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RESEARCH PAPERS: Interior Ballistics

Implementation of Approximate Riemann Solver to Two-Phase Flows in Mortar Systems

[+] Author and Article Information
Ragini Acharya

Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802rza101@psu.edu

Kenneth Kuo

Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802kenkuo@psu.edu

J. Appl. Mech 77(5), 051401 (May 17, 2010) (9 pages) doi:10.1115/1.4001558 History: Received July 23, 2009; Revised January 27, 2010; Posted April 08, 2010; Published May 17, 2010; Online May 17, 2010

This work presents a mathematical model for the two-phase flows in the mortar systems and demonstrates the application of approximate Riemann solver on such model. The mathematical model for the two-phase gas-dynamical processes in the mortar tube consists of a system of first-order, nonlinear coupled partial differential equations with inhomogeneous terms. The model poses an initial value problem with discontinuous initial and boundary conditions that arise due to the design complexity and nonuniformity of granular propellant distribution in the mortar tube. The governing equations in this model possess characteristics of the Riemann problem. Therefore, a high-resolution Godunov-type shock-capturing approach was used to address the formation of flow structure such as shock waves, contact discontinuities, and rarefaction waves. A linearized approximate Riemann solver based on the Roe–Pike method was modified for the two-phase flows to compute fully nonlinear wave interactions and to directly provide upwinding properties in the scheme. An entropy fix based on Harten–Heyman method was used with van Leer flux limiter for total variation diminishing. The three-dimensional effects were simulated by incorporating an unsplit multidimensional wave propagation method, which accounted for discontinuities traveling in both normal and oblique coordinate directions. A mesh generation algorithm was developed to account for the projectile motion and coupled with the approximate Riemann solver. The numerical method was verified by using exact solutions of three test problems. The specific system considered in this work is a 120 mm mortar system, which contains an ignition cartridge that discharges hot gas-phase products and unburned granular propellants into the mortar tube through multiple vent-holes on its surface. The model for the mortar system was coupled with the solution of the transient gas-dynamic behavior in the ignition cartridge. The numerical results were validated with experimental data. Based on the close comparison between the calculated results and test data, it was found that the approximate Riemann solver is a suitable method for studying the two-phase combustion processes in mortar systems.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 5

Calculated z-t diagram of physical variables in the mortar tube with 0 charge increment

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Figure 6

Validation of calculated results by comparison with the measured (a) pressure-time traces at three port locations along the mortar tube and (b) projectile dynamics with measured data for 0 charge increments loading

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Figure 7

Validation of calculated results by comparison with the measured (a) pressure-time traces at three port locations along the mortar tube and (b) projectile dynamics with measured data for four charge increments loading

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Figure 4

Verification of the five-equation approximate Riemann solver by exact solution of the Riemann problem shown by test 3 at t=0.025 s (— exact, ○ calculation with flux limiter)

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Figure 3

Verification of the five-equation approximate Riemann solver by exact solution of the Riemann problem shown by test 2 at t=0.007 s (— exact and ○ calculation with flux limiter)

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Figure 2

Verification of the five-equation approximate Riemann solver by exact solution of the Riemann problem shown by test 1 at t=0.2 s (— exact, ◻ calculation without flux limiter, and ○ calculation with flux limiter)

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Figure 1

Cross-sectional view of the 120 mm mortar system

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