Preliminary Evaluation of Transient CFD for Ascent Aeroacoustic … · Preliminary Evaluation of Transient CFD for Ascent Aeroacoustic Loads and Vibration Environments. Mike Nucci,

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Preliminary Evaluation of Transient CFD for Ascent Aeroacoustic Loads and Vibration Environments

Mike Nucci, Mike Yang, Parthiv ShahATA Engineering, Inc.

Paul BremnerSonelite, Inc.

June 2, 2015

Spacecraft and Launch Vehicles Workshop 2015

Presentation Outline

MotivationUnsteady CFD analysis of expansion ramp at transonic speedsDerivation of Corcos CoefficientsWavenumber analysis of CFD resultsSummaryFuture Work

2


Motivation

1. Locally high, inhomogenous aero loads can drive problematic random vibration environments

2. Limited # Kulites in wind tunnel, under-resolves loading• Compensate with high uncertainty margins or “maxi-max” approach• Could lead to over-conservative vibration qualification levels

3. CFD offers high spatial resolution, everywhere• Define spatial distribution of PSD loading ?• Define spatial correlation of loading ?• Sufficient time length can be limitation => Supplement with testing

4. Do locally high aeroloads really increase random vibration response ?

• What is correct – and practical - use of CFD aeroloads to predict random vibration ?

3


Hybrid RANS/LES Simulation for Ramp

Work performed in support of NASA STTR• Fairly small, “wind tunnel-sized” model is simulated• Goal was to capture representative shock-boundary layer interaction

45-degree ramp modeled with far-field boundary conditions • Periodic boundary conditions through thickness. Simulation effectively two-dimensional

Solved at Mach 0.855.3 million cellsDomain is 10 ramp heights thick

4

Rectangular trip

Ramp

Close-up View of Solution Domain


Analysis of CFD Divided into Four Regions

X=0

X=0.00635

X=0.05 (termination shock)

X=-0.127 (trip)

X=-0.13 (knife edge)

Region 1

Region 2

Region 430 – 38 ramp heights downstream

Region 3

Our focus will generally be on Regions 1, 2, 3


-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3-0.1

-0.05

0

0.05

0.1

0.15

X-Position (m)

Del

ta C

pSpatial Distribution of ΔCp,RMS Predicted by Transient CFD Correlates to Test

6

CFD shows normalized schlieren (density gradient)

Loci/CHEM, hi-resolution, unsteady CFD data being used to explore analysis methods

Robertson, 1971.

Mach 0.85


Corcos model for spatial correlation typically used to define spatial correlation within a flow zone• Correlation coefficients observed in wind tunnel to be robust

and homogeneous within flow zones

• Is this observed in CFD data ?• How does it vary across inhomogeneous flow zones (eg.

shock) ?

Corcos Model Parameters Extracted from CFD

7

Decay coefficients

Convection wavenumber (kc = ω/Uc)

Spacecraft and Launch Vehicles Workshop 2015 8

EXAMPLE Spatial Correlation from CFD resultsSampling 2-pt cross spectra

• 2 point Cross spectrum

– Random pressure collapse to

– Phase defined by convection Uc

– Spatially-decaying coherence

( ) ( ) ykcc

xkcpp

cycx exkeGfG ∆−∆− ⋅∆⋅≅ cos)(2,1 ω

-10.00

-8.00

-6.00

-4.00

-2.00

0.00

2.00

4.00

10 100 1000 10000

Freq (Hz)

Pha

se (R

ad)

PhasePoint49_Point50

Uc = 28 m/s over 10mm

0.01

0.10

1.00

10 100 1000 10000

Freq (Hz)

Coh

eren

ce

Coh 49-50

Cx=0.25 over 10mm

( ) ( ) ( )[ ]fxPfxPEf

fG jj ,,121

*2,1 ∆

=

( )c

c

Uxfxkf∆=

∆=π

φ2

( ) ( ) ( ) ( )

[ ]221

22,1

22,1 ;;

xkc

pppp

cxe

fxGfxGfGf∆−=

=γ


PSD is Highest in Separated Region

9

102 103 104 105

10-2

100

102

Frequency, Hz

Pa2 /H

z

PSD at Three Locations Down Region Centerline

Beginning (X=0.007)Middle (X=0.025)End (X=0.044)

102 103 104 105

10-2

100

102

Frequency, Hz

Pa2 /H

z



102 103 104 105

10-2

100

102

Frequency, Hz

Pa2 /H

z



PSD in Region 1 PSD in Region 2 PSD in Region 3

PSD in Region 4 ~ 1 Pa^2/Hz over entire region


CORCOS COEFFICIENTS DERIVED FROM CFD

10


0

24x 104 0.08

0.10.12

10-2

100

X-position (meters)

Cx along streamline in center of panel

Frequency, Hz

Cx

02

4x 104

0.020.04

0.060.08

10-2

100

X-position (meters)


Frequency, Hz

Cx

0

24x 104

00.02

0.040.06

10-2

100

X-position (meters)


