NASA Technical Reports Server (NTRS) 20070031864: Flow Separation Side Loads Excitation of Rocket Nozzle FEM

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by  NASA Technical Reports Server (NTRS)

Flow Separation Side Loads Excitation of Rocket Nozzle FEM
Kurt B. Smalley NASA MSFC
Dr. Andrew Brown NASA MSFC
Joseph RufNASA MSFC
Dr. John Gilbert UAH
Introduction
Modern rocket nozzles are designed to operate over a wide range of altitudes, and are also
built with large aspect ratios to enable high efficiencies. Nozzles designed to operate over
specific regions of a trajectory are being replaced in modern launch vehicles by those that are
designed to operate from earth to orbit. This is happening in parallel with modern manufacturing
and wall cooling techniques allowing for larger aspect ratio nozzles to be produced.
Such nozzles, though operating over a large range of altitudes and ambient pressures, are
typically designed for one specific altitude. Above that altitude the nozzle flow is
'underexpanded' and below that altitude, the nozzle flow is 'overexpanded'. In both conditions
the nozzle produces less than the maximum possible thrust at that altitude. Usually the nozzle
design altitude is well above sea level, leaving the nozzle flow in an overexpanded state for its
start up as well as for its ground testing where, if it is a reusable nozzle such as the Space Shuttle
Main Engine (SSME), the nozzle will operate for the majority of its life. Overexpansion in a
rocket nozzle presents the critical, and sometimes design driving, problem of flow separation
induced side loads.
If ambient pressure on the outside of the nozzle is at a greater pressure than that of the nozzle
flow, it is possible for the ambient pressure to force its way upstream along the walls causing the
flow to separate from the nozzle wall and a recirculation zone to appear. Recirculation zones
cause adverse pressure gradients within the supersonic flow, thus creating shock waves
extending from the nozzle wall.
If the nozzle flow separates, a pressure differential between the inner and outer nozzle
surfaces is created. If the separation is asymmetric a resulting transverse or 'side load' is
created. Nozzle side loads can cause damage to the nozzle itself as well as to engine support
structures such as the gimbal joint, actuators or thrust adaptor.
Flow separation induced side loads have caused failures during ground testing of multiple
rocket engines. In the SSME, the three coolant feed lines that run down the outside of the
nozzle from the forward to aft manifolds had weld ruptures that were determined to be partially
due to unforeseen high loading from nozzle side loads during hot fire [6]. In the J-2 engine,
gimbal bolts failed in tension from large nozzle side loads during ground testing [8]. Nozzle
flow separation occurs within a nozzle when the ratio of nozzle wall pressure to ambient pressure
falls below a critical pressure ratio. This ratio is passed through during start-up and shut down
transients. For engines that are able to throttle, such as the SSME, the engine can operate steady
state, at or below the critical pressure ratio for a significant amount of time.
In an overexpanded nozzle asymmetric flow separation appears and disappears in a random
manner. Because of this, the characteristics of the side load are usually described in a statistical
manner. Also, when the compliance of the nozzle structure allows for large deformations of the
nozzle to interfere with the internal flow field, an aeroelastic coupling phenomenon can take
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effect. This phenomenon canhave apotentially damaging amplification effect onnozzle
deformations.
In orderto design anozzle to withstand side loads, engineers usually err on the side of
conservatism to ensure the design will withstand the maximum amplitude the nozzle might incur.
Thus,the lack ofan accurate model ofthe rocket nozzle side load will force a designerto use
over conservative empirical models ofthe phenomenon which tend to over-designthe rocket
nozzle. The over-design canresult in aheavy weight and costpenalty onthe nozzle.
With a goal ofcreating accurate predictive models ofthe rocket nozzle flow separation side
load, NASA Marshall Space Flight Center (MSFC) personnel have carried out amulti-year
experimental and analytical investigationinto the phenomenon. One ofthe results ofthese
studies was the formulation ofa fluid dynamic analysis methodology that generates a set of
internal pressure contours for anozzle undergoing steady statetwo nodal-diameter aeroelastic
flow separation for a single instance intime. This methodology was appliedto predictthe
internal pressure field ofa subscale 27" long nozzle that was cold flow tested inthe MSFC
Nozzle TestFacility.
