On the Coupling Between a Supersonic Turbulent Boundary Layer ...

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Boeing document no. D6-81571,. 1994. [42] Frendi, A., and Maestrello,. L., "On the combined effect of mean and acoustic exci- tation on structural response.
NASA

Contractor

Report

201631

On the Coupling Between a Supersonic Turbulent Boundary Layer and a Flexible Structure

Abdelkader Analytical

Frendi Services

Contract

NASl-19700

October

1996

National

Aeronautics

& Materials,

and

Space Administration Langley Research Center Hampton, Virginia 23681-0001

Inc., Hampton,

Virginia

ON THE COUPLING BETWEEN A SUPERSONIC TURBULENT BOUNDARY LAYER AND A FLEXIBLE STRUCTURE Abdelkader Analytical

Services

Frendi & Materials,

Hampton,

Inc.

VA 23666

Abstract

A mathematical

model

and a computer

code

have

been

vibration of an aircraft fuselage panel to the surrounding layer and acoustic fluid. The turbulent boundary layer decomposition equations.

agreement

supersonic

panel.

1.

earlier

and

are

and

flexible

used.

leads

number

Results data.

the

to the

from

this

response

in acoustic

increases

couple

the

that

are

in the

and radiation

damping

acoustic

resulting model

It is shown

to lower

to be due to an increase Mach

averaging

numerical

panel

to fully

flow field, turbulent boundary model is derived using a triple

a conditional

equations

experimental of the

the

applying

acoustic

is believed

Increasing

with

and

existing

full coupling

This

regime.

agreement

panel with

regime,

the

in this

flow variables

Linearized

in good from

of the

developed

on the

damping,

panel

which

is in

work.

Introduction Future

efficient,

civilian

ments,

a substantial

in various Speed

aircraft,

less expensive

subsonic

and

faster

amount fields.

Transport

aircraft

With

noise

and sonic

fatigue.

The

source

of aircraft

interior

fuselage.

These

vibrations

turbulent

boundary

level,

it is imperative

from

the

turbulent

that

mechanics

Early

on the

tural

vibration

either boundary

and

experimental layer.

on

One

development

renewed research

noise

caused

aircraft.

layer

the

phenomenon, effects

of turbulent noise

or empirical

of the

turbulence,

widely

boundary

generation models used

been

pressure

to reduce

pressure

focussed

mainly

on

the

pressure

in the

literature

is the

noise

is transmitted problem

structure field

mostly

interior

understood

the

area

skin of the

in the

fluctuations

to describe

models

outer

noise

least

in the

the

is a challenging

layer

of a High

increasing of the

is the

fuel

require-

to be accomplished

by which

that

more

stringent

fluctuations

in order This

quieter,

development

vibrations

mechanisms

interior.

be

needs

in the have

the

by the

to

of these

work

interests

Therefore,

to the

have

In light

interest

is generally

we understand

interior data

and

the

in turn

the

boundary

involves a fluid mechanics. work

are

layer

aircraft.

(HSCT),

of interior

will

today's

of research

engineering

Civil

or supersonic,

than

in the

Corcos

as it in fluid

on strucand

used

turbulent model

[1].

This tral

model

density

was derived

of the

based

pressure

on experimental

_(w)

describes

distribution

and

the above

equation,

distances

and

Wooldridge

the

the

w¢ = ¢(_)ACNIB(N

frequency

exponential

Ue is the

the

cross

spec-

convection

functions

W_)ezp(-i_)

content

term

ta is the frequency,

[2] the

and gives

as;

r(¢,_,_) where

observations

(or

auto-spectrum),

represents

the

¢ and r/are

the streamwise

velocity.

A and B

(1)

Based

were

A

convection

on

the

represented

and

of the

B

the

pressure

and spanwise

experiments

spatial field.

In

separation

of WiUmarth

by decaying

and

exponentials

of the

form;

N) = where data.

the

constants

In recent [3-10]. that

years,

Graham

13 are arbitrary

many

improvements

[11] performed

for aircraft

to account

a and

interior

for the

noise

problems, of the

that

The

performance

superior

model

was

to these 14].

the Eflmtsov's

derived

models,

This

multidimentional

Gaussian

It is important determine

field

constants

in the

turbulent

is therefore coupling

This

is not important

Monte

Carlo

with

and become

layer

above

(low speeds),

to the

to solve field

models

Since

He

fact

that

this

In addition this

to be

need

surface

high

the

useful

however,

thickness.

experiments.

problem

[12-

a homogeneous,

experimental

pressure

speed

constants

and

can be

of its inability

layer

zero mean.

the

is fixed

proposed concluded

be used for such problems.

method

for compressible

approach

model

pressure

useful.

once

been and

because

attributed

laboratory

layer

all of the

In addition,

boundary

decoupled.

the

have

models

on boundary

was

than

set of experimental

model

various

is inadequate

length

model

process

especially

limited.