Frequency, Hz

Cx

Streamwise Decay Coefficient for Each Region

11

Cx for Region 1 Cx for Region 2 Cx for Region 3

Region 2 shows increase in Cx near shock


0 0.01 0.02 0.03 0.04 0.050

0.5

1

1.5

2

2.5

X-Position (meters)

Cx


3000 Hz10000 Hz25000 Hz40000 Hz

0.06 0.08 0.1 0.12 0.14 0.160

0.5

1

1.5

2

2.5

X-Position (meters)

Cx


3000 Hz10000 Hz25000 Hz40000 Hz

Streamwise Decay Coefficient Down Center of Panel

12

Cx for Region 1 Cx for Region 2 Cx for Region 3

Increase at low frequencies expected due to boundary layer thickness limitation on large eddy correlation length [Ref: Bull, C&R “modified” CORCOS model]


103 1040

0.05

0.1

0.15

0.2

0.25

Frequency, HzSt

dev

/ Mea

n

Normalized Standard Deviation across panel

cxcz

103 1040

0.05

0.1

0.15

0.2

0.25

Frequency, Hz

Stde

v / M

ean


cxcz

103 1040

0.05

0.1

0.15

0.2

0.25

Frequency, Hz

Stde

v / M

ean


cxcz

Normalized Standard Deviation Below 25% For All Frequencies

13

Region 1 Region 2 Region 325%

20%

15%

10%

5%

25%

20%

15%

10%

5%

25%

20%

15%

10%

5%


Decay Coefficients are Similar to Literature in Separated Regions (Expansion Fan, Shock)

14

Attached regions show much lower Cx than shown in literature. Reason currently unknown.


Uc increases through expansion fan but drops to “nominal” value of ~0.65 near termination shock. This makes sense b/c shock is point of reattachment.

15

Typically measure ~0.7(Also VA One default)

1 2

3 4


SPATIAL WAVE-INTEGRATED (AVERAGED) SPATIAL CORRELATION FROM CFD

16


Wavenumber Analysis and Modal Force Spectrum Both Use Area-Avg to Describe Loading

Vibration response controlled by modal force spectrum

– Space-integral (average) over product of pressure CPSD and mode shape

Spatial Fourier transform of pressure (wavenumber spectrum) is similar form:

– Space integral (average) of FSP cross spectrum– Fourier components structure mode shapes Ψr (kx,ky )

17


Wavenumber Analysis Fully Describes Loading

Expected wavenumber spectrum of Corcos spatial correlation model

– Spectrum shape defines “zone-averaged” kc, cx, cy

Modal force spectrum calculated directly from wavenumber spectrum

18

X =

( ),pp k ωΦ ( )r kψ ( ), ,ff rS k ω

Ridge at kc


Structural Mode shapes have 4 wavenumber componentsΨ(km,x ,kn,y ) = +mπ/Lx, +nπ/Ly,-mπ/Lx,-nπ/Lxy,

One peak in wavenumber space per componentExample shown is for simply supported rectangular panel

19

(1,1) Mode (6,6) Mode (10,10) Mode


Modal response greatest at hydrodyn coincidenceClearly seen in wavenumber space

20

(1,1) Mode (6,6) Mode (10,10) Mode


Interpreting Wavenumber Analysis Plots

21

Magnitude scales with autospectrumResults for region straddling shock are shown

-50000

5000

-2000

0

2000

100

Kx (rad/m)

Pressure Amplitude at 1.535433e+04 Hz

Kz (rad/m)

Pres

sure

Am

plitu

de (P

a2 /Hz) Ridge occurs at Kc

Flow is in X-direction


-50000

5000

-2000

0

2000

100

Kx (rad/m)


Kz (rad/m)

Pres

sure

Am

plitu

de (P

a2 /Hz)

-50000

5000

-2000

0

2000

100

Kx (rad/m)


Kz (rad/m)

Pres

sure

Am

plitu

de (P

a2 /Hz)

-50000

5000

-2000

0

2000

100

Kx (rad/m)


Kz (rad/m)

Pres

sure

Am

plitu

de (P

a2 /Hz)

All Three Regions Show Same Wavenumber Shape

22

Region 1 Region 2 Region 3


Interpreting Wavenumber in Kx(Streamwise) Direction (Region 2 shown)

23

-4000 -2000 0 2000 400010-6

10-4

10-2

100

Kx (rad/m)

Pres

sure

Am

plitu

de (P

a2 /Hz)

Kz = 0

5118 Hz 9843 Hz15354 Hz20079 Hz24803 Hz30315 Hz

Apparent wavelength of convectingvorticies is smaller at high frequencies; viz:

( ) ( )

( ) ( )

2

2 2

c

c

cc

Ufk f f

ORfk f

f U

πλ

π πλ

= =

= =

Peak corresponds to Kc

Peak at negative Kx indicates possible recirculation


Interpreting Wavenumber in Kz (cross-flow) Direction (Region 2 shown)

24

-2000 -1000 0 1000 200010-6

10-4

10-2

100

Kz (rad/m)

Pres

sure

Am

plitu

de (P

a2 /Hz)