This paperwill discuss the implementation ofthis coarse butreasonable representation ofthe
pressure field spatial and temporal characteristics onto a structural dynamic finite elementmodel
ofthe nozzle in atime transient analysis. The resulting model structural response isthen
comparedto test to validatethe methodology used to create the pressure field. This comparison
revealed thatthe analysis deformations were significantly higherthan those measured during
testing. Onthe other hand the analytically predicted shape and frequency ofthenozzle response
were both accurate. Ifthe pressure contour is reformulated according to a measurementbased
amplification factor, itis hoped that an accurate yet simplepredictionofthe nozzle response to
the aeroelastic flow separation side load canbe obtained.
Background
To increase their understanding ofnozzle side loads, engineers at MSFC began an
investigationin2000 into the phenomenonthrough atask entitled "Characterization and
." Accurate Modeling ofRocket EngineNozzle Side Loads" [1,2,3], ledby A. Brown. The stated
objective ofthis studywas to develop a methodology to accurately predictthe character and
magnitude ofnozzle side loads. The study included further hot-fire testing ofthe MC-l engine,
cold flow testing ofsubscale nozzles, CFD analyses ofbothhot-fire and cold flow nozzle testing,
and finite element (fe.) analysis ofthe MC-1 engine and cold flow tested nozzles. A follow on
taskincluded an effortto formulate a simplifiedmethodology for modeling a side loadduring a
two nodal diameterfluid/structure interactionfor a single moment intime.
Two cold flow nozzle testarticle were manufactured. The first was athick walled truncated
ideal nozzle that is stiffenoughto not deflectan appreciable amount due to side loads. This
nozzle was used to baseline the pure fluid physics ofthe experiment. The second nozzle, seen in
Figure 1, had the same internal contourbuthad amuch thinner wall. This nozzle was usedto
characterize any fluid structure interaction. Bothnozzles were 26.7" long and 12.4" diameter at
their exitplanes with 30 to 1area ratios.
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Figure 1. Thin Walled Nozzle
A modal testwas performed on boththe NTF nozzle support structure and the thin walled
nozzle itself. Details and results ofthis testing canbe found in [4, 5]. The results ofthe modal
tests were used to determine the natural frequency ofthe thin walled nozzle secondnodal
diametermode as well as to ground a fInite elementmodel ofthe nozzle which was used to aid in
an investigation ofthe nozzle/supportstructure couplingproblem. The fInite elementmodel of
the nozzle and test facility backup structure (see Figure 3) was createdbyMSFC engineering in
MSC.PATRAN. Thehigh fIdelity ofthe model was used to ensure good strainpredictions from
the experimental strain gage locations and was verifIed through comparisonwith the modal test.
Fortime transient response analyses, the facility/nozzle interface was constrained as a cantilever
boundary condition.
Figure 3. FEM ofThin Walled Nozzle
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The cold flow tests were conducted at MSFC inthe Nozzle TestFacility (NTF) as seen in
Figure 2. Compressed dry air was the nozzle working fluid. The nozzles were mountedinthe
testcabin. The pressure inthe cabin was varied viaan ejector system.
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Figure 2. ThickWalled Nozzle in NTF
Sixteen circumferential straingages were mounted onto the flexible walled nozzlejust
downstream ofthe nozzle throat, every 22.5 degrees. Three axial strain gages were mounted
justupstream ofthat. Steady and fluctuating pressures were mounted onto the nozzle in two
axial and two radial planedribs on eachnozzle. Also, four accelerometers were mounted onthe
thick walled nozzle, two onthe thin.
Originally, load cells were to be mounted radialy atthe nozzle facility interface.
Unfortunately, due to anozzle/facility feedback problem during operation, these load cells had to
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be removed to prevent damage to them and the facility. Bothnozzles were tested over a range
ofmass flow rates, inlettotal pressures, test cabin pressures and nozzle pressure ratios. Further
detail onthis testing canbe found in [9, 10].
As expected, the thin walled nozzle showed amuch largerresponse onthe strain gage dataas
well as the fluctuating pressure data. A survey ofthe thin walled nozzle data showedthatfor
everyhigh strainregion during the testing, the nozzle second nodal diameter was the dominant
frequency inthe strain gage data. Further analyses ofthe strain gage data showedthat this
frequency did indeed coincide with atwo nodal diameter shape. The fluctuating pressure data
also showed ahigh nozzle two nodal diameter frequency response.
A discrepancy with the datawas revealed, though, when a comparison ofthe phase between
the strain gage data andthe pressure data revealed thatthey were in phase. This is ninety
degrees offofwhatwould be expected for aresonantcase. This problem ledto the investigators
inabilityto prove with certainty ifthis response truly was aresult ofthe fluid/structure
interaction.
