One - Dimensional Profile Inversion of a Planar Layer Bounded by an Inhomogeneous Impedance Boundary

2006 ◽  
Author(s):  
Fatih Yaman ◽  
Ali Yapar
Keyword(s):  
Planar Layer ◽  
Impedance Boundary ◽  
One Dimensional ◽  
Profile Inversion

Thermoacoustic Stability of Quasi-One-Dimensional Flows–Part I: Analytical and Numerical Formulation

2004 ◽  
Vol 126 (4) ◽  
pp. 637-644 ◽  
Author(s):  
Dilip Prasad ◽  
Jinzhang Feng
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Problem Formulation ◽  
Mean Flow ◽  
Sonic Point ◽  
Impedance Boundary ◽  
One Dimensional ◽  
Natural Modes ◽  
Local Wave ◽  
Numerical Formulation

A numerical method is developed for transient linear analysis of quasi-one-dimensional thermoacoustic systems, with emphasis on stability properties. This approach incorporates the effects of mean flow variation as well as self-excited sources such as the unsteady heat release across a flame. Working in the frequency domain, the perturbation field is represented as a superposition of local wave modes, which enables the linearized equations to be integrated in space. The problem formulation is completed by specifying appropriate boundary conditions. Here, we consider impedance boundary conditions as well as those relevant to choked and shocked flows. For choked flows, the boundary condition follows from the requirement that perturbations remain regular at the sonic point, while the boundary conditions applicable at a normal shock are obtained from the shock jump conditions. The numerical implementation of the proposed formulation is described for the system eigenvalue problem, where the natural modes are sought. The scheme is validated by comparison with analytical and numerical solutions.

Three‐dimensional velocity profile inversion from finite‐offset scattering data

Geophysics ◽  
1981 ◽  
Vol 46 (6) ◽  
pp. 837-842 ◽  
Author(s):  
S. Raz
Keyword(s):  
Velocity Profile ◽  
Three Dimensional ◽  
Scattering Data ◽  
One Dimensional ◽  
Velocity Variations ◽  
Profile Inversion ◽  
Relationship Of ◽  
The Relationship

The reconstruction of three‐dimensional (3-D) velocity variations from finite‐offset scattering data is formulated. Reduction to the limiting cases of zero and small offset distances as well as the case of one‐dimensional (1-D) stratification is given. An inherent increase in complexity is cited and interpreted. The relationship of the proposed inversion to the F-K migration is discussed.

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