Pressure Oscillations In Solid Rocket Motors: Effect of Nozzle Cavity

Transcription

1 Aerotecnica Missili & Spazio, The Journal of Aerospace Science, Technology and Systems Pressure Oscillations In Solid Rocket Motors: Effect of Nozzle Cavity F. Stella a, F. Paglia b a Sapienza - Università di Roma Dipartimento di Meccanica e Aeronautica b Sapienza - Università di Roma Dipartimento di Meccanica e Aeronautica Affiliation: AVIO Spa - Colleferro (RM) Abstract A numerical study of pressure oscillation generated in Solid Rocket Motors (SRM) is presented. As reference problem, the experiment conducted by Anthoine et al. [1] in cold flow has been adopted. Attention is focused on the effect of the cavity located in the vicinity of the nozzle on the flow acoustic coupling and therefore on the consequent pressure oscillations. A parametric study with different cavity volumes has been conducted assuming the flow to be axi-symmetric. Results show that the cavity volume plays an important role in the flow-acoustic coupling mechanism. Indeed, the maximum pressure oscillation magnitude is observed to be highly dependent on the cavity volume and a close to linear dependence of the maximum excited mode against the volume of the cavity is documented. Satisfactory comparisons with experimental data available on the same geometrical configuration are also presented and discussed. 1. Introduction Periodic vortex shedding as a source of acoustic oscillations in Solid Rocket Motors (SRM) has attracted the attention of several researchers during the last decade. The reason for this interest is an unpredicted oscillatory behavior observed in several motors during test firing or during flight. Oscillatory behavior has been observed in the Space Shuttle RSRM (Redesigned SRM), in the Titan IV SRMU (SRM Upgrade) and more recently in the Ariane V P230 [2,3]. These oscillations have been attributed to a periodic vortex shedding due to the presence of frontal thermal protections (PTF). When the vortex-shedding frequency is the same as the natural frequency of the chamber, the pressure oscillation reaches a maximum and this can reduce the overall performances and usability of the launcher. Several experimental and numerical studies in cold-flow [4, 5] have demonstrated the role of the thermal protection in this process. In these experiments, the vortex shedding is produced at the obstacle and pressure oscillations reach large magnitude when the vortex shedding frequency is close to the frequency of one acoustic mode of the duct. The basic mechanism of this process can be described as a feedback loop consisting of the following steps: c AIDAA, Associazione Italiana di Aeronautica e Astronautica the hydrodynamic instability of the shear layer region that develops near a sudden expansion of the geometric configuration (such as the thermal protection); the roll - up and advection of a vortex structure; the impingement of the vortex on a surface located downstream (such as the nozzle head); acoustic propagation from the downstream source; the acoustical triggering and generation of a new vortex structure. In the past, research has been mainly focused on the mechanisms which produce the vortex oscillations, in many cases with the goal of avoiding this phenomenon. Although avoiding the generation of pressure oscillations is probably an optimal solution, in many engineering application a large reduction of the amplitude of oscillation would be considered a satisfactory goal. Anthoine et al. [1] conducted a study of pressure oscillations reduction in a cold flow (i.e. non-reactive flow) problem. In their paper the authors indicate that the level of pressure oscillation is an increasing function of the volume of the cavity. Unfortunately an optimized design of such cavity is not possible in 31

