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Two-phase unsteady flow in solid rocket motors
Aerospace Science and Technology 6 (2002) 413–422 www.elsevier.com/locate/aescte
Two-phase unsteady flow in solid rocket motors Ecoulement diphasique instationnaire dans les moteurs à propergol solide Joël Dupays ∗ Fundamental and Applied Energetics Department, Office National d’Etudes et de Recherches Aérospatiales (ONERA), B.P. 72, 92322, Châtillon Cedex, France Received 20 November 2001; received in revised form 21 June 2002; accepted 12 July 2002
Abstract Aluminized propellants are frequently used in solid rocket motors to increase specific impulse. Unlike the other ingredients, aluminum particles can burn in a significant portion of the chamber and produce a condensed phase that is carried out into the flowfield. Thereby, aluminum particles can affect appreciably combustion instabilities by acting as driving or, on the contrary, as damping mechanisms. Therefore, a reliable stability prediction must include the description of the reactive two-phase flow in the motor. Studies realized on this subject in the ASSM program are reviewed. 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Résumé Les propergols aluminisés sont fréquemment utilisés dans les moteurs à propergol solide pour augmenter l’impulsion spécifique. Contrairement aux autres ingrédients du propergol, les particules d’aluminium peuvent brûler dans une portion significative de la chambre et produire une phase condensée qui est transportée dans l’écoulement. De ce fait, les particules d’aluminium peuvent modifier sensiblement les instabilités de combustion en les amplifiant ou, au contraire, en les réduisant. C’est pourquoi, une prédiction fiable de la stabilité doit inclure la description de l’écoulement diphasique dans le moteur. Les études réalisées sur ce sujet dans le programme ASSM sont présentées. 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Keywords: Solid rocket motor; Combustion instabilities; Two-phase flow; Aluminum combustion; Numerical simulation Mots-clés : Propulsion propergol solide ; Instabilités de combustion ; Écoulement diphasique ; Combustion de l’aluminium ; Simulation numérique
1. Introduction Aluminum powder is frequently used as solid propellant additive to increase specific impulse since aluminum has a high density, a large oxidation reaction energy and its oxidation reduces the oxidizer species H2 O and CO2 to better propulsion fluids, namely H2 and CO. However, the physics of aluminum combustion is very different from other propellant ingredients such as polymeric binder and ammonium perchlorate. Aluminum particles are less volatile and do not burn “instantaneously” and “cleanly” at the propellant surface. The melting of the particles on the surface can lead to the formation of agglomerates that * Corresponding author.
E-mail address: [email protected] (J. Dupays).
ignite, either on or after leaving the propellant surface. Original particles that leave the surface individually burn up within 1 or 2 mm of the surface but the combustion of agglomerates may occur in a significant portion of the chamber. In both cases, the droplet combustion produces aluminum oxide (Al2 O3 ) smoke and residues that are carried into the flowfield. Detailed knowledge of dispersed phase characteristics as residue size, burning time and heat release are essential to improve motor performance and reliability. The presence of these droplets into the flowfield contributes to the motor performance loss via a decrease in nozzle efficiency, possible surface damages from droplet impingement and increases in radiation signature and environmental pollution (including space debris). Inside the motor, these droplets are the source of slag material that may remain in the motor during firing and thereby cause excessive heat-
1270-9638/02/$ – see front matter 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. PII: S 1 2 7 0 - 9 6 3 8 ( 0 2 ) 0 1 1 8 2 - 3
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Nomenclature d d0 f p t T x, y Xi
droplet diameter initial droplet diameter frequency pressure time temperature axial and radial coordinates molar fraction for species i
ing and subsequent insulation erosion where they collect, i.e., mainly into the aft-dome region around the submerged nozzle. Certain induced sloshing motion of this molten liquid slag can lead to control problems and possible vehicle instability. Slag material, when ejected, can be also at the origin of pressure pulses inside the motor that could trigger or amplify instabilities. Aluminum droplet combustion and Al2 O3 residue behavior in the chamber can also affect appreciably combustion instabilities by acting as driving or damping mechanisms. The impact of the dispersed phase behavior on motor operations via its effects on combustion instabilities and slag accumulation is actively studied for the Ariane 5 booster within the ASSM (Aerodynamics of Segmented Solid Motors) research program [2]. As the slag accumulation problem is described in detail in Ref. [37] (see also [14]), this article will focus essentially on the logic followed in this program to address both inert and reactive aspects of dispersed phase-flow oscillation interactions. Although slag accumulation and combustion instabilities are discussed in separated articles, it is worth pointing out that the two aspects are not disconnected since flow oscillations could modify the slag rate, as pioneer works of SNPE Propulsion seem to show [16]. Combustion instabilities have been observed in many solid rocket motors burning with either aluminized or unaluminized propellants. The role of aluminum in these oscillatory behaviors seems to be rather complex and ambiguous. Flow oscillations are expected to interact with the accumulation-agglomeration process on the burning surface, with the ignition and the distributed combustion that may occur in a significant portion of the chamber and finally with Al2 O3 residues in the entire volume of the chamber. The first and the third interactions were identified as damping phenomena while the second is suspected to be a driving mechanism. Their effectiveness would depend essentially on oscillation frequencies, droplet sizes and, for the second interaction, on burning-to-residence time ratio so that the net contribution of aluminum to the global acoustic balance of a motor may be positive or negative. This ambiguous behavior seems to be confirmed by the facts.
α, β κ θ τu τc ω
spatial coefficients of attenuation and dispersion of acoustic energy droplet loading ratio of liquid to gas temperature in the undisturbed state droplet dynamic relaxation time droplet burning time angular frequency
The effectiveness of aluminum in suppressing instabilities was demonstrated especially at high frequencies [5] essentially thanks to the particulate damping effect, the aforementioned third interaction. This effect is now well understood and results from velocity and thermal lags between the gas and the Al2 O3 droplets [35]. For a given frequency, its effectiveness depends on sizes and mass fractions of the condensed phase. As a large share of the droplets are often fine, high frequency oscillations are preferably damped. The first interaction, that is the melting and the thermal inertia of the accumulated aluminum on the burning surface, was also identified as a damping phenomenon. As for the particulate damping, a theoretical foundation for this phenomenon was established [33]. It tends to reduce the response of the combustion to incident pressure disturbances especially at frequencies below 2000 Hz, but as underlined by Price [30], this process is probably of secondary importance compared to the particulate damping due to coarse residues. However, despite these two damping effects, some rocket motors, usually stable with unaluminized propellants, were found to develop instabilities at relatively low frequencies once aluminum powder was introduced in the propellant [3, 4,30]. This oscillatory behavior could be related to the second interaction, the so-called distributed combustion effect as the works of Braithwaite et al. [5] and more recently of Brooks and Beckstead [6] should tend to prove it. As the damping and driving mechanisms cannot be supposed to compensate themselves, reliable stability predictions must include these two contributions and thus must include the description of the reactive two-phase flow in the motor. The task is even more complex for the large segmented booster of Ariane 5 because of the development of a vortex shedding phenomenon locked on the first acoustic mode of the chamber [38,39]. The use of a conventional linear method in this case is no longer relevant and may lead to a troublesome misinterpretation as pointed out in previous works (see, e.g., [24,38,39]). In addition, linear methods cannot predict oscillation levels. Therefore, it was recognized that the numerical simulation of the unsteady compressible two-phase reactive flow will provide the ultimate solutions. Numerical simulation offers also a convenient way
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to identify and test solutions to control and reduce the oscillation levels. The development of a numerical tool for the prediction of oscillation frequencies and levels in the booster is a quite challenging task that requires carreful and gradual validation steps. That is why, after a first validation step restricted to inert particulate flows, reactive particulate flows have been addressed. The two distinct phases of validation are illustrated in separate subsections. Each of them include theoretical, experimental and numerical studies that, taken as a whole, represent an unprecedented effort to understand the impact of the particulate phase on combustion instabilities and, considered individually, often constitute original and pioneering works.
