STUDIES ON INTRINSIC FLUID DYNAMICS ISSUES PERTINENT TO HIGH-PERFORMANCE ROCKETS

ISTP-16, 2005, PRAGUE 16 TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA STUDIES ON INTRINSIC FLUID DYNAMICS ISSUES PERTINENT TO HIGH-PERFORMANCE ROCKETS V.R. Sanal Kumar 1, A. Sameen 2, H.D.Kim 3, T.Setoguchi 4, B.N.Raghunandan 5 and S.Raghunathan 6 1-3 Andong National University, South Korea, 4 Saga University, Japan, 5 Indian Institute of Science, India, 6 The Queen s University of Belfast, UK Corresponding author: rsanal@andong.ac.kr, +82-54-820-6210 Keywords: solid rockets, boundary layer, separation, reattachment Abstract Theoretical studies have been carried out to examine the grain geometry dependent driving forces on flow separation and reattachment in high-performance solid rockets. The parametric studies have been carried out in an inert simulator of a solid rocket motor with divergent port using a two-dimensional standard k-omega turbulence model. It was observed that due to the area fraction blocked by the boundary layer displacement thickness the motor axial velocity increased up to a critical distance from the inlet section and further it altered due to the coupled effect of grain geometry and the motor nozzle, which in turn will alter the separation and reattachment/secondary ignition point. 1 Introduction More sophisticated solid rocket motors (SRMs) require greater accuracy in the prediction and control of peak pressure and pressure rise rate during the ignition transient. This allows and justifies the use of small margin of safety for the engine parts, thus result in high motor mass ratio, in addition to the control and guidance requirement of the vehicle. Ignition transient is defined as the time interval between the application of ignition signal and 1 Scientist/Engineer, Propulsion Group, VSSC/ISRO, India 2 Postdoctoral fellow, Polytechnic University of Madrid, Spain 3 Professor and Head, School of Mechanical Engineering 4 Professor and Chairman, Department of Aerospace Engineering 5 Professor, School of Mechanical Engineering 6 Professor and Head, School of Aeronautical Engineering, Bombardier Aerospace Royal Academy Chair, AF AIAA. the instant at which motor attains its equilibrium or designed operating conditions. An excessive pressurization rate (ignition shock) can cause a failure even when the pressure is below the design limit. Note that the solid propellant grain and many of the motor components are viscoelastic in nature, both the chamber pressure and the rate of pressurization being of prime concern to the rocket motor designers. The discernment of the time-dependent pressure loads, that a propellant grain experiences, is possible only if one possesses a detailed knowledge of the unsteady rocket motor internal flow coupled with the structural response of the propellant and case. Characterization of the bulk internal flow field in any solid rocket motor is complex owing to the fact that the flow is unsteady, multidimensional and reacting. Such a level of numerical sophistication is yet to be realized for ignition transient study. Many modern high-performance solid rockets have grains with sudden expansion/divergence of the combustion port combined with high volumetric loading density, high throat to port area ratio (A t /A p > 0.56) and large length-to-diameter ratio (L/D > 10). The use of new grains with higher performance or more environmentally benign propellants will require systematic combined thermoviscoelastic and fluid dynamics analysis, and further redesign to account for higher structural loads and temperatures, and resulting changes in system instabilities. 1 The motivation for the present study emanates from the desire to explain the phenomena or mechanism(s) 1

V. R. Sanal Kumar, A. Sameen, H. D. Kim, T. Setoguchi, B. N. Raghunandan, S. Raghunathan responsible for the ignition pressure spike, pressure-rise rate, instabilities and pressure oscillations often observed during the static tests and the actual flights of certain class of solid rockets with divergent port. Through empirical techniques, in the Indian industry, increasing the port area of the motor has been proposed as one of the remedies for reducing the unusual ignition pressure spike. Unfortunately, this has reduced the propellant loading density and affected the high-performance nature of the rocket motor due to the envelop restriction. Moreover the intrinsic flow physics during the said period is also not well understood. In an attempt to resolve some of these problems and in the light of new findings substantial revision of the existing idea is required [2-15]. One such problem of urgency is to examine the intrinsic fluid dynamics issues pertinent to flow separation and secondary ignition in SRMs with divergent port geometry. In this paper, inert (unignited) simulators of solid rockets are deliberately selected for parametric analytical studies to examine the various fundamental fluid-dynamics processes pertinent to ignition transient without complications arising from the propellant combustion. Having logical precise relevance to the flow separation and secondary ignition at hand [5], the next step through this paper will be to examine the intrinsic flow physics and the motor dynamics augmenting the pressure spike and pressurization rate in high-performance solid rockets with divergent ports. 