CONCEPTION OF A “SILENT” MORTAR PROJECTILE. PART II – CALCULATIONS OF INTERNAL BALLISTIC PARAMETERS

The paper presents a theoretical description of computer codes for solution of the major question of internal ballistics for a “silent” mortar projectile. The computer codes proved their usefulness by providing the characteristics of a shot for each correct configuration of the projectile and eliminat-ing automatically the solutions not complying with the accepted specifications. Additionally, the structure of the code facilitates the modifications of a system of equations and parameters of the model to assisting a designing process of other systems of firearms.

Investigations on Internal Ballistic Characteristics of Pasty Propellant Rocket Engine

Pasty rocket engines have broad application prospects in the aerospace field. To study the internal ballistic characteristics of the pasty propellant rocket engine, the burning surface change model of pasty propellant was built. The calculation program was developed to calculate the pressure evolution in the combustion chamber, and the experiment was carried out based on a pasty propellant rocket test system. The data calculated by the program are in good agreement with the experiment, the error of the initial pressure peak is only 4.02%, and the internal ballistic characteristics of the rocket engine at each stage were analyzed detailly. The effects of ignition delay time, transport pipeline structure, free volume of the combustion chamber, mass flow rate, and flow velocity of the pasty propellant on internal ballistic characteristics of the pasty propellant rocket engine are investigated. The results indicate that when the ignition delay time increases, the pressure rises faster and the initial pressure peak increases obviously. The transport pipe diameter changes from 11.3 mm to 7.4 mm, and the initial combustion time and residual propellant combustion time decreased by 41.3% and 36.0%. The reduction of the free volume of the combustion chamber can reduce the initial pressure peak and the time to reach the equilibrium pressure. The initial pressure spike and equilibrium pressure rise with the increase of the pasty propellant flow velocity. While the ignition transient decreased with the increase of the pasty propellant flow velocity. The internal ballistic properties can be improved by reducing the ignition delay time, the diameter of the transport pipeline, and the free volume of the combustion chamber, or by increasing the mass flow rate of the pasty propellant rocket engine.

Comparison of cylindrical and non-cylindrical grain internal ballistic behavior of hybrid rocket engines and solid rocket motors

Hybrid rocket engines (HREs) are a chemical propulsion system that nominally combine the advantages of liquid-propellant rocket engines (LREs) and solid-propellant rocket motors (SRMs). HREs in some cases can have a higher specific impulse and better controllability than SRMs, and lower cost and engineering complexity than LREs. For HREs and SRMs, both kinds of rocket engine employ a solid fuel grain, and the chosen grain configuration is a crucial point of their design. Different grain configurations have different internal ballistic behavior, which in turn can deliver different engine performance. A cylindrical grain design is a very common design for SRMs and HREs. A non-cylindrical-grain is a more complex grain configuration (than cylindrical) that has been used in many SRMs, and is also a choice for some HREs. However, while an HRE and an SRM can employ the same fuel grain configuration, the resulting internal ballistic behavior would not be expected to be the same. Pressure-dependent burning tends to dominate in SRMs, while axial flow-dependent burning tends to dominate in HREs. To help demonstrate in a more direct manner the influence of the differing combustion processes on the same fuel grain configuration used by an HRE and SRM, a number of internal ballistic simulations are undertaken for the present study. For the reference SRM cases looked at, an internal ballistic simulation program that has the capability of predicting head-end pressure and thrust as a function of time into a simulated firing is utilized for the present investigation; for the corresponding HRE cases, a simulation program is used to simulate the burning and flow process of these engines. For the present investigation, the two simulation programs are used to simulate the internal ballistic performance of various HREs and SRMs employing comparable cylindrical and non-cylindrical fuel grain configurations. The predicted performance results, in terms of pressure and thrust, are consistent with expectations that one would have for both propulsion system types.

Structural vibrations and internal ballistic modelling of a star-grain solid rocket motor

A numerical model is developed to solve the governing equations for the structural dynamics and internal ballistics of a solid rocket motor (SRM). An explicit finite element method is used to solve for the structural response, and an explicit finite volume method is used to solve for the internal ballistic flow. Together, these two numerical solutions are coupled to model the nonsteady behaviour of axial combustion instability in sleeved cylindrical- and star-grain SRMs. The simulation model is used to predict the axial instability in star-grain SRMs. A parametric analysis is made to record the effects of various parameters on the simulation model. These parameters include the numerical dissipation constant, damping ratio and pulsing strength. It is found that both the numerical dissipation constant and damping ratio can, both artificially and physically, affect the finite element structural response of the motor. The pulsing strength affects only the rate at which the do pressure rises as well as how quickly the limiting wave amplitude is reached. A numerical model is developed to solve the governing equations for the structural dynamics and internal ballistics of a solid rocket motor (SRM). An explicit finite element method is used to solve for the structural response, and an explicit finite volume method is used to solve for the internal ballistic flow. Together, these two numerical solutions are coupled to model the nonsteady behaviour of axial combustion instability in sleeved cylindrical- and star-grain SRMs.The simulation model is used to predict the axial instability in star-grain SRMs. A parametric analysis is made to record the effects of various parameters on the simulation model. These parameters include the numerical dissipation constant, damping ratio and pulsing strength. It is found that both the numerical dissipation constant and damping ratio can, both artificially and physically, affect the finite element structural response of the motor. The pulsing strength affects only the rate at which the do pressure rises as well as how quickly the limiting wave amplitude is reached.The detailed analysis of simulated star-grain SRM axial instability reveals the effect of structural vibrations on burning rate augmentation and wave development in nonsteady operation. The variation in oscillation frequencies about a given grain section periphery, and along the grain with different levels of burnback, influences the means by which the local acceleration drives the combustion and flow behavior. The amount of damping also plays a role in influencing the predicted instability symptoms of the motor.

