An Augmented Approach for the Pressure Boundary Condition in a Stokes Flow

An augmented method is proposed for solving stationary incompressible Stokes equations with a Dirichlet boundary condition along parts of the boundary.In this approach,the normal derivative of the pressure along the parts of the boundary is introduced as an additional variable and it is solved by the GMRES iterative method.The dimension of the augmented variable in discretization is the number of grid points along the boundary which is O(N).Each GMRES iteration(or one matrix-vector multiplication)requires three fast Poisson solvers for the pressure and the velocity.In our numerical experiments,only a few iterations are needed.We have also combined the augmented approach for Stokes equations involving interfaces,discontinuities,and singularities.

Effect of an adverse pressure gradient on the streamwise Reynolds stress profile maxima in a turbulent boundary layer

It is widely accepted that in a turbulent boundary layer （TBL） with adverse pressure gradient （APG） an outer peak usually appears in the profile of streamwise Reynolds stress. However, the effect of APG on this outer peak is not clearly understood. In this paper, the effect of APG is analysed using the numerical and experimental results in the literature. Because the effect of upstream flow is inherent in the TBL, we first analyse this effect in TBLs with zero pressure gradient on flat plates. Under the individual effect of upstream flow, an outer peak already appears in the profile of streamwise Reynolds stress when the TBL continues developing in the streamwise direction. The APG accelerates the appearance of the outer peak, instead of being a trigger.

Boundary normal pressure-based electrical conductivity reconstruction for magneto–acoustic tomography with magnetic induction

As a kind of multi-physics imaging approach integrating the advantages of electrical impedance tomography and ul- trasound imaging with the improved spatial resolution and image contrast, magneto-acoustic tomography with magnetic induction （MAT-MI） is demonstrated to have the capability of electrical impedance contrast imaging for biological tissues with conductivity differences. By being detected with a strong directional transducer, abrupt pressure change is proved to be generated by the gradient of the induced Lorentz force along the force direction at conductivity boundary. A simplified boundary normal pressure （BNP）-based conductivity reconstruction algorithm is proposed and the formula for conductivity distribution inside the object with the clear physical meaning of pressure derivative, is derived. Numerical simulations of acoustic pressure and conductivity reconstruction are conducted based on a 2-layer eccentric cylindrical phantom model using Hilbert transform. The reconstructed two-dimensional conductivity images accord well with the model, thus success- fully making up the deficiency of only imaging conductivity boundary in traditional MAT-MI. The proposed method is also demonstrated to have a spatial resolution of one wavelength. This study provides a new method of reconstructing accurate electrical conductivity and suggests the potential applications of MAT-MI in imaging biological tissues with conductivity difference.

MECHANISM OF BOUNDARY LUBRICATION UNDER POINT CONTACT

The acid number of the mixed solution of 150SN oil and oleic acid characterizes the volume content of oleic acid in the solution, based on which the adsorptive capability of oleic acid is studied on the 45 steel balls and disks. Boundary lubrication tests are carried out on a self designed ball-on-disk machine, The base oil is pure 150SN oil, and oleic acid as additive are added into the lubricant. Disks have surface roughness values （Ra） of 0.8 μn and 0.4 μn. The electrical contact resistance method is used to determine the lubrication status. Hypothesize that the molecular film is monomolecular layer in condensed state and the opposing surfaces are completely separated by molecular film. A boundary lubrication model is established according to experimental results and hypothesizes. The experimental and calculatienal results show that the adsorption of polar molecules on steel surface is the main factor to form the boundary lubrication film. Load and sliding speed contribute little to the friction coefficient of boundary lubrication. The properties of steel surface and additive for the lubricant significantly influence on the characters of boundary lubrication. The smaller the surface roughness value is, the smaller the friction coefficient of the boundary lubrication is.

INVESTIGATION ON THE APPLICATION OF THE BOUNDARY ELEMENT METHOD TO THE SPILL GROOVED THRUST BEARING

An application of the boundary element method (BEM) is presented to calculate the behaviors of a spiral grooved thrust bearing (SGTB). The basic reason is that the SGTB has very complex boundary conditions that can hinder the effective or sufficient applications of the finite difference method (FDM) and the finite element method (FEM), despite some existing work based on the FDM and the FEM. In other to apply the BEM, the pressure control equation, i. e., Reynolds' equation, is first transformed into Laplace's and Poisson's form of the equations. Discretization of the SGTB with a set of boundary elements is thus explained in detail, which also includes the handling of boundary conditions. The Archimedean SGTB is chosen as an example of the application Of BEM, and the relationship between the behaviors and structure parameters of the bearing are found and discussed through this calculation. The obtained results lay a solid foundation for a further work of the design of the SGTB.