2 Overview of the Numerical Methodology Numerical simulations have been carried out with the help of a well-established twodimensional standard k-omega turbulence model. This model is an empirical model based on model transport equations for the turbulence kinetic energy and specific dissipation rate. This code solves standard k-omega turbulence equations with shear flow corrections using a coupled second order implicit unsteady formulation. This model uses a control-volume based technique to convert the governing equations to algebraic equations, which can be Fig. 1. A typical grid system in the computational domain. solved numerically. The viscosity is determined from the Sutherland formula. An algebraic grid generation technique is employed to discretize the computational domain. A typical grid system in the computational region (see Fig.1) is selected after the detailed grid refinement exercises. The grids are clustered near the solid walls using suitable stretching functions. In all the cases, thickness of the first grid cell from the solid surfaces is taken as 0.1 mm. The motor geometric variables and material properties are known a priori. Initial wall temperature, inlet total pressure and temperature are specified. At the solid walls a no-slip boundary condition is imposed. At the nozzle exit a parabolic pressure profile is imposed. The Courant-Friedrichs- Lewy number is initially chosen as 3.0 in all of the computations. Ideal gas is selected as the working fluid. The transient mass addition due to propellant burning is deliberately suppressed in this model to examine the turbulent separated flow features discretely in SRMs with divergent ports. The code has successfully validated with the help of benchmark solutions. 3 Results and Discussion In the present numerical simulation SRMs with different divergent ports are examined. Except for the geometric variables, all other parameters are kept constant in the parametric studies. Figure 2 is demonstrating the influence of port geometry on the axial velocity variations of five different SRMs with same initial and boundary conditions. In the first three cases divergent location (X s ) is varied, in the forth case inlet diameter is increased by 50% and in the fifth case divergence angle, α is increased from 45 o to 64 o. All the results reported are anticipated and giving corroborative evidences of the previous experimental/theoretical findings [4-6]. 2

STUDIES ON INTRINSIC FLUID DYNAMICS ISSUES PERTINENT TO HIGH-PERFORMANCE ROCKETS Fig. 2. Velocity variations along the axis of SRMs showing the peak near the transition location (Baseline values: L/D = 4, X s /d =3, A t /A p = 0.375). It can be seen from Fig.2 that, in cases 2, 3 & 5, the axial velocity (centerline) is relatively high near the divergence location. This can be explained with the help of boundary layer theory. Note that owing to the viscous friction, boundary layer will be formed on the walls (before the transition region) and their thickness will increase in the downstream direction to the divergence location. Since the volume of flow must be the same for every section, the decrease in rate of flow near the walls which is due to friction must be compensated by a corresponding increase near the axis. Thus the boundary layer growth occurs under the influence of an accelerated external flow. As a result, at larger distances from the inlet section velocity will be relatively high and the flow will possibly become turbulent; consequently the boundary layer thickness will suddenly increase leading to the sudden increase in the axial velocity due to the rocket motor port area fraction blocked by the boundary layer displacement thickness. This will cause flow separation far downstream of the divergence region. In the fourth case reported herein shown relatively low velocity at the axis due to the high port area compared to the other four cases reported. As stated in the introduction increasing the port area of a solid rocket motor can reduce the unacceptable ignition pressure spike and pressure-rise rate caused due to the gas dynamics of the upstream narrow port, at the expense of propellant loading density. In the first case flow recirculation tendency, leading to reattachment and secondary ignition, was found very less because location of the transition region was near to the head-end at the forfeit of the propellant loading density. When the transition location was fixed at far downstream of the SRM, the tendency of flow separation was found very high. This will lead to the formation of recirculation bubble and flow reattachment. Note that the flow reattachment will favor secondary ignition and that will cause the flow unsteadiness leading to an unacceptable high-pressure rise rate during the ignition transient period of operation of solid rockets. Hence the prudent selection of the transition location within the given envelop, without diluting the high-performance nature of solid rocket motor, is critical for a designer. Fig. 3. Velocity vectors in an inert simulator of a solid rocket motor with non-uniform port. Fig. 4. Contours of Velocity Magnitude (corresponding to Fig. 3). Fig. 5. Contours of Static Pressure (corresponding to Fig. 3). Fig.6. Contours of turbulent kinetic energy (corresponding to Fig. 3). 3

