Direct numerical simulation of rarefied turbulent microchannel flow

Direct numerical simulation (DNS) has been carried out to investigate the effect of weak rarefaction on turbulent gas flow and heat transfer characteristics in microchannel. The Reynolds number based on the friction velocity and the channel half width is 150. Grid number is 64 × 128 × 64. Fractional time-step method is employed for the unsteady Navier–Stokes equations, and the governing equations are discretized with finite difference method. Statistical quantities such as turbulent intensity, Reynolds shear stress, turbulent heat flux and temperature variance are obtained under various Knudsen number from 0 to 0.05. The results show that rarefaction can influence the turbulent flow and heat transfer statistics. The streamwise mean velocity and temperature increase with increase of Kn number. In the near-wall-region rarefaction can increase the turbulent intensities and temperature variance. The effects of rarefaction on Reynolds shear stress and wall-normal heat flux are presented. The instantaneous velocity fluctuations in the vicinity of the wall are visualized and the influence of Kn number on the flow structure is discussed.     

MHD flow in a rectangular duct with a perturbed boundary

The unsteady magnetohydrodynamic (MHD) flow of a viscous, incompressible and electrically conducting fluid in a rectangular duct with a perturbed boundary, is investigated. A small boundary perturbation $\epsilon$ is applied on the upper wall of the duct which is encountered in the visualization of the blood flow in constricted arteries. The MHD equations which are coupled in the velocity and the induced magnetic field are solved with no-slip velocity conditions and by taking the side walls as insulated and the Hartmann walls as perfectly conducting. Both the domain boundary element method (DBEM) and the dual reciprocity boundary element method (DRBEM) are used in spatial discretization with a backward finite difference scheme for the time integration. These MHD equations are decoupled first into two transient convection–diffusion equations, and then into two modified Helmholtz equations by using suitable transformations. Then, the DBEM or DRBEM is used to transform these equations into equivalent integral equations by employing the fundamental solution of either steady-state convection–diffusion or modified Helmholtz equations. The DBEM and DRBEM results are presented and compared by equi-velocity and current lines at steady-state for several values of Hartmann number and the boundary perturbation parameter.     

Spectral analysis of turbulence based on the DNS of a channel flow

The development and assessment of spectral turbulence models requires knowledge of the spectral turbulent kinetic energy distribution as well as an understanding of the terms which determine the energy distribution in physical and wave number space. Direct numerical simulation (DNS) of turbulent channel flow yields numerical “data” that can be, and was, analyzed using a spatial Fast Fourier Transform (FFT) to obtain the various spectral turbulent kinetic energy balance terms, including the production, dissipation, diffusion, and the non-linear convective transfer terms.     

Electrokinetic and aspect ratio effects on secondary flow of viscoelastic fluids in rectangular microchannels

The secondary flow of PTT fluids in rectangular cross-sectional plane of microchannels under combined effects of electroosmotic and pressure driving forces is the subject of the present study. Employing second-order central finite difference method in a very refined grid network, we investigate the effect of electrokinetic and geometric parameters on the pattern, strength and the average of the secondary flow. In this regard, we try to illustrate the deformations of recirculating vortices due to change in the dimensionless Debye–Hückel and zeta potential parameters as well as channel aspect ratio. We demonstrate that, in the presence of thick electric double layers, significant alteration occurs in the secondary flow pattern by transition from favorable to adverse pressure gradients. Moreover, it is found that for polymer-electrolyte solutions with large Debye lengths, the secondary flow pattern and the shape of vortices are generally dependent upon the width-to-height ratio of the channel cross section. Also, the inspections of strength and average of secondary flow reveal that the sensitivity of these quantities with respect to the electrokinetic, geometric and rheological parameters increases by increasing the absolute value of velocity scale ratio. In this regard, utilizing the curve fitting of the results, several empirical expressions are presented for the strength and average of the secondary flow under various parametric conditions. The obtained relations with the other predictions for secondary flow are of high practical importance when dealing with the design of microfluidic devices that manipulate viscoelastic fluids.     

Direct numerical simulations of localized disturbances in pipe Poiseuille flow

We consider pipe Poiseuille flow subjected to a disturbance which is highly localized in space. Experiments by Peixinho and Mullin have shown this disturbance to be efficient in triggering turbulence, yielding a threshold dependence on the required amplitude as R^-1.5 on the Reynolds number, R. The experiments also indicate an initial formation of hairpin vortices, with each hairpin having a length of approximately one pipe radius, independent of the Reynolds number in the range of R=2000-3000. We perform direct numerical simulations for R=5000. The results show a packet of hairpin vortices traveling downstream, each having a length of approximately one pipe radius. The perturbation remains highly localized in space while being advected downstream for approximately 10 pipe diameters. Beyond that distance from the disturbance origin, the flow becomes severely disordered.     

