WANG Jian-ru，HE Guo-qiang，XU Tuan-wei，LI Jiang，LI Qiang

(College of Astronautics，Northwestern Polytechnical University，Xi’an 710072，China)

0 Introduction

SSRM has the excellent technology characteristics of simple structure and easy to realize large thrust.Therefore，SSRM is able to effectively realize the thrust of the magnitude of 100 tons，even kiloton large solid motor in space launch technology field.However，the unique design structure characteristics of SSRM combustion chamber lead to big difference in ablation of insulation between SSRM and common SRM.Especially，the insulation ablation is more necessary in the afterward-dome.In order to meet the demand of internal ballistic design，usually in the forward end of posterior segment grain adiabatic inhibitor is laid out to maintain the constant mass flow rate.However，as the burning area withdrawing，the existence of adiabatic inhibitor make it inevitable that the adiabatic inhibitor cann＇t burn out with the propellant at the same time，but often lag behind the propellant to a certain height，which make the upstream gas form shrinkage and expansion flow pattern.

The motor has two main forms of abnormal ablation insulation caused by two phase flow.The First is mechanical damage effect on internal insulation in a short period of time，with local concentration and high velocity，for example，ablation under overload condition or ablation caused by sudden acceleration of hot gas in combustion chamber，and the second，with local concentration and low velocity，is cumulative effect of heat increment for a period of time，for example，insulation erosion is aggravated by particle impingement in combustion chamber.In SSRM，the existence of adiabatic inhibitor can accelerate centre area flow velocity in combustion chamber，thus leading to various aggravation of ablation insulation downstream of combustion chamber，belonging to the first abnormal erosion condition mentioned above.

Studies on SSRM are mainly concentrated on the internal flow simulations abroad，but are just at the initial stage in China，and there are no special reports on afterward-dome ablation resulted from end-surface adiabatic inhibitor.With the development of technology on large SSRM，it is crucial to carry out SSRM combustion flow-ablative coupling research work.

For a typical SSRM，this paper deeply analyze several influence factors of sectional adiabatic inhibitor ring on afterward-dome insulation during the combustion process.Through numerical simulation，combining with the existed experimental data，the causes of afterward-dome ablation are revealed.Finally，some design measures and suggestions are put forward to effectively suppress the afterwarddome ablation insulation in SSRMs.

1 Analysis of afterward-dome ablation phenomenon for a typical SSRM

As shown in Fig.1，in a typical two segmented solid rocket motor combustion chamber，adiabaticinhibitor which is arranged on the front end surface of the second grain is employed to limit end burning.The adiabatic inhibitor contour，before and after firing test，is shown in Fig.2.The most severe afterward-dome ablation area，540 mm in diameter，is almost the same diameter as the residual inhibition ring.In order to analyze the extent of insulation ablation，comparison analysis for test data is made between segmented combustion chamber and integral combustion chamber，the data shown in Table 1.With relatively low working pressure and same working time，also the same submerged nozzle structure，the same afterward-dome surface and the same grain conditions，the insulation ablation volume increase 1.6 times due to the existence of residual adiabatic inhibitor.And the most serious ablation area is the same inner diameter as the residual inhibition ring.

Fig.1 A typical structure of the segmented solid rocket motor

Fig.2 Ablation condition of adiabatic inhibitor

Table 1 Data comparison on afterward-dome ablation insulation between segmented combustion chamber and integral combustion chamber

2 Numerical simulations on afterward-dome ablation for a typical SSRM

2.1 Governing equations

The flow process in combustion chamber is a typical process of two-phase flow，and in recent years，the Euler-Lagrangian method is generally used.In order to achieve the two-phase coupling calculation，gas phase governing equation is solved in the Euler coordinates，and droplet tracking is solved in the Lagrangian coordinates.

2.1.1 Governing equations of gas phase

Gas mass conservation equation:

Considering the effect of discrete phase，the momentum conservation equations of gas phase can be written as follows:

Considering the effect of discrete phase，the energy conservation equation for gas phase can be written as:

where，I is the specific internal energy;qprepresents energy source caused by particles interacting;J→is the heat flux，including heat conduction and enthalpy diffusion.

2.1.2 Turbulence model

The standard k-ε turbulence model is used in this paper，which is a semi-empirical formula based on turbulent kinetic energy and dissipation ratio，and also is a kind of high Re number turbulence model.In a small amount of calculation case，it could ensure the calculation accuracy，and it is widely used.In numerical calculation，the two-order precision Roe format is employed to discretize the spatial derivative.In the time direction，the first-order precision stepping scheme is applied.

