Flight Loads

ZONAIR Engineering Modules and Capabilities

The ZONAIR Software Architecture

ZONAIR consists of many submodules for various disciplines that include (1) AIC matrix generation module, (2) 3-D spline module, (3) trim module, (4) aeroheating module, (5) vortex roll-up module and (6) aerodynamic stability derivative module. The interrelationship of ZONAIR with other engineering software systems such as the pre-processor, structural finite element method (FEM), Computational Fluid Dynamic (CFD) method, six degree-of-freedom (6 d.o.f.) and critical loads identification is depicted in the following figure.

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Finite Element Based High-Order Paneling Scheme

The ZONAIR panel model is normally constructed by first descretizing the configuration into many grid points and then connecting these grid points with either the quadrilateral or triangular panels. This type of panel construction is very similar to the structural finite element method. In fact, some of the NASTRAN bulk data cards are directly adopted for ZONAIR input. In order to ensure the continuity of singularity distribution over the entire panel model, unit singularity strength is first assigned at each grid point and piecewisely linear singularity is distributed over the panels, which are surrounding this grid. Such an elementary singularity distribution is shown in Figure FE.1. Clearly, the superposition of the elementary singularity distribution of all grid points can result in a continuous singularity distribution over all panels.

Furthermore, because the four corner points of a quadrilateral panel may not be located on the same plane, each quadrilateral panel is subdivided into six triangular panels for the continuity of panel geometry Figure FE.2.

Figure FE.1 Elementary Singularity
Distribution at Grid Points.

Figure FE.2 Subdivision of a Quadrilateral
Panel into Sub-triangular Panels.

At each panel, both Dirichlet boundary condition and Neumann boundary condition are imposed for solving the source and doublet strengths (Figure FE.3). Also, the zero-force condition is imposed on the wake to satisfy the wake condition.

Figure FE.3 Dirichlet and Neumann Boundary Conditions
on Panels and Zero-Force Condition on Wake Surface.

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No Requirement for Modeling Wake Surfaces

Unlike other high-order panel methods such as PANAIR, VSAERO and QUADPAN where the wake surfaces must be explicitly modeled, ZONAIR requires only the specification of the line segments along the trailing edge of the wing and body where the wake surface starts; no wake surface modeling is required by ZONAIR. These line segments for wake modeling are shown in the following figure. Internally, ZONAIR sweeps these line segments to infinity and creates a flat wake surface. Because an exact solution can be obtained by integrating the wake integral from the line segment to infinity, the wake effects can be included by only evaluating the exact integral solution along each line segment.

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Nastran Bulk Data Input for ZONAIR

The ZONAIR input is very similar to the NASTRAN bulk data input. In fact, some NASTRAN bulk data cards can be directly adopted for ZONAIR modeling. Also, multiple subcases can be specified in one ZONAIR job for different flight conditions. This direct adoption of some NASTRAN bulk data cards for ZONAIR modeling is shown in the following figure.

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Direct Adoption of Off-the-Shelf FEM Pre-Processor for Panel Model Generation

Figure AD.1 presents the comparison between ZONAIR unstructured paneling scheme and PANAIR’s paneling scheme where the advantages of adopting the unstructured grids is shown. Another advantage in using unstructured grids is that it allows arbitrary grid point selection for a given configuration. In order to demonstrate this feature, a sphere is modeled by using regularly spaced/shaped panels (called Regular Panels) and randomly spaced/shaped panels (called Random Panels) whose pressure distribution results are shown in Figures AD.2a and AD.2b, respectively. Clearly, this arbitrary grid point selection capability of the unstructured grids can greatly reduce the user burden in the grid generation process. The similarity between the ZONAIR and MSC.Nastran input format enables the direct adoption of the pre- and post-processors of MSC.Nastran for ZONAIR model generation and result display. There are many off-the-shelf NASTRAN pre- and post-processors such as PATRAN, AML, I-DEAS, FEMAP, etc. that are all capable of importing IGES files from the CAD systems. Therefore, one can generate a ZONAIR aerodynamic model that is based on the surfaces defined by the CAD system, thereby providing tremendous time savings in generation of models.

Figure AD.1 Comparison of ZONAIR and PANAIR Paneling Schemes.

(a) Cp on Regular Panels

(b) Cp on Random Panels

Figure AD.2 Regular and Random Paneling of a Sphere at M=0.0, AoA=0 deg..

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Validation of Subsonic Aerodynamics

NACA RM L51F07 wing-body configuration at M = 0.6, α = 4°

  • Pressures along the body show strong wing-body interference.
  • Good correlation with the wind-tunnel measurements.

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Validation of Supersonic Aerodynamics

Force and Moment Coefficients of a Generic Advanced Fighter M = 1.2 and 2.0 ZONAIR vs. Wind Tunnel Test Results

Pressure Distribution on Generic Advanced Fighter at M = 1.2, α = 4.1 º

  • Whole aircraft with tip missile configuration shows the capability of ZONAIR for accurate supersonic aerodynamics on complex geometry
  • CPU time is only 10 minutes on a 2.4Ghz PC computer.

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Validation of Hypersonic Aerodynamics

Hypersonic Body Employing Bent-Nose Control ZONAIR comparison vs. CFL3D

  • Equivalent Mach number transformation to circumvent the superinclined panel problem.
  • Local pulsating body analogy for flow rotationality effects.
  • Good agreement between ZONAIR and CFL3D on the CKEM body at various bent-nose angles at M = 6.0.

