Slip boundary conditions for rough surfaces

The velocity slip and temperature jump for a two-dimensional rough plate under hypersonic conditions were analyzed using the Direct Simulation Monte Carlo(DSMC)method.Surface roughness was explicitly modeled by introducing various structures on the flat plate.The influences of relative roughness height,which involves the roughness height,roughness spacing,incoming velocity,and the degree of rarefaction,were analyzed and discussed.It is found that with the increase of the relative roughness height,the jump temperature increases,while the slip velocity decreases gradually.The effects of surface roughness on the slip coefficients can be attributed to the change of accommodation coefficients.A new slip model for rough surfaces was established in this paper,which accounts for the coupling effects of gas rarefaction and surface roughness,without the effort to model the surface roughness explicitly.The nitrogen flows in the microchannel,and flows over a blunt cone and an axisymmetric bi-conic body,were simulated under the modified and conventional slip boundary conditions,respectively.The numerical solutions were validated with experimental data.It can be safely concluded that compared with the traditional first-order slip boundary conditions,the modified slip model improves the accuracy of macroscopic properties,especially the heat transfer coefficient.

Structural architecture of Neoproterozoic rifting depression groups in the Tarim Basin and their formation dynamics

The Tarim Basin is the largest, oil-bearing, superimposed basin in the northwest of China. The evolution and tectonic properties of the initial Tarim Basin have been hotly disputed and remain enigmatic. The Neoproterozoic basin is covered by a vast desert and a huge-thickness of sedimentary strata, has experienced multiple tectonic movements, had a low signal to noise ratios(SNRs) of deep seismic reflection data, all of which have posed critical obstacles to research. We analysed four field outcrops, 18 wells distributed throughout the basin, 27 reprocessed seismic reflection profiles with higher SNRs across the basin and many ancillary local 2D and 3D profiles and aeromagnetic data. We found about 20 normal fault-controlled rifting depressions of the Cryogenian and Ediacaran scattered throughout the basin, which developed on the Precambrian metamorphic and crystalline basement. The structural framework is clearly different from that of the overlying Phanerozoic. The rifting depressions consist of mainly half grabens, symmetrical troughs and horst-grabens. From the northeast to southwest of the basin,they are divided into three rifting depression groups with the WNW, ENE, and NW-trends that are mainly controlled by normal faults. The maximum thicknesses of the strata are up to 4100 m. From the Cryogenian to Ediacaran, most of the main inherited faults to active and eventually ceased at the end of the Ediacaran or Early Cambrian, while subsidence centres appeared and migrated eastward along the faults. They revealed that the different parts of the Tarim continental block were in NNE-SSWoriented and NNW-SSE-oriented extensional paleo-stress fields(relative to the present) during the Neoproterozoic, and were accompanied by clockwise shearing. According to the analysis of the activities of syn-sedimentary faults, filling sediments,magmatic events, and coordination with aeromagnetic anomalies, the tectonic properties of the fault depressions are different and are primarily continental rifts or intra-continental fault-controlled basins. The rifting phases mainly occurred from 0.8–0.61 Ga.The formation of the rifting depression was associated with the initial opening of the South Altun-West Kunlun Ocean and the South Tianshan Ocean, which were located at the northern and southern margins of the Tarim Block, respectively, in response to the break-up of the Supercontinent Rodinia and the initial opening of the Proto-Tethys Ocean.

Analytical method of nonlinear coupled constitutive relations for rarefied non-equilibrium flows

It is well known that Navier-Stokes equations are not valid for those high-Knudsen and high-Mach flows, in which the local thermodynamically non-equilibrium effects are dominant. To extend the non-equilibrium describing the ability of macroscopic equations, Nonlinear Coupled Constitutive Relation(NCCR) model was developed from Eu’s generalized hydrodynamic equations to substitute linear Newton’s law of viscosity and Fourier’s law of heat conduction in conservation laws. In the NCCR model, how to solve the decomposed constitutive equations with reasonable computational cost is a key ingredient of this scheme. In this paper, an analytic method is proposed firstly. Compared to the iterative procedure in the conventional NCCR model, the analytic method not only obtains exact roots of the decomposed constitutive polynomials, but also preserves the nonlinear constitutive relations in the original framework of NCCR methods. Numerical tests to assess the efficiency and accuracy of the proposed method are conducted for argon shock structures, Couette flows, two-dimensional hypersonic flows over a cylinder and threedimensional supersonic flows over a three-dimensional sphere. These superior advantages of the current method are expected to render itself a powerful tool for simulating the hypersonic rarefied flows and microscale flows of high Knudsen number for engineering applications.