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AMU_-2001-1004

PREDICTION OF BUSINESS JET AIRLOADS USING THE

OVERFLOW NAVIER-STOKES CODE

Elias Bounajem"

Cessna Aircraft Company, Wichita, Kansas 67215

and

Pieter G. Buning"

NASA Langley Research Center, Hampton, Virginia 23681

Abstract

The objective of this work is to evaluate the

application of Navier-Stokes computational

fluid dynamics technology, for the purpose of

predicting off-design condition airloads on a

business jet configuration in the transonic

regime. The NASA Navier-Stokes flow

solver OVERFLOW with Chimera overset

grid capability, availability of several

numerical schemes and convergence

acceleration techniques was selected for this

work. A set of scripts which have been

compiled to reduce the time required for the

grid generation process are described.

Several turbulence models are evaluated in

the presence of separated flow regions on

the wing. Computed results are compared to

available wind tunnel data for two Mach

numbers and a range of angles-of-attack.

Comparisons of wing surface pressure from

numerical simulation and wind tunnel

measurements show good agreement up to

fairly high angles-of-attack.

Introduction

Computational Fluid Dynamics (CFD)

technology has seen remarkable advances

* Member, AIAA

"*Associate Fellow, AIAA.

Copyright Â© 2001 by the American Institute of Aeronautics and

Astronautics, Inc. All rights reserved.

in the last few years. CFD is used today on a

regular basis to support design efforts in

such areas as aircraft design, propulsion

system design and integration, combustion,

ship design and the automotive industry, to

name a few.

The aircraft industry is a primary customer of

CFD technology. Depending on the task at

hand, the aircraft designer has a wide range

of sophistication to chose from. This range

includes: full modeling of viscous effects as

available in Navier-Stokes type codes; Euler

codes, transonic small disturbances and full

potential codes when viscous effects are not

of primary influence; and finally, linearized

potential flow codes for shock free flows or

when only an approximate answer is being

sought. These codes are implemented with

different types of grids: multiblock, patched

or overset grids if a structured grid approach

is considered, Cartesian and unstructured

grids for unstructured methods. The

literature is rich with publications identifying

the pros and cons of each of these methods.

The bulk of CFD work in the aircraft design

arena has been in the cruise flight regime.

Under these conditions, the airflow is still

attached to the surface with small regions of

separated flow, and CFD calculations are

known to be quite reliable in predicting

aircraft performance characteristics.

Areas which have not received as much

attention are those that deviate from the

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cruise condition. These situations are

encountered when the entire flight envelope

of the airplane is of interest. Here,

combinations of angle-of-attack, Mach and

Reynolds number can be challenging for any

CFD code. High angle-of-attack will cause

the flow to separate. As the high subsonic

regime is approached, the flow will have

numerous shock waves on the wing, pylon,

etc. The interaction of shock waves with the

boundary layer complicates flow patterns

and makes CFD prediction significantly more

difficult. With the presence of large

separated flow regions, the focus shifts more

and more towards turbulence modeling.

Here, the validity of the model's underlying

assumptions becomes critical to the quality

of the solution the CFD code can provide.

The present work aims at evaluating the

applicability of Navier-Stokes CFD

technology to predict off-design airloads on a

business jet configuration. OVERFLOW

[1,10], a NASA research flow solver which

uses the Chimera overset grid approach,.

has been selected for this evaluation.

OVERFLOW offers a wide array of

numerical schemes and turbulence models,

and has been accepted throughout the

aircraft industry as one of the leading Navier-

Stokes codes available.

Grid Generation

The overset grid approach has the

advantage of allowing grid generation of

aircraft components separately, thus

providing grids that conform to the

component topology. Through a hole cutting

procedure and boundary point interpolation,

excess overlap between component grids is

blanked out.

The geometry modeled here is a business

jet configuration with aft fuselage mounted

pylon/nacelles. Figure 1 shows the different

surface grids that make up the current

model. In all fifteen grids, including the outer

box grids, were needed to define the

geometry.

