Hierarchal structure of the simplified Navier-Stokes equations (SNSE) and its mechanical connotation and application

The hierarchial structure and mathematical property of the simplified Navier-Stokesequations (SNSE) are studied for viscous flow over a sphere and a jet of compressible flu-id. All kinds of the hierarchial SNSE can be divided into three types according to theirmathematical property and also into five groups according to their physical content. Amultilayers structure model for viscous shear flow with a main stream direction is pre-sented. For the example of viscous incompressible flow over a flat plate there existthree layers for both the separated flow and the attached flow; the character of thetransition from the three layers of attached flow to those of separated flow is elucidated.A concept of transition layer being situated between the viscous layer and inviscidlayer is introduced. The transition layer features the interaction between viscous flow andinviscid flow. The inner-outer-layers-matched SNSE proposed by the present author inthe past is developed into the layers matched (LsM)-SNSE.

Compressible laminar boundary-layer flows of a dusty gas over a semi-infinite flat-plate

The compressible laminar boundary-layer flows of a dilute gas-particle mixture over a semi-infinite flat plate are investigated analytically. The governing equations are presented in a general form where more reasonable relations for the two-phase interaction and the gas viscosity are included. The detailed flow structures of the gas and particle phases are given in three distinct regions : the large-slip region near the leading edge, the moderate-slip region and the small-slip region far downstream. The asymptotic solutions for the two limiting regions are obtained by using a seriesexpansion method. The finite-difference solutions along the whole length of the plate are obtained by using implicit four-point and six-point schemes. The results from these two methods are compared and very good agreement is achieved. The characteristic quantities of the boundary layer are calculated and the effects on the flow produced by the particles are discussed. It is found that in the case of laminar boundary-layer flows, the skin friction and wall heat-transfer are higher and the displacement thickness is lower than in the pure-gas case alone. The results indicate that the Stokes-interaction relation is reasonable qualitatively but not correct quantitatively and a relevant non-Stokes relation of the interaction between the two phases should be specified when the particle Reynolds number is higher than unity.

Assessment of bursting detection methods with LES database of turbulent channel flows

Validated by comparison with DNS, numerical database of turbulent channel flows is yielded by Large Eddy Simulation (LES). Three conventional techniques: uv quadrant 2, VITA and mu-level techniques for detecting turbulent bursts are applied to the identification of turbulent bursts. With a grouping parameter introduced by Bogard & Tiedemann (1986) or Luchik & Tiederman (1987), multiple ejections detected by these techniques which originate from a single burst can be grouped into a single-burst event. The results are compared with experimental results, showing that all techniques yield reasonable average burst period. However, uv quadrant 2 and mu-level are found to be superior to VITA in having large threshold-independent range.

Performance of a small high-speed liquid jet apparatus

The performance of a small high-speed liquid jet apparatus is described. Water jets of 200m/s to 700m/s have been obtained by firing a deformable lead slug from an air rifle into a stainless steel nozzle containing water sealed with a rubber diaphragm. Nozzle devices of using the impact extrusion (IE) method and cumulation (CU) method are designed to generate jets. The injection sequences are visualized using schlieren photography. The difference between the IE and CU methods in the jet generation is found.

Analysis of micro-indentation problem of a soft film on a hard substrate

Two stages have been observed in micro-indentation experiment of a soft film on a hard substrate. In the first stage, the hardness of the thin film decreases with increasing depth of indentation when indentation is shallow; and in the second stage, the hardness of the film increases with increasing depth of indentation when the indenter tip approaches the hard substrate. In this paper, the new strain gradient theory is used to analyze the micro-indentation behavior of a soft film on a hard substrate. Meanwhile, the classic plastic theory is also applied to investigating the problem. Comparing two theoretical results with the experiment data, one can find that the strain gradient theory can describe the experiment data at both the shallow and deep indentation depths quite well, while the classic theory can't explain the experiment results.

Computation of turbulence-generated noise by large-eddy simulation

The hybrid method of large eddy simulation (LES) and the Lighthill analogy is being developed to compute the sound radiated from turbulent flows. The results obtained from the hybrid method are often contaminated by the absence of small scales in LES, since the energy level of sound is much smaller than that of turbulent flows. Previous researches investigate the effects of subgrid sacle (SGS) eddies on the frequency spectra of sound radiated by isotropic turbulence and suggest a SGS noise model to represent the SGS contributions to the frequency spectra. Their investigations are conducted in physical space and are unavoidably influenced by boundary conditions. In this paper, we propose to perform such calculations in Fourier space so that the effects of boundary conditions can be correctly treated. Posteriori tests are carried out to investigate the SGS contribution to the sound. The results obtained recover the -7/2 law within certain wave-number ranges, but under-estimate the amplitudes of the frequency spectra. The reason for the underestimation is also discussed.

Prediction of particle distribution in isotropic turbulence by large-eddy simulation

The recent application of large-eddy simulation (LES) to particle-laden turbulence requires that the LES with a subgrid scale (SGS) model could accurately predict particle distributions. Usually, a SGS particle model is used to recover the small-scale structures of velocity fields. In this study, we propose a rescaling technique to recover the effects of small-scale motions on the preferential concentration of inertial particles. The technique is used to simulate particle distribution in isotropic turbulence by LES and produce consistent results with direct numerical simulation (DNS). Key words: particle distribution, particle-laden turbulence, large-eddy simulation, subgrid scale model.

