Andrew M. Brown

Wall Pressure Unsteadiness and Side Loads in Overexpanded Rocket Nozzles

Surveys of both the static and dynamic wall pressure signatures on the interior surface of a sub-scale, cold-flow and thrust optimized parabolic nozzle are conducted during fixed nozzle pressure ratios corresponding to FSS and RSS states. The motive is to develop a better understanding for the sources of off-axis loads during the transient start-up of overexpanded rocket nozzles. During FSS state, pressure spectra reveal frequency content resembling SWTBLI. Presumably, when the internal flow is in RSS state, separation bubbles are trapped by shocks and expansion waves; interactions between the separated flow regions and the waves produce asymmetric pressure distributions. An analysis of the azimuthal modes reveals how the breathing mode encompasses most of the resolved energy and that the side load inducing mode is coherent with the response moment measured by strain gauges mounted upstream of the nozzle on a flexible tube. Finally, the unsteady pressure is locally more energetic during RSS, albeit direct measurements of the response moments indicate higher side load activity when in FSS state. It is postulated that these discrepancies are attributed to cancellation effects between annular separation bubbles.

Characterization of Side Load Phenomena Using Measurement of Fluid/Structure Interaction

During ground-tests of most production rocket engines over the last 30 years, large asymmetric transient side loads coming from the nozzle and related steady-state vibrational loads within the nozzle have been measured. The widely varying magnitude of these loads has been large enough to fail interfacing components as well as nozzles in these engines. This paper will discuss a comprehensive test and analysis program that has been undertaken to develop a methodology to accurately predict the character and magnitude of this loading. The project to-date has incorporated analytical modeling of both the fluid flow and the nozzle structure and testing of both full-scale and sub-scale rocket nodes. Examination of the test data indicates that one of the two-nodal diameter structural modes may be interacting with flow separation from the nozzle inside-wall in a self-excited or aeroelastic vibration phenomenon. If verified, this observation will be used to develop a methodology for design and analysis. A fuller understanding of the characteristics of this vibration will provide an increase in the accuracy and confidence of side load predictions, which will be critical for the successful construction of the next generation of low-cost, reliable rocket engines.

Details of Side Load Test Data and Analysis for a Truncated Ideal Contour Nozzle and a Parabolic Contour Nozzle

Two cold flow subscale nozzles were tested for side load characteristics during simulated nozzle start transients. The two test article contours were a truncated ideal and a parabolic. The current paper is an extension of a 2009 AIAA JPC paper on the test results for the same two nozzle test articles. The side load moments were measured with the strain tube approach in MSFC s Nozzle Test Facility. The processing techniques implemented to convert the strain gage signals into side load moment data are explained. Nozzle wall pressure profiles for separated nozzle flow at many NPRs are presented and discussed in detail. The effect of the test cell diffuser inlet on the parabolic nozzle s wall pressure profiles for separated flow is shown. The maximum measured side load moments for the two contours are compared. The truncated ideal contour s peak side load moment was 45% of that of the parabolic contour. The calculated side load moments, via mean-plus-three-standard-deviations at each nozzle pressure ratio, reproduced the characteristics and absolute values of measured maximums for both contours. The effect of facility vibration on the measured side load moments is quantified and the effect on uncertainty is calculated. The nozzle contour designs are discussed and the impact of a minor fabrication flaw in the nozzle contours is explained.

Recovering Aerodynamic Side Loads on Rocket Nozzles using Quasi-Static Strain-Gage Measurements

During over-expanded operation of rocket nozzles, which is defined to be when the exit pressure is greater than internal pressure over some part of the nozzle, the nozzle will experience a transverse forcing function due to the pressure differential across the nozzle wall. Overexpansion occurs during the nozzle start-up and shutdown transient, even in high-altitude engines, because most test facilities cannot completely reproduce the nearvacuum pressures at those altitudes. During this transient, the pressure differential moves axially down the nozzle as it becomes pressurized, but this differential is never perfectly symmetric circumferentially. The character of the forcing function is highly complex and defined by a series of restricted and free shock separations. The subject of this paper is the determination of the magnitude of this loading during sub-scale testing via measurement of the structural dynamic response of the nozzle and its support structure. An initial attempt at back-calculating this load using the inverse of the transfer function was performed, but this attempt was shown to be highly susceptible to numerical error. The final method chosen was to use statically calibrated strain data and to filter out the system fundamental frequency such that the measured response yields close to the correct dynamic loading function. This method was shown to capture 93% of the pressure spectral energy using controlled load shaker testing. This method is one of the only practical ways for the inverse determination of the forcing function for non-stationary excitations, and, to the authors’ knowledge, has not been described in the literature to date.

