Modelling and solutions to the linear stability of a detonation wave in the kinetic frame

Artigo publicado num número especial da revista.The analysis of linear stability of a steady detonation wave is formulated for the first time at the kinetic level in the frame of the Boltzmann equation extended to reacting gases. Within this context and for a reversible reaction, the stability problem is carried out, in agreement with most classical papers on gas detonation, through a normal mode approach for the one-dimensional disturbances of the steady wave solution, and an acoustic radiation condition at the final equilibrium as closure condition. The proposed modelling leads to an initial value problem, constituted by the linearized reactive Euler equations in the perturbed shock frame with related Rankine-Hugoniot conditions, which can be solved by means of a proper numerical technique. An application is provided for an elementary bimolecular reaction.Centro de Matemática da Universidade do MinhoFundação para a Ciência e a Tecnologia (FCT)Italian INDAM-GNF

Numerical study of surface tension driven convection in thermal magnetic fluids

Microgravity conditions pose unique challenges for fluid handling and heat transfer applications. By controlling (curtailing or augmenting) the buoyant and thermocapillary convection, the latter being the dominant convective flow in a microgravity environment, significant advantages can be achieved in space based processing. The control of this surface tension gradient driven flow is sought using a magnetic field, and the effects of these are studied computationally. A two-fluid layer system, with the lower fluid being a non-conducting ferrofluid, is considered under the influence of a horizontal temperature gradient. To capture the deformable interface, a numerical method to solve the Navier???Stokes equations, heat equations, and Maxwell???s equations was developed using a hybrid level set/ volume-of-fluid technique. The convective velocities and heat fluxes were studied under various regimes of the thermal Marangoni number Ma, the external field represented by the magnetic Bond number Bom, and various gravity levels, Fr. Regimes where the convection were either curtailed or augmented were identified. It was found that the surface force due to the step change in the magnetic permeability at the interface could be suitably utilized to control the instability at the interface.published or submitted for publicationis peer reviewe

On buoyant convection in binary solidification

We consider the problem of nonlinear steady buoyant convection in horizontal mushy layers during the solidification of binary alloys. We investigate both cases of zero vertical volume flux and constant pressure, referred to as impermeable and permeable conditions, respectively, at the upper mush???liquid interface. We analyze the effects of several parameters of the problem on the stationary modes of convection in the form of either hexagonal cells or non-hexagonal cells, such as rolls, rectangles and squares. [More ...]published or submitted for publicationis not peer reviewe

Theory for solvent, momentum, and energy transfer between a surfactant solution and a vapor atmosphere

We develop a complete set of equations governing the evolution of a sharp interface separating a volatile-solvent/nonvolatile-surfactant solution from a vapor atmosphere. In addition to a sorption isotherm equation and the conventional balances for mass, linear momentum, and energy, these equations include a counterpart of the Hertz???Knudsen???Langmuir equation familiar from conventional theories of evaporation-condensation. This additional equation arises from a consideration of configurational forces within a thermodynamical framework. While the notion of configurational forces is well-developed and understood for the description of materials, like crystalline solids, that possess natural reference configurations, very little has been done regarding their role in materials, such as viscous fluids, that do not possess preferred reference states. We therefore provide a comprehensive discussion of configurational forces, the balance of configurational momentum, and configurational thermodynamics that does not require a choice of reference configuration. The general evolution equations arising from our theory account for the thermodynamic structure of the solution and the interface and for sources of dissipation related to the transport of surfactant, momentum, and heat in the solution, the transport of surfactant and momentum within the interface, and the transport of solute, momentum, kinetic energy, and heat across the interface. Due to the complexity of these equations, we provide approximate equations which we compare to relations that appear in the literature.published or submitted for publicationis peer reviewe

On the dynamics and linear stability of one-dimensional steady detonation waves

A detailed analysis of the dynamics and linear stability of a steady one-dimensional detonation wave propagating in a binary reactive system with an Arrhenius chemical kinetics of type A + A = B + B is carried out. Starting from the frame of the kinetic theory, the binary reactive mixture is modelled at the mesoscopic scale by the reactive Boltzmann equation (BE), assuming hard sphere cross sections for elastic collisions and step cross sections with activation energy for reactive interactions. The corresponding hydrodynamic limit is based on a second-order non-equilibrium solution of the BE obtained in a previous paper, using the Chapman-Enskog method in a chemical regime for which the reactive interactions are less frequent than the elastic collisions. The resulting hydrodynamic governing equations are the reactive Euler equations, including a rate law which exhibits an explicit dependence on the reaction heat and forward activation energy of the chemical reaction. These equations are used to describe the spatial structure of the steady detonation wave solution and investigate how this structure varies with the reaction heat. The response of the steady solution to one-dimensional disturbances is studied using a normal mode linear approach which leads to an initial value problem for the state variable disturbances in the reaction zone. The stability problem is treated numerically, using an iterative shooting technique to determine the unstable modes. The analysis here developed emphasizes the influence of the chemical reaction heat and activation energy on the linear stability spectra.CMAT-UM, FCT Project Est-C/MAT/UI0013/2011, FEDER Funds - COMPETE, FCT Phd Grant SFRH/BD/28795/200

Theory of detonation with an embedded sonic locus

We address the problem of generalizing sonic conditions to a three-dimensional unsteady self-sustained detonation wave. The conditions are shown to be the characteristic compatibility conditions on the exceptional surface of the governing hyperbolic system of reactive Euler equations. Two equations are derived that are necessary to determine the motion of both the lead shock and the sonic surface. Detonation with an embedded sonic locus is thus treated as a two-front phenomenon: a reaction zone whose domain of influence is bounded by two surfaces, the lead shock surface and the trailing characteristic surface. The geometry of the two surfaces plays an important role in the underlying dynamics. We also discuss how the sonic conditions of detonation stability theory and detonation shock dynamics can be obtained as special cases of the general sonic conditions.published or submitted for publicationis peer reviewe

THEORY OF DETONATION WITH AN EMBEDDED SONIC LOCUS∗

Abstract. A steady planar self-sustained detonation has a sonic surface in the reaction zone that resides behind the lead shock. In this work we address the problem of generalizing sonic conditions for a three-dimensional unsteady self-sustained detonation wave. The conditions are proposed to be the characteristic compatibility conditions on the exceptional surface of the governing hyperbolic system of reactive Euler equations. Two equations are derived that are necessary to determine the motion of both the lead shock and the sonic surface. Detonation with an embedded sonic locus is thus treated as a two-front phenomenon: a reaction zone whose domain of influence is bounded by two surfaces, the lead shock surface and the trailing characteristic surface. The geometry of the two surfaces plays an important role in the underlying dynamics. We also discuss how the sonic conditions of detonation stability theory and detonation shock dynamics can be obtained as special cases of the general sonic conditions