Critical deflagration waves leading to detonation onset under different boundary conditions

High-speed turbulent critical deflagration waves before detonation onset in H2–air mixture propagated into a square cross section channel, which was assembled of optional rigid rough, rigid smooth, or flexible walls. The corresponding propagation characteristic and the influence of the wall boundaries on the propagation were investigated via high-speed shadowgraph and a high-frequency pressure sampling system. As a comprehensive supplement to the different walls effect investigation, the effect of porous absorbing walls on the detonation propagation was also investigated via smoke foils and the high-frequency pressure sampling system. Results are as follows. In the critical deflagration stage, the leading shock and the closely following turbulent flame front travel at a speed of nearly half the CJ detonation velocity. In the preheated zone, a zonary flame arises from the overlapping part of the boundary layer and the pressure waves, and then merges into the mainstream flame. Among these wall boundary conditions, the rigid rough wall plays a most positive role in the formation of the zonary flame and thus accelerates the transition of the deflagration to detonation（DDT）, which is due to the boost of the boundary layer growth and the pressure wave reflection. Even though the flexible wall is not conducive to the pressure wave reflection, it brings out a faster boundary layer growth, which plays a more significant role in the zonary flame formation. Additionally, the porous absorbing wall absorbs the transverse wave and yields detonation decay and velocity deficit. After the absorbing wall, below some low initial pressure conditions, no re-initiation occurs and the deflagration propagates in critical deflagration for a relatively long distance.

Boundary Correlation Functions of the gl(1|1) Supersymmetric Vertex Model

The gl（1/1） supersymmetric vertex model with domain wall boundary conditions （DWBC） on an N × N square lattice is considered. We derive the reduction formulae for the one-point boundary correlation functions of the model. The determinant representation for the boundary correlation functions is also obtained.

SIMULATION OF SUDDEN-EXPANSION AND SWIRLING GAS-PARTICLE FLOWS USING A TWO-FLUID PARTICLE-WALL COLLISION MODEL WITH CONSIDERATION OF THE WALL ROUGHNESS

A two-fluid particle-wall collision model with consideration of wall roughness is pro- posed.It takes into account the effects of the friction,restitution and in particular the wall roughness, and hence the redistribution of Reynolds stress in different directions,the absorption of turbulent en- ergy from the mean motion and the attenuation of particle motion by the wall.The proposed model is used to simulate sudden-expansion and swirling gas-particle flows and is validated by comparing with experimental results.The results show that the proposed model gives better results than those obtained by the presently used zero-gradient condition.Hence,it is suggested that the proposed model should be used as the wall boundary condition for the particle phase in place of the presently used boundary condition.

Drinfeld twist and the domain wall partition function of the eight-vertex model

With the help of the F-basis provided by the Drinfeld twist or factorising F-matrix for the spatial optical soliton model associated with the eight-vertex model, we calculate the partition function for the eight-vertex model on an N ×N square lattice with domain wall boundary condition.

Improvement and application of wall function boundary condition for high-speed compressible flows

In order to develop a wall function boundary condition for high-speed flows so as to reduce the grid-dependence of the simula- tion for the skin friction and heat flux, a research was performed to improve the compressible wall function boundary condition proposed by Nichols. Values of parameters in the velocity law-of-the-wall were revised according to numerical experiments and the expression of temperature law-of-the-wall was modified based on theoretical analysis and numerical simulation. Be- sides, the formula of the heat conduction term in near-wall region was derived so that the coupling between the wall function boundary condition and CFD code was realized more accurately. Whereafter, the application study of the modified wall func- tion was carried out. The numerical case of supersonic turbulent boundary layer on a flat plate illustrated that the modified wall function produces reasonable results of skin friction and heat flux, and profiles of velocity, temperature and turbulent eddy viscosity for coarse grids with the initial wall spacing of y＋〈400, and that the modifications to the original wall function can obviously improve the simulation precision. As for the application of separation flows, it was found from the numerical cases of supersonic cavity flow and hypersonic axisymmetric compression comer that the compressible velocity law-of-the-wall originally established based on the fully-developed attached turbulent boundary layer approximately holds in the near-wall re- gion inside the separation flows, which ensures that reliable skin friction and heat flux can be given by the wall function inside the separation flows, while for the region near separation and reattachment points, the wall function gives results with a rela- tively large error, because the velocity law-of-the-wall used in the wall function takes on obvious deviation from the real ve- locity profiles near the separation and reattachment points.

Lattice Boltzmann Flow Simulation in a Combined Nanochannel

The widely used micro-flow wall-boundary conditions for lattice Boltzmann method(LBM)are evaluated in a force driven combined nanochannel flow.The flow field consists of a two-dimensional nanochannel(mother channel)of an infinite length having flat plates of a finite length inside.The flat plate is set above the bottom wall of the nanochannel with a narrow gap.The flow,thus,develops through this narrow gap(narrower channel)and the other side of the plate(wide gap).The Knudsen number based on the mother channel height is Kn=0.14 whereas the characteristic Knudsen number in the narrower channel is 1.1.To obtain the reference data,the molecular dynamics(MD)simulation is performed with a fully diffusive wall condition.The LBMs are based on the lattice BGK model and with the bounce-back/specular reflection(BSBC)and the diffuse scattering(DSBC)wall boundary conditions.The relaxation time is modified to include sensitivity to Kn.The DSBC shows generally satisfactory results in the test flow cases including fully developed force driven Poiseuille flows,where the BSBC performs worse at Kn>0.5 with a fixed bridge coefficient of b=0.7.This results in its overprediction of the flow rate in the narrower channel region since the characteristic Knudsen number there is 1.1.The MD simulation suggests that the flow develops gradually through the narrower channel region though all the LBM predictions show almost instant flow development.This fact suggests that the relaxation time model needs to have more sensitivity to the locally defined Kn.Further discussions of the BSBC with a different set of models suggest that the regularization process is required for predicting complex nanoscale flows.