2. Inert two-phase flows 2.1. Theoretical aspects and validation As emphasized in the introduction, the attenuation of sound by suspended, inert droplets in a gas is now well understood [35]. Inert droplets are inclined to damp and to disperse the waves by slowing them. The damping is more pronounced when the droplet response time is close to the acoustic time period or, in other words, when the acoustic Stokes number, ωτu , is close to 1. The damping increases with the droplet loading defined merely, in a stagnant medium, as the droplet-to-gas mass ratio per unit volume of the mixture. The dispersion is highest for relatively low Stokes numbers, that is for small droplets and/or for relatively low frequencies. From a numerical viewpoint, this theoretical development offers a convenient support for defining a simple test case for validating the ability of two-phase flow codes to deal with propagating phenomena. Morfouace and Tissier [27], Dupays et al. [13] and Basset et al. [1] used it with success for this purpose. Basset et al. [1] extended also the Temkin and Dobbins’s theory by suppressing the assumption of a stagnant medium and found good agreement between the new theory and their computations. A more elaborate validation is to compare the behavior of numerical codes with the usual 1D acoustic balance approach in a motor geometry [40]. The geometry must be simple enough to permit valuable comparisons. That is why a simple cylindrical port motor called TEP was chosen. The linear stability results are performed for the first axial mode (3162 Hz), so that the classical linear stability integrals are available for comparisons. The 2D computations are performed with the ONERA SIERRA code. The code is based on a two-fluid (Eulerian) approach, well suited for predicting two-way interactions between the phases, especially when the number of droplet class of interest is a priori reduced since a bimodal droplet distribution size is expected in the Ariane 5 booster chamber. Computations are performed in the following way: after convergence toward a steady state solution, the motor is excited close to its first
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axial mode by means of one period of head-end forcing. Then, the response of the flowfield to that perturbation is analyzed in term of frequency and exponential damping. These results are obtained for various model parameter settings as well as for various griddings and are compared to linear results. Parametric studies on the droplet loading κ, the injection velocity and the diameter (i.e., Stokes number) were performed. Droplets and gas are injected in thermal equilibrium. Two mesh sizes were defined. The coarse grid (CG) does not resolve the acoustic boundary layer whereas the fine grid (FG) does. Since no significant influence of the mesh refinement was found, the particulate damping seems to be unchanged by the acoustic boundary layer. A similar weak influence of the injection velocity was found. The dynamical equilibrium seems to be rapidly reached whatever the injection velocity (ranging from characteristic propellant burning rates to the gas velocity) so that the acoustic wave propagates in the same loaded flow. Results for the parametric study on the loading are displayed on Fig. 1. Rather low values of the loading are chosen to take the restrictions of the linear theory into account. The agreement on the frequencies and the particulate damping is very satisfactory. Results remain also very good when the Stokes number is varied via the droplet diameter (see Fig. 1 again). 2.2. The C1xb setup After the first validations of numerical tools using theoretical results, the next step is to compare simulations with experiments. For that purpose, a small, naturally unstable motor called C1xb was designed to develop a vortex shedding phenomenon locked on the first axial mode, as observed in large segmented motors (Fig. 2). Please note that this laboratory facility is only partially representative of these motors, because the shear layer is generated from a chamfered edge of the grain located in the middle of the chamber and the vortex does not evolve above an injecting surface. A very simple internal geometry was retained to facilitate both the interpretation of results and the validation of numerical calculations. To obtain a comprehensive database with which numerical codes can be compared and evaluated, up to 18 transducers, most of them put along the second part of the chamber, were used to monitor the chamber pressure [8,13]. Four composite propellants, with nearly identical burning rates and flame temperatures, were chosen to perform parametric studies on mass fraction and particle diameter. The first, a 79% AP − 21% HTPB propellant, was kept free of particles to serve as reference. Two were loaded with small Al2 O3 particles (about 5 µm) with mass fractions of 5 and 10%, respectively. Because large spherical Al2 O3 particles were not available, the last was loaded with zirconium silicate particles (about 70 µm) with a mass fraction of 5%. In the following discussion, these propellants will be subsequently called Butalite, Butalamine 5% or 10%, and Butalazine. The particle sizes and mass fractions were carefully chosen by resorting to the acoustic balance theory. For the
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Fig. 1. Droplet loading and size effects on frequencies and particulate damping in the TEP motor.
Fig. 2. Above: schematic of C1xb setup (dim in mm), below: power spectral density vs time and frequency for Butalamine 5% and Butalazine firings.
frequency of the first axial mode, which is roughly 700 Hz, small particles should be far more efficient than large particles in damping the oscillations. Moreover, the mass fraction was chosen to observe both vortex shedding and particulate damping.
As expected, vortex shedding was identified during all firings. All tests experienced pressure oscillations with some bursts corresponding to sustained self-excitation on the first acoustic modes. Butalite tests exhibited three bursts, and the other compounds only two, in the second half
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of the burn as though the particles delay the starting of oscillations. The frequency shifts observed on the power spectral density plots establish the reality of the coupling between the acoustics and the vortex roll [38]. In addition, pressure oscillation damping is observed for the Butalamine tests. The increase of the particulate mass fraction leads to a moderate increase of the damping effect, but only in the second burst. Indeed, the third is barely damped, perhaps because of the occurrence of complex wall-eddy-particulate phase interactions at this point in the burn. Results obtained for the Butalazine tests are quite different. Large particles seem to modify the energy distribution inside the chamber, as shown in Fig. 2. At the beginning of the firing, the third axial mode and even the fourth are unstable, to the point that oscillation levels are larger than for the Butalite and Butalamine tests. However, when the vortex shedding is set in motion, and although the third axial mode remains important, oscillation levels remain at moderate values, and are similar to those measured on the Butalite tests. This database was used to validate the SIERRA code. A configuration leading to a sustained self-excitation phenomenon was retained. Computation conditions, such as grid size, numerics, gas and particle properties, and boundary conditions, are described in Ref. [8]. Computations were performed without propellant response models. In spite of this, the comparisons are rather good as shown in Fig. 3 for the Butalamine 5% case. Computations were first conducted for 6-µm particles with three different mass fractions of 5, 10
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and 20%. The magnitude and phase of the Fourier coefficient of the first axial mode, along the chamber axis, highlight the form of this mode in the grain port and the presence of four eddies in the second part of the chamber. This is in agreement with the vorticity contour plot. Oscillation levels were found to be larger with a mass fraction of 10% than with a mass fraction of 5%, whereas, with 20%, oscillations are totally damped (not shown). This result is inconsistent with the linear theory that, of course, cannot predict this threshold effect. By contrast, the frequency shift due to the reduction of the speed of sound in a two-phase medium is well recovered by the computations, and in agreement with both theoretical as well as experimental results [8]. A parametric study on the particle size around 6 µm highlights the drastic sensitivity of the oscillation levels to the particle size, at least when the Stokes number approaches 1 (see Table 1). Unlike the case for single-phase flow, the ratio of the aft-end to head-end oscillation level is larger than 1. The damping is more significant at the head end because the upstream running pressure wave has to travel a greater distance. For all these computations, the signal remains monochromatic and the frequency keeps the same value. For the larger particles, the signal is no longer monochromatic. In accordance with the experimental results, the first three acoustic modes are amplified, and the frequency of the first mode is slightly increased. Coarse particles are swept by the eddies toward the centerline, where the mass concentration increases drastically. As a result, 70-µm particles tend to
Fig. 3. Fourier coefficients of the first mode along the chamber axis. Table 1 Parametric study on particle size for 5% mass fraction Particle diameter, µm – 5 6 6 and 7 7 70 a Polychromatic signal.
Stokes number, ωτu
Frequency, Hz
Head-end pressure oscillation, mbar
Aft-end pressure oscillation, mbar
– 0.33 0.47 0.56 0.64 64.4
731 684 684 684 684 713a
31 30 20 12 8 21
26 30 22 15 11 14
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damp the oscillations with the same efficiency as 6-µm particles, as the accumulation effect due to the preferential concentration mechanism compensates the size effect. In fact, these large particles act less on the acoustics than on the flow itself, because, as in single-phase flow, the ratio of the aft-end to head-end oscillation level is larger than 1. To sum up, the main results deduced from this study are the following: • The influence of the dispersed phase must be taken into account to achieve a reliable stability prediction. • The particle-gas interactions are extremely complex; some threshold effects can be identified. • The increase of the loading does not necessarily accentuate the attenuation of instabilities. • The preferential concentration mechanism of the dispersed phase by the vortex can lead to an accumulation effect, that, in practice, can reveal itself as efficient as the size effect. • Particle size is a sensitive parameter that may act on the oscillation levels and on the energy distribution, so that the distribution size must be described very precisely. Strictly bimodal distributions can be insufficient. A similar numerical study was performed on a cold-flow configuration close to the C1xb geometry by using a Lagrangian approach. The simulations showed similar results concerning the mass loading and Stokes number effects [17]. It is very useful to show the ability of Lagrangian methods to treat unsteady flows because this approach is well suited not only for describing distribution size, but also for describing collision and coalescence phenomena. These phenomena very likely modify the droplet distribution size inside the chamber and thus the global acoustic balance of the motor. In the Ariane 5 booster, these phenomena seem to be important [14,37] and thus should be included in unsteady computations. The main limiting factor of the Lagrangian approach is its high CPU and memory costs for unsteady computations. It is critical for computations in solid rocket chambers where the propellant surface is often significant and needs a lot of injection points to be well described. Leaving aside these aspects that require further work, and provided that the distribution size is well-known, the particulate damping effect in a motor seems to be rather well predicted by numerical simulations.