Cylindrical Shell Submerged in Bounded Acoustic Media: A Modal Approach

The dynamics of a simply-supported cylindrical shell submerged in liquid hydrogen (LH 2 ) and liquid oxygen (LOX) are considered. The shell itself is bounded by a rigid outer cylinder with closed rigid ends. This conOguration gives rise to two ∞uid-Olled cavities{ an inner cylindrical cavity and an outer annular cavity. Such geometries are common in rocket engine design. This study computes the natural frequencies and modes of the ∞uid-structure system by combining the rigid wall acoustic cavity modes and the in vacuo structural modes into a system of coupled ordinary diAEerential equations. Eigenvalue veering is observed near the intersections of the curves representing natural frequencies of the rigid wall acoustic and the in vacuo structural modes. In the case of a shell submerged in LH 2 , system frequencies near these intersections are as much as 30% lower than the corresponding in vacuo structural frequencies. Due to its high density, the frequency reductions in the presence of LOX are even more dramatic. The forced response of the ∞uid-loaded shell subject to a harmonic point excitation is also presented. The forced response in the presence of ∞uid is diAEerent from the response of the structure in vacuo in a variety of ways. The frequency shifts that arise from consideration of the ∞uid alter the order of the resonant response peaks. In some cases, modes that are well separated in the in vacuo case are within close proximity in the ∞uid-loaded case (and vice-versa). The ∞uid-loaded structural responses also contain relatively small resonant peaks corresponding to system modes that are dominated by contributions from the ∞uid.

Probabilistic Component Mode Synthesis of Nondeterministic Substructures

Standard methods of structural dynamic analysis assume that the structural characteristics are deterministic. Recognizing that these characteristics are actually statistical in nature, researchers have recently developed a variety of methods that use this information to determine probabilities of a desired response characteristic, such as natural frequency, without using expensive Monte Carlo simulations. One of the problems in these methods is correctly identifying the statistical properties of primitive variables such as geometry, stiffness, and mass. We present a method where the measured dynamic properties of substructures are used instead as the random variables. The residual flexibility method of component mode synthesis is combined with the probabilistic methods to determine the cumulative distribution function of the system eigenvalues. A simple cantilever beam test problem is presented that illustrates the theory.

Probabilistic Methods to Determine Resonance Risk and Damping for Rocket Turbine Blades

The liquid oxygen–hydrogen J-2X rocket engine, which powers the upper stage of the NASA Space Launch System, is presently undergoing hot-fire testing. Analysis revealed numerous potential resonance issues with hardware in the turbomachinery flowpath, which could be catastrophic for the launch vehicle. This paper describes a series of probabilistic analyses incorporating nondeterministic characteristics of mistuning amplification, blade damping, natural frequency, and speed to assess the risk of failure of turbine blades due to resonance during past and present tests and to determine an appropriate value of damping to use in deterministic forced response analysis. The analyses are the first reported in the literature combining these critical nondeterministic parameters. The new damping determination technique developed here indicates that combining a damping value in the lower 1.5 sigma range with a 3 sigma mistuning amplification value results in a desired total 3 sigma probability of failure. These risk ...

Application of Probabilistic Methods to Assess Risk Due to Resonance in the Design of J-2X Rocket Engine Turbine Blades

The LOX-Hydrogen J-2X Rocket Engine, which is proposed for use as an upper-stage engine for numerous earth-to-orbit and heavy lift launch vehicle architectures, is presently in the design phase and will move shortly to the initial development test phase. Analysis of the design has revealed numerous potential resonance issues with hardware in the turbomachinery turbine-side flow-path. The analysis of the fuel pump turbine blades requires particular care because resonant failure of the blades, which are rotating in excess of 30,000 revolutions/minutes (RPM), could be catastrophic for the engine and the entire launch vehicle. This paper describes a series of probabilistic analyses performed to assess the risk of failure of the turbine blades due to resonant vibration during past and present test series. Some significant results are that the probability of failure during a single complete engine hot-fire test is low (~1%) because of the small likelihood of resonance, but that the probability increases to around 30% for a more focused turbomachinery-only test because all speeds will be ramped through and there is a greater likelihood of dwelling at more speeds. These risk calculations have been invaluable for use by program management in deciding if risk-reduction methods such as dampers are necessary immediately or if the test can be performed before the risk-reduction hardware is ready.

The Response of a Mechanical Oscillator Due to Swept and Dithered Excitation

A single degree-of-freedom oscillator subject to linearly swept and/or dithered excitation is considered. Dither refers to the variation of an excitation frequency about a given nominal, or primary, frequency. Dither in rocket engine turbopump shaft speeds can be an important consideration when analyzing the dynamic response of turbomachinery components such as turbine blades. Results indicate that the incorporation of dithered excitation into a fatigue analysis may extend the predicted fatigue life of the structure by a factor of two or more.

An Efficient Modal Analysis Method for Structures Coupled to Fluid-Filled Cavities

This work discusses the implementation of a component mode synthesis technique for use with geometrically complex acoustic-structure systems. The feasibility of conceptually similar techniques was Orst demonstrated over 30 years ago. Since that time there have been remarkable advancements in computational methods. It is therefore reasonable to question the extent to which component mode synthesis remains a computationally advantageous approach for acoustic-structure systems of practical interest. This study demonstrates that relative to the most recent release of the popular Onite element software package, ANSYS, component mode synthesis techniques have a signiOcant computational advantage when the forced response of an acoustic-structure system is of interest. However, recent improvements to the unsymmetric eigensolver available in ANSYS have rendered component mode synthesis a less e±cient option when calculating system frequencies and modes. The e±ciency and accuracy of the proposed technique is assessed in the context of systems that are relevant to the design of liquid rocket engines.