Numerical Simulation of Coupling Thermal and Mechanical Influence on Submerged Nozzle in Solid Rocket Motor

Abstract

The coupling thermal and mechanical effect on submerged nozzles is important in the design of modern rockets upon thermal loading and aerodynamic pressure. In this paper, a simulation with the subroutine of nonuniform pressure and nonuniform heat transfer coefficient was conducted to study the thermo-structural response of a submerged nozzle at the pressure 6 MPa and stagnation temperature 3200 K. Both the aerodynamic parameters and heat coefficients were obtained through analyzing the flow field. It was found that the thermal loading had an important influence on the stress of throat insert for the solid rocket motor (SRM). The hoop stress increases at first and then decreases with the increase of time for the throat insert. The ground hot firing test of SRM with a submerged nozzle was carried out. The experimental results showed that the structural integrity of the submerged nozzle is very normal during SRM operation. The present method is reasonable, which can be applied to study the thermo-structural response of submerged nozzle for SRM.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

The SRM nozzle always acts as the energy transformation equipment where the chemical energy of the propellant turns into the kinetic energy of gas [1]. In order to shorten the length of a solid rocket motor, the submerged nozzle is adopted in high altitude solid rocket motor [2, 3]. It is classified as a submerged nozzle, as its entrance extends to within the combustion chamber of the SRM. In general, the submerged nozzle is always working under extremely harsh circumstances, such as thermal load, mechanical load, thermo-chemical ablation, and particle-laded flow [4–7]. Hence, the structure integrity is of great importance for the normal operation of the nozzle. Hence, the simulation of the submerged nozzle is carried out to analyze the structure integrity, such as flow simulation, heat transfer simulation, and structure analysis [8].

A variety of recent works account for the growth in knowledge and techniques in the assessment of the structural behavior of SRM nozzles. Kumar et al. [9] undertook an extensive thermo-structural analysis of composite structures, incorporating temperature-dependent properties, and thermal, thermo-chemical and mechanical loads, and subsequently performed a coupled thermo-structural stress analysis of an SRM nozzle comprised of various orthotropic and isotropic materials. Morozov and Beaujardiere [10] investigated the dynamic thermo-structural response of a composite rocket nozzle throat using the commercial finite element code ADINA. It is found that the dynamic response oscillates about the quasi-static response in all cases, and that, in general, the variance in stress magnitudes between the two solution techniques is significant. Tian et al. [11] studied the problems with gap design and contact stress about the SRM nozzle under thermal loading and pressure using the finite element method. Li et al. [12] had a focus on the thermal structural analysis of the nozzle throat insert; the influences of the thermoelastic stress are discussed by the computational software ABAQUS. Zheng [13] studied the thermo-structural analysis and failure behaviors of carbon-carbon composite throat insert. Hu et al. [14] determined the temperature and stress field of the conical trapped joint carbon-carbon nozzle divergent section. Sun et al. [15] studied the thermo-structural response of a typical nozzle with consideration of the structure gap based on the finite element method.YU et al. [16] considered the influence of the fit clearance of the throat insert on the deformation and stress distribution of the nozzle based on the three-dimensional finite element model. The research shows that the fit clearance of throat insert does not change the overall distribution of stress, but can affect the stress on the matching surface. Cozart and Shivakumar [17] performed a finite element axisymmetric stress analysis of a 3-D braided preform ablative composite rocket nozzle, incorporating a material ablation model. In the work of Yoo et al. [18], a kick motor nozzle utilizing spatially reinforced composites was subjected to finite element thermo-elastic analyses following the development of a material model used to homogenize various spatial reinforcement architectures.

To sum up, a large amount of work has been done for investigating the thermo-structural response. However, literature on the thermo-structural response of the submerged nozzle at the initial stages of operation is scarce. This study focuses on the numerical simulation of the submerged nozzle under the condition of internal pressure and thermal loading. It addresses a method for analyzing the thermo-structural response of nozzle using a finite element analysis program and discusses the development of a user subroutine which allows us to model the nonuniform pressure and nonuniform heat transfer coefficients on the wall. Furthermore, the ground hot firing test of SRM is carried out. Finally, some conclusions are drawn in the end.

2. Submerged Nozzle Model

2.1. Geometry

The three-dimensional cyclic symmetry finite element analysis is performed for the submerged nozzle made of different composites. This nozzle consists of five substructures, namely, throat insert made from the punctured carbon-carbon composite, the tape wound 2D silica-phenolic entrance insulator—which isolates the hot gas and metal case, the silica-phenolic liner—which isolates the hot and cooler substructures, divergent insulator made from the silica-phenolic, and metal case made from the titanium alloy, as shown in Figure 1. In Figure 1, the coordinate of $X$-axis is dimensionless by the nozzle length. Furthermore, in order to reduce the thermal stress of the throat insert, the clearance was set up in the internal interface of the throat insert. The values of interface AB, BC, DE, and EF are all 0.05 millimeters.