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Methodology
Basedonthe cold flow results, MSFC personnel formulated a fluid dynamic analysis
methodologythat generates a set ofinternal pressure contours for a nozzle undergoing steady
statetwo nodal-diameter aeroelastic flow separationfor a single instance intime. This
methodology would then be assessed by applying this pressure field in a structural dynamic
transientresponse analysis and comparingthe results withexperimental data.
The first step inthis methodology is to create deformednozzle contours representing the two
nodal diameter shape ofthe nozzle at differentclockingpositions. The highest strain gage
responses were taken from the cold flow testing performed at MSFC NTF and comparingthem
to mass normalized strains from a finite elementmodal analysis ofthe nozzle. The strain gage
responses were taken during run 37_3_sep at 24.6 seconds.
This comparisonyielded a strain scale factor. The mass normalized deflectionofthe modal
analysis was'thenmultiplied bythis scale factor in orderto obtainrepresentative deformations of
anozzle running axially from the combustion chamberto the nozzle exitofthe test article.
A series ofnozzle wall contours was extracted from the finite elementmodel ofthe nozzle
deformed inthe 2ND mode shape. Axial wall contours were extracted at constant
circumferential angles of0,22.5,45,67.5 and 90 degrees. These contours were usedto develop
arepresentative load distribution for the deformed nozzle with separated flow. Symmetry ofthe
2ND deflection shape allowed these locations to be reflected to representthe remainderofthe
nozzle.
The second step ofthe methodology was to generatenozzle internal flow fields for each of
the deformedprofiles. Towardsthis end, atwo-dimensional kinetics (TDK) methodology was
used. The TDK analyses assumedthe nozzles were full flowing, i.e., no separation. Each
contourwas analyzed independently as an axisymmetric nozzle. Nozzle total conditions were
derived from the test data. Wall pressure distributions were extracted from the TDK solutions.
These can be seen inFigure 4.
..,+--~;>'~~-+--I---I-------j---!---+------: r--::-c::-::~,:;-.-----'
-::£::e'"
~'.:t:'
...+--+--I---I-------j~~=-:~:::----+--+-----;
Figure 4. TDKExtracted Wall Pressure Distribution
The separation location was thenestimated. The nozzle flow separates at a locationwhere
the wall pressure is between 0.28 to 0.38 ofambientpressure. Forthis analysis, a value of0.29
was used to choose a separation location. A line representing 0.29 ofthe cabin pressure for the
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testpoint in run 37_3_sep at 24.6 seconds canbe seen inFigure 5. This is atime in which the
testarticle was excited inthe 2ND mode. The location at which each ofthe contourpressure
distributions crossedthe 0.29P curve was set as its separation location.
ambient
The pressure downstream ofeach contour's separation locationwas assumed to rise to 0.98
ofambientpressure. The resulting pressure distributions are shown inFigure 5.
.s r
-->~,'
~
......
~~
- -'::-=-~=:."':~.~
. ---
. . . . . . . -. . . J . . . . .
.,.
Figure 5. Nozzle Wall PressureDistributions with Assumed Separation
This approach assumed 0.29 for the separation location. Values of0.28 to 0.38 could have
also been used. Themagnitude ofthe forces would have been different, butthe relative
magnitudes would have beenthe same.
Dynamic effects were ignored in the flow analysis and thus a fixed wall condition was
... assumed. This is a good assumption becausethe aerodynamics ofthe nozzle change much
quicker thanthe shape ofthe nozzle. This means the nozzle aerodynamics will quickly adjustto
anewwall shape. This assumption allows for the methodologyto produce a model ofsteady
state flow separationwhich is undergoing a fluid/structure interactionwith the nozzle for a single
moment intime. Furthermore, this assumption also allows for the methodology to be validated
viaa structural time transient analysis ofthe nozzle, since the aerodynamics would be able to
keep up with any changes inthe nozzle geometry.
The method ofvalidation for the internal pressure contours for anozzle was to convertthe
pressure contours into force time history forcing functions. These forcing functions are then
applied to the nozzle finite elementmodel ina time transient structural response analysis from
which the nozzle strainresults are compared backto the original testdata. The pressure
contours consist ofabsolute pressure vs. axial location down the length ofthe nozzle for 6
different circumferential clockings.