3. Reactive two-phase flows 3.1. Aluminum combustion modeling The main difference of aluminum combustion in comparison with hydrocarbon fuels is the agglomeration process at the propellant surface and the production of a bimodal droplet size distribution. These droplets consist mainly (80– 90% of mass) of submicron Al2 O3 smoke that can be mod-
eled as a particular gas component. The remainder are Al2 O3 residues, ranging roughly from 20 µm to 200 µm in size, depending on the original aluminum particle size and the degree of agglomeration [12,31,32]. For the Ariane 5 propellant, 1/3 of the total mass undergoes agglomeration. The ideal combustion model should give precise informations on the residue size, the heat release and the burning time. The main input of the model are the sizes of the agglomerates and of isolated droplets, the thermophysical properties of Al, Al2 O3 and Al-containing species and the droplet environment in term of species distribution, temperature, velocity and pressure. The first and second points are the subject of specific studies in the ASSM program [15,26,34,36]. The droplet behavior in a propellant atmosphere is studied numerically [28] since in situ measurements in such a harsh medium are difficult to make. The numerical simulation is also well suited to address both convective and unsteady effects. To date, there is no satisfying combustion model providing residue size, burning time and heat release. The Law’s model [19], for instance, is an appealing, purely academic model able to give all these informations. But, the model is built around a questionable assumption, namely the growing of the oxide lobe during the combustion. While this phenomenon is observed in the laboratory or in a controlled atmosphere, it is probably marginal in reality, as all the visualizations indicate. That is why most reliable models are based on empirical correlations for the burning time and the combustion is stopped for a fixed diameter corresponding to the residue size. Following these approaches, the burning time can be written as [41] τc = k
d0n (aXO2 + bXH2O + cXCO2 )n1 pn2 T n3
(1)
where k is a constant and a, b, c, are the efficiencies of the oxidizers. The values of the parameters proposed by Widener and Beckstead [41] are listed in Table 2. As they have been obtained from theoretical and numerical considerations, a reliable database is needed to confirm these values. To obtain it, ONERA is conducting experiments in real atmosphere with a high-pressure, constant-volume window bomb [36]. This correlation should be valid only for large droplets (agglomerates) for which the reaction is believed to be limited by the diffusion of the oxidizers towards the droplet and the outward flux of gaseous aluminum. However, some studies (e.g., Ref. [18]) seem to show that the assumption of infinite kinetics for the gas-phase reactions could lead to a serious underprediction of the burning time for small aluminum particles. This uncertainty is increased by the fact Table 2 Values of parameters proposed in Ref. [41] (τc in ms, p in atm, d0 in µm) a
b
c
n
n1
n2
n3
k
1
0.58
0.22
1.9
0.39
0.2
1.57
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Fig. 4. Aluminum combustion modeling.
that the burning time for small droplets is less easily measurable. There is a second, more obvious difference between agglomerates and isolated droplets: they do not burn in the same atmosphere. Due to their smaller size, isolated droplets burn close to the surface in an oxidizer-rich environment, while agglomerates burn farther away in an oxidizer-lean environment since much of the available oxidizers, essentially CO2 and H2 O in a propellant atmosphere, has been used for the combustion of smaller droplets before, as illustrated in Fig. 4. Finally, agglomerates can have a heterogeneous composition. They can contain fuel and oxidizer contaminants from the propellant surface as well as excess initial oxide shell mass. Because of all these differences, agglomerates will burn slower than isolated droplets. Recent experimental results obtained by Melcher et al. [25] tend to support these hypothesis. 3.2. Theoretical aspects and validation As mentioned in the introduction, the distributed combustion effect is suspected to be a driving mechanism for acoustic-related instabilities. But there is a lack of theoretical base to prove it. To contribute to the clarification of this uncertainty, Dupays and Vuillot [11], and Dupays [9] studied the mass transfer on the propagation of a plane and smallamplitude acoustic wave in a stagnant two-phase medium. In the first study, the droplet vaporization is supposed to be controlled by the thermal conductivity (droplets vaporize in their vapor) and both phases are in thermal equilibrium in the undisturbed state. In the second study, the process is supposed to be controlled by the diffusion (droplets vaporize in an inert gas) and the gas-droplet mixture is no longer in thermal equilibrium. To represent a combustion chamber atmosphere more closely, the gas temperature can be higher than the droplet temperature. Therefore, the vaporization process produced by the acoustic wave is added to
Fig. 5. Effects of the ratio of liquid to gas temperature on nondimensional coefficients of attenuation and dispersion.
the steady contribution. In both studies, the mass exchange term follows a classical, quasi-steady d2 -law. With the first model, the mass transfer process is found to be either a damping or a driving phenomenon. The governing parameter is the latent heat of vaporization. Its influence is predominant at low acoustic Stokes numbers. These results are well recovered by the computations [11]. With the second model, the author shows similar tendencies but the governing parameter is, in this case, the ratio of the liquid-to-gas temperatures in the undisturbed state (θ ), as displayed in Fig. 5. Results are given for gas and droplet properties describing an aluminized propellant atmosphere. For low Stokes numbers, the coefficient of attenuation α becomes negative as soon as θ is less than 1. On the other hand, if the undisturbed gas-droplet mixture is at a saturated state (θ = 1), mass transfer is a damping phenomenon as
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already shown by Marble [23]. The position and intensity of the maximum of amplification is sensitive to many parameters like the ratio θ , the intensity of the mass transfer and the thermodynamic properties of the droplets and the gas mixture. Even though the generalization of those results to the case of aluminum combustion seems hazardous, these studies give arguments for suspecting distributed combustion to be a rather powerful source of instability. As its effects would be predominant at low frequencies, it could explain the occurrence of instabilities in this frequency range in some large motors burning aluminized propellant. Some of the restrictions of theoretical models must be clearly improved. For instance, the use of an unsteady vaporization model for aluminum droplets instead of the quasi-steady d2 law could give more confidence in the results. The next test cases considered consist of the reactive twophase flow in the TEP geometry. This geometry is useful to test combustion models from the classical d2 -law to better aluminum combustion models, as shown for instance by Daniel [7]. For that purpose, steady computations are sufficient. As no theoretical results are available, a workshop involving three laboratories with three different codes was organized. Participants were IUSTI, SNPE Propulsion and ONERA. The two first participants used an Eulerian approach while ONERA used the Eulerian and Lagrangian solvers of the MSD code. The comparison between these two approaches seems to be very useful because, to some extent, the drawbacks of one approach are the advantages of the other. For the first test case, droplets are supposed to vaporize in their vapor and the mass transfer rate follows the d2 -law. The injected droplet diameter and mass fraction are 30 µm and 18% respectively. The injected velocity is assumed to be at the order of magnitude of the propellant regression rate, namely 10 mm/s. Droplet properties are those of aluminum. The gas and the droplets are injected along the chamber up to the base of the nozzle (see Fig. 1). Pressure at two positions are compared, as well as gas and droplet mass flow rates at the outlet [10]. All of the computations give very similar results. In order to provide more detailled informations, the results are also compared along three grid lines. For instance, Fig. 6 highlights the good agreement between the four computations for the droplet diameter along the grid line i = 50. These results are an encouragement to continue the workshop with a more relevant combustion model. 3.3. Numerical simulations in real motors All the test cases explained are useful to test either the behavior of the combustion model or the ability of the code to deal with propagating phenomena. But the final aim is, of course, to test both aspects in real configurations. A segmented motor, called LP6, prone to parietal vortex shedding (VSP) driven instabilities was chosen for that purpose [20, 21]. To avoid multi-species simulations, droplets were supposed to vaporize and release heat according a d2 -law. The computations were performed with the SIERRA code. Sev-
Fig. 6. Droplet diameter along the grid line i = 50 in the TEP simulations (L stand for Lagrangian).
