Pavel Utkin

Numerical and Experimental Investigation of Detonation Initiation in Profiled Tubes

Detonation initiation in a tube with parabolic contraction and conical expansion was investigated numerically and experimentally. The optimized geometry of conical expansion with sine-shaped wall is proposed. The generalized diagram in the form of detonation curves at the contraction slope angle versus incident shock Mach number plane is presented. For solving the governing Euler equations, the numerical method based on finite volume approach with Godunov flux approximation adapted for multiprocessor systems is used. It has been shown experimentally that the parabolic contraction and conical expansion ensure shock-to-detonation transition in a stoichiometric propane-air mixture under normal conditions at a very low minimal incident shock wave velocity of 680 ± 20 m/s, which approximately corresponds to a Mach number of 2. This result is important for novel jet propulsion systems with detonative burning of fuel-pulse detonation engines.

Numerical Study of Detonation Wave Propagation in the Variable Cross-Section Channel Using Unstructured Computational Grids

The work is dedicated to the numerical study of detonation wave initiation and propagation in the variable cross-section axisymmetric channel filled with the model hydrogen-air mixture. The channel models the large-scale device for the utilization of worn-out tires. Mathematical model is based on two-dimensional axisymmetric Euler equations supplemented by global chemical kinetics model. The finite volume computational algorithm of the second approximation order for the calculation of two-dimensional flows with detonation waves on fully unstructured grids with triangular cells is developed. Three geometrical configurations of the channel are investigated, each with its own degree of the divergence of the conical part of the channel from the point of view of the pressure from the detonation wave on the end wall of the channel. The problem in consideration relates to the problem of waste recycling in the devices based on the detonation combustion of the fuel.

MATHEMATICAL MODELING OF DETONATION PROPAGATION IN A TUBE WITH VARIABLE CROSS SECTION USING UNSTRUCTURED COMPUTATIONAL GRIDS

The finite-volume computational algorithm of the second approximation order for the calculation of two-dimensional flows with detonation waves on fully unstructured meshes with triangular cells is developed. The problem of detonation initiation and propagation in an axisymmetric tube of variable cross section filled with the stoichiometric hydrogen–air mixture is considered. Three geometrical configurations of the tube are investigated, each with its own degree of the divergence of the tube in terms of the pressure produced by the detonation wave at the end wall of the tube. The problem solved relates to the problem of waste recycling in the devices based on the detonation combustion of the fuel.

Toward Second-Order Algorithm for the Pulsating Detonation Wave Modeling in the Shock-Attached Frame

ABSTRACT The article is dedicated to the numerical investigation of gaseous pulsating detonation wave propagation using two approaches. In the first one the problem is solved in the laboratory frame and the detonation is initiated near the closed end of the channel. In the second approach the modeling is carried out in the shock-attached frame. For this purpose we proposed the numerical algorithm for the integration of shock evolution equation using a grid characteristic method. The algorithm is characterized by the second approximation order. The stable, weakly unstable, irregular and strongly unstable modes of detonation wave propagation are investigated using both approaches. The calculation of the stable mode demonstrates that the developed algorithm for the detonation wave modeling in the shock-attached frame has approximately the second approximation order indeed. The obtained results for the weakly unstable mode are in agreement with the linear theory. The qualitative and quantitative differences between two approaches are marked out. The most differences in results are noticed in the strongly unstable mode.

Initiation of detonation in a tube with parabolic contraction and conic expansion

On the basis of results of two and threedimensional numerical simulation, we proposed for the firsttime to use the profiling of axisymmetrictube walls inthe shape of parabolic contraction and conic expansion for initiating the detonation by means of a relatively weak shock wave. The detonation initiationmechanism is revealed, and its basic stages are analyzed. For simulating the propane–air mixture, wefound the paraboliccontraction shape and selectedthe conicexpansion parameters providing the initiation of detonation for the Mach number of an originalshock wave equal to 2.65.According to the theoretical results of V.P. Korobeіnikov, V.A. Levin, and V.V. Markov, the externaldisturbance of a reacting flow can become the cause offormation of a selfsustained detonation [1, 2]. Thesedisturbances can result in substantially nonlinearoscillatory processes due to the instability of the exothermicreaction front. Apparently, only detailednumerical experiments can provide the solution of theproblem under consideration on detonation initiationand indicate ways of its practical realization.Two processes at which the detonation wave can begenerated are wellknown and used in practice; theseare the direct initiation [1] and deflagrationtodetonation transition [3]. In [4] we proposed, investigated,and justified an original approach to shock detonationinitiation with the help of a regular shaped obstacles inplanar channel in which the leading shock wave(LSW) propagates. On the basis of numerical investigations and experiments, we showed that the regularparabolic structure of walls of the channel makes itpossible to reduce considerably the time and the distance before detonation initiation in comparison withthe wall structure in the shape of rectangular irregularities. The subsequent numerical investigation of theshocktodetonation transition (SDT) in an axisymmetric tube with the geometry of the walls investigatedin [4] for the planar case showed that for the Machnumbers in the initiating shock wave (ISW) importantfrom the viewpoint of practical applications, the process differs from that in the planar channel. It provedto be that the local explosion occurs in the region offocus of already the first parabolic element of thestructure instead of in the vicinity of the fifth one asoccurred in [4] for