Multi-Stage Multidisciplinary Design Optimization Method for Enhancing Complete Artillery Internal Ballistic Firing Performance

To enhance the comprehensive performance of artillery internal ballistics—encompassing power,accuracy,and service life—this study proposed a multi-stage multidisciplinary design optimization(MS-MDO)method.First,the comprehensive artillery internal ballistic dynamics(AIBD)model,based on propellant combustion,rotation band engraving,projectile axial motion,and rifling wear models,was established and validated.This model was systematically decomposed into subsystems from a system engineering perspective.The study then detailed the MS-MDO methodology,which included Stage I(MDO stage)employing an improved collaborative optimization method for consistent design variables,and Stage II(Performance Optimization)focusing on the independent optimization of local design variables and performance metrics.The methodology was applied to the AIBD problem.Results demonstrated that the MS-MDO method in Stage I effectively reduced iteration and evaluation counts,thereby accelerating system-level convergence.Meanwhile,Stage II optimization markedly enhanced overall performance.These comprehensive evaluation results affirmed the effectiveness of the MS-MDO method.

An internal ballistic model of electromagnetic railgun based on PFN coupled with multi-physical field and experimental validation

To accelerate the practicality of electromagnetic railguns,it is necessary to use a combination of threedimensional numerical simulation and experiments to study the mechanism of bore damage.In this paper,a three-dimensional numerical model of the augmented railgun with four parallel unconventional rails is introduced to simulate the internal ballistic process and realize the multi-physics field coupling calculation of the rail gun,and a test experiment of a medium-caliber electromagnetic launcher powered by pulse formation network(PFN)is carried out.Various test methods such as spectrometer,fiber grating and high-speed camera are used to test several parameters such as muzzle initial velocity,transient magnetic field strength and stress-strain of rail.Combining the simulation results and experimental data,the damage condition of the contact surface is analyzed.

On the Transient Numerical Simulation of Solid Rocket Motor by Coupling Quasi One⁃Dimension Internal Flow with Three⁃Dimension Propellant Grain Burnback

The quasi one⁃dimension compressible flowfield coupled to the three⁃dimension propellant grain regression solved by the level⁃set method was used to simulate the transient internal ballistics of solid rocket motor.One⁃dimension flowfield instead of three⁃dimension can save computational cost on the premise of calculation accuracy because the radial and azimuthal variations parameters have little contribution to the internal flowfield.The grain regression in real⁃time could provide accurate geometrical information for simulation.A combination of flowfluid solver and grain regression can reappear in a relatively real internal ballistic flowfield,so it is good for further studying the instability of solid rocket motor.For level⁃set equations,the total variation⁃diminishing second⁃order Runge⁃Kutta method for temporal derivatives and a fifth⁃order weighted⁃essentially⁃non⁃oscillatory scheme for spatial derivatives were used.The total variation⁃diminishing MacCormack method was used to discrete the Euler equations in flowfield solver.Two modules of this code were tested in this study:one is the burning rate module and the other is the nozzle erosion module.Results show that the burning rate influenced the solid rocket motor efficiency,and the velocity profile in the chamber was affected by the nozzle shape,and the nozzle erosion could influence the head⁃end pressure spike.

Burning Regression Analysis for 3D Grain Configurations

Grain design is essentially filling a prescribed volume （chamber case） with a certain shape of propellant so as to ensure mission requirements. An infinite number of possibilities exist, covering from two dimensional to three dimensional grain designs. Accurate calculation of grain geometrical properties plays a vital role in performance prediction. In this paper a methodology has been presented for designing 3D grain configuration for Solid Rocket Motors （SRMs）. The design process involves parametric modeling of the geometry in CAD software through dynamic variables that define the complex configuration. Initial geometry is defined in the form of a surface which defines the grain configuration. Grain bum back is achieved by making new surfaces at each web increment and calculating geometrical properties at each step. Geometrical calculations are based on volume and change in volume calculations. Models for Axisymetric and Finocyl grain configuration have been developed. Equilibrium pressure method is used to calculate the internal ballistics. The procedure adopted can be applied to any complex geometry in a relatively simple way for preliminary designing of grain configuration.

