Research On The Chamber Pressure Calculation Method In Highly Metalized Solid Propellant Rocket Motors

In the research of highly metalized solid propellant rocket motors(SRMs),such as the Aluminum-Ice SRM,the metal fuel ramjet and the highly metalized composite propellant SRM,large errors were found when the predicted chamber pressure results were compared with the experimental data.In order to predict the chamber pressure more accurately,the effect of two phase flow and combustion process were introduced to the pressure calculation theory,so as to improve the traditional pressure calculation method.Firstly,the nozzle two-phase flow was simplified to the following models: the frozen flow model,the equilibrium flow model,the constant-lag flow model,the iso-thermal flow model and the constant-particle-temperature model.Under each model,the nozzle mass flow rate formula was obtained,the formula was used to derivate steady pressure formula,so the effect of two-phase flow to the chamber pressure calculation was introduced.Then,according to the 1-D internal ballistic numerical calculation method,the 2-D/3-D numerical chamber pressure calculation method was proposed,the two phase flow effect and the combustion process was considered in the numerical calculation.In the two-phase numerical method,the two-phase product parameters were calculated by the thermodynamic calculation of the propellant,and the calculation was carried out by the FLUENT software.In the numerical calculation considering combustion process,the finite rate/eddy dissipation model was used to simulate the gas phase reaction,while the particle surface reaction model was used to simulate the particle combustion.The reactants at the burning surface boundary were given according to the propellant formulation.The numerical method was used to calculate all the flow parameters,so the steady chamber pressure was acquired.The numerical methods did not get the chamber pressure formula,so the data-fitting method was used in the results of the two-phase numerical calculation and was used to acquire the general pressure formula.The two-phase numerical calculation was used under each steady working state of the SRM,so the nozzle mass flow rate formula was fitted according to these data.The particle mass fraction ? and the particle diameter dp were used as new independent variables in the nozzle mass flow rate formula,and the flow rate formula was used to derivate the pressure formula.The former methods were used to calculate the chamber pressure of some HTPB SRMs with aluminum content varied from 14% to 30%,and an Aluminum-Ice SRM with 50% aluminum content was also used for calculation.The calculated results were compared with the experimental data,The results showed that: 1)Among the pressure formulas obtained according to the two-phase models,the error of the pressure result of the frozen flow model is larger than 15%,and the equilibrium flow model has an error near to 10%,which is close to the traditional pressure calculation formula.The pressure results of the isothermal flow model and the constant particle temperature model showed errors near 5% when compared with the experimental data,and the constant-lag flow model has an error of 5%~10%.2)The numerical results when the two-phase flow effect was considered have errors of pressure less than 5%.3)When the combustion process was considered,the pressure results showed errors less than 6%.4)The pressure formula obtained by the method of data fitting showed results error less than 6% when it was used to the pressure calculation of the HTPB SRMs and the Aluminum-Ice SRMs with 40%~50% aluminum content.Several new pressure calculation method were proposed to improve the traditional pressure calculation method,and when their results are compared with the experimental data,the isothermal flow model and the constant particle temperature model showed relatively accurate chamber pressure results in highly metalized SRMs.The numerical calculation of two-phase flow predict the pressure accurately,based on this method and data fitting,the general pressure formula was obtained,the new formula kept the accuracy of the numerical calculation and is more simple and practical.The numerical calculation of the combustion process is relatively complex and the model is currently inaccurate and the lack of detailed reaction data,so its accuracy is lower than those of the two-phase flow calculation.The two-phase flow numerical calculation and data fitting method are recommended for the pressure calculation of metalized SRMs.