嶋田 徹

This paper describes the development of a numerical simulation system, "Advanced Computer Science on Solid-Rocket-Motor (SRM) Internal Ballistics (ACSSIB)". The objectives of this technology development consist of development of composite-propellant slurry casting-flow simulation, development of local burning-rate correlation with the slurry flow field characteristics, and development of the internal ballistics, i.e., combustion pressure time history, prediction. The ACSSIB have proved itself a promising technology for improvement of SRM reliability and drawn the following conclusions. (1) Hump effect of solid rocket motor combustion is verified by small-scaled motor firing tests and strand burner measurements. (2) Form microscopic observation by microfocus X-ray CT and data deduction by image processing, it is verified that there is a significant correlation between the orientation of coarse AP particles and the burning rate. (3) Development of propellant slurry casting simulation has been successfully conducted. From the casting simulations, it is verified that there is a significant correlation between the angle of the burning direction against the isochrone surface tangent (in plane with the normal) and the burning rate. (4) Development of simulation technique for internal ballistics has been successfully conducted. Simulation results are in good agreement with static firing test results of real motors. Finally, several future technical challenges are identified. Copyright ©2010 by the International Astronautical Federation. All rights reserved.

Discussions are made on the localized erosion of charring ablators used in the expanding part of solid rocket motor nozzles. Such erosion pattern is sometimes seen over liner surface downstream the throat inserts after static firing tests. The major characteristic of the localized erosion is that its shape is groove-like, its erosion amount is very large compared to surrounding region, and its location of occurrence is not simply related to the upstream configuration, such as axial slots or fins of the solid propellant grain. The objective here is to consider the growth mechanism of the localized erosion by reviewing facts reported in the literature on the charring ablators, ablation patterns, and vortical three-dimensional flows in nozzles.

In order to understand the mechanism of the large roll-torque generation in the operating solid rocket motor with axially-slotted propellant grain and the narrow nozzle submergence region, fully three-dimensional Navier-Stokes numerical simulations have been conducted. The several grain configurations are computed and it is found that there are at least two groups of quasi-steady state solutions, one shows large roll torque, and the other shows small one. From the present simulation results, it is observed that the large roll torque is generated due to the interaction of the circling flow around the nozzle inlet with the slot jet exhausting out from the slot end into the aft-end cavity. Although the roll torque evaluated from the computation is one-order higher than that observed in the real fight, the present simulation serves the insight into the qualitative mechanism of the real roll torque generation.

The acoustic combustion instability of solid rocket motor (SRM) is investigated by computational fluid dynamics and compared with theoretical results. The quasi-one-dimensional (Q1D) Euler equations for the unsteady flow inside the combustion chamber and the equation for the thermal conduction inside the solid propellant are simultaneously solved with a quasi-steady flame model near the burning surface. The Runge-Kutta Discontinuous Galerkin (RKDG) method is used as the platform for the flow simulation and the numerical accuracy study is carried out. The conventional second-order Finite Volume Method is verified to give accurate results by the comparison with the third-order RKDG method. The growth rate versus the nozzle entrance Mach number for the attenuation case shows good agreement with the linear theory. For the growing case, it is shown that agreement is good for small Mach numbers. The results of the stability limit show good agreement with the theory for low Mach number. For higher Mach numbers, the stability-limit curve of the present simulation show the dependency on the imaginary part of the response function. Extension to the axisymmetric problem is straightforward and preliminary results have been obtained. © 2007 by the authors.

This paper describes our experiment and computation of roll torque caused by the internal flow of star-perforated solid rocket motor. The roll torque induced by motor internal flow is known from the early days but is not sufficiently understood among rocket scientists in academia and industry. In the background, there is complexity of a three-dimensional vortical flow in combustion chambers. The roll torque occurring in the launch of the Mu-V rocket was reported by the author in the previous paper (Shimada, IAC-06-C4.3.02, Oct.2006), in which the relation with the internal three-dimensional flow was considered. The roll torque was observed in every seven launches during the early operation period of M-14 motor and it was one-order high compared with that of the aerodynamic and/or of thrust misalignment. The cause of the roll torque was discussed on the possibility of Type-I of Knauber's classification, namely the combustion instability, but it was concluded that the possibility of Type-I was small because the mass efflux from the burning surface was relatively large in M-14 and at the same time, no strong sign of combustion instability existed. In this paper, first, the result of a static firing test of a small motor (diameter of 500mm, burning period of 30 seconds, combustion pressure of about 5 MPa, the maximum thrust of about 50 kN, AP/HTPB/Al+MgAl propellant) is described. In this experiment, the swirling component of exhaust plume and the roll torque acting on the motor have been measured. The swirling flow is measured by the lift force acting on the vane which is installed right downstream the nozzle exit. The result shows the swirling has increased for several seconds after the ignition and attenuated gradually after that. On the other hand, roll torque has been evaluated from the balances of the force and the moment among the gravitational force, the suspension force from the test stand, and the two peripheral loads measured at diametrically either side (right and left) of the motor. The results show that the maximum torque has been about 28 N-m at around several seconds after the ignition in the opposite direction of the swirling flow. The evaluated dimensionless torque coefficient is rather a big value of 1.1 × 10-3. Next, discussion is made on whether the roll torque of M-14 is caused by Type-II, i.e., the internal swirling flow due to the grain shape. The M-14 has seven axial slots in each two grain segments. Because the mass efflux from the slots is larger than the remaining parts of the circumference of the cross section, a jet will flow out from each slot into the central port region. At least two possibilities can be considered; one is symmetric and the other is asymmetric secondary flow field in the cross section. It is only the symmetric case that no torque is generated; in which seven pairs of longitudinal vortices should steadily exist. On the other hand, if the symmetric flow is unstable, these jets might merge into one swirling flow which is supposed to be stabler than the symmetric flow. In this paper verification is sought concerning this supposition employing computational fluid dynamics simulations of the three-dimensional internal flow.