V. R. Sanal Kumar, A. Sameen, H. D. Kim, T. Setoguchi, B. N. Raghunandan, S. Raghunathan Note that separation, secondary ignition, boundary layer thickness and turbulence are familiar concepts: yet they are not easy to define in such a way as to cover the detailed flow characteristics encountered in high-performance rocket motors. Figure 3 shows the velocity vectors in an SRM with divergent port during the early phase of ignition transient. Figures 4-6 are the corresponding contours of velocity magnitude, static pressure and turbulent kinetic energy respectively. In Fig.3 the formation of the recirculation bubble is visible at the transition region. The intrinsic flow features at this region during the formation of the recirculation bubble can be discerned in Figs.4-6. When time advances the flow features will change. These effects can be seen in Figs.7-11. (not the center point!) of the recirculation bubble (see Fig. 9) because within the separation bubble, the mean turbulent intensity rises highly especially near the centre of the bubble due to high mixing and large-scale unsteadiness, and it reduces as one move to the reattachment point and over the boundary layer development region. Note that the secondary ignition occurs inside the initial recirculation bubble. Therefore, the size of the recirculation bubble and the location of the eye are important for further study. It is inferred that by inducing high turbulence level (practically by using igniter nozzle wire screens, or by creating artificial roughness to the grain wall without affecting the ballistics!), the position of transition could be Fig. 7. Contours of Total Pressure at time, t = 0.001 s Fig. 10. Contours of Static Pressure at time, t = 0.002 s Fig. 8. Contours of Velocity Magnitude (corresponding to Fig. 7). Fig.11. Contours of Velocity Magnitude (corresponding to Fig. 10). Fig.9. Contours of Turbulence Intensity (corresponding to Fig. 7). In another attempt the influence of igniter jet turbulence intensity on flow separation has been examined in an SRM with divergent port. A case with high-turbulence intensity shows less possibility of flow separation and reattachment. It was also observed that in all the cases the maximum turbulence intensity falls at the eye brought closer to the entry region, or indeed the laminar layer could be entirely eliminated! Separation is mostly an undesirable phenomenon because it entails large energy losses. Note that near to a solid surface flow velocities are low due to the no-slip condition at the wall. Hence in a region where the piezometric pressure is increasing, there are likely to exist certain streamlines, on which there are points whose total pressure is less than the piezometric pressure a little further downstream. When this happens, these streamlines can only reach this further point if 4

STUDIES ON INTRINSIC FLUID DYNAMICS ISSUES PERTINENT TO HIGH-PERFORMANCE ROCKETS their energy is increased by the action of the shear force exerted by adjacent elements of the flow. This condition is satisfied when τ/ y>0, where τ is the local shear stress and y is the distance measured away from the grain wall. This process of energy conversion by the action of viscosity cannot be maintained indefinitely and, if the flow does not manage to negotiate the region of adverse pressure gradient, a point is reached at which the value of τ and hence of u/ y becomes zero at the surface. Downstream of such a point, which is known as a separation point, the velocity u close to the surface becomes negative and so a region of reverse flow is established. Because of their ability to transfer momentum laterally, turbulent flows are more able than laminar flows to negotiate regions of adverse pressure gradients. Whether or not separation actually takes place, the general effect of the adverse pressure gradient is to give rise to a localized region of slow moving fluid stretching away from the wall. Because of the continuity condition, which can be applied over the whole cross-sectional area, the axial flow velocities must necessarily increase elsewhere in order to compensate for this effect. There is therefore a tendency for flows to become increasingly non-uniform whenever positive axial pressure gradients are encountered. Note that the thickness of a turbulent boundary layer is larger than that of a laminar boundary layer owing to greater energy loss in the former. The development of the wall boundary layer in turbulent flow is more complicated than in wholly laminar flow. Initially it takes the form of a laminar layer, but at some position along the rocket motor port there is a transition to a turbulent layer, where a sudden increase in axial velocity can be discerned in Fig.2 (see Cases 2, 3 & 5). The actual position of transition depends on a number of factors including Reynolds number, surface roughness, and the turbulence level of the igniter jet flow entering the motor port. The separated flow characteristics such as size of the separation bubble, flow redevelopment and heat transfer in the recirculation region are known to depend on Reynolds number upstream of the divergent region and its height. In the SRM cases considered here the reattachment point is found to lie around 1.5-3 times of the divergent height, which is in good agreement with bench mark solutions. In the real motor test cases the exact location of the secondary ignition will possibly be altered from the reattachment point due to the