Surface Grids

The first step in the grid generation process

is to generate surface grids for the various

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components. Five components were

identified: wing, fuselage, pylon, nacelle and

wing-body fairing. For the wing, pylon, and

nacelle, the CATIA CAD model was

imported in IGES format into the NASA

Langley GridTool software [2], where a

surface grid was generated. The fuselage

surface grid was generated directly in CATIA

to improve surface grid quality resulting from

projection onto the original geometry. As for

the wing-body fairing (Figure 2), it was

deemed appropriate to represent it with a

combination of collar grids and therefore no

computational surface grid was generated

for this component.

Collar Grids

The next step in the process is to make use

of the collar grid approach [3] in the overlap

region between the various components.

This approach is used to ensure good quality

grids in these areas, to allow for inter-grid

communication through interpolation and to

capture the viscous effects in the juncture all

in the same grid. Collar grids are generated

by identifying the intersection curve between

components and growing a grid onto the

adjacent components.

Collar grids were generated at the pylon-

nacelle and pylon-fuselage junctures. For

the wing-body fairing, a collar grid was

generated at the fuselage-fairing intersection

and at the wing-fairing intersection. A third

grid originating at the model centerline

covered the remainder of the fairing.

The NASA Ames Chimera Grid Tools (CGT)

software package [4] was used to generate

the collar grids, to add wakes to the wing

and pylon grids, and to add a wing tip cap

grid [14]. Another cap grid was required for

the pylon shelf, which extended beyond the

nacelle exhaust plane. To increase

communication with the nacelle grid, the

pylon cap grid was extended upstream and

projected onto the nacelle surface (Figure

3).

Volume Grids

From the body-fitted surface grids, volume

grids were generated with HYPGEN [5-6].

The initial spacing off the surface is equal to

0.00035 inches, which corresponds to a yÃ·

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value of 1 at 10 percent chord from the wing

leading edge.

Communication between the component grid

outer boundaries, and extension of the

computational domain to the far field is

accomplished with two levels of Cartesian

box grids, following an approach used for

other geometries [7-8].

Grid Communication

The PEGSUS 4.0 code [9], developed by

CALSPAN at AEDC, is used to remove

excess overlap between grids and find

interpolation stencils for inter-grid boundary

points. This process effectively connects all

of the overset component and box grids into

one system.

Scriptin.q the Process

It is recognized that this grid generation

process is iterative. Several attempts may be

made to ensure that the surface is

adequately represented and that the number

of orphan points, grid points with no

adequate interpolation stencil, is minimized.

Also, during development phase, the

configuration is constantly changing as more

refinements are introduced. With this in

mind, a set of scripts that performs the tasks

highlighted above is highly desirable. This

allows for making changes to the various

components and then regenerating the

entire grid system with a minimum amount of

user input.

The present work uses a modified set of

scripts, originally developed for a generic

business jet configuration. These scripts

encompass surface grid generation and

refinements, volume grid generation, hole

cutting and interpolation stencil identification.

An example illustrating the script approach is

the generation of the wing-body fairing collar

grids. As shown in Figure 4, this process

starts with wing and fuselage surface grids,

the fairing definition in the form of reference

grids (created in GridTool from the IGES

CAD definition), and grid lines representing

the intersection of the fairing with each of the

fuselage, wing, and symmetry plane.

The first step uses the SURGRD surface

grid generation code [15] from CGT to

AIAA-2001-1004

create collar surface grids, shown in Figure

2. Second, volume grids are generated with

HYPGEN. Finally, CGT utilities are used to

add reflected symmetry planes and smooth

the wake region of the wing-fairing collar.

Flow Solver

The OVERFLOW Navier-Stokes flow solver

is used in this analysis. This code uses an

implicit approximate factorization algorithm

to solve the thin-layer formulation of the

Navier-Stokes equations. For these

calculations, central differencing with

second- and fourth-order artificial dissipation

is used for the Euler terms. Trial runs with

Roe's upwind differencing scheme did not

show improvement over central differencing.