Corcos'

of the Corcos

boundary that

to fit a given

of the

model

rather

used the

random

experimentally, is further

data

to emphasize

the various

to obtain models

studies

idealized

Corcos'

Efimtsov

aircraft

several

approach

study

correlation

extension

of the

from

of the original

a comparative

dependence

recommended

and are chosen

(21

flows,

data the

are determined

structural-fluid in some

speeds

use

of these

the

pressure problem

problems

the

to

is difficult

interaction

engineering

at supersonic

data

coupling

where between

fluid and structure is very important. As was shown by Lyle and Dowell [15], acoustic damping on the structure becomes dominant as the speed is increased from subsonic to supersonic.

This

showed

in a supersonic

of the

that

structural

In order the

complete

appropriate Stokes The

is further response

to account set

With

at higher

the recent

calculations

fluid-structure equations

The fluid

structural

of Wu and

the coupling

Macstrello

term leads

[16] who

to an over-estimate

modes.

differential

requirements the

by the neglecting

conditions.

and

computational

equations.

regime,

for the various

of partial

boundary

equations,

confirmed

for solving

for the

motion

response

advancements

interaction

by

and

the

a problem

in computers, 2

fluid

is described

is given such

effects,

the

the

one needs structure

by the nonlinear nonlinear

will

plate

be dictated

full Navier-Stokes

to solve with

the

Navierequations.

by the

fluid

equations

have

been

integrated

is referred severely the

for a restricted

to in the limited

by the

computational

sible

simple

Since dynamics equations. Eddy

spent

This In DNS,

the

Kolmogorov

limited

to those

subgrid

scales)

in the early

are

the

testing

before

view

point,

DNS

flows,

near-wall

calculation

However,

idea but

for solving expensive

problems

and

a large

Over

infancy,

into

engineering

number over

DNS

of problems.

restriction

is not

but

scales

(or

models

and

need

From

[17]

developed

these

performs models

how

an equivalent

as it is for

DNS.

engineering

numerous;

geometries,

to

extensive

a computational

than

as severe

of LES are

to are

does a poor

been

LES a preferred

it has yet to be used in complex

down scales

small

Though

less expensive

The weaknesses

scales

have

one

these

Large

of resolved

resolved

layers

problems.

do not make

as the

tool

it is still

too

models

are

spatial

etc.

a century

quantities

of averaging

in fluid

by Smagorinsky

[18,20].

In addition,

to various

all the

new models

insight

kind

unresolved.

Reynolds

computationally,

still in their

as the

known

well in free shear

physical

bases

Navier-Stokes

of the unresolved

Recently

data

is in the number

was introduced

size of

developed.

approach

and the

is

is impos-

researchers of the

to resolve

is one order of magnitude

improvements variety

more

such

remain

the

reasonably

by the

being

forms

are coarser

The contribution

layers.

with

can be applied

all these

enough

of the first LES models

and

tool,

simplified

grids

approach

problems

models

DNS

a method

This

to generating

engineering

of a new

be small

boundary

an LES calculation

restricted

LES and

in LES the

performs

i.e.

region,

they

should

One

This model

sophisticated,

the

between

Such

(DNS).

engineering

turbulence

a useful

developing

than the grid size.

Smagorinsky

more

treat

used

however,

is modeled.

1960s.

various

of time

geometries.

can be resolved

been

led to the development

grids

larger

have

being

The difference

scale;

job in wall bounded using

has

LES.

deal

that

use in practical

method

from

and

Simulation

numbers its

to validate

away

a great

effort

Simulation,

scales. the

in order

is decades

have

of Reynolds of this

of flows

Numerical

Therefore,

The uses

flows

DNS

number

as Direct

range

domain.

at this point.

for some

literature

ago,

a time

O. Reynolds

averaged

[21] proposed

mean,

denoted

a decomposition

by an overbar,

of the

and

turbulent

flow

a fluctuation;

1=i+1'. Using the

this

decomposition,

contribution

became

known

used

to solve

only

for the

flow.

from as the a wide

mean

In order

decomposition

he derived the turbulent Reynolds variety

Averaged they

set of equations

fluctuations

(RANS)

problems.

cannot

provide

this deficiency,

for the

mean

had to be modeled.

Navier-Stokes

of engineering

quantities,

to overcome

a new

(a)

W.C.

Since

information

Reynolds

and

new

equations

these

any

quantities

These

and

equations on the

Hussain

have are

dynamics

[22-24]

where

equations

used

been

derived of the a triple

of the form .f = f+.f+f"

to study

small

represents

the

conditional motion. scale

amplitude

averaging Liu [25] used

wavelike

wave

wave motion

eddies.

and

disturbances

(4)

in turbulent

jr" is the turbulent

were used to arrive

at a set of dynamic

a similar

to study

Merkine

approach and

Liu

the

flows.

