عنوان مقاله [English]
Using heat shield, especially in throat area has a significant effect on combustion chamber pressure and thermal efficiency of solid fuel engines, and so many studies have been made in this field. A precise prediction of regression in throat surface is essential to optimum design of high burning time engines. In this study, ablation of graphite nozzle in solid fuel engines is investigated numerically for a special ingredient composite fuel .Navier Stocks equations together with thermodynamic equations inside the engine as well as thermochemical and thermal conductivity equations on nozzle surface are derived and written in their suitable forms and solved to determine the regression rate of nozzle throat surface. Furthermore, a cartridge full size solid motor by polyester binder fuel was tested and the ablation rate was measured by using a 3D scanner. The experimental pressure-time and thrust-time curves were also derived and used as input data for numerical calculations. Comparison between numerical and experimental results shows a satisfactory agreement. The experimental results show that the ablation has maximum value in the inlet area, and in divergent section is approximately constant and its value is 0.2mm. Because of important effect of ablation rate on the geometry of nozzle throat and so on the performance of the engine, the results of this study may have applicable usage in analyzing and designing solid fuel engines.
 A. Agazadeh, M. Adami, Evaluation of ablation and transient heat transfer analysis in ablative insulatur, 14 Annual Conference(International) Mechanical Engineering, 2006, Isfahan University of Technology. (in Persian)
 A. Ragini, K. Kenneth, Effect of Pressure and Propellant Composition on Graphite Rocket Nozzle Erosion Rate, Journal of propulsion and power,Vol. 23, No. 6, November – December 2007.
 P. Li-na and et.al, Effect of combustion gas mass flow rate on carbon/carbon composite nozzle ablation in a solid rocket motor, CARBON 50, pp. 1554-1562, 2012.
 D. Bianchi, Numerical Simulation of Chemical Erosion in VEGA Launcher Solid-Propellant Rocket Motor Nozzles, Propulsion and Energy Forum, Orlando, FL 51st AIAA/ASME/SAE/ASEE joint propulsion conference July 27- 29, 2015.
 D. Bianchi, F. Nasuti, Thermochemical Erosion analysis for Carbon-Carbon Rocket Nozzles, 45th AIAA/ASME/SAE/ASEE joint propulsionconference & Exhibit Denver, Colorado, 2-5 August 2009.
 D. Bianchi, F. Nasuti, Thermochemical Erosion Analysis of Carbon-Carbon Nozzles in Solid-Propellant Rocket Motors,46th IAA/ ASME/ SAE/ ASEE joint propulsionconference &, Nashville , TN Exhibit 25-28 July 2010.
 T. Piyush and Y. Vigor, Chemical Erosion of Refractory Metal Nozzle Inserts in Solid-Propellant Rocket motors, 46th AIAA Aerospace Sciences Meeting and Exhibit, Ren Nevada, 7-10 January, 2008.
 K. Suresh, J. Kushwaha, M. Mondal, A. Kumar, R. K. Jain, G. Rohini, Fabrication and ablation testing of 4D C/C composite at 10 MW/m2 heat flux under a plasma arc heater, Material Science Engineering A 566, pp. 102 -111, 2013.
 F. Nasuti, et. Al, A numerical approach for the study of the gas-surface interaction in carbon-phenolic solid rocket nozzles, Aerospace Science and Technology, pp. 25-31, 27,2013.
 A. Turchi, D. Bianchi, P. Thankre, F. Nasuti, V. Yang., Radiation and Roughness Effects on Nozzle Thermochemical Erosion in Solid Rocket Motors, Journalof propulsion and power Vol. 30, No. 2, March-April 2014.
 C. Bo, Z. Li-Tong, C. Lai-Fei, L. Xin-Gang, Albation of pierced C/C composite nozzles in an oxygen/ethanol combustion gas generator, CARBON 47, pp. 545-550, 2009.
 H. Mohammadiun, M. Mohammadiun, E. Poorshaban, Numerical analysis of thermal conductivity of carbon-carbon Considering the effects of chemical reactions, mass transfer and heat transfer surfac, 8 Annual Conference (International), Iran Air and Space Association Shahin Shahr Isfahan, Malek Ashtar University, 29 February - 1 March 2009. (in Persian)
 L. RE, Pyrolysis kinetics of char forming polymers, Polym Degrad Stab, 1998.
 Y. I. Dimitrienko, I.D. mitrienkov, Effect of Thermomechanical erosion on heterogeneous combustion of composite materials in high-speed flows, Combustion and Flame, pp.122-211, 2000.
 K.A .Hoffmann, S. T. Chiang, Computational fluid dynamics for engineers,engineering education system, 1993.
 H. K. Versteeg, W. Malasekera, An Introduction to Computational Fluid Dynamics, the finite volume method, 2000.
 S.V. Patankar, Numerical Heat Transfer and Fluid Flow, New York, Hemishere, 1980.
 J. Anderson, computational Fluid Dynamics, the basicsith applications, MCgraw-Hill ewyork, 2002.
 Marks standard Handbook for mechanical engineers, Tenth edition, MCgraw-Hill, NewYork, 1997.
 H.G. Landa, Heat conduction in a melting solid, Quarterly Applied Mathematics, Vol.8, No.1, pp. 312-319, 1970.
 J. E. Sunderland, R. J. Groush, Transient Temperature in a melting solid, Transactions of the ASME, Vol. 83, pp. 409- 414, 1961.
 G. P. sutton, O. Biblarz, Rocket propulsion elements, 7th edition, John Wiley & Sons, 2001.
 A. Davenas, Solid rocket propulsion technology, pergamon, vol. 1, 2003.
 B. T. Chang, T. Y Chang, J. S. Hsiao, C. I. Chang, Heat Transfer with Ablation in a Half-Space Subjected to Time Variant Heat Fluxes, Presented at ASME Winter Annual Meeting, Washington, D. C, Papar No.81-WA/HT-34, 1981.
 R. L. Potts, Hybrid Integral/Quasi-Steady Solution of Charring Ablation, AIAA Paper 80-1688, 1990.
 L. Torre, J. M. Kenny, A. M. Maffezzoli, Degradation behaviour of a composite material for thermal protection systems Part Process simulation, J Mater Sci, pp. 33-3145, 1998.
 B. Yan, Z. Chen, J. Zhu, J. Zhang, Y. Jiang, Effects of ablation at different regions in three-dimensional orthogonal C/sic composites ablated by oxyacetylene torch at 1800oc, Journal of materials processing technology 209, pp.3438- 3443, 2009.
 S. Xue-Tao, L. Lei, W. Li, K. Li, Ablation behavior for C/C-zrc composites in a solid rocket motor environment, Ceramics International 41, pp.11793 – 11803, 2015.
 P. Karthikeyan, V.K. Ravindran, S. Hari Krishna, N. Narayanankutty, K.M. Usha, Prediction of erosion characteristics for ablative throat insert liners using ultrasonic velocity measurement, Proceedings of the National Seminar & Exhibition on Non–Destructive Evaluation NDE, December 8- 10, 2011.
 Piyush Thakre, Rajesh Rawat and Richard Clayton, Graphite Nozzle in Solid Propellant Rocket Motor, JOURNAL OF PROPULSION AND POWERE, paper 615, 2012.