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1 – 10 of 52
Article
Publication date: 21 November 2018

Tao Xue, Xiaobing Zhang and K.K. Tamma

A consistent implementation of the general computational framework of unified second-order time accurate integrators via the well-known GSSSS framework in conjunction with the…

Abstract

Purpose

A consistent implementation of the general computational framework of unified second-order time accurate integrators via the well-known GSSSS framework in conjunction with the traditional Finite Difference Method is presented to improve the numerical simulations of reactive two-phase flows.

Design/methodology/approach

In the present paper, the phase interaction evaluation in the present implementation of the reactive two-phase flows has been derived and implemented to preserve the consistency of the correct time level evaluation during the time integration process for solving the two phase flow dynamics with reactions.

Findings

Numerical examples, including the classical Sod shock tube problem and a reactive two-phase flow problem, are exploited to validate the proposed time integration framework and families of algorithms consistently to second order in time accuracy; this is in contrast to the traditional practices which only seem to obtain first-order time accuracy because of the inconsistent time level implementation with respect to the interaction of two phases. The comparisons with the traditional implementation and the advantages of the proposed implementation are given in terms of the improved numerical accuracy in time. The proposed approaches provide a correct numerical simulation implementation to the reactive two-phase flows and can obtain better numerical stability and computational features.

Originality/value

The new algorithmic framework and the consistent time level evaluation extended with the GS4 family encompasses a multitude of past and new schemes and offers a general purpose and unified implementation for fluid dynamics.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 April 1986

G. Billet

A class of flux‐splitting explicit second‐order finite difference schemes is set up. An ‘optimal’ scheme is defined for 1‐D flows and applied to 2‐D flows with CFL being able to…

Abstract

A class of flux‐splitting explicit second‐order finite difference schemes is set up. An ‘optimal’ scheme is defined for 1‐D flows and applied to 2‐D flows with CFL being able to reach 2. The results obtained show that this ‘optimal’ scheme is well adapted to the unsteady flows.

Details

Engineering Computations, vol. 3 no. 4
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 28 October 2013

Cheng Cheng and Xiaobing Zhang

In computational fluid dynamics for two-phase reactive flow of interior ballistic, the conventional schemes (MacCormack method, etc.) are known to introduce unphysical…

Abstract

Purpose

In computational fluid dynamics for two-phase reactive flow of interior ballistic, the conventional schemes (MacCormack method, etc.) are known to introduce unphysical oscillations in the region where the gradient is high. This paper aims to improve the ability to capture the complex shock wave during the interior ballistic cycle.

Design/methodology/approach

A two-phase flow model is established to describe the complex physical process based on a modified two-fluid theory. The solution of model is obtained including the following key methods: an approximate Riemann solver to construct upwind fluxes, the MUSCL extension to achieve high-order accuracy, a splitting approach to solve source terms, a self-adapting method to expand the computational domain for projectile motion and a control volume conservation method for the moving boundary.

Findings

The paper is devoted to applying a high-resolution numerical method to simulate a transient two-phase reactive flow with moving boundary in guns. Several verification tests demonstrate the accuracy and reliability of this approach. Simulation of two-phase reaction flow with a projectile motion in a large-caliber gun shows an excellent agreement between numerical simulation and experimental measurements.

Practical implications

This paper has implications for improving the ability to capture the complex physics phenomena of two-phase flow during interior ballistic cycle and predict the combustion details, such as the flame spreading, the formation of pressure waves and so on.

Originality/value

This approach is reliable as a prediction tool for the understanding of the physical phenomenon and can therefore be used as an assessment tool for future interior ballistics studies.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 March 1994

E. Daniel, R. Saurel, M. Larini and J.C. Loraud

This paper investigates the multi‐phase behaviour of dropletsinjected into a nozzle at two separate wall locations. The physical featuresof the droplets (rate of mass, density and…

Abstract

This paper investigates the multi‐phase behaviour of droplets injected into a nozzle at two separate wall locations. The physical features of the droplets (rate of mass, density and radius) at each injector location are identical. This system can be described by a two‐phase Eulerian—Eulerian approach that yields classical systems of equations: three for the gaseous phase and three for the dispersed droplet phase. An underlying assumption in the two phase model is that no interaction occurs between droplets. The numerical solution of the model (using the MacCormack scheme) indicates however that the opposite jets do interact to form one jet. This inconsistency is overcome in the current paper by associating the droplets from a given injection location with a separate phase and subsequently solving equations describing a multiphase system (here, three‐phase system). Comparison of numerical predications between the two‐phase and the multiphase model shows significantly different results. In particular the multiphase model shows no jet interaction.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 4 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 November 1997

