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EVALUATION METHOD OF THRUST OSCILLATIONS IN LARGE SRM – APPLICATION TO SEGMENTED SRM’s

Séverine Ballereau, Franck Godfroy, Stany Gallier, Olivier Orlandi, Jean Thepenier SAFRAN-SME

(France) e-mail: s.larrieu@safran-sme.fr

Eric Robert, Nathalie Cesco CNES

(France)

ABSTRACT

Large segmented Solid Rocket Motors (SRM) experience pressure oscillations. A number of them, including Ariane 5, Space Shuttle or the Titan family, are reported to exhibit this kind of instability during operation. Pressure oscillations (ODP) in such SRM could be due to many physical phenomena with different origins: the formation of vortex shedding in relation with geometric and ballistic factors, combustion instabilities linked to the combustion of aluminium particles, etc. Since such oscillations could be penalizing for the launcher, SAFRAN-SME (SME) has been conducting extensive studies in the context of R&D programs, under the authority of CNES and together with ONERA to improve pressure oscillation modelling. The aims of the work performed have been: to identify the various origins of these instabilities, to better understand the conditions in which they develop and the mechanism involved, to consider possible coupling phenomena and to assess their ultimate impact on motor operation. Numerous 2D and 3D geometries have been studied, by considering various thermodynamics conditions and numerous models such as turbulence, multi-phase flow, etc. This knowledge is a highly valuable asset when the time comes to design a new motor or even when a modification is planned on existing geometries. At the present time, the knowledge acquired provides a means of defining a research methodology for thrust oscillations in the preliminary design phase for future SRM. This methodology is useful in identifying and predicting, as a first approximation and at a very early stage, critical geometries and time points during firing at which thrust oscillations could occur, which might compromise booster performance. During a second phase, numerical aerodynamic simulations and in some cases experimental tests on subscale motors can be performed to confirm the expected preliminary results and to evaluate the ODP amplitudes. The first part of this paper gives an overview of the methodology employed by SME to study ODP issue in SRMs. Key themes and main findings are presented. The second part is devoted to some implementation examples on well known segmented SRMs. .

47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit31 July - 03 August 2011, San Diego, California

AIAA 2011-6054

Copyright © 2011 by Safran-SME. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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I. ACRONYMS CFD = Computational Fluid Dynamics ODP = Oscillations de Pression (pressure oscillations) SRM = Solid Rocket Motor FTI = Frontal Thermal Insulation MPS = Moteur à Propergol Solide (SRM) AVS = Angle Vortex-Shedding L = Grain length OVS = Obstacle Vortex-Shedding Rc = Bore radius at a given time PVS = Parietal Vortex-Shedding ITHAC = Instabilité thermo-acoustique (Thermal acoustic instability) AM = Acoustic mode

II. Introduction Ever since the start of the Ariane 5 program in

1987 there have been concerns that the segmented architecture of the large solid rocket boosters might induce a pressure oscillation mechanism that could generate thrust oscillations and thus unstable operation. The evaluation of this phenomenon at that time relied heavily on the expertise developed in France, mainly at ONERA (French national aerospace research centre) and within SME, through their work on defence programs for the French weapons procurement agency (the DGA). Expertise in this field was also gained in America on the TITAN motors and on the space shuttle. In the early days of the Ariane 5 program, the available tools for assessing the stability were considered as unsophisticated and consisted mainly of linearised asymptotic methods (acoustic balance) developed on the basis of the reference acoustic modes of the motor’s combustion chamber, considered as a resonating cavity.

At a very early stage, work conducted in United States identified deficiencies in these methods for the new generation of motors whose main characteristic, in addition to their high length to diameter ratio (L/D), was that their propellant grain was divided up into several segments (a production imperative). In contradiction to the stability predicted by the classical acoustic balance, these motors proved to be marginally unstable for their first longitudinal acoustic modes, while at a level that did not compromise the mission. However, considering the size of the motors, the frequencies associated with these acoustic modes were sufficiently low to introduce coupling phenomena with the launcher’s structural modes. Thus, although apparently innocuous, these oscillations had to be controlled.

For these reasons, and since that time, SME has conducted extensive studies in the context of R&D

programs, under the authority of CNES (the French space agency) and in close collaboration with ONERA, to improve drastically the modelling of pressure oscillations in solid rocket motors.