In equation

A combination equations

the near-field

[26] studied 3

shear

fluctuation.

describing

jet noise

development

due

(4),

of time

f and

the wave

to the large-

of noise-producing

large-scale

wavelike

[28] and

Gatski

fine-grained

which RANS

last

few

they

researchers

the models etc.

have

The

is described,

results

The

more

noise

from

Merkine

between

Gatski

[27], Alper

large-scale

[30] calculated shear

coupled

unsteady

coherent

turbulence

remarks

are:

of this paper

are

to a Very

and the

is organized

describes

are given given

Large

as follows;

the

method

in section

in section

developed

in section

or VLES

used

(4) and a summary

the

or DNS, geometry,

mathematical

to solve

of the

the

results

model,

and

Boundary

Layer

triple decomposition as follows;

g represents

Equations

proposed

by W.C.

Reynolds

[24], the

flow

quantities

a flow quantity

and (_) its Favre

(4) averaged

mean

defined

by

- (pg) p When

decomposing

of Morkovin's therefore;

some

(5).

g = .0+ .0+ g" where

by

[32]. The

LES

for any

(2)

of the models

identified

either

be used

of solution

been

has been than

can

acoustic

The extension with the new

Simulation

less costly method

Bastin

Lighthil]'s

have

method

Eddy

production

recently,

structures.

models

RANS

it is computationally

extensively

(3)

unsteady

Liu and

Model

Turbulent

Using the are decomposed

equivalent

tested

section

The

sound

More

with

and

structures

the

layer.

approach

advanced

physics.

VLES

and discussions

Mathematical

2.1

mixing numerous

been

remainder

concluding 2.

flow.

modeling

years,

as being

of using

the

Liu and

in a free turbulent

the jet

contain

advantages

model

shear

structures

jet.

interactions

led to the solution of a wide variety of engineering problems. method to unsteady problems has been made less difficult

because many

in a free

the

a semi-deterministic

to calculate

In the

turbulent

[29] studied

coherent

[31] used

analogy

in a plane

Liu

turbulence

due to large-scale et al.

eddies

and

the

hypothesis

density,

the

[33] which

(5)

turbulent

fluctuations,

has

recently

been

p", verified

are by

neglected Sommer

by et al.

virtue [34],

(6) In equations (4) and (6), (_, p) is the low frequency is the turbulent fluctuation. By

defining

the

total

mean

(4)

part

of the

mean

and

(g")

to be

G =0+0, equation

variation

(7)

becomes g=G+g". 4

(8)

Equation time

(8)

has

a similar

independent In the

mean

derivation

averaging

was

form

while

in (8),

of the

introduced.

to equation G is time

dynamic

Some

(3);

used

of this

>=0

only

difference

is that

in (3),

f is a

dependent.

equations

properties

] =0

(10)-(13),

(u_',

defined

momentum,

CO

P-(y-1)[E-p(U_-I-U_-t-U_+-t-)/2].

(p, Ud, E, P)

e u, p")

axe the

P/(7

1) + p(u_

averaged

-

(12)

represent

turbulent

stress

the

total

fluctuations.

+ u_ + u_)/2.

means The

of the

variables

variable

In equations

(13)

ill)

(e) and

(p, ud, e, p),

is the (12),

total

energy

< 7-dj > is the

tensor,

(14)

Moo [ _,kco.j+-Sg.,,/ _ COU_ COUj'_ --_,-G;_ 20Uk _f,q,] < r,j >=--_ where

Moo,

viscosity, stress

ReL

respectively.

tensor

..

and

and

# axe the freestream The

term

is modeled

Mach

number,

< _i_j - "- " > of equation

in the

same

way.

Reynolds (11)

In equation

number

is similar

(12),

and to the

< :-uuj'" >,

molecular Reynolds

< P-"'uy" > and

H

< _-Ouj > have to be modeled. Invoking the Boussinesq approximation to the

mean

strain-rate

tensor,

leads

that

the Reynolds

stress

tensor

is proportional

to 2

1 (15)

where and

k =< u_-"-u_" > /2 is the S O is the

mean

strain-rate

turbulent tensor

kinetic given

energy,/zt

is the

turbulent

eddy

viscosity

by,

(16)

5

The

turbulent

eddy

viscosity

is obtained

from

the

relation

(17)

_,= c;-_ where

C_ is a constant,

w the

The conservation

specific

equations

dissipation

for k and

rate

(elk)

with

e being

the

dissipation.

w are;

a(pk) + _= (pujk)

au,

a (_,, a_)

(18) (19)

a (_.aw) In equations (18) C_, t = 0.09 (same model model. 2.2

described

and (19), pa = C_npCk/_a) and C,., 1 = C,,,tc2/CCC_t)°'%%), as C_, in the log layer), crk = c% = 2, C_ 2 = 0.83 and _ = 0.41. above

