As part of a NASA/MSFC research program to evaluate the effect of different nozzle contours on the well-known but poorly characterized "side load" phenomena, we attempt to back out the net force on a sub-scale nozzle during cold-flow testing using acceleration measurements. Because modeling the test facility dynamics is problematic, new techniques for creating a "pseudo-model" of the facility and nozzle directly from modal test results are applied. Extensive verification procedures were undertaken, resulting in a loading scale factor necessary for agreement between test and model based frequency response functions. Side loads are then obtained by applying a wide-band random load onto the system model, obtaining nozzle response PSD's, and iterating both the amplitude and frequency of the input until a good comparison of the response with the measured response PSD for a specific time point is obtained. The final calculated loading can be used to compare different nozzle profiles for assessment during rocket engine nozzle development and as a basis for accurate design of the nozzle and engine structure to withstand these loads. The techniques applied within this procedure have extensive applicability to timely and accurate characterization of all test fixtures used for modal test.A viewgraph presentation on a model-test based pseudo-model used to calculate side loads on rocket engine nozzles is included. The topics include: 1) Side Loads in Rocket Nozzles; 2) Present Side Loads Research at NASA/MSFC; 3) Structural Dynamic Model Generation; 4) Pseudo-Model Generation; 5) Implementation; 6) Calibration of Pseudo-Model Response; 7) Pseudo-Model Response Verification; 8) Inverse Force Determination; 9) Results; and 10) Recent Work

Brown, Andrew M.

Ruf, Joe

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Source of Acquisition 
NASA Marshall Space Flight Center 
Calculating Nozzle Side Loads using Acceleration Measurements of Test- 
Based Models 
Andrew M. Brown, Ph.D. 
NASA Marshall Space Flight Center 
Propulsion Structural and Dynamic Analysis, ER41 
MSFC, AL 35812 
Joe Ruf 
NASA Marshall Space Flight Center 
Propulsion Structural and Dynamic Analysis, ER43 
MSFC, AL 35812 
NOMENCLATURE 
Nozzle Test Facility NTF 
Frequency Response Function FRF 
Degree of freedom dof 
MSFC Marshall Space Flight Center 
Power Spectral Density PSD 
Root Mean Square RMS 
ABSTRACT 
As part of a NASAIMSFC research program to evaluate the effect of different nozzle contours on the well-known 
but poorly characterized "side load phenomena, we attempt to back out the net force on a sub-scale nozzle 
during cold-flow testing using acceleration measurements. Because modeling the test facility dynamics is 
problematic, new techniques for creating a "pseudo-model'' of the facility and nozzle directly from modal test 
results are applied. Extensive verification procedures were undertaken, resulting in a loading scale factor 
necessary for agreement between test and model based frequency response functions. Side loads are then 
obtained by applying a wide-band random load onto the system model, obtaining nozzle response PSD's, and 
iterating both the amplitude and frequency of the input until a good comparison of the response with the 
measured response PSD for a specific time point is obtained. The final calculated loading can be used to 
compare different nozzle profiles for assessment during rocket engine nozzle development and as a basis for 
accurate design of the nozzle and engine structure to withstand these loads. The techniques applied within this 
procedure have extensive applicability to timely and accurate characterization of all test fixtures used for modal 
test. 
INTRODUCTION 
A major design driver for rocket engine nozzles is the evaluation of their response to the phenomena known as 
"side loads", which is a substantial transverse load cause by the separation of the internal flow from the side wall 
of the nozzle due to an overexpanded operating condition. Although this operating condition, in which the 
ambient pressure is greater than the internal pressure, generally only occurs at sea level ground testing of the 
engine, the magnitude of the transverse load has caused failures of both nozzle actuating systems [I], and 
sections of the nozzle itself [2]. The topic has been studied in great detail; an excellent overview of the research 
up to 2004 is presented by Ostland [3]. Even though the phenomena is understood on a theoretical level, though, 
a technique for accurately predicting the magnitude and frequency content of the actual forcing function at a 
particular moment in time has not yet been determined. For this reason, researchers at NASNMSFC have 
pursued a series of subscale programs in this context. The most recent investigation, led by J. Ruf, is focusing on 
evaluating the relative difference in side loads between several different subscale nozzle contours using the 
MSFC cold-flow Nozzle Test Facility (NTF). The calculation of the side loads is performed with two methods, both 
of which are based upon techniques applied by German researchers [4]. The first is the measurement of strains 
on a specially designed "strain-tube" that has been calibrated for static weights hung from the strain-tube nozzle 
interface (see figure 1). The second method, which is the subject of this paper, uses the measurement of 
accelerations with a dynamic model of the system to calculate an effective point load that approximates the net 
asymmetric pressure loading on the nozzle. 
