Unstructured-grid methods development for unsteady aerodynamic ...

NASA

Technical

104143

Memorandum

¥

UNSTRUCTURED-GRID UNSTEADY

METHODS

AERODYNAMIC

(_ASA-T_-I04143)

AND

U_ST_UCTUnEn

O_VrL_PH_'JT

F_

UNSTEADY

AERnELASTIC

ANALYSES

DEVELOPMENT AEROELASTIC

ANALYSES

_,

12

N91-3_POS_

AND

AERODYNAMIC (HASA)

FOR

p

CSCL

OIA

G31o2

JOHN

T.

BATINA

ELIZABETH WILLIAM RUSS

M. LEE L.

KLEB

D. RAUSCH

SEPTEMBER

1991

N/ A Nalional Aeronaullc_ SpruceAdmlnislralion

and

IJmgle¥ Roaoateh Cerdef I Inmplon. Virqfnl_ 23665

Unclas 0046090

IJNSTRUCTURED-GRII) UNSTEADY

METIIODS

AERODYNAMIC

John

T.

M.

William NASA

L.

Langley

FOR

AEROEI.ASTIC

ANAI,YSES

Balina

Elizabeth

Hampton,

DEVELOPMENT

AND

Lee Kleb

Research

Virginia

Center

23665-5225

USA

and Russ

D.

Purdue West

Rausch University

l,afayelle,

Iodiana

SumnHiry

47907

aircraft

USA

was modeled

exlension, The unent

current

slalus

of

in Ihe Unsteady

Research

Center

oped

for

unsteady

paper

first highlights

For the

solution

selected

results

pabilily.

The

applications are also code

is descrihed.

which results

with

with

solutions

grid

agreement

equations

two

obtained data

thus

using

of

gives the ca-

of

structural

show

the accuracy.

deformations undergoing

any

formations, structured

rately

the

Considerable

progress

decades

on

methods

fi_r aerodynamic

fix:used

primarily

the Euler namic that

developing

and

move

of

the

of

the ruethc_ts

moving

mesh

moves These

ity of the

procedures

defommtions. assume

that

three

grid

an alternative, make

use

grids

are typically

shears

as the

made

that b_.ly

the applicabil-

or small-amplitude typically

have

physics

in two

triangles

of an assemblage

di-

and

in

of tetrahedra.

of

u_d.

more

adaption

cal time-stepping

where

the temporal

u_d

in cells

tages

over

flw unsteady

structured

geometries

methods

have

grid

methods

which

aerodynamic

ple, the primary is the ability

grid

advantage

to easily such

model

and

several make

aer_velaslic

as the F[A-18

connplicated aircraft

them

analyses.

of the unstructured very

distinct

shown

advanattractive

For exam-

where

determined

by the largest

purpose

of

The

first

selected

of the capability.

the

results The

the

upwind-type

three-dimensional

the time-integration tails

on

and the

explicit spatial

of the and

that

to

of the flow

in

"l_me

time

is as

that

explicit

status

the Unsteady Center. have

been

equations various

artificial

flow

deand

are either dissipation

dissipative. are

t°'-t9

features

are demribed

adaption

are

level

the current

Euler

fluid

cells

steps

accuracy

Research

discretizations

lo-

in grid

time

within

are naturally

governing

temporal

also

demonstrate

with

temporal

may problems

problem.

solvers

solvers

which

adaption

to the same

Langley

which

flow

of was

am used

in the

flow

an order mesh

and larger

of the tinre-dependent

of the central-difference-type or of

steps

is to describe

at NASA

highlights

fi)r solution

gives

size

times

accurate

of as time-accurate

methc, ds development

Branch

paper

step

cells

solution

three

unsteady

are small.

all grid

the paper

of unstructured-grid Aerodynamics

time are large

gradients

by bringing

implicit

I. '_ The

the

maintained

grid methodoh>gy

in Fig.

smaller

3

delta

fine

the physics

can be thought

gradients

13 The

by using

for

and efficiently

accu-

in Fig.

is a highly

temporal grids

in a

more

mesh

if a globally

adaption,

accurately

result

desome

it enables

number.

produced than

unstructured

time. TM Temporal

then unstructured

points

to spatial with

final

in

for a fiat plate

coarse

not

to small

shown

solution

is

does

done

is that

Mach

The

motion

to predict

the original

equations,

grid

bending capability

For example,

flow

freestream

the Euler

Similar

where

flow.

flow.

fewer

be employed

veloped

The

for the

by adapting

magnitude

The

developed

grids. 3-t9 up of

obtained

solution

advantage refinement

motions

configurations.

shearings

mesh

allows

realistic

applications

A third

vortex-dominated

to the instantaneous

geometri-

been

codes.

at a supersonic

was

resolve

Many

assume

has an underlying

of unstruciured

they consist

require l_sition

of solution

algorithms

these

dimensions

methods

of

aerody-

generally

limit

motions

these

has

the _flution

unsteady

consideration.

mesh

two

(CFD)

in CFD

developed

consequently

to rigid-body

past

inslant:meous

under

the

which

mensions

for

methods

being

that

the compulatkmal

work

For

to the

body

assumptions

As

Recent

these

are currently

Furthermore,

structure.

recently

analysis,

the

dynamics

algorithms

to conform

or

over

fluid

equations.