Numerous 2D or 3D parametric studies have been carried out, assuming various ballistic and thermodynamic conditions, and incorporating specific models for turbulence, multi-phase flows, etc.

These studies have identified a number of sources for these instabilities, and have led to a better understanding of the mechanisms, of the conditions which favour their development, of the various possible couplings and their ultimate impact on motor performance. The knowledge acquired during the course of these various studies has been accumulated, and all the sources of instability encountered have been classified.

The instabilities encountered, which are closely related to the specific motor configuration, are expressed as pressure oscillations (ODP) which, in turn, generate thrust oscillations (OdF), and vibration affecting the entire SRM, which might become a concern for the comfort of the payloads carried by the launcher or missile. Simple criteria developed by SME to provide a first approximation of the phenomena allow identification, for a given motor configuration, of the conditions in which each of these exciting sources might become active, in addition to their frequencies and amplitudes. These criteria are a powerful tool before initiating any complex numerical simulation work.

Building on this work, SME has developed a methodology for studying ODP in any solid rocket motor. It draws results from twenty years of work in this specific field and relies on three key components: theory, simulations and testing.

The adopted methodology has been matured primarily on the Ariane 5 SRM studies, since its specific geometry generates a number of different sources of instability concurrently (mainly PVS and OVS). Since each motor is designed to satisfy a specific mission, each has its own instable operating mode and consequently the proposed methodology must be global in scope. Every specific motor, and therefore every related study needs attention, since the multiplicity of involved phenomena (coupling phenomena) and the interaction between them induce a real difficulty for extrapolating from one motor to another one. This led SME to test these tools on different configurations in order to verify their faculty to give representative results. Consequently, motors with a very wide range of sizes, geometries or thermo-ballistic properties have been studied.

Each new motor configuration studied can potentially suffer from a non-steady state

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phenomenon or from couplings unlike any previously studied ones. The various implementations performed by SME have thus contributed to improve the methodology, and to identify the greatest number of phenomena likely to generate ODP.

Today, the SME methodology created draws from twenty years of work in this specific field. By covering a large number of motors with different sizes and geometries, it represents the culmination of considerable research work conducted jointly by ONERA and SME1, 2 and is thus applicable both to firings and to the prediction of behaviour during firings, and can also be employed at the preliminary design phases for new motors.

First part of the paper gives an overview and a brief description of the methodology and tools associated. In order to explain how concern for possible ODP may impact the design of motor and the subsequent phases of the motor development, a summary of the key themes and the main findings are presented. Illustration of how this methodology has been constructed is presented.

The second part of the document is devoted to some methodology implementation examples. The paper focuses on segmented solid rocket geometries applications. Several representative segmented SRM motors encountered all over the world like A5 SRM, SRMU, RSRM…have been considered and results are presented. We have to precise that for all of these foreign SRMs studied, works done are only based on bibliographic data.

III. The SME approach The experience gained during R&D programs, the

expertise acquired in applying knowledge to motors, and the results obtained by our colleagues at ONERA have enabled the SME teams to develop a methodology that specifically addresses the issue of ODP in solid rocket motors. As a preparatory step, SME and ONERA accumulated the knowledge acquired, and drew up a classification of all the possible sources of ODP observed so far in SRM.

Figure 1: The various origins of ODP

A. Classification of ODP in solid rocket motors, according to SME/ONERA When they do not induce a significant deviation

from the operating point, instabilities are expressed as pressure fluctuations around the average value defined by the steady-state operating point. The causes of instability are numerous, and have many origins. In accordance with the terminology proposed by Paul Kuentzmann, they have been classified into two main categories, for clarification purposes:

• combustion instabilities • hydrodynamic instabilities*

Together they are termed “Operating

instabilities”. Figure 1 details the classification. Historically, combustion instabilities were the

first to be detected. The rate of propellant combustion is influenced by the ambient pressure, and this combustion tends to amplify a pressure fluctuation, within a given frequency range. The most traditional instabilities thus result from resonance between combustion and the acoustics of the motor’s chamber, for frequencies of the order of one kilohertz up to a few tens of kilohertz. To study these instabilities, a detailed representation of the flow of gases in the motor’s chamber is not generally necessary: a small perturbations method (linear acoustics theory) is quite sufficient.