Local time stepping, grid sequencing, and

multigrid are used to accelerate

convergence [10].

While steady-state acceleration techniques

were used for these simulations, the mid-

range and high angle-of-attack cases were

largely separated. Total lift coefficient varied

by 0.02 from a mean value in some cases.

It is recognized that a more thorough

analysis of the unsteady aspect of these

flowfields is needed; however, for the

airloads analysis process only averaged

steady loads are desired.

Processinq Requirements

The grid system for this configuration has a

total of 3.9 million points. Solutions were

generated on an SGI Origin 200 with four

processors and 1.8 GB of memory. Each

case required about 260 MB of memory and

30 hours to converge on a single processor,

except for higher angles-of-attack. These

were processed further to get the solution

stabilized within a certain band.

Results and Discussion

A total of six flow conditions are examined in

the current study. These consist of a series

of three angles-of-attack (low, mid-range

and high) at two transonic Mach numbers

above cruise. For each flow condition,

results were obtained using the Baldwin-

Barth [11] and Spalart-AIImaras [12] one-

equation turbulence models, and the k-

omega two-equation turbulence model [13].

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Attempts to use the Menter SST model [16]

were unsuccessful due to wing root grid

issues. Surface pressure coefficients on the

wing are presented at two stations, one

inboard and one outboard. The Reynolds

number matches that at which the

experimental data was collected in the wind

tunnel.

At low angle-of-attack, where the flow

remains attached to the surface, solutions

using the Baldwin-Barth model show surface

pressures in very good agreement with wind

tunnel data (Figure 5), with shock location

and strength well predicted. Spalart-AIImaras

results are similar. The k-omega model

predicts a shock location significantly aft of

the one-equation models. This behavior is

similar to that shown in Reference 13 for

transonic flow over the RAE 2822 airfoil.

For the mid-range angle-of-attack (Figure 6),

Baldwin-Barth results show shock location

and strength are well predicted on the upper

surface inboard station for both Mach

numbers and on the lower surface for the

higher Mach number case. The upper

surface outboard station pressure

comparison shows that the shock position is

about 5 percent chord aft of that measured

in the wind tunnel. Here the flow separates

behind the shock. For the most part the

lower surface predictions are good. Toward

the trailing edge, the calculated pressure

coefficient shows significant unsteadiness,

varying with where the solution is stopped.

This is more noticeable in the high Mach

number case. This behavior is not present in

the Spalart-AIImaras results, where the flow

is better behaved at the trailing edge. The

predictions on the upper surface of the

inboard station are slightly better than

Baldwin-Barth. Again, the k-omega model

predicts the shock location aft of the other

models.

In the high angle-of-attack case (Figure 7),

where a considerable amount of separation

is present, the upper surface rooftop and

shock location predicted by both one-

equation models are fairly good. However,

pressures aft of the shock at the inboard

station do not match the trends of the wind

tunnel data. A lower pressure at the upper

surface trailing edge leads to an acceleration

of the flow on the lower surface approaching

AIAA-2001-1004

the trailing edge. Results for intermediate

stations (not shown here) indicate that this

pattern disappears a short distance outboard

of this station. This could be a result of

solution convergence difficulty at these

extreme conditions. Further investigation of

this issue is required. Although the k-omega

model continues to predict a shock location

too far aft as in the previous cases, the post-

shock pressure levels match wind tunnel

results. The lower surface predictions for all

models remain good.

Support for the aerodynamic loads process

is provided by supplying design loads for

various components of the aircraft such as

the fuselage, nacelle, pylon, etc. This is

done by providing total component load

(e.g., pylon normal force coefficient), or by

providing a running load.

Here, running loads are computed from the

CFD solution by dividing the body into a

number of segments and integrating the

pressure to obtain either a force or a

moment coefficient in these segments. Data

can be presented either as a cumulative total

starting from a specific point, or separately

for each of the segments, as in Figure 8 for

the fuselage. Individual component loads

can also be used to determine the fraction of

the aircraft total load that is being carried by

a particular component (Figure 9).