eral two-phase flow simulations were carried out to study the effects of the Stokes number on the oscillation behavior. As the vortex shedding phenomenon is locked on the first axial mode, the Stokes number was modified via the droplet diameter. Results from two of these computations are displayed in Fig. 7 and compared with a single-phase computation serving as reference. To simulate the production of a condensed phase, droplet combustion was arbitrarily stopped at fixed diameters and, to simplify the study, aluminum droplets and Al2 O3 residues were supposed to have same properties. The first two-phase flow computation involved 30-µm droplets leading to a residue of 3 µm in size (ωτu = 0.001) and the second involved 125-µm droplets leading to a residue of 60 µm in size (ωτu = 0.504). The pressure recording at the head end indicates that oscillation levels are amplified with the smaller droplets and damped with the larger droplets. For the first case, the driving effect induced by the droplet combustion dominates the damping effect resulting from velocity and thermal lags between the gas and the residues. An opposite trend is found for the second case. In this motor, small and large droplets burn into a fairly small portion of the chamber. It can be concluded that, even in a large motor, where the burning-to-residence time ratio is very low, distributed combustion can be a driving mechanism by amplifying flow disturbances in sheared regions near the propellant surface. Unfortunately, there is no theory allowing the prediction of the intensity of this contribution for a given propellant and motor geometry arrangement, to date. The LP6 is a 1/15th simplified subscale motor of the Ariane 5 booster. Compared to the real booster, the head-end face of the third propellant grain is not inhibited and only the VSP develops in the chamber. In the real motor, because of the difference of the regression rate between the inhibitor and the propellant, a protruding annular disk emerges during the burn which generates a second vortex roll called VSO. Recently, reactive two-phase flow computations have been performed in the booster not only to test the code in
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Fig. 7. Vorticity plots and pressure recordings at the head end in the LP6 motor. From left to right: single-phase computation and two-phase computations with 30-µm droplets (residues of 3 µm in size) and 125-µm droplets (residues of 60 µm in size).
this complex configuration but also to highlight the predominant impact of the distributed combustion on the stability of the booster. Details of this study are described in Ref. [22]. As for LP6’s simulations, oscillation levels were drastically increased by adding the droplet combustion. Without droplets, both VSO and VSP coexist but the unsteady behavior seems to be dominated by the VSO. Spectral analysis of the pressure shows a rather wideband spectrum. With burning droplets, oscillation levels are drastically increased and the signal bandwidth is reduced. The combustion near the propellant surface reinforces the VSP and its coupling with the VSO. While LP6’s computations cannot be compared with experimental results, computations in the Ariane 5 booster can be compared with data recorded during static firings at Kourou. First comparisons are very encouraging with respect to the spectral signature and the oscillation levels. That seems to prove the predominant role of the VSPdistributed combustion pair. An open task remains now to use the described aluminum combustion model and to validate the modeling by using simple geometries as the C1xb motor or, more relevant, the LP9 motor, recently designed for studies of the VSP [29].
4. Conclusion All these studies highlight the significant impact of aluminum particles on combustion instabilities. This impact can be shown theoretically or observed experimentally and
numerically. For the Ariane 5 booster, the unsteady behavior seems to be controlled by the interaction between the distributed combustion and the parietal vortex shedding. The merit of the ASSM program is to have permitted the discovery of a phenomenon unsuspected at the beginning of the program and never observed or described elsewhere. However, this result deserves to be confirmed and specified. To achieve this aim, a reliable aluminum combustion model is needed. As the development of a model providing residue size, burning time and heat release in the motor environment is still out of reach, efforts must focus on reliable empirical correlations for burning times and residue size distributions after burnout. Concurrently, a pragmatic and gradual effort of validation is needed.
Acknowledgements This work was performed within the research program ASSM coordinated by ONERA and conducted with the financial support of CNES, Direction des Lanceurs, under the research convention 93/3040. The author express his thanks to P. Kuentzmann who supported and encouraged this synthesis. The author also wishes to acknowledge E. Daniel from IUSTI, J.F. Guéry from SNPE Propulsion, I. Dubois, Y. Fabignon, G. Lavergne, N. Lupoglazoff, M. Prévost, P. Villedieu, F. Vuillot . . . and all his colleagues in the ASSM program for many fruitful discussions.
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References [1] T. Basset, E. Daniel, J.C. Loraud, Analytical and numerical results on the attenuation and dispersion of an acoustic wave through a two-phase flow, Int. J. Num. Meth. Heat Fluid Flow 7 (7) (1997) 722–736. [2] R. Bec, E. Robert, P. Kuentzmann, Y. Fabignon, A survey of French research programs on internal aerodynamics of segmented solid motors, in: 2nd European Conference on Launcher Technology, Rome, Italy, November 21–24, 2000. [3] M.W. Beckstead, Evidences for distributed combustion, in: Proceedings of the 24th JANNAF Combustion Meeting, Vol. I, in: CPIA Pub., Vol. 476, 1987, pp. 1–12. [4] M.W. Beckstead, H.B. Mathes, E.W. Price, F.E.C. Culick, Combustion instability of solid propellants, in: Proceedings of the 12th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, 1969, pp. 203–211. [5] P.C. Braithwaite, M.W. Beckstead, R.L. Raun, Measurements of distributed combustion, in: Proceedings of the 21st JANNAF Combustion Meeting, Vol. I, in: CPIA Pub., Vol. 412, 1984, pp. 177–186. [6] K.P. Brooks, M.W. Beckstead, Dynamics of aluminum combustion, J. Propul. Power 11 (4) (1995) 769–780. [7] E. Daniel, Eulerian approach for unsteady two-phase solid rocket flows with aluminum particles, J. Propul. Power 16 (2) (2000) 309–318. [8] J. Dupays, Contribution à l’étude du rôle de la phase condensée dans la stabilité d’un propulseur à propergol solide pour lanceur spatial, Ph.D. dissertation, Institut National Polytechnique de Toulouse, France, 1996. [9] J. Dupays, Mass transfer effects on sound propagation in a droplet– gas mixture, in: 5th International Symposium on Special Topics in Chemical Propulsion, Stresa, Italy, June 19–22, 2000. [10] J. Dupays, Y. Fabignon, Simulations numériques diphasiques sur le cas TEP. Comparaisons entre plusieurs codes, Internal ONERA report, RT 4/00584 DMAE/ DEFA, 2000. [11] J. Dupays, F. Vuillot, Propagation of acoustic waves in a two-phase vaporizing mixture, J. Propul. Power 18 (1) (2002) 222–224. [12] J. Dupays, Y. Fabignon, O. Orlandi, J.F. Trubert, Combustion of aluminum particles in solid rocket motors, in: 2nd ONERA–DLR Aerospace Symposium, Berlin, Germany, June 15–16, 2000. [13] J. Dupays, M. Prévost, P. Tarrin, F. Vuillot, Effects of particulate phase on vortex shedding driven oscillations in solid rocket motors, AIAA Paper 96-3248, July 1996. [14] J. Dupays, Y. Fabignon, P. Villedieu, G. Lavergne, J.L. Estivalezes, Some aspects of two-phase flows in solid-propellant rocket motors, in: V. Yang, T.B. Brill, W.-Z. Ren (Eds.), Solid Propellant Chemistry, Combustion, and Motor Interior Ballistics, in: Progress in Astronautics and Aeronautics, Vol. 185, AIAA, Reston, 2000, pp. 859–883. [15] J. Duterque, Experimental studies of aluminum agglomeration in solid rocket motors, in: 4th International Symposium on Special Topics in Chemical Propulsion, Stockholm, Sweden, May 27–31, 1996. [16] F. Godfroy, J.F. Guéry, Unsteady Eulerian flow analysis of solid rocket Motor Slag, AIAA Paper 97-2859, July 1997. [17] F. Goncalves de Miranda, J.L. Estivalezes, G. Lavergne, Numerical simulation of droplet dispersion in a cold-flow rocket, AIAA Paper 00-0818, Jan. 2000. [18] M.K. King, Modeling of single particle aluminum combustion in CO2 N2 atmospheres, in: Proceedings of the 17th Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1977, pp. 1317–1328. [19] C.K. Law, A simplified theoretical model for the vapor-phase combustion of metal particles, Combust. Sci. Tech. 7 (1973) 197–212. [20] N. Lupoglazoff, F. Vuillot, Parietal vortex shedding as a cause of instability for long solid propellant motors: numerical simulations and comparisons with firing tests, AIAA Paper 96-0761, Jan. 1996. [21] N. Lupoglazoff, J. Dupays, F. Vuillot, Vortex shedding pariétal en présence de particules en combustion, Internal ONERA report, RTS 1/6182/DSNA/Y, 1999.
