Coupling Heat Transfer and Fluid Flow Solvers for High Area Ratio Rocket Nozzle

Abstract. Turbulent flow separation coupling heat transfer with the solid case in the high area ratio rocket nozzle is simulated with the CFD method and the results are investigated experimentally. The finite volume method, the 2nd order upwind scheme, SST k-ω turbulence model and enhanced wall function are employed to solve the N-S equation and thermal conduction equation. To predict the fluid field and wall temperature distribution, numerical models have been developed considering both solid and fluid regions. Solid and fluid regions work together, each one providing a boundary condition for the other, and the solution to the coupled problem has been attained. In the end， flow in a high area ratio rocket nozzle is simulated, separation is indicated, and in the separation zone the temperature gradient is high. The location of the separation point predicted agreed well with the experimental data, which proved the accuracy of the method of numerical simulation. Keywords: High area ratio rocket nozzle, Fluid-thermal coupled analysis, Numerical simulation, Gas separation, Ground test Main text Nozzle design constitutes an important phase of rocket development. The performance of a rocket depends heavily on its nozzle's effectiveness in converting thermal energy to kinetic energy. To increase the vacuum performance of classical convergent-divergent rocket nozzles, it is desirable to achieve high expansion rate. Modern rocket nozzles are designed to operate over a wide range of altitudes and are typically with large area ratios to ensure high efficiencies at high altitudes. A nozzle's design altitude is where its exit pressure is equal to the ambient pressure. Above that altitude, the nozzle flow is 'underexpanded' and below it, 'overexpanded'. In both conditions the nozzle produces thrust less than the possible maximum value. Usually the nozzle design altitude is well above sea level, leaving the nozzle flow in an overexpanded state for its startup as well as ground testing. Overexpansion in a rocket nozzle presents the critical, and sometimes design driving, problem of flow separation induced side loads. The structure of the liquid-rocket-engine nozzle flowfield generated by the flow separation that may occur because of a strong overexpansion has attracted many experimental and numerical studies In the present study, a new numerical method is adopted in the simulation of the separation flow in the rocket nozzle with high area ratio, carried out in a validated numerical Reynolds-Averaged-Navier-Stokes code, with turbulence computed according to two-equation SST model. In the end, an experiment is conducted to validate the results

Combined Acceleration Methods for Solid Rocket Motor Grain Burnback Simulation Based on the Level Set Method

A detailed study of a set of combined acceleration methods is presented with the objective of accelerating the solid rocket motor grain burnback simulation based on the level set method. Relevant methods were improved by making use of unique characteristics of the grains, and graphical processing unit (GPU) parallelization is utilized to perform the computationally intensive operations. The presented flow traced the expansion of burning surfaces, and then Boolean operations were applied on the resulting surfaces to extract various geometric metrics. The initial signed distance field was built by an improved distance field generating method, and a highly optimized GPU kernel was used for estimating the gradient required by the level set method. An innovative Boolean operation method, thousands of times faster than ordinary ones, was ultimately proposed. Performance tests show that the overall speedup was close to 15 on desktop-class hardware, simulation results were proven to converge to analytical results, and the error boundary was 0.25%

Precise Design of Solid Rocket Motor Heat Insulation Layer Thickness under Nonuniform Dynamic Burning Rate

With the purpose of obtaining optimal designs of the heat insulating layers in solid rocket motors, we have proposed a numerical approach to compute the ideal thickness of the heat insulating layer. The proposed method is compatible with solid rocket motors that have any shape and any manner of erosion. The nonuniform dynamic burning rate is taken into consideration to achieve higher accuracy. A high-performance code is developed that uses triangular geometry as an input to allow exchanging data from any CAD platform. An improved geometric intersection algorithm is developed to generate the required sampling points, saving 35% computation time compared to its open source equivalent. Parallel computing technology is utilized to further improve the performance. All operations of the proposed approach can be executed automatically by programs, eliminating the manual work of gathering data from CAD software in the traditional approach. Validation data shows that the proposed approach saves 3.85% of the mass compared to the ordinary design approach. Performance profiling shows that the implemented code operates within 5 seconds, which is much faster than the unoptimized open source version