2.1.3 Governing equations for discrete phase

At present，most of the two-phase flow using DDM(Discreet Droplet Model)，assuming that the particle position vector as rp，velocity vector as Vp={up，νp，wp}T，energy isIn the Lagrange coordinates，control equations are written in the following form.

where，fpand qprepresent the particle momentum and energy source respectively.

2.1.4 Particle-wall impingement model

In the process of gas flow，submerged wall slag is formed as the high temperature gas liquid particles impinged on inner wall surface and attached to the wall surface.Therefore，that building a model to describe the interaction of high temperature liquid particles and wall is the core of all the questions in this paper.This article can provide reference to Professor Arcoumanis＇results［4］.

2.1.5 Particle diameter distribution

Foreign studies［5－6］show that particle size distribution is logarithmic distribution of doublet in combustion chamber of SRM，of which 70% ～80%are soot particles，with diameter less than 5 μm，and average diameter 1.5 μm or so.Soot particles are very good at stream，and are of no effect on flowing，therefore，the soot particles are used as gas phase.The other 20% ～30%are large particles，with an average diameter varying from 10 μm to 300 μm.This portion of the particles will be deposited in the nozzle back wall region，and making dome insulation ablation become more serious.

2.2 Numerical simulation and calculation method

The software Fluent is applied to couple and solve the above equations，with two order upwind scheme.Boundary conditions included no-slip wall，injection，inlet/outlet pressure and symmetric plane.Structured grid is applied to the computational region，and grid size is 0.8 ～1.2 mm along the axial and radial direction.

For a typical SSRM，under different adiabatic inhibitor residual height condition(see Table 2)，combustion chamber flow analysis is carried out.At the time of 20 s(propellant perforation diameter of 450 mm)，when the adiabatic inhibitor diameters are 150 mm，200 mm and 250 mm，the flow field are analyzed respectively.It is assumed that at the whole calculation burning-restricted layer is made of rigid material，whose motion don＇t need to be taken into account in the flow field.

Table 2 Different calculated conditions for SSRM(the nozzle throat Dia.150 mm)

2.3 Results and analysis

The calculation results under the above three conditions are shown in Fig.3.Condition 1，the calculation re-sults show that the maximum concentration is 25.1 kg/m3at afterward-dome and the maximum scour velocity is 35 m/s.Condition 2，the calculation results show that the maximum concentration is 13.9 kg/m3at afterward-dome and the maximum scour velocity is 34 m/s.Condition 3，the calculation results show that the maximum concentration is 12.9 kg/m3at afterward-dome and the maximum scour velocity is 30.2 m/s.From calculation results，it is drawn that the combustion chamber flow speed increase because of the existence of adiabatic inhibitor，leading to the upstream gas speed increased significantly and gas concentration improved too.As the gas pass through the adiabatic inhibitor，the level of air concentration is significantly higher than other parts along the axis regional to the combustion chamber afterward-dome.In addition，it is also found that along with the insulation layer ablation gradually expanded(i.e.insulation diameter gradually expanded)，the values of area ratio 1 and area ratio 2 in Table 2 increase gradually，which result in flow acceleration phenomena showing a downward trend.

Fig.3 Concentration distribution

Meanwhile，flow concentration also exhibit a reduced tendency，as the height caused by the residual adiabatic inhibitor protruding propellant surface is low，then the gas accelerated degree is lower.For this typical SSRM，in view of the combination effect of submerged nozzle and adiabatic inhibitor，the absolute velocity gained by the numerical simulation is remained at a high level.

［1］and［2］show that the influencing factors of insulation erosion aggravation caused by two phase flow are mainly the particle velocity，concentration and angle in the SRM combustion chamber.For commonly used butyronitrile and EPDM insulation，the ablation rate increases as the flow velocity increases.The flow velocity present a turning point within the range of 25 ～30 mm/s，and subsequent ablation increases rapidly，as shown in Fig.4.Based on this conclusion and combining the above analysis，the flow velocity attached to the afterward-dome insulation is above 30 mm/s which is greater than the speed of the inflection point due to the substantial increase of ablation insulation，which is also a reasonable cause to explain the afterward-dome ablation insulation intensification.