The

Plate

The

out-of-plane

was

derived

by Wilcox

[35] and

plate

displacement,

DA2w

plate

as the

(k-w)

turbulence

Equation w, is given _w

where Young

is known

with The

D is the Modulus, material

and

+ p_,h--_- i- + F_

1" is the structural

A=

The right hand side, 6p, of equation fluids and can be written as

biharmonic

equation,

Ow

plate stiffness obtained from D h the plate thickness and vp the density

by the

= EphS/12(1 Poisson ratio.

damping.

c_

(20)

= 5p

04

The biharmonic

= _-_+ 2o--;/_, +_ (20) represents

- v_), with In equation

Ep being the (20), pp is the

term

is defined

c_

(21)

the pressure

loading

due to the adjacent

6p = f - pb_ with

(p=)

pressure 2.3

being calculated

The

Acoustic

In order arrive

at (see

the

radiated from

the

acoustic model

Radiation

to calculate

the

pressure

in section

and

as

(22) (pbZ)

the

turbulent

(22),

Kirchhoff's

[WU(TR"z')]

dz'dz'27r

boundary

layer

(2.1).

Equation pressure

pa of equation

formula

is used

to

[36] for details)

Pa(z'Y'z't)

= P°° /

/D

(23)

where

the

square

integration

brackets,

domain,

[.], are

D, is the

used

whole

to denote

plate

a retarded

°_ = "_-r.

and wit time,

In equation

(23),

the

i.e.

=', z')] = wil(t - Rtcoo, ',z') R = [(z -

where

to a point (23)

is used

When the

using

3.

the

plate

"I- (z -

(z',

to calculate

boundary

layer

layer

Navier-Stokes

code

order

accurate

volume

finite

that

is based

centrally

split

with

a good

separation. profiles

Two

a smaller

out

state

(25),

normal

a large

mean

that

that

using

and

Pahl

of Simpson's

profile

conditions,

are ones

the

Using turbulent plate

the

This

the

the

presence

In the

following where

those

considered

with

state

mean

of the

minimal velocity

plate,

calculation

boundary

then

is carried

as follows

(25) using

of the

method

pe,

equations

(10)-(13),

is specified

surface

edge

shock,

flexible

is simply

plate

supported.

equation

as

(20)

developed

through layer

is by

a combination

pressure

fields

acceleration

(18),

(19)

fields,

at every

of a leading

steady

in time.

pressure

is repeated

plate

dynamics

and

the

the

edge

and boundary velocity

called

leading

is obtained

step plate

routine In the

The

rule

IMSL 0.25.

for structural

a trapezoidal

new

an

0.05 and

plate's

with

plate

only

flows edge

terms

spatially

retains

an unsteady

domain

results, the

viscous

an implicit,

steady

edge is turbulent.

procedure

computational

a second an upwind

is generally

the leading

generated

acoustic

layer

to obtain

the

to be between

pressure,

and time

boundary

equation.

case

and

previous

shows

in one

acoustic

in space

plate

the

dimensional

domain

supersonic.

rule

This

first

edge

upstream

difference

radiated

with

thin-

uses with

all the

aerodynamic

includes

chosen

region

finite

method

approximation

at the inflow

of the leading

are integrated

the

except

The

between the

a two top

flow in the

downstream

[39].

(23)

to update The

of

coincides

three-dimensional

while

in time

case;

number

amplitude

an implicit

as follows.

equation

expansion

point

+ eR,,(y, z, t).

is a random

integration

Coupling tained

shows

the

while

integrated ttoff

series

are dJscretized

surface.

of the leading

velocity

the

method,

body

for each

domain

downstrean

e is a small

calculation,

laminar,

Equation

and in the far-field.

observer

numerical

terms

splitting

to the

are made

tLa(y,z,t)

[38] and

The

The thin-layer

= In equation

[37].

using

for high-Reynolds-number

using the

solved

are integrated

scheme.

calculations domain

are

flux difference

derivatives

by perturbing

RNNOF

plate

the

(x,y,z)

point

of sound.

a Taylor

0 (when

The convective

The equations

approximation

are obtained

using

speed

of the

pressure,

at R :

as CFL3D

scheme.

on Roe's

differenced.

terms

to be

surface

surface

equations

known

approximate-factorization

viscous

the

an observer

coo is the

of Solution

The turbulent

are

on the

the singularity

from

distance (24),

source).

Method

scheme

both

to calculate

to avoid

is the

In equation

pressure

(23)

is used

z')l] ill

0, z').

the

equation

integrand

with

z') 1 -t- yi

on the

(24)

different

and

these time

is ob-

as boundary the are

acoustic then

step.

used

Figure

mathematical

models.

all the

studied

because is clamped

cases

between

two

rigid

1

4.

Results

and

This a typical given

section is divided into several fully coupled run are presented.

in subsection

and radiation are

on the

response

given

Results The

The

(4.2). and

and

flow

mean

flow

finally

in subsection

structural

parameters

are;

results

on the

response

from two runs at two different

the

effects

of plate

boundary

=

in this

1.98

case

Much

conditions

are taken

from

MaestreUo

Much

number),

Tt

(free-stream

(Total temperature), T,, = 550 R (Wall temperature) and Re/ft number

plate

Case

used

Moo

of coupling

analyzed.