Kx = Kc

5118 Hz 9843 Hz15354 Hz20079 Hz24803 Hz30315 Hz

Peak near Kz=0 indicates no convection in Z-direction

Rounded peaks correspond to lower spatial decay coefficient


Summary

Hybrid RANS/LES simulation performed for ramp at Mach 0.85• Corcos parameters extracted and examined at different regions• Provides insight into how SFP characteristics vary over space• PSD magnitude highest for separated areas (expansion fan and

shock)• Decay coefficients have low (<25%) normalized standard deviation in

space• Uc increases in expansion fan, drops near shock, and approaches

~0.65Uinf after shockWavenumber analysis perform spatial average of CPSD• Similar to modal force spectrum (both are spatial averages over CPSD

and mode shape)• Modal force spectrum directly calculated from wavenumber spectrum

Wavenumber analysis provides physical insight into flow and structural response

25


Future Work

Recovery of structural response for simulated panel• Using direct CPSD of pressure field• Using derived Corcos parameters• Using wavenumber decomposition

How much does presence of shock actually increase structural response? • ATA has just begun Phase II STTR to measure both

surface fluctuating pressures and resulting vibration response in wind tunnel

26


APPENDIX

27


Grid For Hybrid RANS/LES Simulation

28

• Grid has 5.3 million cells– Mesh is an unstructured trim cell mesh with hanging nodes

• Domain is 2.5” thick (10x ramp height) with 40 cells through the thickness and periodic boundary conditions on the sides



29

• Large refinement region surrounding entire ramp• Smaller refinement region surrounding near-body region

and anticipated shock location



30

• Turbulent trip is modeled to provide similar incoming boundary layer to experiment

• Geometry to be analyzed is similar to experiment - 45 degree ramp with height of 0.25” at Mach 0.85

• Near wall spacing results in a y+ < 100– Wall law viscous boundary condition used– Reynolds number is 8.9e6

Turbulent Trip 45 Degree Ramp


Boundary Conditions

31

Farfield

FarfieldFarfield

Viscous WallSymmetry Symmetry

Periodic


Entire solution domain

32


Trip in front of ramp

33


Ramp with trip

34


Mach Contours Show Expected Termination Shock

X=0

X=0.00635

X=0.05X=-0.127

X=-0.13


PSD is Highest in Separated Region

36

102 103 104 105

10-2

100

102

Frequency, Hz

Pa2 /H

z



102 103 104 105

10-2

100

102

Frequency, Hz

Pa2 /H

z



102 103 104 105

10-2

100

102

Frequency, Hz

Pa2 /H

z



102 103 104 105

10-2

100

102

Frequency, Hz

Pa2 /H

z




Region 1 (Ahead of Shock)

37

-4000 -2000 0 2000 400010-6

10-4

10-2

100

Kx (rad/m)

Pres

sure

Am

plitu

de (P

a2 /Hz)

Kz = 0

5118 Hz 9843 Hz15354 Hz20079 Hz24803 Hz30315 Hz


Region 3 (Aft of region 2)

38

-4000 -2000 0 2000 400010-6

10-4

10-2

100

Kx (rad/m)

Pres

sure

Am

plitu

de (P

a2 /Hz)

Kz = 0

5118 Hz 9843 Hz15354 Hz20079 Hz24803 Hz30315 Hz


( ) ( )

( ) ( )

2

2 2

c

c

cc

Ufk f f

ORfk f

f U

πλ

π πλ

= =

= =


Region 4 (Downstream of Shock)Kc increases with frequency

39

-4000 -2000 0 2000 400010-6

10-4

10-2

100

Kx (rad/m)

Pres

sure

Am

plitu

de (P

a2 /Hz)

Kz = 0

5118 Hz 9843 Hz15354 Hz20079 Hz24803 Hz30315 Hz


( ) ( )

( ) ( )

2

2 2

c

c

cc

Ufk f f

ORfk f

f U

πλ

π πλ

= =

= =


Region 1 (Ahead of Shock)Peak near Kz=0 indicates no significant convection in Z-direction except for small amount in –Z direction

40

-2000 -1000 0 1000 200010-6

10-4

10-2

100

Kz (rad/m)

Pres

sure

Am

plitu

de (P

a2 /Hz)

Kx = Kc

5118 Hz 9843 Hz15354 Hz20079 Hz24803 Hz30315 Hz


Region 3 (Aft of Region 2)

41

-2000 -1000 0 1000 200010-6

10-4

10-2

100

Kz (rad/m)

Pres

sure

Am

plitu

de (P

a2 /Hz)

Kx = Kc

5118 Hz 9843 Hz15354 Hz20079 Hz24803 Hz30315 Hz


Region 4 (Downstream of Shock)Peak near Kz=0 indicates no significant convection in Z-direction except for small amount in –Z direction

42

-2000 -1000 0 1000 200010-6

10-4

10-2

100

Kz (rad/m)

Pres

sure

Am

plitu

de (P

a2 /Hz)

Kx = Kc

5118 Hz 9843 Hz15354 Hz20079 Hz24803 Hz30315 Hz

Documents

Preliminary Evaluation of Transient CFD for Ascent Aeroacoustic … · Preliminary Evaluation of Transient CFD for Ascent Aeroacoustic Loads and Vibration Environments. Mike Nucci,