feedin pipe (alumitfum, t > 12 mm) 
solid nozzle 
(aluminium, t = 11.5 mm) 
- .  
- \ 
strain gauges bending tube 
for two directions (aluminium, t = 1 mm) 
Figure 1. Schematic of Side loads test setup 
MODEL GENERATION 
The first step in the process was to generate a computer model of the nozzle test article and the nozzle test 
facility (NTF) to which it is attached (figure 2). Initial attempts to create a finite element model of the facility, a 
complicated structure composed of ducts, lines, stiffening rods, flow straighteners, and other poorly defined 
elements that have been slowly added onto for the last decade was unsuccessful; a natural frequency agreement 
of closer than 20% could not be achieved for the primary modes. Additional later attempts at modeling the nozzle 
test article only with a detailed finite element model and representing the boundary conditions accurately also 
were concluded to be pointless, as the representation of the enormous impact of the boundary conditions could 
not possibly be represented by a spring accurately and there was no need for the detailed finite element model of 
the nozzle test article. 
Figure 2 Photo of facility without strain tube or nozzle 
At this point, a presentation on the LMS Virtual.Lab@ software was made to MSFC personnel; one of the features 
of the software was implementation of "pseudo-models" generated entirely from modal test data. Although this 
type of model offers some tremendous benefits, little discussion of application of the technique is documented, 
aside from a recent paper by Carnes, et. al [5]. The basis of the technique is fairly simple as applied in the finite 
element code NASTRAN. First, mass, spring, and damper scalar elements are connected from ground to 
"spoints" to simulate each natural frequency, where the values taken from the parameter identification curve fit of 
the modal test are used for the values of modal mass, stiffness, and damping. The "spoint" is a non-physical 
"scalar" degree of freedom (dof) that can be referred to by multi-point constraint equations (MPC's). In this case. 
the spoints represent the generalized degrees of freedom {q) in the standard modal transformation. 
The dynamic response of the physical degrees of freedom, therefore, can be expressed by generating a MPC 
equation directly from each row of equation (1). The "pseudo-model" generated in this manner is accurate 
dynamically, and is created without the necessity of creating a geometry based finite element model. 
One of the advantages of using this method is that a very small number of physical points require testing, since 
only the dynamic response of a few points may be of interest. The primary restriction is that the number of tested 
degrees of freedom equal to or exceeds the number of modes retrieved from the modal test to ensure that they 
can be defined independently. In this case, a modal test performed with a large number of degrees of freedom 
was originally intended on being the basis of the pseudo-model. Later in the process though, when correlation 
with a shaker test (discussed below) was necessary, an abbreviated modal test with only 6 nodes (three dofs per 
node) was performed. These points are shown in red on figure 3. As some slight changes in the facility 
configuration were noted between the two modal tests that caused changes at the fundamental system 
frequencies, the abbreviated test was chosen as necessary for the pseudo-model instead. A subset of 16 modes 
with high values of independence as calculated using the Modal Assurance Criteria were selected from the FRF 
curve fits to keep the number of modes less than the number of dofs. As with all dynamic modeling and 
characterization, the selection of the dofs and modes are important in fhe ultimate accuracy of the results, and 
this probably affects the ultimate answers for this analysis as well. Enough correlation with measured results was 
obtained, though, as discussed below, that this pseudo-model was deemed accurate enough for this study. 