Coupled

properties

In the subsection (4.1) results from to existing experimental data are

effects

(4.5)

are

Fully

the

(4.4),

radiation

a Typical

and

(4.3),

In subsection

acoustic

From

subsections. Comparisons

In subsection

axe discussed.

numbers

4.1

Discussions

=

[40]. 563

R

= 3.73xi06 (Reynolds

per foot). A titanium plate is used in this study with the following parameters;

length, a -- 12 inches, width b = 6 inches, thickness h = 0.062 inches, density per unit area pph - 2.315x10 -s Ibf-scc2/in3, stiffnessD - 345. Ibf-inand damping r - 7.4x10 -4 lbf.sec/in s. The parameter e of equation (25) is set to 0.25. The plate is oriented such that

the

length,

The vertical

computational directions,

83 x 53 x 83. while ft

a, is along

used

respectively,

Equally

upstream

streamwise

domain spaced

grid stretching

vertical

the

is used

of the

direction

inflow

direction.

is 2 x 1 x 2 ft

the

number

points

are

of points

used

in the vertical

boundary.

is located

used

in the

6000 Hz) to both

the

level

numerical

advanced

turbulence

experimental

fluctuation

on the

measurement

that

based

the

structure

with

Effect The

plate

flow

step;

plate,

layer,

and

the

layer plate

little

the

center

the

with

effect

on the

response

of the

an

indication

that

shown

in Fig.

the

lower

of added before 4.4

uncoupled

plate

13. This plate

out. the

is directly 11 shows

the

center

for both

the

two

PSDs. layer.

on Fig.

one

critical

9 show

for

a good (25)

levels.

plate

fluid. back PSD

is higher

response

result

is important significantly

where

noise

Therefore

one

on noise

of Mach

in the

control

reduction

same

the

of the

fully

coupled.

The the

plate

whole

case

for interior

noise

is typically to consider

vibration response

to notice range.

and

at that

This

therefore

in higher

considerations.

both

plate

is

less

[42], this difference would peak responses occurs. As

results

interior the

layer There

frequency

structure

latter

cases.

It is important

on the

uncoupled

the

time

This

boundary

uncoupled displacement

the

at each

fluid flow.

The PSD

through

turbulent

calculation,

since

of the

response

the

turbulent

and

as those

on the

This is expected

damping

techniques

the

other

to the

coupled

overpredicts

needs

are

In the into

12 for the two cases.

in more

are

calculation,

transmitted

Figure

plate

In flexible

communicated

results

analysis

frequencies weight.

deciding

Effect

point

e of equation

of full coupling

the surrounding

boundary

is shown

calculation

effects

carried

fleld

the

turbulent

in this the

is not

between

coupling

higher

an uncoupled

depended

are

determined

response. Based on the results obtained by Frendi and MaestreUo be even greater at higher excitation levels where shifting in the the

surface

at this

that

parameter

experimentally

field and

with

at the plate

of the plate

used

are

pressure

to as uncoupled.

the

expected

level

of Fig.

an

Recent

of the

peak

frequencies

The

and

frequencies.

to mention results

to be due

resolution

behavior

of the

numerical

range.

to access

acoustic sides

response

or no difference

has

at high

frequency

4.1,

The

is believed

grid

similar

It is important

frequency

calculations

radiated

fluctuations

is little

Hz.

properties

In order

on both

the

case is referred pressure

fuselage.

agreement

plate

two

boundary

however

better

(4.1).

communicates

turbulent

agreement

[41] show

in subsection

for this

Higher

Coupling

mean

of a flexible

in better

up to 2000

experiments

in subsection

boundary

presented

in level

used.

[40]. The

on the

range

decrease

model

Concorde

of Maestrello

's location

to obtain

of

result

on the

results

This rapid

turbulence

would

to that

are in the

can be adjusted

given

model

on the

agreement

rapidly. and

measurements

pressure

4.3

decreases

resolution

noise

difficult

levels,

In other

levels, and

response

noise

as

words,

particularly

expensive

of a fully

at

in terms

coupled

plate

to be used.

Number

Two Mach number cases have been studied, 1.98 and 3.03, using the mean flow properties given in the above subsections. Figure 14 shows the PSD of the surface pressure at the

center

of the two

plate

displacement

cases

is higher, Mach

of the

number.

Lyle and

response

at low Fig. Dowell

for the

frequencies.