Structural vibrations and internal ballistic modelling of a star-grain solid rocket motor

A numerical model is developed to solve the governing equations for the structural dynamics and internal ballistics of a solid rocket motor (SRM). An explicit finite element method is used to solve for the structural response, and an explicit finite volume method is used to solve for the internal ballistic flow. Together, these two numerical solutions are coupled to model the nonsteady behaviour of axial combustion instability in sleeved cylindrical- and star-grain SRMs. The simulation model is used to predict the axial instability in star-grain SRMs. A parametric analysis is made to record the effects of various parameters on the simulation model. These parameters include the numerical dissipation constant, damping ratio and pulsing strength. It is found that both the numerical dissipation constant and damping ratio can, both artificially and physically, affect the finite element structural response of the motor. The pulsing strength affects only the rate at which the do pressure rises as well as how quickly the limiting wave amplitude is reached. A numerical model is developed to solve the governing equations for the structural dynamics and internal ballistics of a solid rocket motor (SRM). An explicit finite element method is used to solve for the structural response, and an explicit finite volume method is used to solve for the internal ballistic flow. Together, these two numerical solutions are coupled to model the nonsteady behaviour of axial combustion instability in sleeved cylindrical- and star-grain SRMs.The simulation model is used to predict the axial instability in star-grain SRMs. A parametric analysis is made to record the effects of various parameters on the simulation model. These parameters include the numerical dissipation constant, damping ratio and pulsing strength. It is found that both the numerical dissipation constant and damping ratio can, both artificially and physically, affect the finite element structural response of the motor. The pulsing strength affects only the rate at which the do pressure rises as well as how quickly the limiting wave amplitude is reached.The detailed analysis of simulated star-grain SRM axial instability reveals the effect of structural vibrations on burning rate augmentation and wave development in nonsteady operation. The variation in oscillation frequencies about a given grain section periphery, and along the grain with different levels of burnback, influences the means by which the local acceleration drives the combustion and flow behavior. The amount of damping also plays a role in influencing the predicted instability symptoms of the motor.

Comparison of cylindrical and non-cylindrical grain internal ballistic behavior of hybrid rocket engines and solid rocket motors

Hybrid rocket engines (HREs) are a chemical propulsion system that nominally combine the advantages of liquid-propellant rocket engines (LREs) and solid-propellant rocket motors (SRMs). HREs in some cases can have a higher specific impulse and better controllability than SRMs, and lower cost and engineering complexity than LREs. For HREs and SRMs, both kinds of rocket engine employ a solid fuel grain, and the chosen grain configuration is a crucial point of their design. Different grain configurations have different internal ballistic behavior, which in turn can deliver different engine performance. A cylindrical grain design is a very common design for SRMs and HREs. A non-cylindrical-grain is a more complex grain configuration (than cylindrical) that has been used in many SRMs, and is also a choice for some HREs. However, while an HRE and an SRM can employ the same fuel grain configuration, the resulting internal ballistic behavior would not be expected to be the same. Pressure-dependent burning tends to dominate in SRMs, while axial flow-dependent burning tends to dominate in HREs. To help demonstrate in a more direct manner the influence of the differing combustion processes on the same fuel grain configuration used by an HRE and SRM, a number of internal ballistic simulations are undertaken for the present study. For the reference SRM cases looked at, an internal ballistic simulation program that has the capability of predicting head-end pressure and thrust as a function of time into a simulated firing is utilized for the present investigation; for the corresponding HRE cases, a simulation program is used to simulate the burning and flow process of these engines. For the present investigation, the two simulation programs are used to simulate the internal ballistic performance of various HREs and SRMs employing comparable cylindrical and non-cylindrical fuel grain configurations. The predicted performance results, in terms of pressure and thrust, are consistent with expectations that one would have for both propulsion system types.

Numerical Evaluation of the Use of Aluminum Particles for Enhancing Solid Rocket Motor Combustion Stability

The ability to predict the expected internal behaviour of a given solid-propellant rocket motor under transient conditions is important. Research towards predicting and quantifying undesirable transient axial combustion instability symptoms typically necessitates a comprehensive numerical model for internal ballistic simulation under dynamic flow and combustion conditions. On the mitigation side, one in practice sees the use of inert or reactive particles for the suppression of pressure wave development in the motor chamber flow. With the focus of the present study placed on reactive particles, a numerical internal ballistic model incorporating relevant elements, such as a transient, frequency-dependent combustion response to axial pressure wave activity above the burning propellant surface, is applied to the investigation of using aluminum particles within the central internal flow (particles whose surfaces nominally regress with time, as a function of current particle size, as they move downstream) as a means of suppressing instability-related symptoms in a cylindrical-grain motor. The results of this investigation reveal that the loading percentage and starting size of the aluminum particles have a significant influence on reducing the resulting transient pressure wave magnitude.