SUN Lin,BAI Jianqiang,ZHAO Yu,HUI Weihua,CHENG Chen

(1.Northwestern Polytechnical University,Science and Technology on Combustion,Internal Flow and Thermo-Structure Laboratory,Xi'an 710072,China;2.No.713 Institute,China Shipbuilding Industry Corporation,Zhengzhou 450015,China;3.Henan Key Laboratory of Underwater Intelligence Equipment,Zhengzhou 450015,China;4.Shanghai Academy of Spaceflight Technology (SAST),China Aerospace and Technology Corporation (CASC),Shanghai 201109,China;5.Jin Tong Ling Technology Group Co.,Ltd,Nantong 226001,China)

Abstract：Nozzle insert is the most important component of a solid rocket motor.Since 1960s,carbon/carbon composite was used widely.It always sustains thermal load,mechanical load and chemical load.The ablation rules of the nozzle insert,especially the regression rate and mechanism of the throat,are of great importance to maintain the rocket working normally.By adopting theoretical analysis numerical simulation and experiment,the ablation process of a solid rocket motor nozzle insert made of carbon/carbon composite was investigated.In theoretical aspects,the precise ablation process was proposed.From the point of energy conservation,a balanced equation was set up to describe the complex process on the ablation surface,between the flow field and the solid material.The ablation process was finally divided into two parts,chemical ablation and mechanical erosion.With the help of MSC Marc,a nonlinear analysis commercial software,this process was simulated.Meanwhile,simplified boundary conditions were employed and accurate material properties were chosen to ensure the simulation process effective.The regression rates of the whole ablation surface were analyzed.Results show that compared with the other parts,the severest ablation part is at the front of the throat,because this part bears both chemical and mechanical impact.The average regression rate is about 0.068 mm/s.Ground firing test was performed.By using micro-CT technology,the average regression rates of the ablation surface were gained.Comparison between the numerical results and the test results show that the numerical results are larger than the test results by about 20%.It was considered that the numerical process ignores the ignition process and the tailing process of the solid rocket motor.Therefore,the regression rates should be larger,and the numerical analysis was proven to be effective.

Key words：throat insert;Carbon/Carbon composites;ablation;surface energy balance simulation;micro-CT

0 Introduction

The nozzle of a solid rocket motor (SRM) normally withstands a high temperature of approximately 3500 K and a high pressure of 5～15 MPa,the erosion scouring of condensed-phase particles and thermal corrosion of high-temperature gas during the operation.Under such harsh condition,the motor should ensure high reliability during the whole operating process.Nowadays,modern high-tech warfare has set higher pursuit on the development of science and technology.To be specific,a SRM should bear larger load,provide greater thrust,withstand higher gas temperature and achieve further range,which has set increasingly high requirements on throat insert materials.Owing to a series of superiorities including favorable mechanical performances,physical properties and ablation resistance,carbon-carbon (C/C) composites now have witnessed extensive applications as SRM nozzle inserts[1].

Scholars all over the worlds have experienced gradually perfected research process on C/C composite insert ablation mechanisms from simple ablation only considering thermal sublimation of materials,simple single-component chemical reaction ablation and gas-phase chemical reaction in the early studies to complex ablation process by taking into account simple chemical reaction ablation,complex-component chemical reaction ablation and coupled two-phase-flow mechanical erosion.Moreover,they only focused on the ablation of homogeneous materials in early studies and now investigated the ablation of anisotropic materials,and now they predict the numerical values reliably and accurately while relying on the statistics of experimental data in early days.

Keswani S T,Kuo K K et al preliminarily established the calculation model for the prediction of C/C nozzle ablation rate,in which the effects of diffusion and chemical kinetics on ablation regression speed were taken into account[2-4].The model also included mass and energy equilibrium relation on the material surface and transient heat conduction of the insert materials and took into account the contributions of different gas components on ablation as well as the influences of the combustor pressure,the nozzle surface roughness and the density of C/C composites on ablation.Acharyal R,Kuo K K et al improved the regression model of the nozzle surface and examined the influencing rules of pressure on ablation rate under high-pressure condition.According to the results,they pointed out that thermal chemical play a more important role than mechanical erosion during the ablation process of the SRM insert,and the regression speed of thermal chemical ablation is under combined control of gas-phase diffusion and chemical reaction kinetics[5-6].Moreover,they suggested that the ablation rate can be calculated via harmonic averaging.During the calculation,the gas zone can be divided into inviscid core region and turbulence boundary layer,and the reactions of H2O,CO2and OH with solid carbon were considered in chemical reaction.Finally,the engineering prediction formula of the ablation rate is further improved based on the analysis of the influencing rules of the operating parameters.The Laboratory of Composite Thermal Structure (LCTS) and the Institute of Fluid Mechanics,Toulouse (IMFT),in France,have performed a lot of research on the micro-structure and multi-scale ablation model of C/C composites and explored the calculation method of the ablation of C/C composite.By dividing C/C composites into macroscopic,mesoscopic and microscopic scales,Lachaud J,Vignoles G L et al investigated the oxidation process of C/C composites in the air and observed the surface morphology at micro-scale under a scanning electron microscope;further,they extracted some geometrical parameters for the establishment of mathematical model and analyzed the difference of the ablation morphologies under different control mechanisms[7-12].Aspa Y,Vignoles G L et al focused on the operating environment of SRM insert and investigated the ablation mechanism of 4D C/C composites,in which heterogeneous oxidation reaction of H2O and CO2with C/C was considered.Additionally,the surface regression rules of the composites at micron/millimeter scales were examined and the surface regression at these two scales was simulated using volume of fluid (VOF) method[13-16].