15. This

This result

two

cases.

at the

plate

However

is attributed is consistent

[43] who showed

that

The two center

at high

show

little

10

the

the

The

response

for Mao with

number

and

PSDs

between

damping

of Frendi

Mach

identical.

or no difference

in acoustic

the results

increasing

are nearly

frequencies,

to an increase with

PSDs

-- 1.98

increasing

Maestrello

increases

the

[42] and the

acoustic

damping cases.

on the Since

pressure 4.5

PSDs

Effect

17 shows

lent boundary response plate The

shows

for

due mainly to show

side are

a higher show

simply

supported

effect

A model

the

three

the

two

radiated

involving

be made

plate

changing

using

this

other

lower The

plate

radia(4.1).

plate

from

plate

objective

radiated

properties

frequency.

(such

to lower

indicated

of this

on the

supported

content

is also

turbu-

displacement

modal

frequency level

in order

the

The simply

at the lowest

parameter

approach

18.

in the

19.

and acoustic as in subsection

of the

Fig.

response

a shift

Fig.

any

of the

the PSD

A slightly

resolution,

of changing

that

couples

and

is

calculation pressure

as mass,

to analyze

their

a supersonic

test

of the

experimental

code. results

boundary

have

been

The

given

by

layer.

layer

a flexible

number

damping

radiated be used made

the

the

boundary

pressure to assess

to support

results

is important

increases

lowers

carried this

for the structural

Additional

• As the

Mach

results

both

of the plate

• Changing

boundary

calculations

• Full coupling calculations.

acoustic

turbulent

with

field has been developed. A three dimensional code The code is a modified version of CFL3D. Extensive

dimensional

turbulent

for the the

is field.

stiffness,

effect

on

the

Remarks

capability

existing

case.

vibration

center

as expected,

and

can

pressure

flow properties

However,

content also

calculations

Concluding

identical.

pressure

the radiated acoustic to solve this model. and

nearly frequency

frequencies

direct

radiated

at low frequencies,

on plate

at the

radiated

the

damping...etc) radiation field.

conditions

the same mean

of the pressure

to lack of frequency

the

Additional

5.

of edge using

PSDs

natural

of the

frequencies

effect

a different

lower

PSDs

the the

layer

shows

of the

Conditions

are made

that

the PSDs

in the response

identical.

Edge

to access

16 shows

or no difference

are nearly

two calculations

Figure

Figure

is little

of Plate

In order tion,

structure.

there

the

model

response

showed

acoustic

conditions

show

20

good

summarizes

agreement

pressure

response

damping

especially of the

Figure

and

and

with

fluctuations

in

that;

for accurate

response

out.

plate

has been written two dimensional

on the plate

high

plate

and acoustic

radiation

increases.

The

modes.

changes

frequency content. This shows that the best noise reduction mechanisms.

the

response

and

the

a computational tool can Further test runs can be

this idea.

Acknowledgements The author of NASA Thomas me

during

would

Langley Gatski the

like to acknowledge

Research

Center

for his availability course

under

the support contract

to discuss

the

of this work.

11

of the

NASl-19700. problem

Structural

Acoustics

I would

and the

helpful

Branch

like to thank advice

Dr.

he gave

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yf i Leading edge

i_

_

_111

i shock 5

I

Navier Stok_--_'_

i D_2w + pphWtt + l'w t = p-. p+

I

+

I+x

:+.,.,o +1--.,..,_,° --I-.,o,o +: x0

xo+ L i

.

P®rr

P :'_'.UD

Figure

1: Two

dimensional

X

[w_ (,;,x', z')] _

dx'dz'

computational

domain

15

and the

mathematical

model.

0.30

I

I

I

!

0.15

_ I_ '

II '

l'

-

1

i

0.00

k -0.15

i

-0.30 0.000

l

0.025

0.050 _r"qe,

Figure the

center

2a:

Time of the

history

of the

T

turbulent

plate.

16

0.075

O. 1O0

sec

boundary

layer

surface

pressure

at

0.0010

/

'

,

,

r 0"0005 "_.

1

i!

0.0000

j

-0"0005

I

-0.0010

/

i

0.000

0.025

0.050 Time,

Figure

2b:

Time

history

of the

,

center

17

0.075

O. O0

sec

plate

displacement

response.

0.0008

O.O0O4

-O.OOO4

Figure

2c:

Time

history

of the

radiated

pressure

18

one

foot

away

from

th_ plate

center.

....

125

I

........

I

'

'

'

121

1t7

C!] -o

t12 fl_

108

104

100 100

1000 Frequency,

Figure pressure

3a:

Power

at the

Spectral

center

Density

(PSD)

of the plate.

19

10000 Hz

of the turbulent

boundary

layer

surface

10

10

10

-8

-9

-10

N

-1-

c •-

10

10

10

10

-11

#V

-12

-13 -

-14 0

1000

2000 Frequency,

Figure

3b:

_J

Power Spectral

Density

(PSD)

3000

4000

Hz

of the center plate displacement

20

response.

9° h ....

I

........

I

........

8O

7O

D

m -o

_-_ 6O fl_

5O

4O

50

....

I

........