Robust Three-Dimensional Level-Set Method for Evolving Fronts on Complex Unstructured Meshes

With a purpose to evolve the surfaces of complex geometries in their normal direction at arbitrarily defined velocities, we have developed a robust level-set approach which runs on three-dimensional unstructured meshes. The approach is built on the basis of an innovative spatial discretization and corresponding gradient-estimating approach. The numerical consistency of the estimating method is mathematically proven. A correction technology is utilized to improve accuracy near sharp geometric features. Validation tests show that the proposed approach is able to accurately handle geometries containing sharp features, computation regions having irregular shapes, discontinuous speed fields, and topological changes. Results of the test problems fit well with the reference results produced by analytical or other numerical methods and converge to reference results as the meshes refine. Compared to level-set method implementations on Cartesian meshes, the proposed approach makes it easier to describe jump boundary conditions and to perform coupling simulations

An Approach to Analysing Erosive Characteristics of Two-Channel Combustion Chambers

To acquire the erosive characteristics of two-channel combustion chambers, a quasi-one-dimensional internal ballistics model is proposed. Combining the model with two different erosive burning models, the modified L-R expression, and the Mukunda-Paul expression, the flow parameters and the internal ballistics performance of a test solid rocket motor are computed. The results show good agreement with experimental data. According to the results, the more severe the erosion is, the earlier, longer, and gentler the tail-off stage becomes. During the tail-off stage, the dramatic drop of pressure leads to a low normal burning rate and makes it easier for erosion burning to occur. For this reason, notable erosive burning might appear during tail-off if the case-to-throat area ratio is extremely low. The results also show that flows in the inner channel and the outer channel are similar but not identical. This leads to different erosive burning behaviours in the two channels. Also, the two erosive burning rate models involved in this paper are compared. It seems that the M-P expression provides better results than the modified L-R expression does, since it reveals the threshold phenomena. Besides, the M-P expression has great advantages for its universality for most propellants and different SRM geometries

Extended Application and Experimental Verification of a New Erosive Burning Model Coupled Heat Transfer between Gas and Grain Based on a Star-Grain Solid Rocket Motor

The estimation of erosive burning is of great importance for the internal ballistics computation of a solid rocket motor (SRM) with a large aspect ratio. Because of the variety of parameters affecting erosive burning, most of the erosive burning models developed in earlier years usually contain unknown constants that need to be identified by a trial-and-error procedure for each SRM. Based on an SRM with a cylindrical grain, a new erosive burning model, which coupled the heat transfer between the gas and grain, was proven to be effective previously. To expand the scope of application of this model, in this paper, earlier and new erosive burning models were used in the transient one-dimensional internal ballistics computation, to obtain the internal ballistics for a star-grain SRM. A comparison between the computational and experimental results indicated that both the earlier and new erosive burning models can obtain results with good accuracy for a star-grain SRM. The paper shows that with no constants to be identified, the Ma model is easy to use and has the potential to predict the erosive burning rate before a firing test

efficient simulation of grain burning surface regression

The computation of grain burning surface regression plays a very important role in the internal ballistic performance evaluation of solid rocket motor, however, the traditional methods such as geometry-based one could not handle the self-intersection and characteristic geometric element disappearing problems. This paper presents an effective and efficient framework to simulate 3D grain burning surface regression with level set method which is combined with Fast Marching technique to constrain the calculation area only around the burning surface. At last, a typical grain example is given by our framework to verify our method's effectiveness and efficiency. © (2012) Trans Tech Publications.The computation of grain burning surface regression plays a very important role in the internal ballistic performance evaluation of solid rocket motor, however, the traditional methods such as geometry-based one could not handle the self-intersection and characteristic geometric element disappearing problems. This paper presents an effective and efficient framework to simulate 3D grain burning surface regression with level set method which is combined with Fast Marching technique to constrain the calculation area only around the burning surface. At last, a typical grain example is given by our framework to verify our method's effectiveness and efficiency. © (2012) Trans Tech Publications