Carlos Chiquete

Receptivity of plane idealized one-reaction detonation to three-dimensional perturbations

Solution of the initial-value problem for small three-dimensional perturbations in a plane idealized one-dimensional detonation is presented as an expansion into modes of discrete and continuous spectra in the case of three-dimensional perturbations. The result provides a tool to predict initial amplitudes of the unstable modes depending on the initial perturbation. An example of initial perturbation introduced into the reaction zone is discussed. It is shown that the discrete spectrum stemming from the solution of the initial-value problem for an idealized onereaction detonation is equivalent to the spectrum of the conventional normal-mode approach.

Stability of detonation in a circular pipe with porous walls

A stability analysis is carried out taking into account slightly porous walls in an idealized detonation confined to a circular pipe. The analysis is carried out using the normal-mode approach and corrections are obtained to the underlying impenetrable wall case results to account for the effect of the slight porosity. The porous walls are modelled by an acoustic boundary condition for the perturbations linking the normal velocity and the pressure components and thus replacing the conventional no-penetration boundary condition at the wall. This new boundary condition necessarily complicates the derivation of the stability problem with respect to the impenetrable wall case. However, exploiting the expressly slight porosity, the modified temporal stability can be determined as a two-point boundary value problem similar to the case of a non-porous wall.

Biorthogonal eigenfunction system for supersonic inviscid flow past a flat plate

In order to illustrate the application of the biorthogonal eigenfunction system to receptivity problems and to multimode decomposition, a study case is chosen so that all steps of the method are accompanied by analytical solutions. The receptivity of an inviscid supersonic ∞ow past a ∞at plate to localized periodic-in-time perturbations emanating from the wall is revisited within the scope of the method of the biorthogonal eigenfunction system for linearized Euler’s equations. In addition, application of the biorthogonal eigenfunction system to projection of computational results onto modes of continuous spectra is shown.