2 32 F. Stella, F. Paglia SRM. In fact the nozzle cavity is usually built to allow directional control by means of nozzle inclination, moreover the cavity volume and shape changes with time since the solid propellant stored therein burns during the service life of the motor. For these reasons the cavity shape cannot be designed as an Helmholtz resonator and then the motor cannot benefit from the dissipative effect of such device. As matter of fact the choice of the geometry was conducted with the idea to reproduce the cavity of P230 SRM of Ariane V (geometry C in the present paper). In their paper Anthoine et al. [1] presented experimental and numerical results in non-reactive flow. Comparison of the numerical results with the experimental tests show that globally the frequencies are well simulated by the numerical code despite the fact that the pressure oscillation levels are largely overestimated; in fact oscillation levels obtained from the numerical simulations were one order of magnitude larger than the experimental ones. The authors explained this quite large difference in terms of a three-dimensional effect resulting during the vortex ring travel from the inhibitors to the nozzle head that becomes unstable in the azimuthal direction and gives an incoherent acoustic pressure feedback to the inhibitors. This explanation is not very satisfactory from a physical point of view. In account of the transport velocity, the traveling time of the vortex ring from the obstacle to the nozzle head is around s. This time seems too small for a sufficient growth of the azimuthal disturbance, starting from the small disturbances that can be introduced from axialsymmetric geometrical condition. Moreover, Anthoine et al. [1] did not present any validation of the numerical results, but only a comparison with experiments showing nearly one order of magnitude difference on oscillation levels, clearly indicating the limits of the numerical simulations presented. For these reasons, there is a need for a more detailed investigation in order to give a clearer picture of the phenomenon that is being considered. The main goal of the present paper is to analyze and discuss the effect of the cavity volume near the submerged nozzle on the pressure oscillation levels by means of axi-symmetric numerical simulations. A parametric study with different cavity volumes will be conducted and compared with available experimental and numerical data [1]. The validity of axial-symmetric flow conditions will be a-posteriori evaluated. 2. Physical Problem The problem under study intends to reproduce the phenomenon of pressure oscillations typical of SRM. The physical domain is sketched in figure 1 and can be described as a long circular duct with a submerged nozzle placed at one end. A large cavity is present near the inlet section of the nozzle. An obstacle in the form of one annular ring is placed inside the duct upstream of the nozzle, in order to simulate the presence of thermal protection protrusion, that is the main source of pressure oscillations in SRM. Since axi-symmetric flow conditions have been assumed, all numerical simulations will be conducted under this hypothesis. One of the goals of the present work is to compare and validate results against those found by Anthoine et al. [1], for this reason both the geometry and the boundary conditions are the same as those used in that paper. The computational domain is sketched in figure 2, showing the geometrical dimensions (given in mm). According to [1], walls are considered adiabatic and air at 285 K is injected at uniform velocity axially through the inlet section of the computational domain (figure 3) imposing a constant mass flow rate of 0.3 kg/s. The absolute outlet pressure at the nozzle exit is 10 kpa. The bottom part of the computational domain is the axis of symmetry while the other boundaries (i.e. upper part of the computational domain, the obstacle, the cavity and the nozzle) are defined as non-slip walls at a temperature of 285 K. Although the experiments have been conducted using a non-reactive flow (usually called cold flow), it can reproduce and explain the acoustic interaction between vortices generated by the annular ring and the nozzle cavity. 3. Mathematical Formulation 3.1. Numerical Simulations The commercial CFD code FLUENT has been used for all the numerical simulations. FLUENT uses a control-volume-based technique for discretization and numerical solution of field equations. This approach has the merit, among others, of ensuring that the discretized forms preserve the conservation properties of the partial differential equations. A segregated algorithm has been chosen to solve the conservation equations. Using this approach, the equations are solved sequentially, but since they are nonlinear and the phenomenon unsteady, several iterations of the solution loop must be performed before a converged solution is obtained for each time step. Turbulence has been modeled using a Monotonically Integrated Large Eddie Simulation (MILES) approach [6, 7]. The convective terms in the equations for momentum and energy are discretized using a second-order upwind scheme. The PISO algorithm has been used to achieve the pressurevelocity coupling and an implicit discretization of time derivatives has been also chosen. For sake of conciseness we do not report further details of the numerical code and discrete formulation, the reader can obtain further information from the FLUENT user s manual [8]