[figure omitted; refer to PDF]

On the one hand, in order to obtain the steady flow filed, the axisymmetric numerical simulation was carried out by a finite volume method, based on a pressure solver. A standard $\kappa -\epsilon$ model was used to make the gas phase equation as a closed system. On the other hand, there exist two kinds of thermal boundary conditions for structure simulation, i.e., the adiabatic condition between the outermost structural steel and the air, and the forced convection from the inner flow. For thermal-structural simulation, the heat transfer coefficient along the wall should be provided by means of fluid software. The result is shown in Figures 4–6, respectively. Figure 4 shows the temperature distribution, gradually decreasing along the wall. Figure 5 shows the force convective coefficient between hot gas and wall. As can be seen, the maximum value of the forced convection coefficient is about 8266 W/(m²∙K), and the minimum value is about 324 W/(m²∙K). It is noticed that the variation curve of the heat transfer coefficient presents a peak at the upstream of the throat insert. Figure 6 shows the pressure distribution, gradually decreasing along the wall, because of the gas exhaust flow.

[figure omitted; refer to PDF]

The throat insert is the one subjected to the most severe thermal and mechanical loading, which provides an appropriate case for study. Furthermore, the hoop stress is the most important stress component. Figure 10 displays the hoop stress of the throat insert at different times. It is clear that the position of the maximum hoop compressive stress is upstream at the convergent section of the throat insert, because of the maximum heat transfer coefficient in the upstream of throat insert, the temperature difference is large, and the thermal expansion deformation of throat insert is obvious. Secondly, the position of the maximum hoop tensile stress is at the inner fillet of the throat insert. In order to avoid the damage of throat insert during the test, the radius of the inner fillet can be properly increased. Thirdly, the hoop stress increases at first and then decreases with time for the throat insert. Finally, during the working operation, the maximum hoop compressive stress of throat insert is 6.1 s, and its value is 103.9 MPa, which is less than 180 MPa of compress strength. The maximum hoop stress 34.8 MPa of throat insert is 20.1 s, and its value is 34.8 MPa, which is less than 115 MPa of tensile strength. Both maximum hoop compressive stress and maximum tensile stress yield the material strength.

[figures omitted; refer to PDF]

The contact stress of forward and backward interface in the throat insert has an important influence on the stress distribution and the safety of nozzle during the operation. In particular, both forward gap AB and backward gap EF are very important in Figure 1. Therefore, the value of forward gap AB in Figure 1 is 0.05 millimeters, and the one of backward value EF is 0.05 millimeters. Figure 11 shows the distribution of contact stress for the throat insert at time 28 seconds. It indicates that the value of contact stress is larger at the front face AB, and the value of contact stress is smaller at the back face EF. This is the reason that the gas temperature at upstream is much higher than the one at downstream for throat insert. In order to ensure the reliability of the throat insert, the interface gap of the front face of the throat insert can be properly increased, and the interface gap of the back face can be reduced.

[figure omitted; refer to PDF]

3.4. Experimental Verification of Structural Integrity for the Throat Insert

On the condition of combustion chamber pressure 6 MPa and stagnation temperature 3200 K, the ground hot firing test of SRM with the submerged nozzle was carried out, and the working time was 28 s. In addition, the design values of interface AB, BC, DE, and EF, as shown in Figure 1, are all 0.05 millimeters. The structural integrity of the submerged nozzle is normal. Figure 12 shows the structure of the throat insert after the test of the submerged nozzle. During the SRM operation, the performance of the submerged nozzle yields the requirement of SRM. Meanwhile, the test value of hoop strain for a metal case is $1258\mu \epsilon$ at time 28 s, and the computational value is $1164\mu \epsilon$, as shown in Figure 13, Point A. It can be seen that the computational value is equivalent to the test value. Furthermore, it can be shown that the method of thermo-structure response of submerged nozzle developed in this paper is reasonable. The structure design and interface clearance of throat insert is valid. The distribution of stress field and temperature field for the throat insert are sound, which yields meet the material strength.

[figure omitted; refer to PDF][figure omitted; refer to PDF]

4. Conclusion

In this paper, the thermo-structure response of three-dimensional submerged nozzle under the condition of thermal loading and pressure was investigated. The ground firing test of SRM has been completed. Some conclusions can be drawn as follows:

(1)

Thermal loading is found to have the most dominating influence on the thermal stress of nozzle

(2)

The hoop stress of throat insert increases at first and then decreases with the increase of time

(3)

In order to ensure the reliability of the submerged nozzle, the design of throat insert clearance and structure is extremely important

Acknowledgments

This article was funded by Xi’an Modern Chemistry Research Institute, China.