In contrast, hydrodynamic instabilities are caused by unstable flow, features vortex-type structures. This type of instability may be independent of any reactive phenomenon: they have thus been visualised and characterised through the use of test set ups which operate with air. The hydrodynamic instability is controlled by the flow velocity field, which has a first-order dependency on the geometry and on the thermodynamic properties of the combustion gases, and not on the average pressure†.

Unlike combustion instabilities, hydrodynamic instabilities are highly sensitive to any change in the geometry. Effective study of these instabilities demands labour-intensive numerical simulation work, although simplified approaches can provide useful information. * The prefix hydro- does not infer that the flow is liquid; the phenomenon is strictly gaseous. The use of this prefix is useful in that it emphasises the incompressible nature of this type of instability (in contrast to the compressible nature of acoustics) † For a solid rocket motor, pressure and velocity are, generally speaking, uncoupled due to the presence of the sonic throat

Hydrodynamic

instabilities

AVS OVS PVS

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The first task to be performed when considering a new motor geometry is thus to refer to this classification. In function of the motor data, consulting the classification provides an approximate identification of the phenomena that might occur, and does not omit any. However, in actual motors, the situation will usually prove to be much more complex than the simple classification described above, since different types of instability can co-exist, or couple together. Moreover, it is not intuitively apparent to deduce from initial assumption which type(s) of instabilities will be present in a given configuration. This simple classification is thus insufficient.

One of the fundamental points catered for by the SME methodology is that each motor has its own profile of unstable operation, and this must be studied in detail, since extrapolation often proves to be dangerously unreliable. In view of the complexity of the phenomena which induce ODP, SME’s methodology does not rely on this classification, nor on a single IT tool, nor even on an expert system. Instead, it is based on a compilation of theoretical know-how specific to each source of instability, and on a set of experimental and numerical tools (see Figure 2).

Figure 2: Fundamentals of the methodology

B. SME methodology Firstly, for a given motor, the entire firing sequence must be considered and especially its steady state operation. Indeed, it is important to emphasise that the instabilities are characterised by fluctuations around an average value, and that these fluctuations are dependent on the aforementioned average value.

As stated in the previous section, it is possible to determine quickly which type of instability is likely to occur in a motor, at least with regards to the hydrodynamic instabilities, as a function of the chamber’s internal geometry:

� Elongated: Parietal Vortex Shedding (PVS), intrinsic instability of the Taylor flow in elongated motors, possible

� Presence of a sudden divergence in the combustion surface (Sharp angle): Angle Vortex Shedding (AVS) possible

� Emergent obstacle in the flow: Obstacle Vortex Shedding (OVS) possible

� etc.

This simple examination is then completed by a preliminary design-type analysis, during which:

• The motor’s steady-state behaviour is

determined for the entire firing sequence. This involves determining how the surface regresses, and the various ballistic and thermodynamic parameters.

• Commercial software (such as ABAQUS©) is

used to calculate the acoustic modes and how they change as the firing progresses.

• For hydrodynamic instabilities, SME has

defined, via a “stability analysis”, a set of criteria for evaluating fairly accurately the possible presence of PVS, or OVS combined with PVS, and in a more empirical manner, AVS, or OVS alone.

These criteria permit us to draw the theoretical

hydrodynamic frequencies shape evolution with time. Indeed, for large L/Rc SRM ratio but also when grain surface, nozzle throat dimension and thermodynamic data lead to hydrodynamic modes close to acoustic longitudinal modes3-4, an unsteady flow may appear. Thus, levels can reach high values because of a coupling between both frequencies.

As the chamber geometry grows with the surface burnback, several hydrodynamic modes are defined in order to identify a family of hydrodynamic frequencies curves. Less steady hydrodynamic modes are excited. Their values are deduced from experience and from all the experimental results obtained with already studied similar SRMs. Each corresponding intersection with acoustic modes curves can thus define the formation of a new peak of instabilities. That means that apparition times of each burst of instabilities are fixed by known hydrodynamics data and the motor geometry. This theory has been defined in a very specific simplified case. But with some adaptations, it is possible to determine an equivalent flow which can then be applied to more complex geometries of motors (segmented, with cavities…)5,6.

An application of such an analysis, is given on Figure 3 for the LP6 SRM, 1/15th A5 SRM mock-up with pure PVS.