3 Pressure Oscillations In Solid Rocket Motors: Effect of Nozzle Cavity Data Monitoring Data monitoring is a very delicate issue for obtaining a good estimation in terms of spectrum frequencies and amplitudes. Due to the complexity of the phenomenon under study, a long initial transient has been simulated. In this initial phase, the mechanism of feedback is built-up in the computational domain. After this initial transient, the data acquisition is started. Due to the complex oscillatory behavior of the flow, data monitoring is conducted for a time window longer than 1.31s and 131,072 samples were used during data processing. Pressure and velocity components have been acquired at different control points placed in the computational domain. In particular, one of these points has been chosen near the inlet section (x = 11.5 mm; y = 38 mm) to match the sampling point used by Anthoine et al. [1] (point A in figure 4). All the results presented are based on data acquisition at this point. The sampling frequency of the numerical simulation is 100 khz and simulations of the statistically stationary phase have been carried out for nearly two seconds of physical time (this requires nearly two weeks of numerical simulation on a P4). The study of the frequency response of the pressure oscillation data is based on a spectral analysis conducted by means of Fast Fourier Transform. The amplitude of pressure oscillations is usually evaluated by means of: P RMS (k) = P(k) 2 In the following of the paper, in order to match the same parameter adopted by Anthoine et al. [1], results will be presented in terms of P RMS /P Mean. 4. Validation of numerical results A validation of numerical set up has been conducted by means of a mesh sensitivity analysis and a comparison with available experimental and numerical results [1] is also carried out to assess the reliability of the achieved results Mesh sensitivity analysis Four different computational meshes have been employed for grid validation, ranging from 3950 (mesh M0) up to mesh points (mesh M3). Since one of the most important phenomenon encountered is the instability of the shear layer produced by the obstacle, the mesh size in the y direction (orthogonal to the tip) in proximity of the obstacle (figure 5) is a good indicator of the quality of the mesh adopted. The typical mesh size near the tip and the total number of mesh points, for the different meshes tested, are given in table 1. Pressure spectra which will be presented in the following section, show that the frequency and normalized amplitude (hereafter denoted as P RMS /P Mean ) Table 1 Main data for mesh sensitivity analysis Mesh Cells s (mm) M M M M of the most excited modes can be clearly determined. Therefore, the sensitivity analysis has been accomplished by comparing with each other the values of the most excited frequencies and of their amplitude P RMS /P Mean obtained with the different computation meshes. Tables 2 and 3 give a complete view of the results obtained for the first four modes. From the first view, it is clear that mesh M0 and M1 do not satisfactory predict the amplitude of pressure oscillations and, to a less extent the corresponding frequency values. On the contrary mesh M2 and M3 give accurate values for these quantities. It worth noting that for the first peak, that is the most important from an engineering point of view, mesh M2 and M3 give a difference of 0.5% in the frequency values and a difference of 2.3% on the amplitude. On the basis of these results and also considering the limitations due to computational costs, mesh M2 has been chosen for the numerical simulations presented in this paper. Table 2 Mesh sensitivity: comparison of frequenty peaks Mesh I Peak II Peak III Peak IV Peak (Hz) (Hz) (Hz) (Hz) M M M M Table 3 Mesh sensitivity: comparison of P RMS /P mean Mesh I Peak II Peak III Peak IV Peak M M M M Comparison with experimental data As mentioned above, the present numerical results, obtained using the mesh M2, have been compared with published experimental and numerical data [1]. A detailed assessment is given in Table 4. The first, and usually most important peak, is at 402 Hz and differs by about 2% from the experimental one at 410 Hz.