ADJUSTMENT OF WIND AND PRESSURE FIELDS IN THE BOUNDARY LAYER

The vertical transport of mass at the top of the boundary layer is considered as a link between the boundary layer and free atmosphere.The adjustment of the wind and pressure fields in the boundary layer is studied under the consideration of the interaction between the boundary layer and free atmosphere.The vertical motion at the top of the boundary layer is evaluated.The results show that the distinguished differ- ences of the present results from classical Ekman layer do exist and they are discussed in the paper.

Experimental study for frequency spectrum of turbulent boundary layer pressure fluctuation

An experimental study on TBL (turbulent boundary layer) pressure fluctuation frequeny spectrum of a revolution body is presented. With the measured results, a relation of convective frequency fo of the models is obtained. Relations of turbuleat wall-pressure fluctuation spectrum in transition region and development region to frequency and speed are obtained also

Noise radiation of an elastic plate excited by the turbulent boundary layer pressure fluctuations

A unified theory for calculating the noise radiation of an infinite elastic plate excited by the turbulent boundary layer pressure fluctuations is presented . Using the wave number frequency transfer function to desribe the whole system , consisting of the plate and the liquid loading, a general expression of the cross spectrum was derived. It is an integral in the complex wave number plane and leads to a sum of the residues at the poles of two types. One pole introduced by the convective ridge of the pressure fluctuations yields a direct transfer component , which is an evanescent wave in liquid because the pole lies in the high wave number region . The other poles introduced by the transfer function of structure produce the radiation field components with the resonance modes of a liquid loaded plate. The pole positions and their residues can be computed approximately by use of the Resonance Scattering Theory . For the case of hydrodynamic noise, where the range of the frequency-thickness product of interest is relatively low , the symmetric zero-order mode dominates the noise radiation.

Effect of rare earth cerium on brittleness of simulated welding heat-affected zones in a reactor pressure vessel steel

The welding coarse-grained heat-affected zones（CGHAZs） in the undoped and Ce-doped samples of SA508CL-3 reactor pressure vessel steel were simulated using a Gleeble 1500 D thermomechanical simulator with a peak temperature of 1320 oC at the heat inputs of 30, 50 and 100 kJ /cm, respectively. The ductile-to-brittle transition temperature（DBTT） of the simulated CGHAZs was evaluated along with microstructural and microchemical characterizations. The results indicated that Ce could substantially lower the DBTT of the CGHAZs by its microstructural and microchemical effects. After the thermal cycling of welding, the microstructure in the Ce-doped samples was apparently finer than that in the undoped samples, regardless of the lath bainite obtained at the heat inputs of 30 and 50 kJ /cm or the granular bainite acquired at the heat input of 100 kJ /cm, leading to lower DBTTs for the Ce-doped samples. Moreover, grain boundary segregation of Ce occurred apparently in the Ce-doped samples and exhibited a non-equilibrium characteristic. The segregation of Ce could play an important role in lowering the DBTT of CGHAZs or toughening the CGHAZs.

Regularity of Solutions to the Navier-Stokes Equations with a Nonstandard Boundary Condition

In this paper we are concerned with the regularity of solutions to the Navier-Stokes equations with the condition on the pressure on parts of the boundary where there is flow. For the steady Stokes problem a result similar to L q-theory for the one with Dirichlet boundary condition is obtained. Using the result, for the steady Navier-Stokes equations we obtain regularity as the case of Dirichlet boundary conditions. Furthermore,for the time-dependent 2-D Navier-Stokes equations we prove uniqueness and existence of regular solutions,which is similar to J.M.Bernard＇s results[6]for the time-dependent 2-D Stokes equations.

Study of Simple Hydrodynamic Solutions with the Two-Relaxation-Times Lattice Boltzmann Scheme

For simple hydrodynamic solutions, where the pressure and the velocity arepolynomial functions of the coordinates, exact microscopic solutions are constructedfor the two-relaxation-time (TRT) Lattice Boltzmann model with variable forcing andsupported by exact boundary schemes. We show how simple numerical and analyticalsolutions can be interrelated for Dirichlet velocity, pressure and mixed (pressure/tangential velocity) multi-reflection (MR) type schemes. Special care is taken toadapt themfor corners, to examine the uniqueness of the obtained steady solutions andstaggered invariants, to validate their exact parametrization by the non-dimensionalhydrodynamic and a “kinetic” (collision) number. We also present an inlet/outlet“constant mass flux” condition. We show, both analytically and numerically, that thekinetic boundary schemes may result in the appearance of Knudsen layers which arebeyond the methodology of the Chapman-Enskog analysis. Time dependent Dirichletboundary conditions are investigated for pulsatile flow driven by an oscillating pressuredrop or forcing. Analytical approximations are constructed in order to extend thepulsatile solution for compressible regimes.