Prediction of the ODP

Tests

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• Since all the possible origins of instability must be examined, SME has also defined criteria that indicate the possible presence of combustion instability, either a classical pressure coupling or ITHAC10.

Before initiating a labour-intensive simulation, it is advisable to examine the risk associated with the presence of a given instability. However, the criteria (which are the criteria necessary) provide guideline information only and the analysis must be completed by performing aerodynamic simulations to check the relevance of the preliminary analysis. Moreover, the only way to access the ODP amplitudes is to perform numerical simulations, using the most suitable modelling. Once again, experience is the most valuable resource: knowing when to activate a given model demands a full understanding on a theoretical, experimental and numerical level. It should be stressed that adopting the most complex modelling for this type of simulation may be counter-productive: the results may be controlled entirely by purely numerical aspects, or by poorly-controlled data, without the inherent physics having been understood. Consequently, an initial run-through of the firing is performed using SME’s MOPTI© software7, which is pre-programmed to consider surface burnback, calculation of the acoustic modes and the establishment of the network of hydrodynamic frequencies. The entire firing sequence, or, as a minimum, the subassembly in which instabilities are suspected, is explored by performing simulations, using simplified meshes and modelling, both for calculation cost reasons and for the reasons mentioned above. These simulations provide an initial picture of the ODP for the instants at which they appear, with their frequencies and amplitudes.

Depending on the results of the MOPTI© phase, some time points or periods of the firing sequence are then further investigated by detailed simulation work using the CPS_P® software8, involving finer meshes and more complex modelling and including, as required: combustion of aluminium, effects of turbulence, PTF vibration, response of the propellant, combustion noise, surface burnback, etc. This full analysis can then form the basis for the construction of a scenario that describes the non-steady-state behaviour of the motor studied, an analysis in which numerical simulation plays an important role, but is not the sole contributor. Indeed, it would currently be misleading to pretend to be able to provide a complete scenario based only on calculation and assumptions (before firing) which

describes within a few percents: time of onset / amplitudes / frequencies. However, it is perfectly possible to provide an overview of the non-steady state behaviour, and more importantly, it is possible to provide information that is essential for avoiding ODP when designing a new motor, at least during certain phases.

LP6 Geometry

Figure 3: Application of a PVS criterion to the LP6 motor- Comparison of the theoretical

hydrodynamic frequencies (obtained via the SME stability analysis) with the hydrodynamic

frequencies (obtained experimentally)

IV. Some methodology implementation examples In order to have a better understanding of this approach, this part of the document is devoted to some methodology implementation examples. The paper focuses on segmented solid rocket geometries applications. Several representative segmented SRM encountered all over the world like A5 SRM, SRMU, RSRM…have been considered to test these tools on different configurations and results are presented. The goal of these studies was to verify their faculty to give representatives results.

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Acoustic modes

Hydrodynamic modes

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A. MPS P230 – Ariane 5 Solid Rocket Motors 1. Actual geometry

The MPS P230 has a segmented geometry9 (cf. Figure 4) as the propellant grain is distributed in three segments (noted S1, S2, S3). Segment S1 mainly participates to the takeoff. The other segments burn together during 120 seconds and participate to the “cruise” phase. For ballistic reasons, the two main segments S2 and S3 have thermal insulations at the front. They act as combustion inhibitors (front thermal insulation) on the corresponding faces of the propellant. In that way, they participate in the definition of the combustion surface associated with the desired thrust law.

Figure 4 : A5 SRMs design

Ariane 5‘s SRM operation time is about 2 minutes. During this time, the steady operation is affected by an unsteady phenomenon that occurs in the combustion chamber and generates pressure oscillations levels10. Several bursts of pressure instabilities are noted on the three first longitudinal modes at certain time. Figure 5 represents an example of experimental results concerning the unsteady behaviour of the motor during all phases of functioning (pressure oscillations as a function of time and frequency). Each burst of instabilities is associated to a hydrodynamic frequency organization around the longitudinal acoustic mode of the combustion chamber.

As can be noted, main bursts of instabilities appear on the first longitudinal acoustic mode during the second half part of the functioning, with increasing maximum pressure oscillations levels. But the presence of earlier bursts on higher longitudinal acoustic modes can also be seen.