4 34 F. Stella, F. Paglia Very good agreement is obtained for the frequencies of the other peaks. It should be noted that these frequencies were not explicitly reported by Anthoine et al. [1] but have been extracted from the graphical data presented in their paper. The computed frequency values obtained by [1] are also in good agreement with their experimental results (Table 4). However this is not the case for the relative pressure fluctuation reported in Table 5. It is shown that the numerical predictions of Anthoine et al. [1] differ from the experimental ones by an order of magnitude. On the contrary, there is a remarkably good agreement between the numerical P RMS /P Mean provided by the present simulations and the experimental results. A comparison of the relative pressure fluctuation at the first four peaks with experimental results of [1] (Table 5) shows also that in correspondence of the first peak, at 410 Hz, the present numerical results overestimate, by about 13%, the experimental ones. This difference decreases to 11% using data obtained from mesh M3. Since the differences between the numerical and the experimental data are small, the present results indicate that the flow is adequately described by an axis-symmetric model. Thus, the suggestion that three-dimensional effects were responsible for poor numerical predictions in evaluating the magnitude of the pressure fluctuations seems not to be correct. Finally, it has to be pointed out that not only the peaks but also the overall spectra which will be presented in the next section compares well with the experimental ones obtained by Anthoine et al. [1] Table 4 Obtained frequencies: comparison with experimental and numerical data (data are extracted from the pictures presented in [1] ) Peak Present Exp. [1] Num. [1] (Hz) (Hz) (Hz) I II III IV Table 5 P RMS /P mean : comparison with experimental and numerical data (data are extracted from the pictures presented in [1]) Peak Present Exp. [1] Num. [1] I II III IV The nozzle cavity effect As previously explained the main goal of the present paper is to investigate the important role that the nozzle cavity volume has on the pressure fluctuations level in SRM. In order to study this problem, the flow in four different nozzle cavity geometries has been numerically simulated. The different geometries are sketched in figure 6. Nozzle C is the submerged nozzle corresponding to the reference cavity and corresponds to the one adopted by Anthoine et al. [1]. For the nozzle B the cavity volume is reduced by 50% while in the nozzle D the cavity volume is increased by 50%. The nozzle A is the convergent - divergent section without a cavity and, under the assumption that the cavity volume is responsible for the amplification of pressure fluctuation, the best result is obviously forecasted for this geometry. In order to see the maximum effect, the signal obtained with the nominal geometry (C) has been compared with the one obtained without a cavity (A). Figures 7 and 9 indicate that a quite impressive reduction, of approximately two orders of magnitude, is obtained in the case of the first mode (410 Hz). Moreover, observing the same figures it is clear that there is a strong alteration of the oscillation behavior. For configuration A, the most severe oscillation mode is no longer at the resonant frequency of the combustion chamber (410 Hz) but is at the much higher frequency of 1013 Hz. This frequency is possibly related to the transport time of flow disturbances in the main stream starting from the obstacle and reaching the nozzle head. A first simple evaluation of this phenomenon may be made taking in account the velocity downstream the obstacle on the symmetry axis (v = 73 m/s) and of the distance between the obstacle and the nozzle head (l = 71mm). The associate frequency (f = v/l) is 1028 Hz, that is very close to the one found in the numerical simulations. There is a significant benefit in analysing the results also from the point of view of the maximum relative amplitude of oscillations. In configuration A the maximum amplitude, that is relative to the frequency of 1013 Hz, is (table 6), that is in any case smaller than the value of obtained in the case C for the most excited oscillation mode at 402 Hz. In terms of applications to the SRM technology a double benefit is observed: first the reduction of the amplitude of oscillations and second an increase of the frequency of oscillation, a change that is usually better tolerated by payloads. Unfortunately, due to constructive reasons not in all cases it is possible to avoid or reduce the presence of this cavity in SRM. The results obtained with geometry B (smaller cavity) and D (larger cavity) have been compared with those obtained with geometry C. Figures 8, 9 and 10 show that the behaviour in terms of frequencies of oscillation for cavity B and D is quite similar to that of