I

1O0

1000 Frequency,

Figure 3c: Power the plate center.

Spectral

......

Density

(PSD)

21

10000 Hz

of the radiated

pressure

one foot away from

1.2

C9 O_ c1. CU

Figure

4a:

Probability • at the

center

distribution of the

of the turbulent

plate.

22

boundary

layer

surface

pressure

1.2

0.9

O 0_

0.6

0.3

0.0 -0.002

0.000 Wj

Figure

4b:

Probability

distribution

of the

23

0.002

[rt

center

plate

displacement

response.

1.2

0.9-

O

0.6-

0.3

0.0 -0.005

Figure

4c:

Probability plate

0.005

distribution

of the radiated

center.

24

pressure

one foot

away

from

the

1.2

(0)

'

'

'

1

I

1.0

0.8

O O

0.6 e_ e_

0.4

0.2 0.0

_

0.00

,

0.05

0.10

0.15

0.20

_', ft

1.2

I

I

I

I

1

1.0

0.8 0

0.6

0 ci. a.

n,-

0.4

0.2 0.0

0.00

0.05

0.10

0.15

0.20

1?, ft

Figure direction,

5: Two-point (b)

in the

correlations spanwise

of the

wall pressure;

direction.

25

(a)

in the

streamwise

0.0 0.000

0.025

0.050 _,

Figure

6:

0.075

0.100

msec

Auto-correlation

of the

26

wall pressure.

i::1

(1) I (.n

i

(1) I

8 {'_

I

t'_

I I _P

_o

o _,=ll

2'7

35

......

|

......

i

........

I

5O

25 fA

2O

15

10

5

........

I

I

........

I

10

........

100

I

i

•

1000

i

t

iI,

1OOOO

y÷

Figure 8: Mean velocity -Numerical results.

profile, A Experimental

28

results

(Maestrello

[40]),

10

-9 l

I

___

10

-10

Experimental

(Ref.

[40])

Numerical m

10

-11

--

I

!2

N

T

-... ._c

" I

10

-12

_/I

vl

f \1

/

II Ii II I

10

i{

I

-14 \1

iII_

i!

I 1_ l

10

-15

, ,,,,I,,,,

,,,,,

,1 I

1000

r,_',

9:

Comparison displacement

of the

Power

Spectral

response.

29

I I I I II

I

, ,,,_,li,,

2000 Frequency,

I

rill

I

, , ,,

0

Figure

I

,,

3000

, ,

I!

4000

Hz

Density

(PSD)

of the

center

plate

125

II

!

a I J

a

a

___

Experimental

__

Numerical

!

!

!

!

!

(Ref.

! i

[40])

120

115 m "t3

v

n

110

105

1 O0 1 O0

1000 Frequency,

Figure

10: Comparison ary

layer

of the Power Spectral surface

pressure

at

the

10000 Hz

(PSD)

Density center

30

of

the

of the turbulent

flexible

plate.

bound-

....

I

--

'

'

......

I

I

,

i

i

i

|

i I

Uncoupled

121 .......... Fully Couolec

117

rm ,--7

112

108

104.

I00 100

1000 Frequency,

Figure 11: Comparison of the PSDs of the surface for the uncoupled and coupled cases.

31

10000 Hz

pressure

a.t,the center

of the plate

-7

10

10

-8 __Uncoupled .......

I0

N

I-

Plcte

Fully

Couplet

P!ote

-9

-I0

10

c-

V

-11

lO

10

-12

|

',:,,:.,' '_,'1

!

0

I

I

I

i

I

|

f

I

I

I

I

I

I

i

I

1000

I

I

I

I

!

!

I

I

i

i

2000 Frequency,

Figure 12: Comparison of the PSDs uncoupled and coupled cases.

I

I

I

I

I

3000

I

!

t

!

i

•

" I

[

|

i

4000

Hz

of the center plate displacement

32

for the

l

i

I

!

i

i

I

,

i

I

i

i

i

i

I

i

7O C_

Uncoupled Fully

Couplet

2O 1O0

1000 Frequency,

10000 Hz

Figure 13: Comparison of the PSDs of the radiated plate for the uncoupled and coupled cases.

33

pressure one foot away from the

109

-

103

r',n

98 n

92

Mcch

Numbe-

__3.03

86

....... 1.98 i_

'lll

8O

I

I I I 'Ill

100

JI

1000 Frequency,

0000 Hz

Figure 14: Comparison of the PSDs of the surface pressure at the center of the plate for two different Mach numbers.

34

10

-8

I [

I

J

!

|

Math

I

j

Number

__3.03

10

.........

1.98

°,:°

10

-16 0

2000

4000 Frequency,

Figure different

15: Comparison Mach numbers.

of the

PSDs

of the

35

6000

8000

Hz

center

plate

displacement

for two

100

I

I

I

I

]

I I

Mach

I

I

I

Number"

_303 8O

.......