Generally, pressure oscillations that appear during the firing are due to a complex coupling between the combustion and the internal aerodynamics in the boosters’ combustion chamber. In the case of the Ariane 5 SRMs, longitudinal acoustic modes are

excited by vortex shedding generated by different sources (Figure 76):

- Surface Vortex Shedding phenomenon (PVS), which may appear for large L/Rc ratio,

- Obstacle Vortex Shedding phenomenon (OVS), due to the presence of obstacles in the flow such as the S3 front thermal face protection.

- Angle Vortex Shedding over inter-segment cavities (AVS),

- Other effects (turbulence …)

Time

Static Pressure

Time

Static Pressure

Figure 5 : MPS steady/unsteady pressure delivery curve with time

These Vortex shedding frequencies follow

hydrodynamic characteristics whose measured variations are due to the combustion chamber evolution.

Figure 6 : MPS P230 - Elementary vortex shedding phenomena

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Consequently, the first step in analyzing the behaviour of the motor is to determine the complete combustion chamber profile at each time of the operation. In that way, the whole operating phase of the motor has been simulated. For this point, a very good estimation of all the elements of the internal geometry of the motor at each computed time must be known. In the present case, a reference firing test in terms of average unsteady behaviour over all bursts of instabilities has been chosen. Steady behaviour has been analyzed and reproduced (cf Figure 7 A) in order to determine ballistics data and propellant geometry definition vs time11. The grain geometry for each combustion time is defined on the basis of a surface burn back computation, integrating the results of SME firing test exploitations (hump effect and scale factors). In parallel, front thermal inhibitor shape evolution with time in terms of erosion and deformation in the flow has also be taken into account in order to have the best possible geometrical description.

Once this first step was realized, the equivalent Taylor-Culick flow was determined. Results obtained in terms of theoretical hydrodynamic family of frequencies curves with time are plotted on Figure 7 B and compared with experimental values. This analysis underlines the fact that potential crossing between less steady hydrodynamic modes and the first acoustics one can only occur in the second part of the operation.

CFD simulations have also been realized on several points chosen during the supposed unsteady part of the operation. Each point of CFD computation fits exactly on a theoretical hydrodynamic curve: theoretical aspects of the analysis, adapted to our motor configuration, perfectly explain the results obtained on A5 SRMs temporal spectrum.

A very good coherence is thus demonstrated between SME criterion / Experimental / Computed temporal spectrum. A scenario to the A5 unsteady behaviour can thus be given.

Time

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(A) - Steady-state behaviour determination for

the entire firing sequence

20 30 40 50 60 70 80 90 100

% Burned Mass

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(B) - Comparison of the theoretical hydrodynamic frequencies (obtained via the SME methodology) with the measured hydrodynamic frequencies and

computed temporal spectrum (CFD studies)

(C) – CFD - Vorticity for two phases flow

Figure 7 : MPS P230 SME methodology application

2. Without Front thermal inhibitor

A second loop in A5 SRMs unsteady behaviour computations was performed. In this part, a new version without face inhibitor as the one used on the third segment is examined so that pure PVS (without any coupling with an other vortex source) can be studied. This configuration doesn’t exist anymore and has never been tested. As the suppression of S3 FTI was an idea to limit pressure oscillations amplitudes, this configuration may have some technological interests. The goal of this additional study is to determine, with the methodology presented how the unsteady behaviour (amplitudes but also temporal spectrum) can be affected by such a modification. Consequently, the entire SME analysis is rerun without taking into account the third segment FTI. Results thus obtained are presented on Figure 8. The new family of hydrodynamic frequencies curves is plotted on Figure 8 B. CFD computations have also been realized in order to complete our analysis. Focus on these results allows to establish perfect coherence between theoretical and computed temporal spectrum.

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CFD Computed Frequencies Hydrodynamic Frequencies without FTI

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Hydrodynamic Frequencies without FTI Hydrodynamic frequencies with FTI

