Aslan Kasimov

Spinning instability of gaseous detonations

We investigate hydrodynamic instability of a steady planar detonation wave propagating in a circular tube to three-dimensional linear perturbations, using the normal mode approach. Spinning instability is identified and its relevance to the well-known spin detonation is discussed. The neutral stability curves in the plane of heat release and activation energy exhibit bifurcations from low-frequency to high-frequency spinning modes as the heat release is increased at fixed activation energy. With a simple Arrhenius model for the heat release rate, a remarkable qualitative agreement with experiment is obtained with respect to the effects of dilution, initial pressure and tube diameter on the behaviour of spin detonation. The analysis contributes to the explanation of spin detonation which has essentially been absent since the discovery of the phenomenon over seventy years ago.

On the dynamics of self-sustained one-dimensional detonations: A numerical study in the shock-attached frame

In this work we investigate the dynamics of self-sustained detonation waves that have an embedded information boundary such that the dynamics is influenced only by a finite region adjacent to the lead shock. We introduce the boundary of such a domain, which is shown to be the separatrix of the forward characteristic lines, as a generalization of the concept of a sonic locus to unsteady detonations. The concept plays a fundamental role both in steady detonations and in theories of much more frequently observed unsteady detonations. The definition has a precise mathematical form from which its relationship to known theories of detonation stability and nonlinear dynamics can be clearly identified. With a new numerical algorithm for integration of reactive Euler equations in a shock-attached frame, that we have also developed, we demonstrate the main properties of the unsteady sonic locus, such as its role as an information boundary. In addition, we introduce the so-called “nonreflecting” boundary condition at the far end of the computational domain in order to minimize the influence of the spurious reflected waves.

State of Detonation Stability Theory and Its Application to Propulsion

We present an overview of the current state of detonation stability theory and discuss its implications for propulsion. The emphasis of the review is on the exact or asymptotic treatments of detonations, including various asymptotic limits that appear in the literature. The role that instability plays in practical detonation-based propulsion is of primary importance and is largely unexplored, hence we point to possible areas of research both theoretical and numerical, that might help improve our understanding of detonation behavior in propulsion devices. We outline the basic formulation of detonation stability theory that starts from linearized Euler equations, describe the algorithm of solution, and present an example that illustrates typical results.

Asymptotic theory of evolution and failure of self-sustained detonations

Based on a general theory of detonation waves with an embedded sonic locus that we have previously developed, we carry out asymptotic analysis of weakly curved slowly varying detonation waves and show that the theory predicts the phenomenon of detonation ignition and failure. The analysis is not restricted to near Chapman–Jouguet detonation speeds and is capable of predicting quasi-steady, normal detonation shock speed versus curvature (

Turing patterns and long-time behavior in a three-species food-chain model

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A stationary circular hydraulic jump, the limits of its existence and its gasdynamic analogue

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Model for shock wave chaos.

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Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models.

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Mode selection in weakly unstable two-dimensional detonations

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THEORY OF DETONATION WITH AN EMBEDDED SONIC LOCUS

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