Some Chinese scholars adopted mesoscopic/microscopic composites modelling technique,interface reconstruction,and electronic scanning technique to examine the ablation process and mechanisms of C/C composites at mesoscopic/microscopic scale[18-21].Based on two-phase flow theory and empirical formula,Chang Yan et al[22]established the calculation model of mechanical erosion of 2D axial-symmetrical C-based materials and investigated the distribution rules of droplet trajectory and mechanical erosion as well as the effects of Al mass concentration in the propellant and the combustor pressure on mechanical erosion.Li Qiang et al[23]examined the ablation surface,microscopic structure and ablation mechanism of 4D C/C composites under an electronic scanning microscope,and concluded that the ablation-induced passivation of fibre ends,the formation of lamelliform matrix and particle impact mass flow rate imposed larger effect on the ablation of C/C composites than particle impact velocity in particle impact region.Comparing the ablation experimental results of oxygen/kerosene supersonic flame under two different operating conditions with and without aluminium,Zha Bolin et al[24]found that the ablation volume of the radial fibres of axially-weaved C/C composites was in direct proportion to the concentration of particles.Liu Yang et al[25]focused on the ablation behaviours of 4D-weaved C/C composites under high-velocity high-concentration scouring condition in a SRM and concluded that mechanical erosion effect became a main reason for the ablation of C/C materials after the particle velocity reached a certain threshold.Based on the ablation morphology of the specimen,they discussed several damage modes at the interface between carbon rods and fibre beams and analyzed the reason why the interface was easily destroyed.

Currently,scholars have established a great number of numerical analysis models regarding the ablation behaviors of C/C composites by taking into account chemical reaction and particle erosion,thereby exhibiting certain precision and satisfying the engineering requirement.In this study,by combining test and numerical simulation,the ablation behavior of C/C composite nozzle insert was analyzed.First,using MSC Marc software,the ablation model of C/C composite was established based on the principle of surface energy equilibrium for further ablation analysis;next,the ablation test was performed,and 3D reconstruction models of C/C composite nozzle insert before and after ablation were obtained so as to gain accurate knowledge of the ablation condition at different positions in the nozzle.Results show that the present numerical analysis results fit well with the test data,which can adequately validate the accuracy of the present numerical simulation.

1 Model establishment

1.1 Geometric model

The research emphasise on the ablation of throat insert under the action of high-temperature high-pressure gas when the SRM nozzle operates.Using finite element analysis software,the ablation interface regression condition of the nozzle insert under the action of high-temperature gas in the motor is investigated via simulation so as to obtain some key physical parameters such as the ablation rate.

The specific size of the SRM nozzle under the present simulation is shown in Fig.1.During the simulation,the diameter of the nozzle throat,the maximum combustor pressure,mean pressure,the density of the propellant,and the theoretical combustion temperature of the propellent are 10.2 mm,6.84 MPa,6.233 MPa,1.93 g/cm3and 3300 K,respectively;the motor operate at 7.5 s.

The 3D model of the SRM nozzle as shown in Fig.1 is constructed in CAD software.Since the thermal environment of the nozzle is fully symmetrical,only 1/4 of the nozzle is simulated for simplifying the solving process,as shown in Fig.2.

1.2 Mesh generation

Afterwards,the model is meshed into a lot of hexahedral elements,as shown in Fig.3.Finally,113 072 nodes and 102 600 units in total are generated after mesh generation.

Fig.1 Engineering drawing of the throat model

1.3 Model of materials

The changes of the SRM nozzle materials mainly including pyrolysis,water vaporization and carbon deposition are investigated via simulation.Therefore,the material parameters in initial state and charred state and the material parameters of the vaporized gas should be set during the definition of materials attributes.The specific materials parameters in different states are shown in Table 1 and Fig.4.