additional influence of the igniter ballistics, ignition delay and the propellant combustion etc.. Note that for pinpointing the exact location of the secondary ignition point one has to consider the intrinsic fluid dynamics and combustion aspects of the rocket motor and its allied igniter. Therefore, in the process of identifying which phenomenon or a combination of phenomena was causing the pressure spike, pressure-rise rate, and pressure oscillations in SRMs with divergent port, the importance of hither-to unexpected features of the internal ballistics of high-performance solid rocket motors has come to the foreground. Through these findings the ballisticians can explore possible remedies (like boundary layer breakers) for eliminating the unacceptable pressure spikes and the pressure oscillations often experienced in high-performance rockets to a certain extent without diluting its highperformance. 4 Concluding Remarks The fact that a separated flow region is formed downstream of a sudden expansion area is easy to appreciate. Rather less obvious is the fact the flow may separate from a surface which has no discontinuities of curvature. The process of separation is associated with large rates of dissipation of mechanical energy and so the avoidance of separation is an important factor in the design of internal flow systems. We concluded that due to the area fraction blocked by the boundary layer displacement thickness the SRMs axial velocity will be increasing up to a critical distance from the inlet section and further it will alter depends upon the port geometry and the nozzle-end effect, which in turn will alter the separation and reattachment/secondary ignition point. We also 5

V. R. Sanal Kumar, A. Sameen, H. D. Kim, T. Setoguchi, B. N. Raghunandan, S. Raghunathan concluded that the location of the reattachment point and/or secondary ignition and the features of the recirculation bubbles are sensitive to the igniter jet turbulence intensity. The implication of the secondary ignition can be quite serious for a practical rocket. Note that an error in pinpointing the secondary ignition point can lead to significant errors in the thrust-transient prediction of SRMs. Further study of these phenomena is warranted. Acknowledgement This work was supported by the Korea Science and Engineering Foundation (KOSEF) under the overseas research program. References [1] Sanal Kumar, V.R., Thermoviscoelastic characterization of a composite solid propellant using tubular test, Journal of Propulsion and Power, Vol.19, No.3, 2003, pp. 397-404. [2] Peretz, A., Kuo, K. K., Caveny, L. H., & Summerfield, M. Starting transient of solid propellant rocket motors with high internal gas velocities, AIAA. Journal, Vol. 11, No. 12, 1973, pp. 1719-1729. [3] Johnston, W.A., A numerical procedure for the analysis of the internal flow in a solid rocket motor during the ignition transient period, AIAA Paper, No. 91-1655, 1991. [4] Sanal Kumar, V. R., Unnikrishnan, C., Kim, H.D., Raghunandan, B. N., and Setoguchi, T., 2004, Simulation of flame spread and turbulent separated flows in solid rockets, AIAA paper, AIAA 2004-3375. [5] Raghunandan, B.N., Sanal Kumar, V.R., Unnikrishnan, C and Sanjeev, C., Flame spread with sudden expansions of ports of solid rockets, Journal of Propulsion and Power, Vol. 17 (1), 2001. [6] Raghunandan, B. N., Madhavan, N. S., Sanjeev, C and Sanal Kumar, V. R., Studies on flame spread with sudden expansions of ports of solid propellant rockets under elevated pressure, Defence Science Journal, Vol. 46, No.5, Nov. 1996, pp 417-423. [7] Manson, D.R., Folkman, S.K., Behring, M.A, Thrust oscillations of the space shuttle solid rocket booster motor during static tests, AIAA paper. No. AIAA 79-1138. [8] Lupoglazoff,N., Vuillot,F., Dupays,J., and Fabignon,Y., Numerical simulation of the unsteady flow inside Ariane 5 P230 SRM booster with burning aluminium particle, 2 nd European Conference on Launcher Technology, Rome, Italy, 2000. [9] Brown, R.S., Dunlup, R., Young, S.W., and Waugh, R.C., Vortex shedding as a source of acoustic energy in segmented solid rockets, Journal of Spacecraft and Rockets 18(4), 1981, 312-319. [10] Salita, M., Modern SRM Ignition Transient Modeling (Part 1): Introduction and Physical Models, AIAA Paper, No. AIAA 2001-3443, 2001. [11] Luke, G. D., Eager. M. A., and Dwyer, H. A., Ignition transient model for large aspect ratio solid rocket motors, AIAA paper, No. AIAA 96-3273. [12] Kubotta, N., Survey of rocket propellant and their combustion characteristics, Progress in Astronautics and Aeronautics, AIAA, Eds: Kuo, K.K and Summerfield, M.., Vol.90, Ch.1, 1982. [13] Caveny, L. H., Kuo, K. K. and Shackelfold, B. W., "Thrust and Ignition Transients of the Space Shuttle Solid Rocket Motor," Journal of Spacecraft and Rockets, Vol. 17, No. 6, pp. 489-494, November - December, 1980. [14] Fabignon, Y., Dupays, J., Avalon. G., Vuillot, F., Lupoglazoff, N., Casalis, G and Prevost, M, Instabilities and pressure oscillations in solid rocket motors, Aerospace Science and Technology, 7, 2003, 191-200. [15] Sanal Kumar, V. R., Kim, H.D., Raghunandan, B. N., Sameen. A., Setoguchi, T., and Raghunathan, S, A Phenomenological Introduction of Fluid-throat in High-Velocity Transient Motors, 41st AIAA/ ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Arizona, USA, 10-13 July 2005, AIAA Paper No. AIAA 2005-4147. 6