直方槽道中重力对颗粒相二次流的影响

采用Eulerian／Lagrangian方法模拟直方槽道中气粒两相流动过程。气相采用大涡模拟方法,直接求解大尺度涡运动,小尺度涡采用标准的Smagorinsky亚格子模式模拟,壁面采用幂次率应力模型代替无滑移边界条件。颗粒相采用轨道模型求解。大涡模拟预报的气相平均速度与DNS结果相吻合。结果表明,在直方槽道流向截面,气相存在二次流现象。受气相二次流的作用,颗粒相也存在类似于气相的二次流现象,并考察了重力对颗粒相二次流的影响。     

Pressure distributions of gaseous slip flow in straight and uniform rectangular microchannels

This paper presents analytical derivations of the pressure distribution in straight and uniform rectangular microchannels in the slip flow regime and new experimental data in those channels. The flow is to be steady state, two-dimensional, isothermal, and to have negligible transverse velocities with a first order slip boundary condition. The measured pressure distributions of airflows are compared with newly derived analytical results. There is close agreement between the measurements and calculation by the slip flow formula. The dimensionless location of the maximum deviation from the linear pressure distribution is found analytically and compared with the measurements. This dimensionless location of the maximum deviation increases with the increasing pressure ratios in the slip flow regime. The effect of several parameters such as the channel aspect ratio and the Knudsen number on the locations of maximum deviation from linearity are investigated. The nonlinearity of the pressure distribution is also discussed.     

Measurement-integrated simulation of wall pressure measurements using a turbulent model for analyzing oscillating orifice flow in a circular pipe

The development of a highly functionalized orifice flowmeter with high accuracy under realistic conditions is desired. This paper presents a method for analyzing oscillating air flow through an orifice in a circular pipe. A measurement-integrated (MI) simulation using a standard k–ε model was used to reduce the computation time. In a previous study, the feedback law of the MI simulation was determined by considering the effect of the computational fluid dynamics (CFD) grid on contracted flow. However, the previous method required the measurement of inlet flow rate, which is not feasible in many applications. Therefore, an MI simulation was proposed that only requires wall pressures, which are much simpler to measure than flow rate. In this MI simulation, the wall pressure downstream of an orifice was measured, and a new proportional–integral controller feedback algorithm was developed to control the inlet flow rate in the computed flow field. The proposed MI simulations were performed for steady and oscillatory flow rates up to 10 Hz. It was found that this MI simulation provides accurate solutions at a significantly shorter computation time than conventional CFD analysis.     

Effects of planar inlet plenums on the hydrodynamically developing flows in rectangular microchannels of complementary aspect ratios

The effects of planar inlet plenum geometry on the developing flow fields in two rectangular microchannels of reciprocal aspect ratios (H/W ∼2.75 and ∼0.40) were investigated for Re _D =  1–100 using micro particle image velocimetry (μPIV). These two microchannels were made by a precision sawing and silicon microfabrication techniques. Both the velocity profiles and centerline velocity developments were clearly resolved and extracted along the axial distance from μPIV results. The entrance lengths were found from the centerline velocities using a decaying exponential fitting function where the centerline velocity reaches 99% of the fully developed centerline velocity. The proposed fitting function showed excellent agreement with the experimental results. The planar plenum was shown to cause an upstream predevelopment resulting in the significant reductions in the entrance lengths. Two entrance length correlations were proposed in the forms of Atkinson et al.’s (AIChE J 15:548–553, 1969) and Chen’s (J Fluids Eng 95:153–158, 1973) correlations. The proposed entrance length correlations showed that acquired constant portion and slope of the entrance lengths showed 23–27 and 70–81% reductions for H/W =  2.75 while the entrance length correlation for H/W =  0.40 showed 69–73% increase and 41–63% decrease in the constant portion and slope, respectively.     

Unsteady RANS modelling of flow past a rectangular cylinder: Investigation of Reynolds number effects

The unsteady flow field around a two-dimensional rectangular prism with a fineness ratio (chord-to-thickness) of 5.0, is studied using Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations. A noncommercial unstructured flow solver is used in the simulations at various Reynolds numbers (from 26,000 to 1,850,000 based on the chord length), two different angles of attack (0° and 4°) and low Mach number (0.1). A grid-convergence study is presented in order to investigate the dependence of the flow solution on the spatial and temporal discretization. Results obtained with one- and two-equation turbulence models are compared, including models based on the Explicit Algebraic Reynolds Stress (EARSM) approach. The aim of this work is to assess the capability of the computationally efficient two-dimensional URANS calculations to predict the features of complex massively separated flow around this type of geometry. A further goal is to use numerical simulations to investigate the strong Reynolds number effects observed in wind-tunnel experiments. Satisfactory agreement with the wind-tunnel data is obtained for several test cases, but only the turbulence model based on the EARSM approach captured the significant lift increase at non-zero angles of attack due to variation of Reynolds number. This phenomenon is shown to be related to the progressive upstream migration of the time-averaged shear-layer reattachment location on one side of the rectangular cylinder. The effects of the Reynolds number on the mechanism of vortex shedding are also explored in the simulations.     