[22] N. Lupoglazoff, F. Vuillot, J. Dupays, Y. Fabignon, Numerical simulations of the unsteady flow inside Ariane 5 P230 SRM booster with burning aluminum particles, in: 2nd European Conference on Launcher Technology, Rome, Italy, November 21–24, 2000. [23] F.E. Marble, Some gasdynamic problems in the flow of condensing vapors, Astronaut. Acta 14 (1969) 585–613. [24] H.B. Mathes, Assessment of chamber pressure oscillations in the shuttle solid rocket booster motors, AIAA Paper 80-1091, July 1980. [25] J.C. Melcher, H. Krier, R.L. Burton, Burning aluminum particles inside a laboratory-scale solid rocket motor, AIAA Paper 01-3947, July 2001. [26] F. Millot, B. Glorieux, J.C. Rifflet, Measurements of the physicochemical properties of liquid alumina using contactless techniques, in: V. Yang, T.B. Brill, W.-Z. Ren (Eds.), Solid Propellant Chemistry, Combustion, and Motor Interior Ballistics, in: Progress in Astronautics and Aeronautics, Vol. 185, AIAA, Reston, 2000, pp. 777–788. [27] V. Morfouace, P.-Y. Tissier, Two-phase flow analysis of instabilities driven by vortex shedding in solid rocket motors, AIAA Paper 952733, July 1995. [28] O. Orlandi, Y. Fabignon, Numerical simulation of the combustion of a single aluminum particle in a propellant gas, in: 2nd European Conference on Launcher Technology, Rome, Italy, November 21–24, 2000. [29] M. Prévost, J. Maunoury, P. Prévot, Campagne d’essais du montage LP9, démonstrateur du vortex shedding pariétal (VSP), Internal ONERA report, RF 2/5500.12 DMAE/Y, 1999. [30] E.W. Price, Comments on “Role of aluminum in suppressing instability in solid propellant rocket motors”, AIAA J. 9 (5) (1971) 987–990. [31] H. Ruiz, J.G. Kratz, Granulométrie de la phase condensée, programme ASSM5, Technical report SNPE n◦ 4842/96/SNPE/DFP/CER, 1996. [32] M. Salita, Quench bomb investigation of Al2 O3 formation from solid rocket propellants (Part 2): Analysis of data, in: Proceedings of the 25th JANNAF Combustion Meeting, Vol. 1, 1988, pp. 185–197. [33] M. Summerfield, H. Krier, Role of aluminum in suppressing instability in solid propellant rocket motors, in: Problems of Hydrodynamics and Continuum Mechanics, Sixtieth Anniversary Volume, Society for Independent and Applied Mathematics, Philadelphia, PA, 1969, pp. 703–717. [34] M.T. Swihart, L. Catoire, Thermochemistry of aluminum species for combustion modeling from ab initio molecular orbital calculations, Combust. Flame 121 (1/2) (2000) 210–222. [35] S. Temkin, R.A. Dobbins, Attenuation and dispersion of sound by particulate relaxation processes, J. Acoust. Soc. Am. 40 (2) (1966) 317–324. [36] J.F. Trubert, Agglomeration and combustion of aluminum particles in solid rocket motors, in: 2nd European Conference on Launcher Technology, Rome, Italy, November 21–24, 2000. [37] P. Villedieu, J. Hylkema, G. Lavergne, B. Platet, Y. Fabignon, M. Vardelle, J.F. Guéry, F. Godfroy, P. Le Helley, L. Jacques, Slag accumulation in solid-propellant rocket motors with a submerged nozzle, in: 2nd European Conference on Launcher Technology, Rome, Italy, November 21–24, 2000. [38] F. Vuillot, Vortex shedding phenomena in solid rocket motors, J. Propul. Power 11 (4) (1995) 626–639. [39] F. Vuillot, P.-Y. Tissier, R. De Amicis, Stability prediction for large segmented solid-propellant rocket motors, in: 5ème Symposium International sur la Propulsion dans les Transports Spatiaux, Paris, France, 22–24 mai, 1996. [40] F. Vuillot, T. Basset, J. Dupays, E. Daniel, N. Lupoglazoff, 2D Navier– Stokes stability computation for solid rocket motors: rotational, combustion and two-phase flow effects, AIAA Paper 97-3326, July 1997. [41] J.F. Widener, M.W. Beckstead, Aluminum combustion modeling in solid propellant combustion products, AIAA Paper 98-3824, July 1998.
Two-phase unsteady flow in solid rocket motors Ecoulement diphasique instationnaire dans les moteurs à propergol solide Joël Dupays ∗ Fundamental and Applied Energetics Department, Office National d’Etudes et de Recherches Aérospatiales (ONERA), B.P. 72, 92322, Châtillon Cedex, France Received 20 November 2001; received in revised form 21 June 2002; accepted 12 July 2002
Abstract Aluminized propellants are frequently used in solid rocket motors to increase specific impulse. Unlike the other ingredients, aluminum particles can burn in a significant portion of the chamber and produce a condensed phase that is carried out into the flowfield. Thereby, aluminum particles can affect appreciably combustion instabilities by acting as driving or, on the contrary, as damping mechanisms. Therefore, a reliable stability prediction must include the description of the reactive two-phase flow in the motor. Studies realized on this subject in the ASSM program are reviewed. 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Résumé Les propergols aluminisés sont fréquemment utilisés dans les moteurs à propergol solide pour augmenter l’impulsion spécifique. Contrairement aux autres ingrédients du propergol, les particules d’aluminium peuvent brûler dans une portion significative de la chambre et produire une phase condensée qui est transportée dans l’écoulement. De ce fait, les particules d’aluminium peuvent modifier sensiblement les instabilités de combustion en les amplifiant ou, au contraire, en les réduisant. C’est pourquoi, une prédiction fiable de la stabilité doit inclure la description de l’écoulement diphasique dans le moteur. Les études réalisées sur ce sujet dans le programme ASSM sont présentées. 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Keywords: Solid rocket motor; Combustion instabilities; Two-phase flow; Aluminum combustion; Numerical simulation Mots-clés : Propulsion propergol solide ; Instabilités de combustion ; Écoulement diphasique ; Combustion de l’aluminium ; Simulation numérique
1. Introduction Aluminum powder is frequently used as solid propellant additive to increase specific impulse since aluminum has a high density, a large oxidation reaction energy and its oxidation reduces the oxidizer species H2 O and CO2 to better propulsion fluids, namely H2 and CO. However, the physics of aluminum combustion is very different from other propellant ingredients such as polymeric binder and ammonium perchlorate. Aluminum particles are less volatile and do not burn “instantaneously” and “cleanly” at the propellant surface. The melting of the particles on the surface can lead to the formation of agglomerates that * Corresponding author.
E-mail address: [email protected] (J. Dupays).
ignite, either on or after leaving the propellant surface. Original particles that leave the surface individually burn up within 1 or 2 mm of the surface but the combustion of agglomerates may occur in a significant portion of the chamber. In both cases, the droplet combustion produces aluminum oxide (Al2 O3 ) smoke and residues that are carried into the flowfield. Detailed knowledge of dispersed phase characteristics as residue size, burning time and heat release are essential to improve motor performance and reliability. The presence of these droplets into the flowfield contributes to the motor performance loss via a decrease in nozzle efficiency, possible surface damages from droplet impingement and increases in radiation signature and environmental pollution (including space debris). Inside the motor, these droplets are the source of slag material that may remain in the motor during firing and thereby cause excessive heat-
1270-9638/02/$ – see front matter 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. PII: S 1 2 7 0 - 9 6 3 8 ( 0 2 ) 0 1 1 8 2 - 3
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Nomenclature d d0 f p t T x, y Xi
droplet diameter initial droplet diameter frequency pressure time temperature axial and radial coordinates molar fraction for species i
ing and subsequent insulation erosion where they collect, i.e., mainly into the aft-dome region around the submerged nozzle. Certain induced sloshing motion of this molten liquid slag can lead to control problems and possible vehicle instability. Slag material, when ejected, can be also at the origin of pressure pulses inside the motor that could trigger or amplify instabilities. Aluminum droplet combustion and Al2 O3 residue behavior in the chamber can also affect appreciably combustion instabilities by acting as driving or damping mechanisms. The impact of the dispersed phase behavior on motor operations via its effects on combustion instabilities and slag accumulation is actively studied for the Ariane 5 booster within the ASSM (Aerodynamics of Segmented Solid Motors) research program [2]. As the slag accumulation problem is described in detail in Ref. [37] (see also [14]), this article will focus essentially on the logic followed in this program to address both inert and reactive aspects of dispersed phase-flow oscillation interactions. Although slag accumulation and combustion instabilities are discussed in separated articles, it is worth pointing out that the two aspects are not disconnected since flow oscillations could modify the slag rate, as pioneer works of SNPE Propulsion seem to show [16]. Combustion instabilities have been observed in many solid rocket motors burning with either aluminized or unaluminized propellants. The role of aluminum in these oscillatory behaviors seems to be rather complex and ambiguous. Flow oscillations are expected to interact with the accumulation-agglomeration process on the burning surface, with the ignition and the distributed combustion that may occur in a significant portion of the chamber and finally with Al2 O3 residues in the entire volume of the chamber. The first and the third interactions were identified as damping phenomena while the second is suspected to be a driving mechanism. Their effectiveness would depend essentially on oscillation frequencies, droplet sizes and, for the second interaction, on burning-to-residence time ratio so that the net contribution of aluminum to the global acoustic balance of a motor may be positive or negative. This ambiguous behavior seems to be confirmed by the facts.