If accurate, CFD solutions are invaluable for

the aerodynamic loads process because

they provide distributed surface pressures

which can be analyzed component-by-

component. These supplement wind tunnel

data from extensive pressure taps or

component balances, both expensive

experimental techniques.

Conclusion

A Navier-Stokes flow solver, OVERFLOW,

has been successfully used for the

prediction of aerodynamic loads on a

business jet configuration. Three turbulence

models were evaluated at above-cruise

Mach numbers and low to high angles-of-

attack. Overall, results show the Baldwin-

Barth and Spalart-AIImaras models providing

the closest match to experimental results.

The k-omega turbulence model predicts the

shock location and flow separation farther aft

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than the one-equation models. Further

investigation of isolated flow patterns at the

middle and high angle-of-attack cases is

needed.

References

1. P.G. Buning, et al., "OVERFLOW User's

Manual, Version 1.8," NASA Langley

Research Center, Hampton, VA, Feb. 1998.

2. J. Samareh-Abolhassani, "GridTool: A

Surface Modeling and Grid Generation

Tool," NASA CP-3291, 1995.

3. S.J. Parks, P.G. Buning, J.L. Steger, and

W.M. Chan, "Collar Grids for Intersecting

Geometric Components Within the Chimera

Overlapped Grid Scheme," AIAA 91-1587,

June 1991.

4. W.M. Chan, "Manual for Chimera Grid

Tools," NASA Ames Research Center,

Moffett Field, CA, Oct. 1998.

5. W.M. Chart and J.L. Steger,

"Enhancements of a Three-Dimensional

Hyperbolic Grid Generation Scheme," Appl.

Math. and Comput., Vol. 51, pp. 181-205,

1992.

6. W.M. Chan, I.-T. Chiu, and P.G. Buning,

"User's Manual for the HYPGEN Hyperbolic

Grid Generator and HGUI Graphical User

Interface," NASA TM 108791, Oct. 1993.

7. D.G. Pearce, et al., "Development of a

Large-Scale Chimera Grid System for the

Space Shuttle Launch Vehicle," AIAA 93-

0533, Jan. 1993.

AIAA-2001-1004

8. R.L. Meakin, "Moving Body Overset Grid

Methods for Complete Aircraft Tiltrotor

Simulations," AIAA-93-3350, July 1993.

9. N.E. Suhs and R.W. Tramel, "PEGSUS

4.0 User's Manual," AEDC-TR-91-8, Arnold

Engineering Development Center, Arnold

AFB, TN, Nov. 1991.

10. D.C. Jespersen, T.H. Pulliam, and P.G.

Buning, "Recent Enhancements to

OVERFLOW," AIAA 97-0644, Jan. 1997.

11. B.S. Baldwin and T.J. Barth, "A One-

Equation Turbulence Transport Model for

High Reynolds Number Wall-Bounded

Flows," AIAA 91-0610, Jan. 1991.

12. P.R. Spalart and S.R. AIImaras, "A One-

Equation Turbulence Model for Aerodynamic

Flows," La Recherche Aerospatiale, No. 1,

1994, pp. 5-21.

13. J.E. Bardina, P.G. Huang, and T.J.

Coakley, 'q'urbulence Model Validation,

Testing, and Development," NASA TM

110446, April 1997.

14. S.E. Rogers, H.V. Cao, and T.Y. Su,

"Grid Generation For Complex High-Lift

Configurations," AIAA 98-3011, June 1998.

15. W.M. Chan and P.G. Buning, "Surface

Grid Generation Methods for Overset Grids,"

Computers and Fluids, Vol. 24, No. 5, 1995,

pp. 509-522.

16. F.R. Menter, 'q-wo-Equation Eddy

Viscosity Turbulence Models for Engineering

Applications," AIAA J., Vol. 32, Nov. 1994,

pp. 1299-1310.

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