Simulated solid propellant slurry containing lead sphere tracers is experimentally cast into a double circular cylinder container. During the casting, the temperature and the pressure environment has been mimicked to an actual composite solid propellant casting of solid rocket motors. X-rays are projected on to the slurry flow from two directions and penetration images are recorded by a flat panel detector and an X-ray image intensifier. By suppressing the mutual interference of the X-rays, the two-directional X-ray photography has been successfully conducted. Using the time series data of the X-ray images from the two directions, the identification of each tracer particle in space and time has been done and their three-dimensional paths have been computed. From these procedures, the flow field or the velocity field inside the slurry flow, which is invisible usually, has been estimated. © 2007 American Institute of Physics.

X 線撮影と画像解析を用いて,鉛玉トレーサを含む模擬固体推進薬スラリの二重円筒内部三次元流れ場を可視化した. X 線を互いに直角な二方向から供試体に投影し,透過X 線をフラットパネル検知器とX 線イメージインテンシファイアを用いてビデオに記録した. X 線の相互干渉を抑制することによって,二方向同時撮影が良好に行われた.二方向X 線像の時系列画像データから各トレーサ粒子の空間及び時間的な識別を行い,更に較正用マーカー情報を用いた座標変換を行うことで,トレーサ粒子の刻々の三次元実座標を算出した.これらの手順によって,通常では見ることのできないスラリ流内部の流れ場を可視化し,さらに速度場の推算を行った.

Three-dimensional, single-phase (equilibrium two-phase) flows inside a solid rocket motor at three burn-back grain configurations are studied by computational fluid dynamics (CFD) analyses of the Reynolds-averaged Navier-Stokes equations (RANS). The major concern is the relationship between the flow field and the circumferentially periodic erosion pattern arising in the inlet region of the nozzle, which will be of help for the better understanding of the surface recession mechanism. Obtained results for the first two cases show that, since the mass flux of slot phase is notably large compared with that of fin phase, a remarkable inter-phase gap in the amount of convective heating appears either in the throat or the exit cone. The peak heating rate appears, commonly to all cases, azimuthally in the slot phase and axially at the expansion ratio of about 0.9 upstream of the throat. The flow, which comes out of a slot into a fin base region, spreads toward the fin central part under the influence of the pressure gradient in the circumferential direction, and forms vortical flow tube of opposite rotation mutually with the flow which swirls out of the next slot. At fin phase, since proportionality relation is accepted between the total mass recession per unit area and the total convective heat mass transfer per unit area, it is considered that corrosion is dominant ablation mechanism. On the other hand, in slot phase, there exists surface recession which cannot be explained only by corrosion around a nozzle inlet nose. This surface recession has a very high possibility of having occurred by abrasion by the aluminum/alumina particles contained in the flow which comes out of axial slot of grain and collides with the TPS surface. It is expected that periodic erosion pattern which synchronized with axial slots observed after static-firing test is the result of such a mechanism ruling over. In both the throat and the exit cone, it is thought irrespective of a phase that the effect of mechanical erosion is very small and corrosion or so-called "chemical attack" is the dominant mechanism of surface recession.

There are unique flow-induced phenomena about solid rocket motors (SRM) whose mechanisms have not been fully understood. The generation of roll torque acting on SRM and peculiar ablation patterns of a nozzle liner surface are taken as examples. By reviewing the open literature, it is found that very few systematic prediction methods exist on these phenomena. Roll torque has been observed during the burning of the first-stage motor of the Mu-V rocket in all six flights since 1997. The cause of the roll torque is sought by evaluating the acoustic effect with mass efflux and combustion response, but sufficiently consistent results have not been obtained. The ablation pattern called striation and cross-hatching has been observed on many specimens in the ablation tests, on reentry , objects after recovery, and on the inner surface of SRM nozzle exit cone. The mechanism of the occurrence of these phenomena is discussed. The existence of the longitudinal vortices is essential for the striation, but for the cross-hatching, whether or not it is an indispensable condition is a pending issue.