Figure 3. Strain tube (wrapped in insulation) and nozzle test article in the NTF 
FRF VERIFICATION 
The next step in the process was to validate that a load applied on the pseudo-model yielded the correct 
response. This step consisted of connecting electromagnetic shakers to the structure along the transverse axes, 
applying a measured input force "burst-random" spectrum, and measuring the acceleration response at the same 
locations as would later be measured during the actual side-loads test. The force spectrum is then applied to the 
pseudo-model and the response is compared with the measured response, which should be identical. Vertical 
and horizontal shakers were applied at points 3 and 4 in figure 3 and the response was measured at points 1 and 
2. Analytically, a unit load was initially applied to the pseudo-model in the vertical direction at point 4, a frequency 
response analysis executed, and the FRF for the response at point 2 to this load examined. The FRF was then 
compared with the measured FRF. Even after resolving issues with correctly comparing test output units (G's) 
with analysis units, a discrepancy in the output could be seen. This discrepancy was reduced by imposing a 
factor of 0.553 on the input load. The factor was determined by comparing the peak levels of the FRF at the 
fundamental frequency family around 78 Hz. The cause of this error is not known, but could be due to differences 
in the exact point of load application on the test article versus the application point in the pseudo-model, off-axis 
excitation, or some other cause, such as unnecessarily repetitive unit conversion routines within the LMS software 
which reads and write the test data and the pseudo-model information. The resulting pseudo-model FRF 
matches the test article FRF in the fundamental frequency region fairly well (figure 4), but it is in error at the 
region around the 12'~ mode at 272 Hz (figure 5). Further investigation is planned to evaluate the source of these 
errors. 
.................. 
scaled model 
I I I I I I 
70 80 90 100 110 120 
Frequency (hz) 
Figure 4. Flange vertical input tip vertical response FRF scaled model vs. measured comparison 
Frequency (hz] 
Figure 5. Overall FRF comparison 
The second step in the verification process was using the same procedure for comparing the random response of 
the pseudo-model to the actual structural response for the shaker tests. For the measured input force spectrum 
(figure 6) applied by the shaker at the flange, the comparison of the pseudo-model and measured responses are 
shown in figure 7 and 8. As expected from the FRF results, the measured response matches well in the region of 
the fundamental system frequencies but is a bit off at the 272 Hz mode. 
N 
f 
N 
P 
50 100 150 200 250 300 350 400 
Frequency (hz) 
Figure 6. Shaker test vertical force input spectrum 
Nozzle t ~ p  y accelsration response to flange y 441b rrns input 
Using 6 node modal test based model (I6 most Independent modes) 
10' 
10" 
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- 
rn 
Y 
10.~ 
I I I I I I I 
60 
1 
80 100 120 140 160 180 2M) 
Frequency (hz) 
Figure 7 Shaker test response comparison 
Nozzle tip y accelerat~on response to flange y 441b rrns Input 
Frequency (hz) 
Figure 8 Shaker test response comparison overall 
For verification, the same procedure was followed for lateral response and excitation. Similar results are 
obtained, although a slightly different load scale factor was required. This did give some additional confidence 
that a given level of input on either the pseudo-model or the test article would give generally the same 
acceleration response, so the next step in the procedure, inverse force determination, could now be pursued. 
INVERSE FORCE DETERMINATION 
The goal of the methodology was to provide an accurate magnitude of an equivalent single force, applied at a 
given point on the test facility and nozzle system, that would induce the response that was measured during side 
load testing . For convenience, the location of this force was chosen to be the strain tube nozzle interface (points 
3 and 4), as those were the points that the shaker were attached to as well as the points where the loads for the 
static methodology for obtaining the side load were applied. In practice, the load is the result of an overall time 
and spatially varying pressure field over the inside of the nozzle, but the peak resolved load obtained using this 
assumption can be used for both configuration comparison and design. 
Initially, an up-to-date method for determining the side load value using singular value decomposition of the 
inverse of the FRF matrix was attempted using the "Inverse Force Determination" module within LMS Virtual Lab. 