Analytical calculations of Eulerian and Lagrangian time correlations in turbulent shear flows

The Taylor series expansion method is used to analytically calculate the Eulerian and Lagrangian time correlations in turbulent shear flows. The short-time behaviors of those correlation functions can be obtained from the series expansions. Especially, the propagation velocity and sweeping velocity in the elliptic model of space-time correlation are analytically calculated and further simplified using the sweeping hypothesis and straining hypothesis. These two characteristic velocities mainly determine the space-time correlations.

DNS and LES of turbulent channel flow with hydrophobic surface

Hydrophobic surface benefits for drag reduction. Min and Kim[1] do the first Direct Numerical Simulation on drag reduction in turbulent channel flow. And Fukagata and Kasagi[2] make some theoretical analysis based on Dean[3]'s formula and some observations in the DNS results. Using their theory, they conclude that drag reduction is possible in large Reynolds number. Both Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are performed in our research. How the LES behaving in the turbulent channel flow with hydrophobic surface is examined. Original Smagorinsky model and its Dynamical model are used in LES. The slip velocities predicted by LES using Dynamical model are in good agreement with DNS as shown in the Figure. Although the percentage of drag reduction predicted by LES shows some discrepancies, it is in the error limit for industrial flow. First order and second order moments of LES are also examined and compared with DNS's results. The first-order moments is calculated well by LES. But there are some discrepancies of second-order moments between LES and DNS. [GRAPHICS]

Computation of flow over a rotating body on unstructured Chimera mesh

Flow around moving boundary is ubiquitous in engineering applications. To increse the efficienly of the algorithm to handle moving boundaries is still a major challenge in Computational Fluid Dynamics (CFD). The Chimera grid method is one type of method to handle moving boundaries. A concept of domain de-composition has been proposed in this paper. In this method, sub-domains are meshed independently and governing equations are also solved separately on them. The Chimera grid method was originally used only on structured (curvilinear) meshes. However, in a problem which involves both moving boundary and complex geometry, the number of sub-domains required in a traditional (structured) Chimera method becomes fairly large. Thus the time required in the interior boundary locating, link-building and data exchanging also increases. The use of unstructured Chimera grid can reduce the time consumption significantly by the reduction of domain(block) number. Generally speaking, unstructured Chimera grid method has not been developed. In this paper, a well-known pressure correction scheme - SIMPLEC is modified and implemented on unstructured Chimera mesh. A new interpolation scheme regarding the pressure correction is proposed to prevent the possible decoupling of pressure. A moving-mesh finite volume approach is implemented in an inertial reference frame. This approach is then used to compute incompressible flow around a rotating circular and elliptic cylinder. These numerical examples demonstrate the capability of the proposed scheme in handling moving boundaries. The numerical results are in good agreement with other experimental and computational data in literature. The method proposed in this paper can be efficiently applied to more challenge cases such as free-falling objects or heavy particles in fluid.

Effects of rainfall infiltration on the stability of soil slopes

Slope failure due to rainfall is a common geotechnical problem. The mechanics of rainfall induced landslides involves the interaction of a number of complex hydrologic and geotechnical factors. This study attempts to identify the influence of some of these factors on the stability of soil slope including rainfall intensity, hydraulic conductivity and the strength parameters of soil.

Comparisons of static, quasi-static and dynamic 3D porous media scale network models for two-phase immiscible flow in porous media

A dynamic 3D pore-scale network model is formulated for investigating the effect of interfacial tension and oil-water viscosity during chemical flooding. The model takes into account both viscous and capillary forces in analyzing the impact of chemical properties on flow behavior or displacement configuration, while the static model with conventional invasion percolation algorithm incorporates the capillary pressure only. From comparisons of simulation results from these models. it indicates that the static pore scale network model can be used successfully when the capillary number is low. With the capillary increases due to the enhancement of water viscosity or decrease of interfacial tension, only the quasi-static and dynamic model can give insight into the displacement mechanisms.

Effects of temperature on the threshold of phosphorus for algal blooms

Algal blooms, worsening marine ecosystems and causing great economic loss, have been paid much attention to for a long time. Such environmental factors as light penetration, water temperature, and nutrient concentration are crucial in blooms processes. Among them, only nutrients can be controlled. Therefore, the threshold of nutrients for algal blooms is of great concern. To begin with, a dynamic eutrophication model has been constructed to simulate the algal growth and phosphorus cycling. The model encapsulates the essential biological processes of algal growth and decay, and phosphorus regeneration due to algal decay. The nutrient limitation is based upon commonly used Monod's kinetics. The effects of temperature and phosphorus limitation are particularly addressed. Then, we have endeavored to elucidate the threshold of phosphorus at different temperature for algal blooms. Based on the numerical simulation, the isoquant contours of change rate of alga as shown in the figure are obtained, which obviously demonstrate the threshold of nutrient at an arbitrary reasonable temperature. The larger the change rate is, the more rapidly the alga grows. If the phosphorus concentration at a given temperature remains larger than the threshold the algal biomass may increase monotonically, leading to the algal blooming. With the rising of temperature, the threshold is apparently reduced, which may explain why likely red tide disasters occur in a fine summer day. So, high temperature and sufficient phosphorus supply are the major factors which result in algal growth and blowout of red tide.