α, β κ θ τu τc ω
spatial coefficients of attenuation and dispersion of acoustic energy droplet loading ratio of liquid to gas temperature in the undisturbed state droplet dynamic relaxation time droplet burning time angular frequency
The effectiveness of aluminum in suppressing instabilities was demonstrated especially at high frequencies [5] essentially thanks to the particulate damping effect, the aforementioned third interaction. This effect is now well understood and results from velocity and thermal lags between the gas and the Al2 O3 droplets [35]. For a given frequency, its effectiveness depends on sizes and mass fractions of the condensed phase. As a large share of the droplets are often fine, high frequency oscillations are preferably damped. The first interaction, that is the melting and the thermal inertia of the accumulated aluminum on the burning surface, was also identified as a damping phenomenon. As for the particulate damping, a theoretical foundation for this phenomenon was established [33]. It tends to reduce the response of the combustion to incident pressure disturbances especially at frequencies below 2000 Hz, but as underlined by Price [30], this process is probably of secondary importance compared to the particulate damping due to coarse residues. However, despite these two damping effects, some rocket motors, usually stable with unaluminized propellants, were found to develop instabilities at relatively low frequencies once aluminum powder was introduced in the propellant [3, 4,30]. This oscillatory behavior could be related to the second interaction, the so-called distributed combustion effect as the works of Braithwaite et al. [5] and more recently of Brooks and Beckstead [6] should tend to prove it. As the damping and driving mechanisms cannot be supposed to compensate themselves, reliable stability predictions must include these two contributions and thus must include the description of the reactive two-phase flow in the motor. The task is even more complex for the large segmented booster of Ariane 5 because of the development of a vortex shedding phenomenon locked on the first acoustic mode of the chamber [38,39]. The use of a conventional linear method in this case is no longer relevant and may lead to a troublesome misinterpretation as pointed out in previous works (see, e.g., [24,38,39]). In addition, linear methods cannot predict oscillation levels. Therefore, it was recognized that the numerical simulation of the unsteady compressible two-phase reactive flow will provide the ultimate solutions. Numerical simulation offers also a convenient way
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to identify and test solutions to control and reduce the oscillation levels. The development of a numerical tool for the prediction of oscillation frequencies and levels in the booster is a quite challenging task that requires carreful and gradual validation steps. That is why, after a first validation step restricted to inert particulate flows, reactive particulate flows have been addressed. The two distinct phases of validation are illustrated in separate subsections. Each of them include theoretical, experimental and numerical studies that, taken as a whole, represent an unprecedented effort to understand the impact of the particulate phase on combustion instabilities and, considered individually, often constitute original and pioneering works.
2. Inert two-phase flows 2.1. Theoretical aspects and validation As emphasized in the introduction, the attenuation of sound by suspended, inert droplets in a gas is now well understood [35]. Inert droplets are inclined to damp and to disperse the waves by slowing them. The damping is more pronounced when the droplet response time is close to the acoustic time period or, in other words, when the acoustic Stokes number, ωτu , is close to 1. The damping increases with the droplet loading defined merely, in a stagnant medium, as the droplet-to-gas mass ratio per unit volume of the mixture. The dispersion is highest for relatively low Stokes numbers, that is for small droplets and/or for relatively low frequencies. From a numerical viewpoint, this theoretical development offers a convenient support for defining a simple test case for validating the ability of two-phase flow codes to deal with propagating phenomena. Morfouace and Tissier [27], Dupays et al. [13] and Basset et al. [1] used it with success for this purpose. Basset et al. [1] extended also the Temkin and Dobbins’s theory by suppressing the assumption of a stagnant medium and found good agreement between the new theory and their computations. A more elaborate validation is to compare the behavior of numerical codes with the usual 1D acoustic balance approach in a motor geometry [40]. The geometry must be simple enough to permit valuable comparisons. That is why a simple cylindrical port motor called TEP was chosen. The linear stability results are performed for the first axial mode (3162 Hz), so that the classical linear stability integrals are available for comparisons. The 2D computations are performed with the ONERA SIERRA code. The code is based on a two-fluid (Eulerian) approach, well suited for predicting two-way interactions between the phases, especially when the number of droplet class of interest is a priori reduced since a bimodal droplet distribution size is expected in the Ariane 5 booster chamber. Computations are performed in the following way: after convergence toward a steady state solution, the motor is excited close to its first
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axial mode by means of one period of head-end forcing. Then, the response of the flowfield to that perturbation is analyzed in term of frequency and exponential damping. These results are obtained for various model parameter settings as well as for various griddings and are compared to linear results. Parametric studies on the droplet loading κ, the injection velocity and the diameter (i.e., Stokes number) were performed. Droplets and gas are injected in thermal equilibrium. Two mesh sizes were defined. The coarse grid (CG) does not resolve the acoustic boundary layer whereas the fine grid (FG) does. Since no significant influence of the mesh refinement was found, the particulate damping seems to be unchanged by the acoustic boundary layer. A similar weak influence of the injection velocity was found. The dynamical equilibrium seems to be rapidly reached whatever the injection velocity (ranging from characteristic propellant burning rates to the gas velocity) so that the acoustic wave propagates in the same loaded flow. Results for the parametric study on the loading are displayed on Fig. 1. Rather low values of the loading are chosen to take the restrictions of the linear theory into account. The agreement on the frequencies and the particulate damping is very satisfactory. Results remain also very good when the Stokes number is varied via the droplet diameter (see Fig. 1 again). 2.2. The C1xb setup After the first validations of numerical tools using theoretical results, the next step is to compare simulations with experiments. For that purpose, a small, naturally unstable motor called C1xb was designed to develop a vortex shedding phenomenon locked on the first axial mode, as observed in large segmented motors (Fig. 2). Please note that this laboratory facility is only partially representative of these motors, because the shear layer is generated from a chamfered edge of the grain located in the middle of the chamber and the vortex does not evolve above an injecting surface. A very simple internal geometry was retained to facilitate both the interpretation of results and the validation of numerical calculations. To obtain a comprehensive database with which numerical codes can be compared and evaluated, up to 18 transducers, most of them put along the second part of the chamber, were used to monitor the chamber pressure [8,13]. Four composite propellants, with nearly identical burning rates and flame temperatures, were chosen to perform parametric studies on mass fraction and particle diameter. The first, a 79% AP − 21% HTPB propellant, was kept free of particles to serve as reference. Two were loaded with small Al2 O3 particles (about 5 µm) with mass fractions of 5 and 10%, respectively. Because large spherical Al2 O3 particles were not available, the last was loaded with zirconium silicate particles (about 70 µm) with a mass fraction of 5%. In the following discussion, these propellants will be subsequently called Butalite, Butalamine 5% or 10%, and Butalazine. The particle sizes and mass fractions were carefully chosen by resorting to the acoustic balance theory. For the
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Fig. 1. Droplet loading and size effects on frequencies and particulate damping in the TEP motor.
Fig. 2. Above: schematic of C1xb setup (dim in mm), below: power spectral density vs time and frequency for Butalamine 5% and Butalazine firings.
frequency of the first axial mode, which is roughly 700 Hz, small particles should be far more efficient than large particles in damping the oscillations. Moreover, the mass fraction was chosen to observe both vortex shedding and particulate damping.
