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- W2326867579 abstract "The first computational results for transverse mode acoustic instability in circular geometry are presented. The computations are performed on unstructured computational mesh with a 2-D explicit Euler solver based on upwind discretization on a control volume. The flow of particles was modeled by Eulerian formulation. Gas and solid phase fluxes are computed with Riemann solvers. Time dependent injection rate is determined by using linear response function. The stable and unstable limit cycles are obtained so that numerical validation of existence and stability for the transverse modes are performed . † Ph.D., Research Engineer ‡ Professor, Member AIAA INTRODUCTION Circular geometry is frequently used in solid and liquid rocket motor cavities. The existence and stability for the transverse modes for circular cylinder was performed by Culick and Yang [1]. Culick used approximate analysis in his study and he employed method of time averaging for the solution of nonlinear wave equations. He also analyzed the higher order mean flow and acoustics interactions for transverse modes with the same methodology. In this study the problem is analyzed with computational fluid dynamics (CFD) approach. The CFD was successfully used for the analysis of longitudinal combustion instabilities in solid rocket motors. On the other hand computation of instabilities on transverse modes with CFD is untouched area. In the first part of this study linear stability analysis is given for different particle sizes holding solid phase fraction constant. In the second part the numerical computations are presented LINEAR STABILITY ANALYSIS METHOD The first step in applying the linear stability is to find the radial and transverse mode shapes of the circular geometry. The mode shapes for the 3-D form of the geometry, namely, circular cylinder geometry, is available in literature [2], therefore the 2-D mode shapes are extracted from this source. As for the circular cylinder that is presented in Figure 1, there are two possible normal modes for each frequency, and these are: ( ) ( ) θ κ π ψ m r J x L l ms m n cos cos = (1) ( ) ( ) θ κ π ψ m r J x L l ms m n sin cos = (2) with l=0,1,2,..., m=0,1,2,..., s=0,1,2,... The wave number is defined as" @default.
- W2326867579 created "2016-06-24" @default.
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- W2326867579 date "2003-06-26" @default.
- W2326867579 modified "2023-09-27" @default.
- W2326867579 title "Numerical Computation of Non-Linear Transverse Mode Acoustic Instability in Circular Geometry Confining Two-Phase Mixture" @default.
- W2326867579 cites W2079772543 @default.
- W2326867579 doi "https://doi.org/10.2514/6.2003-5087" @default.
- W2326867579 hasPublicationYear "2003" @default.
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