Figure 8 : MPS P230 SME without third segment FTI methodology application

Comparison with the real configuration (with inhibitor) shows that there is a time of the functioning from which hydrodynamic frequencies become completely different. In the real configuration, the more the inhibitor profile protrudes in the flow, the more hydrodynamic frequencies deviate from the theoretical ones linked to the pure PVS. Same patterns can be noticed on second and third longitudinal acoustic modes. Further analyses have been performed, they have shown that the presence of inhibitor indeed leads to some modifications of the flow along the third segment and then changes the hydrodynamic frequencies. When inhibitor is too inclined or not protruding enough in the flow, PVS is the driving mechanism leading to instabilities. In that case an adapted linear stability can be applied and driven parameters are linked to grain geometries, ballistic and thermodynamics data. On the opposite, when inhibitor sufficiently stands out in the flow, OVS is generated and associated to the PVS already present along the third segment. From this time, vortex structures are modified (cf. Figure 9) and unsteady operation is driven by a new parameter linked to the inhibitor behaviour during the firing. Consequently hydrodynamic frequencies evolution not only depend on Klemmung effect but also on this new parameter. As inhibitor shape regresses slower than propellant, hydrodynamic frequencies gradient is less important. Values remain at the proximity of acoustic modes, it’s the reason why jumps in frequencies are fewer than in the configuration without FTI. Modifications observed on the temporal spectrum are then linked to the inhibitor shape evolution during firing. These aspects have been integrated in the

developed SME criterion in order to be able to predict in which way temporal spectrum may be affected if inhibitor could have a different behaviour.

Rotationnal field (focus S3)

Without FTI With FTI

Rotationnal field (focus S3)

Without FTI With FTI

Figure 9 : MPS P230 - Impact of protruding inhibitor on the unsteady flow

B. SRMU – TITAN IV SRMs The second segmented geometry used to test our tools is the SRMU. SRMU (Solid Rocket Motor Upgrades) are TITAN IV solid rocket boosters.

Figure 10 : SRMU design (US bibliography)

Like the MPS P230, the motor geometry is segmented (cf. Figure 10) as the propellant grain is also distributed in three segments (noted S1, S2, S3). Segment S1 is a star grain and mainly participates to the takeoff. But, contrary to the MPS P230, segment S1 keeps burning until the end of the firing. The other segments burn together for more than two minutes and participate to the “cruise” phase. SRMU geometry doesn’t integrate any face thermal inhibitor. By this way and despite slight differences in length and external diameter, SRMU SRMs configuration is more similar to the MPS P230 configuration without FTI. Consequently, unsteady behaviour should be close to the one computed previously.

Figure 11 represents an example of two experimental results concerning the unsteady

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behaviour of the motor during all phases of functioning (extracted from US literature).

SRMU’s operation time is more than 130s. Like the MPS P230 several bursts of pressure instabilities are noted mainly on the first longitudinal mode and also on the second half part of the firing. Each burst of instabilities is associated to a hydrodynamic frequency organization around the longitudinal acoustic mode of the combustion chamber. The highest ODP levels are obtained during the first peak, when S1 burns. Amplitudes of the following peaks then decrease with time. There is no more instability at the beginning of the tail off, after 110s.

Figure 11 : SRMU steady/unsteady pressure delivery curve with time (US bibliography)

Without any other vortex shedding source, and like the MPS, SRMU length and geometry are largely favourable to pure PVS formation. Focus on L/Rc ratio evolution vs time allows us to observe that the most unsteady operation part is likely to be between 40s et 110s of the firing. Before 40s, this ratio is too high and turbulent effects are strong. Despite a favourable geometry for PVS formation, vortex sheddings then created should degenerate before crossing the nozzle throat. After 115s, L/Rc criterion for PVS formation is not respected anymore: pressure oscillations amplitudes should decrease and pure PVS disappear. To complete this first approach, SME methodology has been applied. First, with US literature data the SRMU geometry has been analyzed. Steady behaviour has been reproduced (cf Figure 12 A&B)

in order to determine accurate ballistics data and propellant geometry definition vs time.

From 0s -> to 110s

(A) SME surface regression construction

SRMU v02

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Par, Données SRMU(PQM-1' pressure profile (90°F NominalBallis tics ) aiaa943284)

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Mot. SME v02

Measuredpressure

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(B) - Steady-state behaviour determination for

the entire firing sequence

(C) - Comparison of the theoretical hydrodynamic frequencies (obtained via the SME methodology) with the measured hydrodynamic frequencies and

computed temporal spectrum (CFD studies)

59s

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(D) – CFD - Vorticity for two phases flow

Figure 12 : SRMU - SME methodology application

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An adapted equivalent Taylor-Culick flow was determined. Results obtained in terms of theoretical hydrodynamic family of frequencies curves with time are plotted on Figure 12 C and compared with combustion chamber first acoustic mode values.