5 Pressure Oscillations In Solid Rocket Motors: Effect of Nozzle Cavity 35 Table 6 Nozzle cavity volume and amplitude of maximum energetic mode Case Cavity vol. Freq. P RMS /P mean (m 3 ) (Hz) A B C D cavity C even if the values of frequencies are slightly changed (Table 6). In terms of amplitude of oscillations the effect is more relevant. A reduction of the original cavity volume, cavity C, to around half of the value, cavity B, leads to a reduction in the maximum pressure by a factor of around 1.8. On the other hand, when the original cavity volume is doubled (cavity D) the maximum amplitude of pressure fluctuations is increased by a factor of around 2.1% (Table 6). Therefore the amplitude of the most energetic pressure oscillation mode is clearly a function of the cavity volume. This dependence seems to be nearly linear as shown in figure 11. It is worth giving a short description of the complex dynamic of the vortex structures in the core of the SMR and inside the nozzle cavity, since this represents the driving mechanism for the observed amplification of the pressure oscillation. The process begins with a vortex (P), see figure 12a, impinging on the nozzle head and splitting into two separate vortices (P1 and P2 in figure 12b). The interaction of vortex P with the boundary layer on the solid wall produces secondary, counter-rotating, vorticity (S). This is in agreement with what is observed by many authors [9 11] in the well known case of the interaction between a vortex ring with a plane wall. Subsequently, the vortex P2 merges with vortex L1, in this way P2 feeds L1 compensating viscous dissipation, so a constant intensity of L1 is maintained on the average. The counter-rotating vorticity S is driven by the induced velocity of L1 to loop around L1 itself. This produces a clearly visible up-and-down movement of the center of L1. An example of an instantaneous vorticity snapshots supporting the author s interpretation is reported in Fig. 13 where some of the main structures sketched in Fig. 12 can be detected. On the basis of the analysis of consecutive frames, an approximate evaluation of the period associated with this movement has been also made, resulting in an approximate time period of s, corresponding to a frequency of 417 Hz, that is very close to the value of 402 Hz found using spectral analysis. 6. Conclusions The effect of the nozzle cavity volume on the pressure amplitude oscillations has been numerically studied using a general-purpose CFD code. The present axi-symmetric numerical approach has been validated against experimental results. The discrepancy between the previous available numerical calculation and experimental results, has been decreased from an overestimate of one order of magnitude to about 13%. Thus the previously held belief that three-dimensional effects were responsible for the difference is, in fact, not correct. Moreover the precision found in the numerical prediction indicates the high level of accuracy that has been obtained using a proper numerical approach together with a very fine computational mesh. The importance of the cavity around the nozzle has been demonstrated by showing a linear dependence of the amplitude of the maximum excited mode on the volume of the cavity. This has important implications for further development in SRM technology. Finally, the basic mechanism of mass injection and expulsion in and from the nozzle cavity has been evidenced and the main dynamics have been correlated with the results obtained from the spectral analysis. REFERENCES 1. J. Anthoine, J.M. Buchlin, J.F. Guery : Effect of Nozzle Cavity on Resonance in Large SRM: Numerical Simulations, Journal of Propulsion and Power 19 (3) , K.W. Dotson, S. Koshigoe, K.K. Pace : Vortex shedding in large solid rocket motor without inhibitors at the segment interfaces, Journal of Propulsion and Power 13 (2) , S.Scippa, P.Pascal and F. Zainer : Ariane - 5 MPS: Chamber pressure oscillations full scale firing results analysis and further studies, AIAA Paper , F. Culick, K. Magiawala: Excitation of acoustic modes in a chamber by vortex shedding, Journal Sound and Vibration 64 (3) , R. Dunlap, R.S. Brown: Exploratory experiments on acoustic oscillation drive by periodic vortex shedding, AIAA Journal 19 (3) , C. Fureby and F.F. Grinstein: Monotonically Integrated Large Eddy Simulation of free shear flows, AIAA Journal 37, 544, F.F. Gristen., C. Fureby: Recent progress on MILES for high Reynolds number flows, Journal of Fluid Engineering, , Fluent v documentation. Fluent.Inc. 9. T.L.Doligaski, J.D.A. Walker : The boundary layer induced by a convected two-dimensional vortex, Journal Fluid Mech. 139, J.D.A. Walker, C. R. Smith, A.W. Cerra, T.L. Doligaski: The impact of a vortex ring on a wall, Journal of Fluid Mech , P. Orlandi, R. Verzicco: Vortex rings impinging on walls: axisymmetric and three dimensional simulations, Journal of Fluid Mech. 256, , 1993.

6 36 F. Stella, F. Paglia Figure 1. Physical problem Figure 2. Adopted geometry (R1 = 13 mm, R2 = 15 mm) Figure 3. Boundary conditions adopted for the numerical simulations

7 Pressure Oscillations In Solid Rocket Motors: Effect of Nozzle Cavity 37 Figure 4. Sampling point A Figure 5. Mesh size near the obstacle (mesh M2) Figure 6. Different nozzle geometries studied numerically. Cavity C is the nominal geometry

8 38 F. Stella, F. Paglia Figure 7. Pressure spectrum obtained with cavity A Figure 8. Pressure spectrum obtained with cavity B

9 Pressure Oscillations In Solid Rocket Motors: Effect of Nozzle Cavity 39 Figure 9. Pressure spectrum obtained with cavity C Figure 10. Pressure spectrum obtained with cavity D

10 40 F. Stella, F. Paglia Figure 11. Amplitude of the most energetic modes as a function of nozzle cavity volume

11 Pressure Oscillations In Solid Rocket Motors: Effect of Nozzle Cavity 41 Figure 12. Sketch of the interaction between the different vortex structures in the nozzle cavity Figure 13. Istantaneous contour plot of the vorticity magnitude showing some of the relevant structures produced from the interaction of the flow with the nozzle cavity.