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.

The SRM nozzle always acts as the energy transformation equipment where the chemical energy of the propellant turns into the kinetic energy of gas [

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. [

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.

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

Model of submerged nozzle.

Some reasonable assumptions are considered as follows to simplify the geometry model:

The outer surface of the nozzle has no heat exchange

The pure gas steady gas is considered, the flow field is steady

The contact thermal resistance is totally ignored for the simulation

The complicated phenomena of erosion and pyrolysis behavior of the erosion and heat insulation materials are neglected

The radiation heat transfer is not considered

There are three kinds of materials for the submerged nozzle, which are titanium alloy, silica-phenolic, and carbon-carbon composite. Silica-phenolic and carbon-carbon materials are treated as homogeneous and orthotropic, and their properties are related to temperature. The properties of titanium alloy, silica-phenolic, and carbon-carbon materials are shown in Tables ^{-1}.K^{-1}), ^{-1}.K^{-1}), ^{-1}), ^{3}).

Material properties of titanium alloy.

4500 | 7.955 | 7.89E-6 | 725.7 | 1.1E6 | 0.34 |

Material properties of silica-phenolic composite.

300 | 1650 | 0.61 | 0.52 | 6.0E-6 | 6.0E-6 | 1.0E3 | 1.2E4 | 8.2E3 | 5.1e3 | 2.1e3 | 0.22 | 0.12 |

500 | 0.72 | 0.71 | ||||||||||

800 | 0.86 | 0.85 | 8.0E-6 | 8.0E-6 | 1.2E3 | 8.1E3 | 6.3E3 | 3.1e3 | 800 | |||

1100 | 1.3 | 1.1 |

Material properties of carbon-carbon composite.

300 | 1890 | 65.8 | 86.5 | 1.3E-6 | 1.2E-6 | 920 | 42.5E3 | 64.8E3 | 22.5E3 | 20.6E3 | 0.22 | 0.11 |

500 | 60.6 | 84.2 | 1001 | |||||||||

800 | 59.5 | 81.2 | 1279 | |||||||||

1100 | 55.1 | 71.2 | 1487 | |||||||||

1400 | 51.3 | 62.5 | 1.4E-6 | 1.3E-6 | 1567 | |||||||

1700 | 1785 | |||||||||||

2000 | ||||||||||||

2300 |

A properly sized mesh can generate more accurate results and reduce the computing resources for the thermo-structural simulation. A 1/12th 3D symmetric model is used in this paper for the simulation. The cylindrical coordinate system is adopted to impose symmetric constraints on the symmetric surface. Figure

Mesh generation.

The simulation for the submerged nozzle is subjected to both thermal and mechanical excitations during the period of analysis. To solve the problem of thermal-structure, both the fluid software and structure software are employed. The first stage entails the aerodynamics of flow on the surface of the nozzle. The second stage supplies the temperature and stress distribution for structure. The flow diagram of the simulation is presented in Figure

Flow diagram of simulation.

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 ^{2}∙K), and the minimum value is about 324 W/(m^{2}∙K). It is noticed that the variation curve of the heat transfer coefficient presents a peak at the upstream of the throat insert. Figure

Temperature distribution about the steady field of SRM, K.

Heat transfer coefficient of the inner surface in Figure

Pressure distribution about the steady field of SRM, Pa.

For the submerged nozzle, the distribution of temperature was obtained at times 28 s based on the finite element method on the conditions of thermal loading, as shown in Figure

Temperature distribution under the thermal loading at time 28 s, K.

For the submerged nozzle, the distribution of Von Mises stress was obtained at 28 s based on the same method on the condition of pressure, as shown in Figure

Von Mises stress distribution under the pressure at time 28 s, MPa.

On the condition of the thermal loading and pressure, the distribution of Von Mises stress was obtained at time 28 s for the submerged nozzle, as shown in Figure

Von Mises stress distribution of submerged nozzle at 28 s under thermal loading and pressure, MPa.

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

Hoop stress of throat insert at different times: (a) at 1.3 s, (b) at 4.1 s, (c) at 6.1 s, (d) at 10.1 s, (e) at 15.1 s, (f) at 20.1 s, (g) at 24.1, (h) at 28.0 s, MPa.

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

Distribution of contact stress for throat insert at 28 s, MPa.

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

Throat insert after the ground hot firing test.

Hoop strain distribution of metal case with simulation.

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:

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

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

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

As most of the data in this manuscript were related to trade secrets, I cannot provide them completely. In the future, if necessary, I can share some data with the reviewers or readers.

The authors declare that they have no conflicts of interest.

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