A scenario to the SRMU unsteady behaviour can thus be given. As expected, potential crossings between less steady hydrodynamic modes and first acoustics one are located in the second part of the operation. Comparison with experimental values shows a good coherence in terms of hydrodynamic frequencies gradient evolution in all firing phases. CFD simulations have also been realized on several points chosen around main peaks. Each point of CFD computation fits exactly with the theoretical hydrodynamic lattice. Both levels and frequencies then computed are very closed to experimental ones. Several views on CFD simulations rotational field permit us to have an idea of the flow organization evolution with time. PVS is clearly identified. It mainly appears along the third grain surface in the last part of the firing with a critical point formation closer and closer of the nozzle with time. As a conclusion, SRMU has first an unsteady behaviour because of its length and geometry which are favourable to PVS formation. It depends on the grain position and shape, during operation. In our case of pure PVS instability, hydrodynamic frequencies evolution with time depends on the grain geometry, burning surface value, nozzle throat value and erosion. Bursts’ appearance times are driven by these parameters.

C. RSRM – Shuttle SRM The final SRM unsteady behaviour analysed in

this paper is the RSRM space shuttle boosters.

Figure 13 : RSRM design

Literature review on RSRM has been analyzed. It is composed of four segments (cf Figure 13). With the data encountered, each grain geometry has been designed to match with corresponding theoretical surface evolution (Figure 15 A). Note that contrary to

the SRMU, each segment has face inhibitors with different sizes. Like for previous SRMs, steady behaviour has been reproduced in order to determine accurate ballistics data and propellant geometry definition vs time. In order to have a complete definition of the combustion chamber geometry, some assumptions have been done concerning each grain face inhibitor shape (both in terms of erosion and deformation in the flow).

Figure 14 represents an example of experimental results concerning the unsteady behaviour of the motor during all phases of functioning. Maximum pressure oscillations levels appear between 78s and 100s of the firing on the first longitudinal acoustic mode with hydrodynamic frequency organization between 14,5 et 17 Hz. Just before, we can note some frequency organizations on the second longitudinal acoustic mode from 50s till the end of the firing with frequencies between 27 and 30Hz and lower amplitudes.

Figure 14 : RSRM unsteady pressure delivery curve with time (US bibliography)

Once the steady state behaviour was reproduced, the adapted equivalent flow was determined in order to obtain hydrodynamic family of frequencies curves with time. Results are plotted on Figure 15 C. Several points of simulations have also been done at different times from 50s up to 100s. Each computation has been analyzed in terms of amplitude and frequency evolution and results are reported on the same graph.

By comparing theoretical/experimental and CFD results we can remark that hydrodynamic curves determined with the methodology fully explain the experimental temporal spectrum profile. Indeed, Figure 15 C results show: • Potential frequency crossing on the first

longitudinal mode only after 80s

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• Potential presence of second longitudinal mode just before and after 50s.

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(C) - Comparison of the theoretical hydrodynamic frequencies (obtained via the SME methodology) with computed temporal spectrum (CFD studies)

70s

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(D) – CFD computation – Vorticity for two phases flow

(D) – CFD computation –Particles concentration

for two phases flow

Figure 15 : RSRM - SME methodology application

Hydrodynamic frequencies gradient is coherent

with experimental results. With a laminar model, amplitudes obtained via

CFD simulations are over-estimated, especially between 50s and 70s where L/Rc ratio is very high. Consequently, the use of a turbulent model becomes mandatory to reach representatives amplitudes.

Computed vorticity field allows us to see that grain geometry generates PVS but OVS is obviously generated by protruding thermal insulators. OVS generated by the first FTI seems to go to the centre of the canal and degenerate. Couplings between PVS and OVS produced by the second and the third FTI occur, especially on the aft segment.

Two phases flow simulations show particles packed around vortices (low Stokes number) which follow the gas flow. A lower particles concentration is observed in the centre of vortices. A high concentration in the aft-end can also be noted.

V. Conclusions Numerous physical phenomena that contribute to

the formation of pressure oscillations can appear during solid rocket motor operation. Since the frequencies associated with these instabilities can couple with the launcher’s structural modes, these oscillations must be controlled. For these reasons, SAFRAN-SME (SME) has conducted extensive studies to improve pressure oscillation modelling in solid rocket motors. Over the past twenty years, SME has gained experience by conducting these studies and by analysing the application of its findings on motors. This experience and expertise, collated with the knowledge and results obtained by our colleagues at ONERA, has been converted by SME into a methodology that addresses the problem of ODP for a large number of motor configurations.