As this module was unable to read the test measured power spectral density (PSD) data, though, it made 
accurate determination of the input PSD very difficult. Therefore, a "brute-force" iterative method for determining 
the force was chosen to ensure that results would be obtained in a timely manner. This method involved 
assuming an input frequency spectrum, applying this loading onto the pseudo-model using MSCIPatranB and 
NXINastranB, and comparing the response PSD with the measured response PSD using MatlabB. The input 
spectrum was then altered based on this comparison until the model and measured results matched qualitatively. 
A comparison of the measured PSD at one time point with the model response PSD is shown in Figure 9 and the 
model input PSD generating this response is shown in figure 10. Parameters chosen for the measured PSD were 
a Nyquist frequency of 10,240 Hz (sampling rate of 20 KHz), block size of 32768, and a bandwidth of 0.625 Hz, 
which yields a block length of 1.6 seconds. Different parameter choices would yield slightly different PSD shapes, 
but this was the smallest block size that yielded a generally smooth PSD. The root mean square (RMS) of the 
input spectrum could then be calculated and reported as the net side load. 
Frequency (ha) 
Figure 9. Comparison model, measured nozzle tip response PSD's for test on Marl, 06,1144sec 
Figure 10. Iteratively generated input force PSD 
I I I I I I 
- 
- 
- 
- 
0.5 - 
I 
Oo 
I I I I I I 
50 100 150 m, 250 300 350 4W 
Although iterative and somewhat tedious, the ability to quickly transfer information between the various software 
programs using modern I10 capabilities allowed the methodology to be used in a fairly repeatable and timely 
fashion. Once the methodology was arrived at, side loads were generated for several test conditions chosen 
according to maximum side load measurements obtained using the static method and for different pressure field 
conditions. These results are shown in table 1. 
450 
Frequency (hz) 
Table I. Side Load Calculations for selected Test Points 
CONCLUSION 
March 1,2006 
367 sec 
1144 sec 
1009 sec 
242 sec 
A modal-test based pseudo-model was used to back calculate side load on a sub-scale rocket nozzle using an 
iterative inverse load identification methodology. Although many errors in the process are evident, a reasonable 
value of loading was obtained that can be used for design and relative comparison purposes. The methodology 
chosen resulted from the inadequacy of existing methods for dealing with the test configuration and limitations in 
measurement capability inside the nozzle itself. In addition to providing useful data for the determination of rocket 
nozzle side loads, the limitations noted here of both the pseudo-modeling and the iterative inverse force 
determination method, along with their advantages, should be helpful for research and development studies of 
similar structures that are difficult to model and whose dynamic characteristics only are of interest. As most test- 
fixtures fall into this category, implementing and refining the techniques investigated in this paper should prove to 
be of great value in quickly and accurately assessing the dynamics of these structures. 
RMS Side Load (Ib) Thrust Optimized 
nozzle contour, 
Nozzle Pressure Ratio 
(chamber pressure1 
ambient pressure) 
38 
66 
38 
unknown 
13.8 
16.9 
6.8 
12.1 
REFERENCES 
1 Rocketdyne Engineering, "Side Load Test And Analysis," North American Rockwell, Rocketdyne Engineering, 
Canoga Park, CA, Presentation, 1974. 
2 Larson, Edward W., Ratekin, Gary H. and O'Conner, George M., "Structural Response To The SSME Fuel 
Feedline To Unsteady Shock Oscillations," Rockwell International, Rocketdyne Division, Canoga Park, CA. 
3 Ostlund, Jan, Supersonic Flow Separation with Application to Rocket Engine Nozzles, Doctoral Thesis, Royal 
Institute of Technology, Stockholm, Sweden, 2004 
4 Frey, M, et. al, Subscale Nozzle Testing at the P6.2 Test Stand, 36th AIAA Joint Propulsion Conference, 17-19 
July 2000, Huntsville, Alabama 
5 Hopkins, R.N., Carne, T.G., "Combining Test-Based and Finite Element-Based Models in Nastran," 22nd 
International Modal Analysis Conference, January 26-29, Dearborn, MI, 2004. 


Calculating Nozzle Side Loads using Acceleration Measurements of Test-Based Models

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