T. Basset, E. Daniel and J.C. Loraud

Presents validation of the Eulerian approach for unsteady two‐phase flows, whose behaviour depends on the coupling between the two phases, on the basis of the study of…

Abstract

Presents validation of the Eulerian approach for unsteady two‐phase flows, whose behaviour depends on the coupling between the two phases, on the basis of the study of attentuation and dispersion of an acoustic wave propagating into a one dimensional two‐phase flow. This approach and the corresponding numerical aspects are accurate enough for later applications in more complex geometries, where “vortex shedding” phenomena take place. Attenuation and dispersion of a pressure wave in a two‐phase medium of rest was previously studied by Temkin and Dobbins. Present work is an extension of this theory to the case of a two‐phase flow. This theoretical approach leads to a numerical solution of the problem. Compares the derived results with those obtained from a direct numerical simulation based on MacCormack scheme in a finite volume formulation. Verifies that analytical and numerical approaches are in good agreement.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 7 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 2 March 2015

Qiao Luo and Xiaobing Zhang

In engineering applications, gas-solid two-phase reaction flow with multi-moving boundaries is a common phenomenon. The launch process of multiple projectiles is a typical…

Abstract

Purpose

In engineering applications, gas-solid two-phase reaction flow with multi-moving boundaries is a common phenomenon. The launch process of multiple projectiles is a typical example. The flow of adjacent powder chambers is coupled by projectile’s motion. The purpose of this paper is to study this flow by numerical simulation.

Design/methodology/approach

A one-dimensional two-phase reaction flow model and MacCormack difference scheme are implemented in a computational code, and the code is used to simulate the launch process of a system of multiple projectiles. For different launching rates and loading conditions, the simulated results of the launch process of three projectiles are obtained and discussed.

Findings

At low launching rates, projectiles fired earlier in the series have little effect on the launch processes of projectiles fired later. However, at higher launching rates, the projectiles fired first have a great influence on the launch processes of projectiles fired later. As the launching rate increases, the maximum breech pressure for the later projectiles increases. Although the muzzle velocities increase initially, they reach a maximum at some launching rate, and then decrease rapidly. The muzzle velocities and maximum breech pressures of the three projectiles have an approximate linear relationship with the charge weight, propellant web size and chamber volume.

Originality/value

This paper presents a prediction tool to understand the physical phenomenon of the gas-solid two-phase reaction flow with multi-moving boundaries, and can be used as a research tool for future interior ballistics studies of launch system of multiple projectiles.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 July 1995

Raafat G. Saadé and Semaan Sarraf

In Northern Regions, ice covers that form on rivers, streams, and lakeswith the onset of winter, cause various problems related to winter navigationand pollution dispersion among…

Abstract

In Northern Regions, ice covers that form on rivers, streams, and lakes with the onset of winter, cause various problems related to winter navigation and pollution dispersion among others. Warm water, from industrial plants, discharged into these rivers cause partial or total melting of the ice cover over considerable distances. The present work investigates the melting of a thin non‐uniform ice cover subject to varying water and air temperatures under turbulent flow conditions. A two‐dimensional depth averaged turbulence model coupled with a heat transfer model is used to simulate laboratory conditions of ice cover melting. Computational results were compared with experimental investigations. The average melting of the ice cover was found to be in close agreement with the experimental measurements with the exception of the leading edge region.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 5 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 August 1996

E.Y.K. NG and S.Z. LIU

This paper introduces a novel algorithm for solving the two‐dimensional Euler and Navier‐Stokes compressible equations using a one‐step effective flux vector‐splitting implicit…

Abstract

This paper introduces a novel algorithm for solving the two‐dimensional Euler and Navier‐Stokes compressible equations using a one‐step effective flux vector‐splitting implicit method. The new approach makes a contribution by deriving a simple and yet effective implicit scheme which has the features of an exact factorization and avoids the solving of block‐diagonal system of equations. This results in a significant improvement in computational efficiency as compared to the standard Beam‐Warming and Steger implicit factored schemes. The current work has advantageous characteristics in the creation of higher order numerical implicit terms. The scheme is stable if we could select the correct values of the scalars (λ±ξ and λ±η) for the respective split flux‐vectors (F± and G±) along the ξ− and η−directions. A simple solving procedure is suggested with the discussion of the implicit boundary conditions, stability analysis, time‐step length and convergence criteria. This method is spatially second‐order accurate, fully conservative and implemented with general co‐ordinate transformations for treating complex geometries. Also, the scheme shows a good convergence rate and acceptable accuracy in capturing the shock waves. Results calculated from the program developed include transonic flows through convergence‐divergence nozzle and turbine cascade. Comparisons with other well‐documented experimental data are presented and their agreements are very promising. The extension of the algorithm to 3D simulation is straightforward and under way.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 6 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 2 August 2013

