characteristics. DARcorporation, 1989. ISBN 978-1-884885-52-5.