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Aft Body Wake Effects

ZONAIR is capable of modeling the flow separation after truncated-end bodies by placing a point source singularity in the body wake region. By specifying the base pressure (Cpb) as an additional input, the strength of this point source singularity along with all unknowns on panels can be solved together.

Computed wake shape for a LMSC Rattayya’s blunt body at α  = 0 º and M = 0.0 (view of the meridian plane)

Without Wake Model

With Wake Model

Comparison of surface pressure distributions for a cone-cylinder body (L/d = 3.3) at α = 0 º and M = 0.0 and Cpb = -2.4

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Multibody Interference Effects

  • Busemann Biplane at a design Mach number (M = 1.75 and α = 0°) where the shock-expansion theory predicts the nullification of wave drag due to the perfect cancellation of Mach waves.

  • Excellent agreement between ZONAIR and shock-expansion theory is obtained.

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Wave Drag Predicitons

The objective of the wind tunnel test is to determine the wave drag reduction of the GAF with a modified aft body section (denoted as H-18) from the baseline GAF (denoted by H-17). Both wind tunnel models use an underbody “blade sting” for supplying the jet flow and have sealed inlets. The difference in measured drag between these two models is assumed to be caused by the afterbody modification. The purpose of this ZONAIR analysis is to validate this assumption by establishing four ZONAIR models; H-17 + blade sting, H-18 + blade sting, H-17 without blade sting, H-18 without blade sting.

Good agreement between ZONAIR and measured wave drag indicates that the blade sting effects on incremental wave drag measurements are small.

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Ground Effects

ZONAIR employs a "mirror-image" approach where the ground is treated as a mid-plane between two mirror-image bodies and can compute the complete flow field solutions allowing for the visualization of the flow field solutions.

Compact Kinetic Energy Missile (CKEM) Flying 5-Inches Above the Ground at Mach 2.0 ZONAIR vs. CFL3D Results

Notice the shock reflection off of the ground. Good agreement of the pressure distribution on the body surface and in the flow field is observed. For this case, ZONAIR takes about 10 minutes of CPU time on a 550 MHz PC computer, whereas, CFL3D takes about 10 hours.

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Aeroheating Analysis

A finite-element-based streamline module called ZSTREAM that adopts the inviscid surface velocities generated by ZONAIR as input to yield high quality streamline solutions.

Once the streamlines are obtained, the aeroheating analysis can be performed along each streamline using a simple one-dimensional boundary layer method.

The one-dimensional hypersonic boundary layer method is developed based on the similarity solutions of compressible (laminar/turbulent) boundary layer methodology of Eckert/Boeing, RhorMa and the White-Christoph methods.

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Wake Relaxation

A flat wake generated from wing cuts into body which creates singularities within the computation. The wake relaxation generates a curved wake surface that removes the problem.

Gun-Launched Projectile with Oblique Wing at M=0.6 and α = 4.0 º

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3D Spline Module

The 3D Spline module establishes the displacement/force transferal between the structural Finite Element Analysis (FEA) model and the ZONAIR aerodynamic model. It contains four powerful spline methods that jointly assemble a spline matrix. These four spline methods include:

  • Thin Plate Spline
  • Infinite Plate Spline
  • Beam Spline
  • Rigid Body Attachment methods

The spline matrix provides the x, y and z displacements and slopes in three dimensions at all aerodynamic grids.

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Static Aeroelastic/Trim Module

ZONAIR's static aeroelastic/trim module provides trim solutions and flexible loads.


  • Employs the modal approach for solving the trim system of the flexible aircraft. The modal approach establishes a reduced-order trim system that can be solved with much less computer time than the so-called “direct method”.
  • Capable of dealing with a determined trim system as well as the over-determined trim system (i.e., more unknowns than the number of trim equations). The solutions of the over-determined trim system are obtained by using an optimization technique that minimizes a user-defined objective function while satisfying a set of user-defined constraint functions.
  • For a symmetric configuration (about the x-z plane), the Trim Module requires only that one-half of the configuration be modeled, even for an asymmetric flight condition.
  • Generates the flight loads on both sides of the configuration in terms of forces and moments at the structural finite element grid points. Output are Nastran FORCE and MOMENT bulk data cards that can be used in subsequent detailed stress analyses.

Static Aeroelastic Deformation

Stress Distribution

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Pressure Mapping from CFD Mesh to ZONAIR Panels

ZONAIR has a robust capability to map the CFD imported pressures onto the ZONAIR panels.


  • Interpolation of the surface pressure coefficient from the CFD surface mesh onto the ZONAIR panels and utilization of this pressure to generate the rigid loads for trim analysis.
  • Transfer of these rigid loads from the ZONAIR panel to the structure finite element grid points using ZONAIR's spline module.
  • Interpolates the surface velocities that are used for the streamline calculation for aeroheating analysis.

Comparison of Cp between the CFD results and the interpolated ZONAIR results on the X-34 at M = 10, α =5°.

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AIC Correction Module for Accurate Flexible Loads Generation

The AIC correction module computes an AIC weighting matrix to modify the ZONAIR computed AIC matrix for accurate flexible loads generation.


  • Adopts the force/moment correction method by Giesing et al. and the downwash correction method by Pitt and Goodman.
  • The AIC weighting matrix generated by the force/moment correction method is computed by matching the wind-tunnel measured section loads.
  • The AIC weighting matrix generated by the downwash correction method is computed by matching the surface pressures that are either measured by wind-tunnel test or compute by CFD.
  • The corrected AIC matrix can be used to provide flexible loads due to structural deformation for trim analysis.

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A Brief Comparative Study of Panel Codes

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