Mohammed Q. Al‐Odat

In this study, the purpose was to introduce two‐dimensional hyperbolic heat conduction equations in order to simulate the fast precooling process of a cylindrically shaped food…

Abstract

Purpose

In this study, the purpose was to introduce two‐dimensional hyperbolic heat conduction equations in order to simulate the fast precooling process of a cylindrically shaped food product with internal heat generation. A modified model for internal heat generation due to respiration in the food product was proposed to take the effect of relaxation time into account. The obtained governing equations were solved numerically using an efficient finite difference technique. The influence of Biot number and heat generation parameters on thermal characteristics was examined and discussed. The results based on hyperbolic model were compared with the classical parabolic heat diffusion model. The present numerical code was validated via comparison with analytical solution and a good agreement was found.

Design/methodology/approach

The obtained governing equations were solved numerically using an efficient finite difference technique.

Findings

The influence of Biot number and heat generation parameters on thermal characteristics was examined and discussed. The results based on hyperbolic model were compared with the classical parabolic heat diffusion model. The present numerical code was validated via comparison with analytical solution and a good agreement was found.

Originality/value

Two‐dimensional analysis of fast precooling of cylindrical food product based on hyperbolic heat conduction model has not been investigated yet.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 2 October 2017

Junaid Godil and Ali Kamran

The capability to predict and evaluate the motor pressure during each phase by means of a numerical analysis can significantly increase the efficiency of the preliminary design…

Abstract

Purpose

The capability to predict and evaluate the motor pressure during each phase by means of a numerical analysis can significantly increase the efficiency of the preliminary design process with a reduction of both the motor development and operational costs. This paper aims to perform numerical simulation to analyze the ignition transient in solid rocket motor by solving Euler equation coupled with some semi-empirical correlations. These relations take into account the main phenomena affecting the ignition transient. Coupling relationships include the heat transfer of the gas to the propellant and erosive burning rate relationship.

Design/methodology/approach

The current research effort divides motor into series of control volumes along the port axis, and the variation of port area, burning surface and burning rate along the port are taken into account. A set of governing equations are then solved using explicit, time-dependent, predictor-corrector finite difference method. The numerical model helps to capture and embed shock wave associated with igniter flow within the solution. Second-order artificial viscosity dampens out the numerical oscillations due to sharp gradient within the flow field. The developed computer code predicts the start-up characteristics of motor. The study also provides comparison of simulation results with in-house experimental motor.

Findings

Simulations are performed with and without erosive burning to demonstrate that the flow model is a good physical approximation of motor. Numerical results calculated by this model without erosive burning are not in good agreement with experimental results. This minor discrepancy has motivated the inclusion of erosive burning in numerical model. The simulated results are then compared with the experimental data for head-end and rear-end pressure. The agreement between simulation and experiment is remarkable. In summary, major finding of this study is that unsteady quasi-one-dimensional gas dynamic model can capture the flow field in the motor during ignition transient effectively.

Research limitations/implications

Unsteady quasi-one-dimensional gas dynamic model can capture the flow field in the motor during ignition transient effectively. However, in systems where two- and three-dimensional effects are pre-dominant, one would require to develop a more elaborate, multi-dimensional model which will allow for further understanding of the flow behavior and eventually lead to modeling of rocket motors with more complex geometries.

Practical implications

The close agreement between experimental and simulation results can be considered as forced to some degree, because the general mathematical model of erosive burning contains a free variable erosive burning exponent. However, in future, this variable can be established a priori by erosive burning tests.

Originality/value

The solid propellant ignition process consists of series of rapid events and must be completed in a fraction of a second. An understanding of the dynamics of ignition has become increasingly vital with the development of larger and more sophisticated solid propellant rocket motors. This research effort provides the simulation framework to predict and evaluate the motor pressure during each phase by means of a numerical analysis, thus significantly increasing the efficiency of the preliminary design process with a reduction of both the motor development and operational costs.

Details

Aircraft Engineering and Aerospace Technology, vol. 89 no. 6
Type: Research Article
ISSN: 1748-8842

Keywords

1 – 10 of 52