Fig.4 Charring ablative rate increases with the increase of particle velocity［2］

3 Method research on reducing afterwarddome ablation

According to the above analysis results，the reason resulted in segmented solid engine rear head ablation volume increase is mainly that the existence of the residual adiabatic inhibitor accounts for the particle velocity increasing in the combustion chamber，thus making afterward-dome ablation insulation more serious.Therefore，the main way to reduce SSRM afterward-dome ablation is to reduce the gas flow speed，making its value below the inflection point value which is subjected to the insulating layer charring and ablative rate increasing with the particle velocity.

Through the analysis of experimental phenomena and the results of numerical simulation，the ratio between adiabatic inhibitor inner diameter area and propellant perforation area，and the ratio between adiabatic inhibitor inner diameter area and nozzle throat area as well as the structed form of nozzle constitute the main factors to aggravate afterward-dome ablation insulation.Therefore，on the basis of the above results the improved model analysis is carried out，the specific calculation conditions are shown in Table 3.Area ratio 1 represent the ratio of adiabatic inhibitor inner diameter area and the propellant inner diameter.Area ratio 2 represent the ratio of adiabatic inhibitor inner diameter and nozzle throat inner diameter.

Table 3 Different calculated conditions for updated SSRM(the nozzle throat Dia.300 mm)

For the improving SSRM configuration，flow field analysis is carried out.The relationship between adiabatic inhibitor height and particle concentration and velocity size in the afterward-dome is obtained by three kinds of different condition of adiabatic inhibitor height，as shown in Fig.5.The calculation results are shown in Table 4.

Calculation results show that:

(1)Condition 1，there is no adiabatic inhibitor，the gas fail to form the acceleration phenomenon in the joint slot parts，when taking into account the gas within a larger bore diameter(the area ratio between propellant perforation diameter and the nozzle throat)，the gas velocity is only 1.5 m/s in the afterward-dome region.

(2)Condition 2，with the height between the residual adiabatic inhibitor and the propellant surface continually increase，the velocity accelerates as the gas flowing through the adiabatic inhibitor，because the area ratio between the adiabatic inhibitor and the nozzle throat is 7.11 which is still larger(compared with the value in Table 1)，thus generating smaller effects on the subsequent flow acceleration，so the flow velocity is improved slightly to 2.0 m/s comparing with Condition 1.

Fig.5 Particle concentration distribution in the afterward-dome

Table 4 Calculated results for different conditions

(3)Condition 3，the height difference gradually increase and the area ratio between adiabatic inhibitor and nozzle throat is further reduced，which would cause the acceleration phenomenon more obvious for the gas in the segmented joint slot(shown in Fig.5).Although the gas velocity in the afterward-dome increase，but only 2.2 m/s，cann’t lead to speed getting bigger promotion.Reference［3］reports that the submerged nozzle would reduce the degree of afterward-dome ablation to a certain extent.Therefore，through the contrast analysis of the three kinds operating data in Table 2 and Table 4，the gas velocity in the afterward-dome is greatly reduced due to the improved SSRM by using a submerged nozzle，the flow velocity is still relatively low even with the similar area ratio between adiabatic inhibitor and throat area.

4 Conclusions

During the working process of SSRM，the combustion chamber gas velocity accelerate to a certain extent due to the existence of adiabatic inhibitor，making two-phase flow gas concentration to be increased，as a result that a certain range of combustion chamber afterward-dome insulation ablation volume become larger comparing with an integral SRM.Through analysis in this paper，the following measures and suggestions are proposed for the structure design of SSRM so as to reduce the dome insulation ablation caused by gas flow.

(1)In the SSRM，with the existence of adiabatic inhibitor，the insulation ablation rate increases multiply as the afterward-dome gas velocity increasing to over 30 m/s，which cause a significant impact to the dome insulation ablation margin，so we should pay more attention to this phenomenon.

(2)In order to reduce the acceleration phenomenon of local airflow caused by the residual adiabatic inhibitor protruding from the burning surface，to reduce the ablation of afterward-dome，the height difference between adiabatic inhibitor and burning surface during working process should be reduced as much as possible.

(3)For different motors，in order to reduce the airflow velocity in the downstream flow field after adiabatic inhibitor，the ratio between inner diameter area of adiabatic inhibitor and nozzle throat area should be increased as much as possible，thus the afterward-dome ablation insulation can be decreased.

(4)In the SSRM，the use of submerged nozzle reduce afterward-dome ablation effectively，which reduce the acceleration of gas speed due to adiabatic inhibitor protruding to flow field greatly.

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