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Because of the multiplicity of phenomena which induce ODP, and the interaction between them, our methodology does not rely on a simple approach that indicates the possible presence of a particular source of instabilities, nor on a single IT tool, nor even on an expert system. Instead, it is based on a compilation of theoretical know-how specific to each source of instability, and on a set of experimental and numerical tools, which can construct a scenario that describes the non-steady state behaviour of the motor studied, in order to identify the time points at which the phenomena are likely to occur.

If work on numerical models is still necessary to obtain accurate information about ODP amplitudes, the methodology offers practical solutions for reducing these amplitudes in existing motors, or suggests workable modifications to displace them to an operating time point that is less penalizing for the launcher.

This tool is now available both to enable firings and to predict the behaviour during firings. It can also be used during the preliminary design phases for new motors. In this latter case, the aim of the methodology developed is to design a new motor by integrating the issue of ODP right from the initial phases of work, in order to construct a launcher that is as vibration-free as possible.

VI. Acknowledgements These studies were conducted by SNPE

Matériaux Energétiques (SME) in the context of CNES’s R&D work in collaboration with our partner, ONERA, whom we would like to thank. We would particularly like to thank, via this publication, our colleagues P. Cloutet, D. Ballion, P. Della Pieta, M.J. Kratz at SME, in addition to G. Casalis, M. Prévost and Y. Fabignon at ONERA, for their contribution to this work.

VII. References 1 Vuillot F., "Vortex shedding phenomena in solid rocket motors", J. of Propulsion and Power, Vol. 11, No. 4, pp 626-639, July-August 1995. 2 Y. Fabignon, J. Dupays, G. Avalon, F. Vuillot, N. Lupoglazoff, G. Casalis and M. Prevost, "Instabilities and pressure oscillations in solid rocket motors", Aerospace Science and Technology, Volume 7, Issue 3, April 2003, Pages 191-200

3 Culick, F.E.C, “The Stability of One-Dimensional Motions in a Rocket Chamber”, Combustion Science and Technology, Vol 7, pp. 165-175, 1973 4 Culick, F.E.C, “The Stability of Three-Dimensional Motions in a Rocket Chamber”,Combustion Science and Technology, Vol 10, pp. 109-124, 1975 5 J. Griffond "Instabilité pariétale et accrochage aéroacoustique dans les conduits à parois débitantes simulant les moteurs à propergol solide d'Ariane 5" - PhD Thesis, ENSAE/ONERA, 2001 (in French) 6 F. Chedevergne, G. Casalis “Thrust oscillations in reduced scale motors, part II: a theoretical approach” 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and exhibit, juillet 2005. J Dupays « Contribution à l’étude du rôle de la phase condensée dans la stabilité d’un propulseur à propergol solide pour lanceur spatial » - PhD Thesis, ONERA, 1996 (in French) 7 P. Le Breton, D. Ribereau, F. Godfroy - « SRM Performance analysis by coupling bidimensional surface burnback and pressure field computations” AIAA 98-3968 July 13-15, 1998/Cleveland 8 P. Durand, B. Vieille, H. Lambaré, P. Vuillermoz, G. Bouré, P. Steinfield, F. Godfroy, J.F. Guéry – “CPS: A three-dimensionnal CFD Numerical Code Dedicated to Space Propulsive Flows”. 36th Joint Propulsion Conference and Exhibit, AIAA/ASEE/ASME/SAE, AIAA Paper 2000_3864, Huntsville, AL, 2000. 9 S. Ballereau, F. Godfroy, Two minutes inside the ARIANE 5’s SRMs : Effetc of different sources of pressure oscillations during operation, IAC-09-C4.2.2, South of Corea, 2009. 10 S. Gallier, F. Godfroy, Aluminum combustion driven instabilities in solid rocket motors, Journal of propulsion and power, volume 25-2, march-april 2009

11 D. Ribéreau, P. Le Breton, S. Ballereau - « Casting Process Effect on Composite Solid Propellant Burning Rate” - 37th AIAA/ASME/SAE/ASEE Joint Propulsion - Conference and Exhibit - 8-11 July 2001 - Salt Lake City, Utah