Numerical Prediction of Interior Ballistics Performance of Projectile Accelerator Using Granular or Tubular Solid Propellant

Two‐dimensional axisymmetric interior ballistics simulations in projectile acceleration systems that use granular or long slotted tubular solid propellants are performed using the solid/gas two‐phase fluid dynamics code of the Euler‐Lagrange approach. For validation, the simulation results are compared with experimental data for tubular solid propellants. In the series of the interior ballistics simulations, the propellant grain size and shape effects on the firing performance of 50 mm gun are numerically investigated. The propellant grain size and shape affect the energy release rate of the solid propellant charged in the chamber, the projectile kinetic energy at the muzzle, and even the fluctuations of the chamber pressure history. An appropriate burning surface area of the propellant grain exists, so that the projectile can achieve the maximum kinetic energy from the released energy of the solid propellant. Based on the simulation results, guidelines are proposed for the grain size design that enables the propellant energy to be used efficiently.     

Experimental Investigation on the Holdup Distribution of Oil‐Water Two‐Phase Flow in Horizontal Parallel Tubes

An experimental investigation was conducted to study the holdup distribution of oil and water two‐phase flow in two parallel tubes with unequal tube diameter. Tests were performed using white oil (of viscosity 52 mPa s and density 860 kg/m³) and tap water as liquid phases at room temperature and atmospheric outlet pressure. Measurements were taken of water flow rates from 0.5 to 12.5 m³/h and input oil volume fractions from 3 to 94 %. Results showed that there were different flow pattern maps between the run and bypass tubes when oil‐water two‐phase flow is found in the parallel tubes. At low input fluid flow rates, a large deviation could be found on the average oil holdup between the bypass and the run tubes. However, with increased input oil fraction at constant water flow rate, the holdup at the bypass tube became close to that at the run tube. Furthermore, experimental data showed that there was no significant variation in flow pattern and holdup between the run and main tubes. In order to calculate the holdup in the form of segregated flow, the drift flux model has been used here.     

Generation of Two‐Phase Air‐Water Flow with Fine Microbubbles

Aiming at the development of a low‐cost technology for multipurpose water and surface treatment in the chemical industry and beyond, using microbubbles, a novel scheme of liquid‐gas interaction within a specially designed bubble generator was tested. Its efficiency for the production of microbubbles with a size distribution in the micron range is confirmed. The basic element of the device is a vortex chamber with water supply through tangential ducts, while the gas (air) is introduced in a highly turbulent swirling flow of water in radial direction through the orifice in the gas supply duct, located on the chamber axis. Bubble diameters, bubble velocities in the pipe flow and effect of the output pressure on the bubble size distribution were studied.     

Explicit Critical Pressure Ratio for Choked Two‐Phase Homogeneous Nozzle Flow

The throat‐to‐stagnation critical pressure ratio for a frictionless and adiabatic nozzle flow of a homogeneous, nonflashing two‐phase mixture can only be expressed as the numerical solution of a transcendental equation. A simple, physically plausible approximation is herein proposed, which fits well over the whole range of mass flow qualities.     

Simulation and Experimental Validation of Two‐Phase Flow in an Aerosol Counter‐Flow Reactor using Computational Fluid Dynamics

A simulation of the hydrodynamic behavior of an aerosol‐counter flow reactor was conducted using an Euler‐Lagrange method. The simulation results were then verified with experiments. The process simulated was a separation process required during the production of biodiesel (fatty acid methyl ester). In this process, the liquid ester/glycerol phases are continuously injected through a hollow cone nozzle with an overpressure of 10⁶ Pa into the reactor, operated at 15000 Pa. The liquid is atomized because of the pressure drop and a liquid particle spray is generated with an inlet velocity of 44.72 m/s. Water vapor of temperature 333 K is injected tangentially through two side, gas inlets with an inlet velocity of 1.2 m/s. Excess methanol is subjected to a mass transfer from the liquid phase into the gas phase, which is withdrawn through the head of the reactor and condensed in an external condenser unit. The stripping of the methanol off the liquid leads to a sharp interface between the glycerol and the ester phase, which can then be easily separated by gravity or pumping. The gas velocity field, pressure field and the liquid particle trajectories were calculated successfully. Simulated dwell time distribution curves were derived and analyzed with the open‐open vessel dispersion model. Experimental dwell time distribution curves were measured, analyzed with the open‐open vessel dispersion model, and compared with the simulated curves. A good consistency between simulated and measured Bodenstein numbers was achieved, but 25 % of the simulated particles exited at the reactor's head, contrary to experimental observations. The difference between simulated and measured dwell times was within one order of magnitude.     