As expected, vortex shedding was identified during all firings. All tests experienced pressure oscillations with some bursts corresponding to sustained self-excitation on the first acoustic modes. Butalite tests exhibited three bursts, and the other compounds only two, in the second half
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of the burn as though the particles delay the starting of oscillations. The frequency shifts observed on the power spectral density plots establish the reality of the coupling between the acoustics and the vortex roll [38]. In addition, pressure oscillation damping is observed for the Butalamine tests. The increase of the particulate mass fraction leads to a moderate increase of the damping effect, but only in the second burst. Indeed, the third is barely damped, perhaps because of the occurrence of complex wall-eddy-particulate phase interactions at this point in the burn. Results obtained for the Butalazine tests are quite different. Large particles seem to modify the energy distribution inside the chamber, as shown in Fig. 2. At the beginning of the firing, the third axial mode and even the fourth are unstable, to the point that oscillation levels are larger than for the Butalite and Butalamine tests. However, when the vortex shedding is set in motion, and although the third axial mode remains important, oscillation levels remain at moderate values, and are similar to those measured on the Butalite tests. This database was used to validate the SIERRA code. A configuration leading to a sustained self-excitation phenomenon was retained. Computation conditions, such as grid size, numerics, gas and particle properties, and boundary conditions, are described in Ref. [8]. Computations were performed without propellant response models. In spite of this, the comparisons are rather good as shown in Fig. 3 for the Butalamine 5% case. Computations were first conducted for 6-µm particles with three different mass fractions of 5, 10
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and 20%. The magnitude and phase of the Fourier coefficient of the first axial mode, along the chamber axis, highlight the form of this mode in the grain port and the presence of four eddies in the second part of the chamber. This is in agreement with the vorticity contour plot. Oscillation levels were found to be larger with a mass fraction of 10% than with a mass fraction of 5%, whereas, with 20%, oscillations are totally damped (not shown). This result is inconsistent with the linear theory that, of course, cannot predict this threshold effect. By contrast, the frequency shift due to the reduction of the speed of sound in a two-phase medium is well recovered by the computations, and in agreement with both theoretical as well as experimental results [8]. A parametric study on the particle size around 6 µm highlights the drastic sensitivity of the oscillation levels to the particle size, at least when the Stokes number approaches 1 (see Table 1). Unlike the case for single-phase flow, the ratio of the aft-end to head-end oscillation level is larger than 1. The damping is more significant at the head end because the upstream running pressure wave has to travel a greater distance. For all these computations, the signal remains monochromatic and the frequency keeps the same value. For the larger particles, the signal is no longer monochromatic. In accordance with the experimental results, the first three acoustic modes are amplified, and the frequency of the first mode is slightly increased. Coarse particles are swept by the eddies toward the centerline, where the mass concentration increases drastically. As a result, 70-µm particles tend to
Fig. 3. Fourier coefficients of the first mode along the chamber axis. Table 1 Parametric study on particle size for 5% mass fraction Particle diameter, µm – 5 6 6 and 7 7 70 a Polychromatic signal.
Stokes number, ωτu
Frequency, Hz
Head-end pressure oscillation, mbar
Aft-end pressure oscillation, mbar
– 0.33 0.47 0.56 0.64 64.4
731 684 684 684 684 713a
31 30 20 12 8 21
26 30 22 15 11 14
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damp the oscillations with the same efficiency as 6-µm particles, as the accumulation effect due to the preferential concentration mechanism compensates the size effect. In fact, these large particles act less on the acoustics than on the flow itself, because, as in single-phase flow, the ratio of the aft-end to head-end oscillation level is larger than 1. To sum up, the main results deduced from this study are the following: • The influence of the dispersed phase must be taken into account to achieve a reliable stability prediction. • The particle-gas interactions are extremely complex; some threshold effects can be identified. • The increase of the loading does not necessarily accentuate the attenuation of instabilities. • The preferential concentration mechanism of the dispersed phase by the vortex can lead to an accumulation effect, that, in practice, can reveal itself as efficient as the size effect. • Particle size is a sensitive parameter that may act on the oscillation levels and on the energy distribution, so that the distribution size must be described very precisely. Strictly bimodal distributions can be insufficient. A similar numerical study was performed on a cold-flow configuration close to the C1xb geometry by using a Lagrangian approach. The simulations showed similar results concerning the mass loading and Stokes number effects [17]. It is very useful to show the ability of Lagrangian methods to treat unsteady flows because this approach is well suited not only for describing distribution size, but also for describing collision and coalescence phenomena. These phenomena very likely modify the droplet distribution size inside the chamber and thus the global acoustic balance of the motor. In the Ariane 5 booster, these phenomena seem to be important [14,37] and thus should be included in unsteady computations. The main limiting factor of the Lagrangian approach is its high CPU and memory costs for unsteady computations. It is critical for computations in solid rocket chambers where the propellant surface is often significant and needs a lot of injection points to be well described. Leaving aside these aspects that require further work, and provided that the distribution size is well-known, the particulate damping effect in a motor seems to be rather well predicted by numerical simulations.
3. Reactive two-phase flows 3.1. Aluminum combustion modeling The main difference of aluminum combustion in comparison with hydrocarbon fuels is the agglomeration process at the propellant surface and the production of a bimodal droplet size distribution. These droplets consist mainly (80– 90% of mass) of submicron Al2 O3 smoke that can be mod-
eled as a particular gas component. The remainder are Al2 O3 residues, ranging roughly from 20 µm to 200 µm in size, depending on the original aluminum particle size and the degree of agglomeration [12,31,32]. For the Ariane 5 propellant, 1/3 of the total mass undergoes agglomeration. The ideal combustion model should give precise informations on the residue size, the heat release and the burning time. The main input of the model are the sizes of the agglomerates and of isolated droplets, the thermophysical properties of Al, Al2 O3 and Al-containing species and the droplet environment in term of species distribution, temperature, velocity and pressure. The first and second points are the subject of specific studies in the ASSM program [15,26,34,36]. The droplet behavior in a propellant atmosphere is studied numerically [28] since in situ measurements in such a harsh medium are difficult to make. The numerical simulation is also well suited to address both convective and unsteady effects. To date, there is no satisfying combustion model providing residue size, burning time and heat release. The Law’s model [19], for instance, is an appealing, purely academic model able to give all these informations. But, the model is built around a questionable assumption, namely the growing of the oxide lobe during the combustion. While this phenomenon is observed in the laboratory or in a controlled atmosphere, it is probably marginal in reality, as all the visualizations indicate. That is why most reliable models are based on empirical correlations for the burning time and the combustion is stopped for a fixed diameter corresponding to the residue size. Following these approaches, the burning time can be written as [41] τc = k
d0n (aXO2 + bXH2O + cXCO2 )n1 pn2 T n3
(1)
where k is a constant and a, b, c, are the efficiencies of the oxidizers. The values of the parameters proposed by Widener and Beckstead [41] are listed in Table 2. As they have been obtained from theoretical and numerical considerations, a reliable database is needed to confirm these values. To obtain it, ONERA is conducting experiments in real atmosphere with a high-pressure, constant-volume window bomb [36]. This correlation should be valid only for large droplets (agglomerates) for which the reaction is believed to be limited by the diffusion of the oxidizers towards the droplet and the outward flux of gaseous aluminum. However, some studies (e.g., Ref. [18]) seem to show that the assumption of infinite kinetics for the gas-phase reactions could lead to a serious underprediction of the burning time for small aluminum particles. This uncertainty is increased by the fact Table 2 Values of parameters proposed in Ref. [41] (τc in ms, p in atm, d0 in µm) a
b
c
n
n1
n2
n3
k
1
0.58
0.22
1.9
0.39
0.2
1.57
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419
Fig. 4. Aluminum combustion modeling.