References

[1] P. F. Melia, "Flow and ablation patterns in Titan IV SRM aft closures," 31st Joint Propulsion Conference and Exhibit,DOI: 10.2514/6.1995-2878, .

[2] E. R. Joyce, M. P. Snyder, "Solid rocket motor design for a high altitude composite rocket," 45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit,DOI: 10.2514/6.2009-5083, .

[3] M. Angelone, F. Mascanzoni, C. Milana, "Technological and programmatic development of Zefiro 40 solid rocket motor," 48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit,DOI: 10.2514/6.2012-4213, .

[4] B. C. Yang, A Theoretical Study of Thermo-Mechanical Erosion of High-Temperature Ablatives, 1992.

[5] Y. W. Guan, J. Li, Y. Liu, "Ablation characteristics and reaction mechanism of insulation materials under slag deposition condition," Acta Astronautica, vol. 136 no. 4, pp. 80-89, DOI: 10.1016/j.actaastro.2017.02.001, 2017.

[6] J. Li, M. F. Guo, X. Lv, Y. Liu, K. Xi, Y. W. Guan, "Erosion characteristics of ethylene propylene diene monomer composite insulation by high-temperature dense particles," Acta Astronautica, vol. 145 no. 2, pp. 293-303, DOI: 10.1016/j.actaastro.2018.01.055, 2018.

[7] Y. Liu, Y. W. Guan, J. Li, "Insulator ablation modes in different impact conditions of alumina droplets onto wall surfaces," Acta Astronautica, vol. 153 no. 6, pp. 138-145, DOI: 10.1016/j.actaastro.2018.10.032, 2018.

[8] Q. Li, P. J. Liu, G. Q. He, "Fluid-solid coupled simulation of the ignition transient of solid rocket motor," Acta Astronautica, vol. 110 no. 3, pp. 180-190, DOI: 10.1016/j.actaastro.2015.01.017, 2015.

[9] R. R. Kumar, G. Vinod, S. Renjith, G. Rajeev, M. K. Jana, R. Harikrishnan, "Thermo-structural analysis of composite structures," Materials Science and Engineering A, vol. 412 no. 1-2, pp. 66-70, DOI: 10.1016/j.msea.2005.08.065, 2005.

[10] E. V. Morozov, J. Beaujardiere, "Numerical simulation of the dynamic thermostructural response of a composite rocket nozzle throat," Composite Structures, vol. 91 no. 4, pp. 412-420, DOI: 10.1016/j.compstruct.2009.04.006, 2009.

[11] S. P. Tian, G. J. Tang, D. K. Li, D. C. Yuan, "Gap design of solid rocket motor nozzle structures," Journal of Propulsion Technology, vol. 26 no. 5, pp. 448-451, 2005.

[12] S. L. Li, F. Zhang, B. Xiong, "Influences factor analysis of thermal structure on motor throat," Structure and Environment Engineering, vol. 40 no. 2, pp. 56-63, 2013.

[13] Q. Zheng, Thermo-Structural Analysis and Failure Behavior of C/C Composite Throat, 2011.

[14] J. H. Hu, S. H. Meng, X. L. Chang, C. H. Xu, H. Chen, "Temperature and stress field analysis of conical trapped joint C/C nozzle divergent section," Journal of Solid Rocket Technology, vol. 35 no. 1, pp. 64-68, 2012.

[15] L. Sun, F. T. Bao, N. Zhang, W. Hui, S. Wang, N. Zhang, H. Deng, "Thermo-Structural Response Caused by Structure Gap and Gap Design for Solid Rocket Motor Nozzles," Energies, vol. 9 no. 6,DOI: 10.3390/en9060430, 2016.

[16] X. J. Yu, S. Yu, Y. Wang, Y. Yang, "Thermo-structure coupled computation for the influence of fit clearance on the stress distribution of composite nozzle," 2018 Joint Propulsion Conference,DOI: 10.2514/6.2018-4486, .

[17] A. B. Cozart, K. N. Shivakumar, "Stress analyses of a 3-D braided composite ablative nozzle," 40th Structures, Structural Dynamics, and Materials Conference and Exhibit,DOI: 10.2514/6.1999-1277, .

[18] J. S. Yoo, I. H. Cho, C. G. Kim, "Thermoelastic analysis of a kick motor nozzle incorporating spatially reinforced composites," Journal of Spacecraft and Rockets, vol. 40 no. 1, pp. 83-91, DOI: 10.2514/2.3918, 2003.