Development of multicomponent lattice Boltzmann flux solver for simulation of compressible viscous reacting flows

In this paper, the multicomponent lattice Boltzmann flux solver (LBFS) is developed for simulation of two-dimensional compressible viscous reacting flows. This work is based on the existing LBFS for simulation of single-component compressible flows. The present solver applies the finite volume method to discretize the multicomponent Navier-Stokes equations and evaluates the numerical flux at the cell interface by local solution of the lattice Boltzmann equation. To evaluate numerical flux, the original non-free parameter D1Q4 model in the existing LBFS is extended to the multicomponent counterpart in which the total density at the cell interface is computed directly by summing the density distribution functions, and the densities of different species are calculated from the mass fractions at the left and right sides of cell interface. The internal energy is evaluated from the enthalpy which considers the different physical properties of the species, and the temperature at the cell interface is obtained by Newton iteration. In addition, an improved switch function which takes into account the reacting effects and aspect ratio of the grid is introduced to control the numerical dissipation. Several benchmark problems are simulated to validate the present multicomponent LBFS. It is shown that the present solver is carbuncle-free for the unfavorable aspect ratio grid in the test cases here and has a satisfied performance for simulation of multicomponent compressible viscous reacting flows.

Figure 1

Definition of a finite control volume (fixed in space).

Figure 2

The discrete particle velocity of multicomponent non-free parameter D1Q4 model.

Figure 3

Local coordinate system at the cell interface.

Figure 4

The switch function calculation process.

Figure 5

The different aspect ratios of the grid with (a) large aspect ratio and (b) unit aspect ratio.

Figure 6

Computational domain for shock-induced combustion flow.

Figure 7

Temperature contours with shock wave detachment distance.

Figure 8

Comparison of pressure contours by using different schemes.

Figure 9

Pressure and temperature profiles along the stagnation line.

Figure 10

Mass fractions of main species profiles along the stagnation line.

Figure 11

Comparison of switch function contours: (a) without grid modification and (b) with grid modification.

Figure 12

Comparison of temperature contours near the symmetric axis by using different schemes: (a) Roe scheme without chemical reaction, (b) Roe scheme with chemical reaction, (c) AUSM+ scheme without chemical reaction, (d) AUSM+ scheme with chemical reaction, (e) LBFS without chemical reaction, and (f) LBFS with chemical reaction.

Figure 13

Computational domain for hypersonic air chemical nonequilibrium flow.

Figure 14

Pressure contours with shock wave detachment distance.

Figure 15

Mass fractions of different species along the centerline.

Figure 16

Temperature contours of hypersonic air chemical nonequilibrium flow.

Figure 17

Switch function contours of hypersonic air chemical nonequilibrium flow.

Figure 18

Mass fraction contours of different species: (a) species ${\mathrm{N}}_2$, (b) ${\mathrm{O}}_2$, (c) N, (d) O, (e) NO, and (f) $\mathrm{N}{\mathrm{O}}^{+}$.

Figure 19

Configuration of simplified dual combustion chamber (unit: mm).

Figure 20

Computational domain for supersonic combustion flow of ethylene.

Figure 21

Comparison of the pressure distribution on the chamber wall: (a) upper surface and (b) lower surface.

Figure 22

Temperature and switch function contours of the chamber: (a) temperature contours and (b) switch function contours.

Figure 23

Mass fraction contours of species CO and $\mathrm{C}{\mathrm{O}}_2$: (a) species CO and (b) species $\mathrm{C}{\mathrm{O}}_2$.