that the burning time for small droplets is less easily measurable. There is a second, more obvious difference between agglomerates and isolated droplets: they do not burn in the same atmosphere. Due to their smaller size, isolated droplets burn close to the surface in an oxidizer-rich environment, while agglomerates burn farther away in an oxidizer-lean environment since much of the available oxidizers, essentially CO2 and H2 O in a propellant atmosphere, has been used for the combustion of smaller droplets before, as illustrated in Fig. 4. Finally, agglomerates can have a heterogeneous composition. They can contain fuel and oxidizer contaminants from the propellant surface as well as excess initial oxide shell mass. Because of all these differences, agglomerates will burn slower than isolated droplets. Recent experimental results obtained by Melcher et al. [25] tend to support these hypothesis. 3.2. Theoretical aspects and validation As mentioned in the introduction, the distributed combustion effect is suspected to be a driving mechanism for acoustic-related instabilities. But there is a lack of theoretical base to prove it. To contribute to the clarification of this uncertainty, Dupays and Vuillot [11], and Dupays [9] studied the mass transfer on the propagation of a plane and smallamplitude acoustic wave in a stagnant two-phase medium. In the first study, the droplet vaporization is supposed to be controlled by the thermal conductivity (droplets vaporize in their vapor) and both phases are in thermal equilibrium in the undisturbed state. In the second study, the process is supposed to be controlled by the diffusion (droplets vaporize in an inert gas) and the gas-droplet mixture is no longer in thermal equilibrium. To represent a combustion chamber atmosphere more closely, the gas temperature can be higher than the droplet temperature. Therefore, the vaporization process produced by the acoustic wave is added to
Fig. 5. Effects of the ratio of liquid to gas temperature on nondimensional coefficients of attenuation and dispersion.
the steady contribution. In both studies, the mass exchange term follows a classical, quasi-steady d2 -law. With the first model, the mass transfer process is found to be either a damping or a driving phenomenon. The governing parameter is the latent heat of vaporization. Its influence is predominant at low acoustic Stokes numbers. These results are well recovered by the computations [11]. With the second model, the author shows similar tendencies but the governing parameter is, in this case, the ratio of the liquid-to-gas temperatures in the undisturbed state (θ ), as displayed in Fig. 5. Results are given for gas and droplet properties describing an aluminized propellant atmosphere. For low Stokes numbers, the coefficient of attenuation α becomes negative as soon as θ is less than 1. On the other hand, if the undisturbed gas-droplet mixture is at a saturated state (θ = 1), mass transfer is a damping phenomenon as
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already shown by Marble [23]. The position and intensity of the maximum of amplification is sensitive to many parameters like the ratio θ , the intensity of the mass transfer and the thermodynamic properties of the droplets and the gas mixture. Even though the generalization of those results to the case of aluminum combustion seems hazardous, these studies give arguments for suspecting distributed combustion to be a rather powerful source of instability. As its effects would be predominant at low frequencies, it could explain the occurrence of instabilities in this frequency range in some large motors burning aluminized propellant. Some of the restrictions of theoretical models must be clearly improved. For instance, the use of an unsteady vaporization model for aluminum droplets instead of the quasi-steady d2 law could give more confidence in the results. The next test cases considered consist of the reactive twophase flow in the TEP geometry. This geometry is useful to test combustion models from the classical d2 -law to better aluminum combustion models, as shown for instance by Daniel [7]. For that purpose, steady computations are sufficient. As no theoretical results are available, a workshop involving three laboratories with three different codes was organized. Participants were IUSTI, SNPE Propulsion and ONERA. The two first participants used an Eulerian approach while ONERA used the Eulerian and Lagrangian solvers of the MSD code. The comparison between these two approaches seems to be very useful because, to some extent, the drawbacks of one approach are the advantages of the other. For the first test case, droplets are supposed to vaporize in their vapor and the mass transfer rate follows the d2 -law. The injected droplet diameter and mass fraction are 30 µm and 18% respectively. The injected velocity is assumed to be at the order of magnitude of the propellant regression rate, namely 10 mm/s. Droplet properties are those of aluminum. The gas and the droplets are injected along the chamber up to the base of the nozzle (see Fig. 1). Pressure at two positions are compared, as well as gas and droplet mass flow rates at the outlet [10]. All of the computations give very similar results. In order to provide more detailled informations, the results are also compared along three grid lines. For instance, Fig. 6 highlights the good agreement between the four computations for the droplet diameter along the grid line i = 50. These results are an encouragement to continue the workshop with a more relevant combustion model. 3.3. Numerical simulations in real motors All the test cases explained are useful to test either the behavior of the combustion model or the ability of the code to deal with propagating phenomena. But the final aim is, of course, to test both aspects in real configurations. A segmented motor, called LP6, prone to parietal vortex shedding (VSP) driven instabilities was chosen for that purpose [20, 21]. To avoid multi-species simulations, droplets were supposed to vaporize and release heat according a d2 -law. The computations were performed with the SIERRA code. Sev-
Fig. 6. Droplet diameter along the grid line i = 50 in the TEP simulations (L stand for Lagrangian).
eral two-phase flow simulations were carried out to study the effects of the Stokes number on the oscillation behavior. As the vortex shedding phenomenon is locked on the first axial mode, the Stokes number was modified via the droplet diameter. Results from two of these computations are displayed in Fig. 7 and compared with a single-phase computation serving as reference. To simulate the production of a condensed phase, droplet combustion was arbitrarily stopped at fixed diameters and, to simplify the study, aluminum droplets and Al2 O3 residues were supposed to have same properties. The first two-phase flow computation involved 30-µm droplets leading to a residue of 3 µm in size (ωτu = 0.001) and the second involved 125-µm droplets leading to a residue of 60 µm in size (ωτu = 0.504). The pressure recording at the head end indicates that oscillation levels are amplified with the smaller droplets and damped with the larger droplets. For the first case, the driving effect induced by the droplet combustion dominates the damping effect resulting from velocity and thermal lags between the gas and the residues. An opposite trend is found for the second case. In this motor, small and large droplets burn into a fairly small portion of the chamber. It can be concluded that, even in a large motor, where the burning-to-residence time ratio is very low, distributed combustion can be a driving mechanism by amplifying flow disturbances in sheared regions near the propellant surface. Unfortunately, there is no theory allowing the prediction of the intensity of this contribution for a given propellant and motor geometry arrangement, to date. The LP6 is a 1/15th simplified subscale motor of the Ariane 5 booster. Compared to the real booster, the head-end face of the third propellant grain is not inhibited and only the VSP develops in the chamber. In the real motor, because of the difference of the regression rate between the inhibitor and the propellant, a protruding annular disk emerges during the burn which generates a second vortex roll called VSO. Recently, reactive two-phase flow computations have been performed in the booster not only to test the code in
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Fig. 7. Vorticity plots and pressure recordings at the head end in the LP6 motor. From left to right: single-phase computation and two-phase computations with 30-µm droplets (residues of 3 µm in size) and 125-µm droplets (residues of 60 µm in size).
this complex configuration but also to highlight the predominant impact of the distributed combustion on the stability of the booster. Details of this study are described in Ref. [22]. As for LP6’s simulations, oscillation levels were drastically increased by adding the droplet combustion. Without droplets, both VSO and VSP coexist but the unsteady behavior seems to be dominated by the VSO. Spectral analysis of the pressure shows a rather wideband spectrum. With burning droplets, oscillation levels are drastically increased and the signal bandwidth is reduced. The combustion near the propellant surface reinforces the VSP and its coupling with the VSO. While LP6’s computations cannot be compared with experimental results, computations in the Ariane 5 booster can be compared with data recorded during static firings at Kourou. First comparisons are very encouraging with respect to the spectral signature and the oscillation levels. That seems to prove the predominant role of the VSPdistributed combustion pair. An open task remains now to use the described aluminum combustion model and to validate the modeling by using simple geometries as the C1xb motor or, more relevant, the LP9 motor, recently designed for studies of the VSP [29].
4. Conclusion All these studies highlight the significant impact of aluminum particles on combustion instabilities. This impact can be shown theoretically or observed experimentally and
numerically. For the Ariane 5 booster, the unsteady behavior seems to be controlled by the interaction between the distributed combustion and the parietal vortex shedding. The merit of the ASSM program is to have permitted the discovery of a phenomenon unsuspected at the beginning of the program and never observed or described elsewhere. However, this result deserves to be confirmed and specified. To achieve this aim, a reliable aluminum combustion model is needed. As the development of a model providing residue size, burning time and heat release in the motor environment is still out of reach, efforts must focus on reliable empirical correlations for burning times and residue size distributions after burnout. Concurrently, a pragmatic and gradual effort of validation is needed.
Acknowledgements This work was performed within the research program ASSM coordinated by ONERA and conducted with the financial support of CNES, Direction des Lanceurs, under the research convention 93/3040. The author express his thanks to P. Kuentzmann who supported and encouraged this synthesis. The author also wishes to acknowledge E. Daniel from IUSTI, J.F. Guéry from SNPE Propulsion, I. Dubois, Y. Fabignon, G. Lavergne, N. Lupoglazoff, M. Prévost, P. Villedieu, F. Vuillot . . . and all his colleagues in the ASSM program for many fruitful discussions.
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