Inorderto apply the original pressure contours in atime transient analysis, the contours first
had to be manipulated in orderto give them the correct spatial discretization. To spatially
discretize the pressure contours downto a manageable number ofapplication points, six planes
moving axially down the nozzle were chosen. Eachplane was roughly 3.18" apart. Around each
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plane, 16 nodes were then chosen as points offorce excitation for the transient analysis, making
atotal of96 excitation locations symmetricallyplaced aroundthe nozzle. An illustration ofthese
points canbe seenin Figure 7.
Figure 7. Nozzle Model Excitation Points
Next, the ambientpressure within the test diffuser was subtracted outofthe contours. Inthe
case ofthis experiment, this pressure was 1.7psi. This was done to produce the gage pressure
acting across the nozzle wall. Itshould be noted thatthe subtraction ofthe ambientpressure
from the pressure field negated the pressure field withinthe plane atthe end ofthe nozzle,
.., making it zero. This fact allowed for the subtraction ofthe last plane ofexcitationpoints from
the analysis. Finally, the pressure contours were interpolatedto span a full 360 degrees, creating
a two nodal diameter shape.
Afterthe spatial interpolation, the time transient aspect ofthe forcing function was applied.
This was achieved by calculatingthe meanpressure around each axial plane inthe pressure field.
Eachvalue inthe pressure field matrix was then given atime varying componentby
fluctuating it around its respective mean value. This was done by simply multiplying eachpoint
by
Pt{j,i)=mO)+(p0)-mO»)*sin(2*n*78.4*t(i)),
where Pf(iJ) is the fluctuating wall pressure in both circumferential clockingposition 0) and
time (i), PO) is the static wall pressure, mO) is the meanpressure around a circumferential plane
and t(i) is atime array. The frequency ofoscillationwas chosen as the analytical two nodal
diameter mode. The excitationpoints ofinterestwere then extracted out ofthe full pressure field
matrix.
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The pressure field nexthad to betransformed into a force field in orderto be applied to the
nodes withinthe model. This transformation was done by calculating an effective areaaround
eachnode and multiplying eachpressure forcing function by its effective area.
It should be noted thatone additional manipulation was necessary to manipulate the pressure
fields'into realistic time variantrepresentations. At the second-to-Iastplane ofexcitation down
the nozzle, a sinusoid could not be used to truly representthe time variant nature ofthe force
field.
As the separation planepasses each individual point inthis plane, the pressurejumps from
the ambientto the pressureupstream ofthe separation bubble. This transition happens very
rapidly. The pressure at any givenpointwill then remain constant until the separationplane
passes again. Forthis reason, a square wave was chosento represent the time variantaspect of
the forces inthis plane. The circumferential loading distributionfor a singletimepointin the
analysis along the 6 chosenplanes canbe seen in Figure 8.
..
~
i
-Ill!!
I
1'0 !iD '00 .......:m
!i~l/\j\j .''---~~S~"..~.93o-'C~~'"''
•
~·o 5J ~a:: ·so XI) 25D X:I'J E It:
h90
!:~I/Y ~.'".:
1 I
o,50 so 100 '50 200 25CJ n 39l 3050 50 tOO 150 D) 25D 150
Anglll ""9l-
Figure 8. Circumferential Loading Distribution For a Single
The forces were applied to their respective node points in a non-initial conditiontransient
analysis inthe commercial code NASTRAN. The time durationfor the analysis was chosento
ensurethatthe analysis would obtain a steady state solution, from which the maximum strains
would beused to compare backto the test. The time step ofthe analysis was chosento be
0.0001 seconds with 256 time steps. This number oftime steps allowed for a Fast Fourier
Transformto be performed onresults, enabling Power Spectral Density operations during post
processmg.
The analytical magnitudes ofthe analysis are dependant onthe damping value used inthe
analysis. Forthat reason, two damping values were used intwo separate analyses in hopes to
boundthe analytical results. The fust damping value used was the pure modal damping of0.22
percent critical damping obtained through the impactmodal test. This value, in a resonant
condition, is used as a minimum damping that should existinthe structure during operation.
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The second damping value used as the upperboundvalue was obtainedby a quality factor
calculationperformed on boththe straingage and accelerometer data. The quality factor canbe
calculated as follows:
Q= Fn
F2-Fl
where F is the resonantfrequency ofinterest and F, and F2 are the frequencies ofthe 'li power
n
points ofthatresonantpeak. For apower spectral density curve, the F and F values lie at 1/-.)2
j 2
the F amplitude. The quality factor canthen be related to the critical damping ratio as follows:
n
1
(= 2Q·
Thoughthis calculation gives only arough estimation onthe true damping value ofthe nozzle
during operation, itwas thoughtto be accurate enough inthis applicationto act as an upper
bound. Thequality calculationrevealed thatthe experimental damping factor was roughly 0.8
percent critical damping. The operational modal damping value was found to be slightly larger
thanthe impacttest modal damping.