Three‐Dimensional Simulation of Pressure Fluctuation in a Granular Solid Propellant Chamber within an Ignition Stage

The effects of the conditions of the ignition system in the propellant chamber of a gun system using a granular solid propellant are numerically investigated with respect to ignition performance criteria such as the differential pressure generation between the breech and the projectile base. Simulations, in which the length of the primer and the igniter mass are varied, are performed using a solid/gas two‐phase fluid dynamics code for three‐dimensional calculation of gas flow and discrete solid propellant particles. This code simulates the igniter combustion in the primer, the movement of burning solid propellant grains, and the formation of pressure gradients inside the chamber in the ignition process. The differential pressures between the breech and the projectile base measured in experiments are well predicted by the simulations for various igniter conditions. In the process of igniting the solid propellant, the propellant grains are accelerated toward the projectile base by the igniter gas flows from the primer vents. Fixed‐particle simulation is also carried out in order to examine the effects of the movement of the solid propellant grains on the chamber pressure profile. The simulated results reveal that the movement of solid propellant grains causes differential pressure fluctuations, which depend on the discharge from the primer vents and the locations of these vents.     

Computational Fluid Dynamics Modeling of Gas‐Liquid Two‐Phase Flow around a Spherical Particle

Microscale studies, which can provide basic information for meso‐ and macroscale studies, are essential for the realization of flow characteristics of a packed bed. In the present study, the effects of gas velocity, liquid velocity, liquid‐solid contact angle, and liquid viscosity on the flow behavior were parametrically investigated for gas‐liquid two‐phase flow around a spherical particle, using computational fluid dynamics (CFD) methodology in combination with the volume‐of‐fluid (VOF) model. The VOF model was first validated and proved to be in good agreement with the experimental data. The simulation results show that the film thickness decreases with increasing gas velocity. This trend is more obvious with increasing operating pressure. With increasing liquid velocity, the film thickness tends to be uniform on the particle surface. The flow regime can change from film flow to transition flow to bubble flow with increasing contact angle. In addition, only at relatively high values does the liquid viscosity affect the residence time of the liquid on the particle surface.     

Distribution of Two‐Phase Flow across 2.7‐mm Vertically Split U‐Type Junctions

A visual observation of the two‐phase flow across vertically split U‐type junctions and its flow redistribution inside two 2.7‐mm diameter smooth tubes with curvature ratios (2R/D) of 3 and 7, respectively, are reported. The range of mass flux is between 100 and 700 kg/m²s and quality (x) ranges from 0.001 to 0.5. The ratio of liquid distribution between the upper and lower outlet legs is related to the inlet flow pattern, but its influence is reduced at higher mass flux. The difference in liquid flow rates in the lower and upper legs is significantly affected by gravity at a small inlet mass flux, but this difference becomes less profound when the inlet mass flux is increased. The difference between the liquid flux in the upper and lower leg is reduced for the smaller curvature radius due to the reduced effect of gravity between the upper and lower legs. However, there is no consistent trend of gas flow distribution across the U‐type junction as compared to liquid flow distribution. The air mass flux in the upper and lower legs always increase with an increase in both gas quality and the total mass flux.     