198

rr_

6O fi_

4O

2O 100

Figure the

plate

16: Comparison for two different

i000

of the Mach

10000

Frequency,

Hz

PSDs of the numbers.

radiated

36

pressure

one

foot

away

from

125

I

....

Plate

........

I

Boundcries

___

Clamped

.......

Simply

120 Suppcr:ea

11,5 r_ 'o

s

: ii 110

.::,:.:,

ii: i.,"....."

105

IO0

'.°°

I

'

i

°.

I

I J

I

I

I

I'

'

100

1000 Freq_e,_cy,

Figure for two

17: Comparison edge conditions

_ I J

of the PSDs of the plate.

0000 Hz

of the surface

37

pressure

at the

center

of the

plate

-7

10

10

-8

I

tI

I

|

I

I

I

I

I

_

|

I

I

|

|

|

i

..:

I

t

_

I

I

#lcte

I

|

|

I

I

$

|

I

L

|

I

I

I

I

_

I

I

Roundcries

!i

o-9 i.J:l_ ,_'.._._

_

Clcrnped

.......

Simoly

o Suppor:_d

N

"t" c

10-10

I

10

'

1

_IIIflff_llrJt

0

r

1000

r

f

f

_

I

f

_

!

t

t

itlrllt_l_tll

2000 Frequency,

Figure 18: Comparison conditions of the plate.

i!..

of the PSDs

.3000

ii

'

4000

Hz

of the center plate displacement

38

for two edge

100

1

!

I

I

I

I

l

1

_

1

I

I

I

I

I

I

I

I

I

I

I

go

80

70 r_

60 V

0._

50

4O Clampe_

30

...........

Simply

Supported

20 10000

Figure 19: Comparison of the PSDs of the plate for two edge conditions of the plate.

39

radiated

pressure

one foot

away

from

the

U

O

0

..,,...,

O i=,

N

i=,

REPORT

DOCUMENTATION

PAGE

Form

Approved

OMB

No.

0704-0188

Public repotting burden for this coIleot_n of in_ormat=0n is estimated to average 1 hour pet ret4_0_se, _',cluding the time 'lot revmwmg instruct_rta, searching existing 0ala sources. gathering and mainla_ing the data needed, and coml[_eting and revmw_g the collection of information Send comments regarding this burden estimate or any other aspect of this colteotion of information, including suggestions fc_ re0ucing this burden, to Washington Hla_:lUarle_ Services, Directorate for Inlon'nat=onO_eratmrrs and Repoffs. 1215 Jefferson Davis Highway. Suite 1204. Arlington. VA 22202-4302, and to the Offce of Management arcl Budget. Paperwork Re0uctK_ Pro mct (0704-0188). Wast_ngton. DC 2C_03. 1. AGENCY

USE

ONLY

(Leave

blank)

2. REPORT

DATE

3. REPORTWPE

October 1996 4. TITLE

AND

AND

DATES

COVERED

Contractor Report

SU_TiTIJE

5.

On the Coupling Between a Supersonic Turbulent Boundary Layer and a Flexible Structure

FUNDING

NUMBERS

C NAS1-19700 WU 537-06-37-20

6. AUTHOR(S)

Abdelkader

Frendi

7. PERFORMINGORGANIZATIONNAME(S)AND ADDRESS(ES) Analytical

Services

Hampton,

VA

& Materials,

8. PERFORMING ORGANIZATION REPORT NUMBER

Inc.

23666

9. SPONSORING I MONITORING AGENCYNAME(S) ANDADDRESS(ES)

10.

SPONSORING/MONITORING AGENCY

National Aeronautics and Space Administration Langley Research Center Hampton, VA 23681-0001

REPORT

NUMBER

NASA CR-201631

11. SUPPLEMENTARY NOTES Langley Technical Monitor: Final Report 12a.

D_i

HII_UTION

I AVAILABILITY

Kevin P. Shepherd

STATEMENT

12b.

DISTRIBUTION

CODE

Unclassified - Unlimited Subject Category 71

13.

ABSTRACT

(Maximum

200

words)

A mathematical model and a computer code have been developed to fully couple the vibration of an aircraft fuselage panel to the surrounding flow field, turbulent boundary layer and acoustic fluid. The turbulent boundary layer model is derived using a triple decomposition of the flow variables and applying a conditional averaging to the resulting equations. Linearized panel and acoustic equations are used. Results from this model are in good agreement with existing experimental and numerical data. It is shown that in the supersonic regime, full coupling of the flexible panel leads to lower response and radiation from the panel. This is believed to be due to an increase in acoustic damping on the panel in this regime. Increasing the Mach number increases the acoustic damping, which is in agreement with earlier work.

14. SUBJECT YP.HMS

15.

High-Speed Research, High-Speed Civil Transport, Acoustic Damping, Plate Response, Coupling

Supersonic,

Turbulent,

NUMBER

OF PAGES

41 16.

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CODE

A03 17.

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