rigidly

deforms.

cal

developing

or deforming that

made

analysis.t'2

Navier-Stokes

mesh

been

computational

and aeroelaslic the

the

on

has

wing

grid

for adaptive

is a conical Inlroductkm

limit

and

for a transport-type

grid

which

the

inlets

a structured of geometrical

aircraft grid

deforming

simple

grid way

to treat

surface

assumptions

edge canopy

the methodology

mesh

such

as

engine With

a complete-vehicle The

leading as the

this level

of complete

of the deforming

2.

includes effects.

is thai

the

with

as well

to achieve

advantage

to move

in Fig.

natural

also

power

difficult

way

An example

involve

modeling

A second

depicted

grid

comparisons

and

tails,

vertical

engine

it is extremely

complexity.

configuration

Comparisons

a structured

grid.

the wings

and

The

to simulate

fl_r a general

the accuracy

These

verifies

The

three-dimensional

flows.

to determine

methodology.

which

devel-

amt then

the fuselage.

nozzles

developed

features

and

unsteady

being

been

and

Langley

an:dyses.

have

various

and

experimental

the unstructured g_xt

Euler

demonstrate

[x_th steady

made

that

demonstrate

are

aeroelastic

solvers

develop

al NASA

methods

,rod

the flow

methods

Branch

These

aerodynamic

of the unsteady

for

and

unstnJcturcd-grid

Aertv, lynamies

by including

horizontal

Both

discussed equations.

procedures

are

for Dealso

Fig

given. and

The selected

results

three-dimensional

I

Unstructured

that are presented

appficatkms

for both

surface

demonstrate

sleady

grid for F/A

two-

and unsteady

IX fighter

lime

step may

tated

by the CFL

flows. Comparisons are also made with soluticms obtained using a structured grid c(_le and with experimental d;tla Io determine

tile residual

the accuracy

scribed

of the unstructured

grid

methodology.

Central-Difference-Type The using

unsteady

Euler

a finite-volume

tmstructurcd The

algorithm

of

type flow

solver.

explicitly

to prevent

high-frequency tire

blend

conceptually

imd thus With

this

solver,

oscillations

uncoupled

of

anti

and fourth

lively.

biharmonic

operator

The

four-stage,

scheme

at the first stage.

in time

and

in cell

volumes

more,

includes

this explicit-scheme

CFI,

number

of 2_22.

the CFI+ number residtnal

with

equations lions_

;tre

damping

uses

c:ltiorls,

by a k_al

however,

tile time-accuracy

a global

lime

using

stability

time step

requirement.

The

difference

splitting

on structured

a spatially

spatial split

similar

referred

discretization

this

account

is that

Further-

to a

to steady-state, implicitly

l_ivrts.

These

several

local

at each lq)r

is usually maxirnlurl

the

implicit

used

de-

the

the

flow

grid

solver.

a so-called splitting

of Roe. 2t These

local

alThe

fluxof van

tlux-split

wave-propagation

diseretizations

flux-

for use

involves

they capture sh_k within the shirk

these

or

flux-vector

splitting

for

ahernatively

unstructured

charac-

waves sharply with structure. A further

are naturally

additional parameters

dissipative

artificial dissipation to control the di.,,si-

patron.

"rhc Euler explicit

etluali(ms

Runge-Kutta

relaxation ordering

are

meth_xl

integrated

in time

(described

in the previous

time-imegration

prcx:edure.

scheme

Is The

the elements

that

involving

procedure

make

using

up the unstructured

tions.

The

stream

to downstream

first

sweep

is performed

in the direction

and the _cond

and thus allows the selection of the step size based accuracy of the problem being considered, rather

I_)h+t

numerical

stability

lime

may

of

re-

from

and an appropriate independent

supersonic

relaxation

of the

be used step

of numerical

flows

scheme

algorithm. for rapid

the second

Consequently, convergence

issues.

up-

sweep

is unconditionally

size may be selected stability

from

is from downstream

step-

steps

purely

sweep

using

global

by mesh

upstream to downstream The solution is obtained by sweeping two limes through the mesh as dictated by stability considera-

This

becausc

section)

a Gauss-Seidel

For

appli-

an

either

is implemented

unnecessary.

grid

allowable

present

to upstream.

time

unsteady

as

developed

itera-

Jacobi

.'tceelerated

The

_hemes

solver

on either

of the flow and one grid point

advantage

of may

step,

flux-vector

to ;Is :m upwiv_l-type

I.eer 2° or the flux-difference

teristics ;it most

time

be solved

either

to upwind

of

based

discreliTations

adaption

Solver

may and

In. lS-Iq The

meshes.

approach

varying

Flow

differencing

i,, thus

temporal

dic-

version

section.

Euler equations

upwind

or an implicit

for ct|anges

by the

s_ep size analysis,

unsteady

using

and,

is evalu-

is limited

ix furtfier stepping,

allowable

stage

correslxmding

aver:lging

grid

The by

accurate

In this

tnesh.

size that

by

to steady-stale and h_al

scheme.

c(mvergencc

approximately

a stant|artl,

using

to at'cotlall

condition

be increased

the maximum

as determined

a step

involves

is hu'ger th:m that

a time

Alternatively,

and consequently do not require terms or tile adjustment of free