Fig.2 3D model of the throat insert

Fig.3 Mesh generation results of the throat insert

(a)Specific heat capacity of the original (b)Specific heat capacity of the charred

(c)Specific heat capacity of the gas (d)Thermal conductivity of the charred

Table 1 Physical parameters of the materials in different states

2 Establishment of numerical model

SRM throat insert materials under the ground ignition condition obey two basic principles,i.e.energy conservation and mass conversion.Based on the principle of surface energy balance (SEB) in commercial software Marc,the surface contraction process during ablation and erosion processes can be determined according to thermal conduction heat flow entering into the materials and surface temperature.In addition to thermal conduction heat flow,SEB also considers convective heat flow generated by blowing effect induced by mass injection,radiation balance,a kind of enthalpy flow rate form under the diffusion of the chemical material molecules at the boundary layer,three kinds of enthalpy flows of the related mass transfer form in thermal chemical ablation caused by gas and thermal inner decomposition,three kinds of enthalpy flows relate to thermo-chemical ablation,the mechanical erosion caused by liquid or solid-phase particles and the elimination of surface liquid state structure.

Fig.5 Illustration of SEB on the ablation surface of C/C composites

By overall considering above influencing factors,the SEB equation consists of the following items: convective term,a kind of enthalpy flow formed by the chemical material molecules at the boundary layer,the enthalpy flow in the related mass transfer formed by thermo-chemical erosion induced by gas,the enthalpy flow caused by internal thermal decomposition,the enthalpy flow formed by blowing effect induced by mass injection,the enthalpy flow corresponding to thermochemical ablation induced by particle impact,the thermal effect corresponding to mechanical erosion induced by particle impact,the enthalpy flow induced by the elimination of surface liquid-state structure (or liquid removal),the radiation equilibrium term and the heat transfer term.To be specific,the SEB equation can be found in reference[26].

Afterwards,using CAE software,numerical simulation is performed on the ablation process of C/C composite insert for subsequent geometrical model establishment,material model establishment,mesh generation,boundary condition determination,operating condition input,calculation analysis and post-processing.

3 Comparison and analysis of results

3.1 Firing test results

The present hot-run test process is described in detail in reference[27].Before and after hot-run test,3D model of the throat insert is reconstructed using μ-CT technique.After the hot-run test,the models before and after the test are superposed to gain in-depth knowledge of the ablation conditions at different points on the insert surface,and the results are shown in Fig.6 and Fig.7.

Fig.6 3D reconstruction results using μ-CT

Fig.7 The ablation rate of the inner surface of the throat insert in axial direction

3.2 Simulation results

The regression of the throat insert is gradually expanded as the ablation process continued.Moreover,the ablation at the throat is most intensive,with the maximum regression.Next,the throat ablation rates at different moments are calculated,as shown in Table 2.

It can be observed that the ablation rate of the nozzle insert increase steadily with the time at a decreasing rate.The increasing rate of the ablation rate is fairly low after approximately 7 s.It can be predicted that the ablation rate gradually tend to be stable as the ablation process continue.

Table 2 Ablation rates at different moments

Through analysis,it can be concluded that the rise of the temperature field inevitably lead to the increase of the reaction rate at a macro-perspective,thereby gradually enhancing the ablation rate.In terms of reaction process,when the motor exactly start to operate,the reaction temperature is low and the diffusion rate is obviously higher than the chemical reaction rate.The ablation process is controlled by chemical reaction,which is referred to as dynamic mechanism.At a high reaction temperature,the oxidation process increase steadily,while the oxidation components are insufficient in supply;accordingly,the transport rate of oxidation components to the material surface play a limit role,and the ablation process is controlled by the diffusion mechanisms[2-3].In conclusion,the transition of the ablation mechanism result in the change of macro-ablation rate.

3.3 Comparison and analysis

The experimentally-measured mean ablation rate reach a maximum of 0.056 mm/s,while the present calculated value is 0.068 mm/s,with a relative error of 21.4%.The simulation result is slightly larger than the experimental value.During actual operation process,the engine operates 7.5 s.The ablation rate is low at the beginning and end of the motor operation,which overall lower the mean ablation rate.During the present simulation,the condition at the beginning and end of the motor operation is not taken into account,and the overall simulation is performed in the format of high-temperature gas flow ablation.Thereby regression rate produced by simulation is higher than that in the experimental value.

4 Conclusions

In this paper,we adopted three methods,i.e.theoretical analysis,numerical simulation and experiment analysis to conduct the research.Through theoretical analysis,the ablation process is investigated.By numerical simulation,a simulation model of high reliability is established.Based on experiment analysis,3D construction of the throat of both before and after the firing test is adopted to gain the regression rates of the whole ablation surface.In comparison,the numerical results are larger than the test results by about 20%.It is considered that the numerical process ignores the ignition process and the tailing process of the solid rocket motor.Therefore,the regression rates should be larger,and the numerical analysis is proven to be effective.

Acknowledgements:Manuscript presented at the International Astronautical Congress,IAC-20,'The CyperSpace Edition','12-14 October 2020'.Copyright by IAF.