Accuracy of Safety Valve Two‐Phase Mass Flow Capacity Sizing

The method specified in ISO/CD 4126–10 exhibits the highest accuracy compared to other models used in industry and academia. At the same time it allows for an oversizing of the necessary relief area under all test conditions. The average or statistical reproductive accuracy is characterized by an unacceptable logarithmic scatter of about 80 %.     

Toward Understanding of Two‐Phase Eccentric Helical Reactor Performance

Mass transfer investigations in a two‐phase gas‐liquid Couette‐Taylor flow (CTF) reactor and a numerical flow simulation are reported. The CTF reactor is characterized by high values of the mass transfer parameters. Previous mass transfer investigations have yielded high values of the volumetric mass transfer coefficients (of the order of 10^–1 s^–1) and the specific interfacial area, compared to those obtained in a stirred tank (10³ m² m^–3). In order to intensify mass transfer in the CTF reactor, an eccentric rotor (rotating inner cylinder) was used. In the eccentric annulus with rotating inner cylinder, due to frequent variation of the hydrodynamic flow field parameters, nonlinear hydrodynamic conditions occurred. These conditions can influence the rate of mass transfer. The experimental results of benzaldehyde oxidation in an eccentric CTF reactor confirmed an increase in mass transfer, as against a concentric CTF reactor. Numerical simulation of the Couette‐Taylor (helical) flow was performed in a concentric and in an eccentric annulus. Calculation of parameters such as velocity, static pressure, kinetic energy and energy dissipation rate revealed a significant effect of gap eccentricity on the flow behavior.     

Modeling of Two‐Phase Flashing Flow of Multicomponent Mixtures in Large Diameter Pipes

A two‐phase flashing flow model is developed to predict the distributions of pressure, temperature, velocity and evaporation rate in a transfer line, which is a typical example of a two‐phase flow pipe in the petrochemical industry. The model is proposed based on the pressure drop model and the multi‐stage flash model. The results indicate that pressure drop, temperature drop, and change of evaporation rate mainly occur in the transition section and the junction site of the transfer line. The predictions of the model have been tested with reliable field data and the good agreement obtained may lead to a better understanding of the two‐phase flashing flow phenomenon, as well as demonstrating the feasibility of applying the model into the design and optimization of pipelines.     

Analysis of Liquid Jet Breakup in One‐ and Two‐Phase Flows

The phenomenon of breakup of a jet into drops has been applied mainly to separation technologies in the chemical, pharmaceutical, and metallurgical industries. The paper deals with the experimental analysis directed at the breakup of polymer solutions flowing through an orifice nozzle. The analysis of the breakup and atomization of a liquid jet by a high‐speed gas jet is presented. Additionally, non‐Newtonian effects on the breakup of the liquid jet into drops were studied using the microphotography method. In the experiments, various aqueous solutions of polyacrylamide were used. The polymer solutions studied were power‐law fluids. Analysis of the photographs of the jet breakup showed that the length of the jets depends on the liquid and gas flow rates and on the concentration of the polymer used. High‐molecular‐weight polymers added to a solvent lead to changes in the rheological properties of the liquid and the breakup length of the jet.     

Phase Distribution Measurements during Transient Bubbly Two‐Phase Flow in a Vertical Pipe

An experimental procedure for investigating transient bubble flow for an adiabatic air/water system with vertical upward flow in a pipe is presented. The results of the measured local transient two‐phase flow parameters are shown along a pipe length of approx. four meters. From the measured radial phase distributions under steady and under transient conditions one can draw conclusions about the interfacial forces. Here, the effects indicate the action of forces such as a transverse lift force and a time dependent force like the virtual mass force during the transient. For modelling the transverse lift force which seems to play a dominant role for that flow regime the formulation of Zun was chosen and it was implemented into the commercial CFD‐Code Fluent Release 4.4.4 via user‐defined subroutines. Finally, results from the simulation of the steady states of start and end conditions of an experimental measured transient are shown.     