Finocyl Grain Design and Optimization Using Sequential Quadratic Programming

Design technique of 3D Finocyl grain configuration for Solid Rocket Motors, including its performance prediction and optimization is discussed. In doing so, the design objectives and constraints are set, geometric parameters of Finocyl grain are identified, and performance prediction parameters are calculated, thereafter the preliminary design is completed and optimal design is reached. For every grain design, it is necessary that the minimum possible mass of propellant is used to produce the required thrust within a certain limit of burning time. By using this technique of design and optimization, the vital parameter of propellant mass is optimized to its minimum value, yet vital parameter of thrust is attained in the required burning time with the fixed length and diameter of motor. Especially a geometrical model of grain configuration is developed by using various combinations of ellipsoid, cone, cylinder, sphere, torus and inclined plane. With the diameter of the motor fixed, the Finocyl Grain geometry totally depends on sixteen independent variables. Each of these variables has a bearing on explicit characteristic of Finocyl grain design and optimization. Changing the value of each of these variables brings significant effects on the performance. Due to such attributes of Finocyl grain configuration, compromises will result. Overall optimal design is ensured through assigning and analyzing a suitable range of geometric parameters satisfying the requirements of minimum mass of propellant and ensuring sound values for internal ballistic parameters while remaining within the design constraints of thrust, burning time, length and diameter of chamber case.

Design and Optimization of 3D Radial Slot Grain Configuration

Upper stage solid rocket motors （SRMS） for launch vehicles require a highly efficient propulsion system. Grain design proves to be vital in terms of minimizing inert mass by adopting a high volumetric efficiency with minimum possible sliver. In this arti- cle, a methodology has been presented for designing three-dimensional （3D） grain configuration of radial slot for upper stage solid rocket motors. The design process involves parametric modeling of the geometry in computer aided design （CAD） software through dynamic variables that define the complex configuration. Grain bum back is achieved by making new surfaces at each web increment and calculating geometrical properties at each step. Geometrical calculations are based on volume and change-in-volume calculations. Equilibrium pressure method is used to calculate the internal ballistics. Genetic algorithm （GA） has been used as the optimizer because of its robustness and efficient capacity to explore the design space for global optimum solution and eliminate the requirement of an initial guess. Average thrust maximization under design constraints is the objective function.

A Hybrid Optimization Approach for SRM FINOCYL Grain Design

This article presents a method to design and optimize 3D FINOCYL grain （FCG） configuration for solid rocket motors （SRMs）. The design process of FCG configuration involves mathematical modeling of the geometry and parametric evaluation of various independent geometric variables that define the complex configuration. Virtually infinite combinations of these variables will satisfy the requirements of mass of propellant, thrust, and burning time in addition to satisfying basic needs for volumetric loading fraction and web fraction. In order to ensure the acquisition of the best possible design to be acquired, a sound approach of design and optimization is essentially demanded. To meet this need, a method is introduced to acquire the finest possible performance. A series of computations are carried out to formulate the grain geometry in terms of various combinations of key shapes inclusive of ellipsoid, cone, cylinder, sphere, torus, and inclined plane. A hybrid optimization （HO） technique is established by associating genetic algorithm （GA） for global solution convergence with sequential quadratic programming （SQP） for further local convergence of the solution, thus achieving the final optimal design. A comparison of the optimal design results derived from SQP, GA, and HO algorithms is presented. By using HO technique, the parameter of propellant mass is optimized to the minimum value with the required level of thrust staying within the constrained burning time, nozzle and propellant parameters, and a fixed length and outer diameter of grain.

Design and optimization of solid rocket motor Finocyl grain using simulated annealing

The research effort outlined the application of a computer aided design(CAD)-centric technique to the design and optimization of solid rocket motor Finocyl(fin in cylinder) grain using simulated annealing.The proper method for constructing the grain configuration model,ballistic performance and optimizer integration for analysis was presented.Finocyl is a complex grain configuration,requiring thirteen variables to define the geometry.The large number of variables not only complicates the geometrical construction but also optimization process.CAD representation encapsulates all of the geometric entities pertinent to the grain design in a parametric way,allowing manipulation of grain entity(web),performing regression and automating geometrical data calculations.Robustness to avoid local minima and efficient capacity to explore design space makes simulated annealing an attractive choice as optimizer.It is demonstrated with a constrained optimization of Finocyl grain geometry for homogeneous,isotropic propellant,uniform regression,and a quasi-steady,bulk mode internal ballistics model that maximizes average thrust for required deviations from neutrality.