Results
FromtheNASTRAN forced response transientanalysis, strainresults were obtained inthe
nozzle circumferential and axial directions atthe nozzle cold flow strain gage locations. The
results were inthe form ofstraintime history and were later converted into strain spectral density
plots. The analytical circumferential straintime histories and PSD can be seeninFigures 9 and
10. The comparable test circumferential stain gage data canbe seen inFigures 11 and 12
respectively. To viewthe experimental data, the ASRl commercial software PC Signal was
used.
Not! rJode8036 Nod 8024 Nod 8012
1"00 \500 1500 1500
1lX() 100) 100) 100)
500 .AhAA~ c 500 !'
;:;!; 0 ~e 0 ~
.~ -500 VVVV~ Ii -500 ~
·100) -100) ·100) -100)
·1500 ·1500 .1500 .1500
0 005 0 015 02 0 005 01 015 O~ 0 005 01 015 O~ 0 005 01 015 02
Iff.( .cj Time(.c) Tm..(.c) Tim.(.c)
Figure 9. Analytical Circumferential Strain TimeHistory Results
10
j 0043
10,....---------,
···21 ; .
.
······· ....... .....······, ....., .
00 :0 100
n
F, ~)
I
II
Figure 10. Analytical Circumferential Strain PSD Results
I
pr37_3b_seplJ7.datBlockSize=4096.NoofBlock=1.BW=2.50.Time=24.6to25.0000.Window-Type:Hamming. Oveilap:0%. 3121/20074:02:42PM
sg·H045 RawTi~History 00sg-H067 RawTimeHistory 00sg-HOSO RawTimeHistory 00sg-Hl12 RawTimeHistory
1100 M 11 M 11 M 11 M
500 500 500 500
t: t: t: t:
0 ~ ~ ~ 0 ~
'5 '5 '5 '5
-500 -500 -500 -500
-1100
24.60024.7 24.B 24.9 25.000
Time(Sec)
Figure 11. Experimental Circumferential Strain Time History Results
pr37_3b_sep07.dal.BlockSize=4096.NoofBlock-1.BW.2.50.Time·24.6to25.0000.Window-Type:Hamming. Overlap:0%. 3/21/20074:05:20PM
1.0e+dB~045 RawPSD.RMS'6~1166 1.0e+dB~067 RawPSD.RMS'4~7324 10e+dB~090 RawPSD.RMS'35~5934 1.0e+0~H112 RawPSD.RMS=4~.537
1.0e+004 1.0e+004 1.0..004 1.0e+004
1.0e+OO3 N 1.0e+003 N 1.0e+OO3 N 1.0e+OOJ
~ ~ ~
1.Oe+002 1.0..002 1.0e+002
1.0e+001 't2: 1.0e+001 't2: '2t: 1.0e+00l
1.0e+000 '5 1.0e+000 '5 '5 1.0e+000
1.Oe-00 1.0e-001 1.0e-00
1.0e-0~.0!=:::0~2O~40~60,-'::::80~10~0~120
1.Oe-00ij.00 20 40 60 80100120 1.Oe-00ij.00 20 40 60 80100120
Frequency[Hz) Frequency(Hz) Frequency(Hz)
Figure 12. Experimental CircumferentialStrain PSD Results
Itcan be seen inboththe strain spectral densities and time histories, the frequency content of
the test vs. the analysis compare welL This was to be expected since the forcing functions were
craftedto have the same frequency as the analytical two nodal diameter mode.
Itcan also be seen inthe comparison betweenthe analytical strainvalues andthe testvalues
thatbothhave two nodal diameter shapes. This canbe seenthrough the clocking ofthe strain
gages. Both sets ofdata showa definite trend ofincreasing from a noise floor to the highest
amplitude and back again over 180 degrees. Eventhe relative amplitudes from gageto gage are
similar.
The greatest difference betweenthe analytical and experimental results can be seen in the
straintime history circumferential amplitudes. The analytical amplitudes are almost 100%
greaterthan that ofthe test. It should be noted againthat the analytical magnitudes are
dependantonthe damping value used inthe analysis. Inthis particularrun, the puremodal
damping of0.22 percent critical damping was used.