Using NSGA‐II and TOPSIS Methods for Interior Ballistic Optimization Based on One‐Dimensional Two‐Phase Flow Model

In order to meet the design demands of new gun systems or new types of projectiles, the interior ballistic charge design seems especially important. In this paper, a one‐dimensional two‐phase flow model is presented. The model describes the transient combustion of granular propellants in a gun, and pressure waves are considered as an objective. This study adopts a hybrid method to solve the problem. In the first stage, the non‐dominated sorting genetic algorithm (NSGA‐II) with “a “filter” is employed to approximate a set of Pareto‐optimal solutions. In the subsequent stage, a multi‐attribute decision‐making (MADM) approach is adopted to rank these solutions from the best to the worst. The ranking of Pareto‐optimal solutions is based on the technique ordered preference by similarity to ideal solution (TOPSIS) method. In TOPSIS method each objective needs a corresponding weight coefficient, and a practical problem is introduced. Both the entropy method and linear analysis method are adopted to get two sets of weights for the objectives, respectively. The two pairs of final, best compromise solutions are compared for satisfying the designer’s aim. For the analysis of the results, a two‐phase flow interior ballistic model for design optimization is established, and the hybrid approach could get a reasonable design scenario.     

3‐D Simulations of an Internal Airlift Loop Reactor using a Steady Two‐Fluid Model

Three‐dimensional (3‐D) simulations of an internal airlift loop reactor in a cylindrical reference frame are presented, which are based on a two‐fluid model with a revised k‐? turbulence model for two‐phase bubbly flow. A steady state formulation is used with the purpose of time saving for cases with superficial gas velocity values as high as 0.12 m/s. Special 3‐D treatment of the boundary conditions at the axis is undertaken to allow asymmetric gas‐liquid flow. The simulation results are compared to the experimental data on average gas holdup, average liquid velocity in the riser and the downcomer, and good agreement is observed. The turbulent dispersion in the present two‐fluid model has a strong effect on the gas holdup distribution and wall‐peaking behavior is predicted. The CFD code developed has the potential to be applied as a tool for scaling up loop reactors.     

Void Fraction Measurement for Two‐Phase Flow Using Electrical Resistance Tomography

Measurement of void fraction of two‐phase flows remains a challenging area. In this paper the application of an electrical resistance tomography (ERT) system for this purpose has been studied. A new approach through the direct use of the voltage data measured by the ERT system is presented. The measured voltage data are first compressed through a feature extraction, and a polynomial regression procedure is followed to obtain the relationship between the void fraction and the feature extracted. Both simulation and experiment are carried out to verify the approach. The methodology of the new approach, simulation and experimental results are presented in the paper.     

Characterization of Air‐Water Two‐Phase Vertical Flow by Using Electrical Resistance Imaging

The characterization of air‐water two‐phase vertical flow in a 12 m flow loop with 1.5 m of vertical section is studied by using electrical resistance tomography (ERT). By applying a fast data collection to a dual‐plane ERT sensor and an iterative image reconstruction algorithm, relevant information is gathered for implementation of flow characteristics, particularly for flow regime recognition. A cross‐correlation method is also used to interpret the velocity distribution of the gas phase on the cross section. The paper demonstrates that ERT can now be deployed routinely for velocity measurements and this capability will increase as faster measurement systems evolve.     

Numerical Simulation of the Hydrodynamics of Gas/Solid Two‐Phase Flow in a Circulating Fluidized Bed with Different Inlet Configurations

The gas/solid flow characteristics in a circulating fluidized bed with two different inlet configurations were investigated by numerical simulation based on an Eulerian approach. In order to describe the interaction between the gas phase and the solid phase and the influence of the solid phase on the gas turbulence, a source term formulation with a more reasonable physical meaning was introduced. The simulation results were validated by the experimental data; then, the model was employed to examine the effect of the inlet configuration on the gas and solid feeding. The simulation results showed that, using the side feeding system, the distributions of solid flow and concentration were highly variable both over the column cross‐section and along the column height. However, such variations can be improved by using the elbow inlet system where the gas and solid are fed from the bottom.