Abstract
Based on the kinetic theory, a three-dimensional multiple-relaxation-time discrete Boltzmann model (DBM) is proposed for nonequilibrium compressible reactive flows where both the Prandtl number and specific heat ratio are freely adjustable. There are 30 kinetic moments of the discrete distribution functions, and an efficient three-dimensional thirty-velocity model is utilized. Through the Chapman–Enskog analysis, the reactive Navier–Stokes equations can be recovered from the DBM. Unlike existing lattice Boltzmann models for reactive flows, the hydrodynamic and thermodynamic fields are fully coupled in the DBM to simulate combustion in subsonic, supersonic, and potentially hypersonic flows. In addition, both hydrodynamic and thermodynamic nonequilibrium effects can be obtained and quantified handily in the evolution of the discrete Boltzmann equation. Several well-known benchmarks are adopted to validate the model, including chemical reactions in the free falling process, thermal Couette flow, one-dimensional steady or unsteady detonation, and a three-dimensional spherical explosion in an enclosed cube. It is shown that the proposed DBM has the capability to simulate both subsonic and supersonic fluid flows with or without chemical reactions.
Highlights
Reactive flows encompassing a wide variety of nonlinear, unsteady, and nonequilibrium processes are common in nature and industry.1 more than four-fifths of mankind’s utilized energy is generated from the exothermic reactive flows.2 In the past few decades, considerable research has been devoted to reactive flows, including supersonic and hypersonic flows related to the supersonic aircraft, rocket engine, detonation engine, supersonic combustion ramjet, etc
In 2017, Gan et al proposed a 3D discrete Boltzmann model (DBM) for compressible flows without reaction based on the single-relaxationtime Boltzmann equation, fixing the Prandtl number Pr = 1.42 In this work, we extend the model to 3D reactive flows and present a multiple-relaxation-time (MRT) method to make the Prandtl number adjustable
A 3D MRT DBM is presented for reactive flows where both the Prandtl number and specific heat ratio are freely adjustable
Summary
Reactive flows encompassing a wide variety of nonlinear, unsteady, and nonequilibrium processes are common in nature and industry. more than four-fifths of mankind’s utilized energy is generated from the exothermic reactive flows. In the past few decades, considerable research has been devoted to reactive flows, including supersonic and hypersonic flows related to the supersonic aircraft, rocket engine, detonation engine, supersonic combustion ramjet, etc. In 2020, Shu et al developed a simplified sphere function-based gas-kinetic flux solver for compressible viscous reacting flows.37 This model applies the finite volume method to discretize the multi-component NS equations and computes numerical flux at the cell interface by using local solution of the Boltzmann equation. Instead of using two sets of distribution functions, in 2012, Prasinari et al extended a consistent LBM38 by introducing correction terms, recovering the third- and fourth-order moments, and describing the temperature field.30 These pure models are all limited to low Mach number flows. In 2017, Gan et al proposed a 3D DBM for compressible flows without reaction based on the single-relaxationtime Boltzmann equation, fixing the Prandtl number Pr = 1.42 In this work, we extend the model to 3D reactive flows and present a multiple-relaxation-time (MRT) method to make the Prandtl number adjustable.
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