A noncausal framework for model-based feedback control of spatially developing perturbations in boundary-layer flow systems. Part II: numerical simulations using state feedback

We present numerical results illustrating the successful state feedback control of a spatially developing boundary-layer flow system. Control is applied using the noncausal framework developed in Part I of this study. After addressing some important regularization issues related to the proper treatment of the infinite-dimensional nature and semi-infinite spatial extent of the present system, we compute the state-feedback control gains according to the equations developed in Part I at several spanwise wavenumbers β. We then inverse transform the result to obtain spatial convolution kernels for determining the control feedback. The effectiveness of the controls computed using these feedback kernels, which are well resolved on the computational grid and spatially localized in the spanwise direction, is tested using direct numerical simulation of the boundary-layer flow system. A significant damping of the flow perturbation is observed, which is of the same order as the damping that arises when applying significantly more expensive iterative adjoint-based control optimization schemes.     

A FORTRAN program to compute vertical magnetic field of a horizontal rectangular loop on n-layered earth for em depth sounding

A FORTRAN program is described to compute the vertical magnetic field anywhere inside or outside a rectangular loop which carries a sinusoidally varying current and is horizontally placed on the surface of a n-layered earth. The program utilizes the concept of reciprocity and the known solution for a horizontal magnetic dipole source placed over a n-layered half-space. The computing algorithm is executable on a minicomputer like PDP 11/40 and as such is useful to many geoscientists who do not have access to mainframe computer, for computing model data to fit and interpret field observations from electromagnetic depth sounding experiments.     

An algebraic-Q4 turbulent eddy viscosity model: Boundary layer flow over a flat plate and flow in a pipe

An algebraic turbulent eddy viscosity model is proposed based on a length scale model coupled with the turbulent viscosity expression of the renormalization group theory of turbulence. The eddy viscosity is presented as a solution of a quartic equation. The new length scale model is based on boundary layer characteristics (displacement thickness, shape factor). The model is applied to transitional boundary layer flow over a flat plate and to flow in a smooth pipe. Predictions for the laminar-turbulent transition, and integral characteristics, such as the total skin friction coefficient, mean velocity profile across the boundary layer, and the friction coefficient in a pipe, are found to be in good agreement with experimental data.     

固体火箭发动机喷管两相流场与结构温度场一体化数值模拟与软件实现

为准确、高效地进行固体火箭发动机的喷管结构设计与性能分析,考虑两相流场和结构温度场之间的相互影响,采用有限差分方法求解二维轴对称两相欧拉方程组,进行喷管气体-颗粒两相无黏流动数值模拟;采用有限元法求解二维轴对称瞬态导热微分方程,进行喷管复合结构温度场数值模拟;根据面向对象编程思想,采用VC+ +以人机交互的工作方式实现喷管内型面和结构设计,并完成有限差分网格和有限元网格的自动划分和显示;通过数值模拟方法与面向对象软件设计方法的有效结合,实现二维轴对称喷管两相无黏流场和复合结构温度场的一体化数值模拟. 数值模拟结果表明,该方法有助于在统一的软件平台上充分利用计算机辅助技术完成喷管性能与结构的综合评估,可以用于固体火箭发动机喷管的工程设计.     

Binary collision of drops in simple shear flow at finite Reynolds numbers: Geometry and viscosity ratio effects

The collision of two equal-size drops in an immiscible phase undergoing a shear flow is simulated over a range of viscosity ratios (??) and different geometries. The full Navier-Stokes equations are solved by a finite difference/front tracking method. Based on experimental data, different cases were simulated by changing the offset, size of drops, and viscosity ratio. The distance between drop centres along the velocity gradient direction (z) was measured as a function of time. It was found that ??z increases after collision and reaches a new steady-state value after separation. The values of ??z, during the interaction, increases with increasing initial offset. Our results show that the time of approaching of drops at low initial offset is greater than the other cases, but the maximum deformation is the same for equal drop sizes. The deformation decreases with decreasing the size of drops. As the initial offset increases, the drops rotate more quickly and the available contact time for film drainage decreases. We found that the trajectories of drops in the approaching stage are different owing to the different initial offsets. However, after the drops come into contact, it observed that they follow the same trajectories. As ?? increases, the drops rotate more slowly, and the point at which the drops separate is delayed. The trajectories of drops become more symmetric with the increased ??.     

Scalability of parallel spatial direct numerical simulations on intel hypercube and IBM SP1 and SP2

The implementation and performance of a parallel spatial direct numerical simulation (PSDNS) approach on the Intel iPSC/860 hypercube and IBM SP1 and SP2 parallel computers is documented. Spatially evolving disturbances associated with laminar-to-turbulent transition in boundary-layer flows are computed with the PSDNS code. The feasibility of using the PSDNS to perform transition studies on these computers is examined. The results indicate that PSDNS approach can effectively be parallelized on a distributed-memory parallel machine by remapping the distributed data structure during the course of the calculation. Scalability information is provided to estimate computational costs to match the actual costs relative to changes in the number of grid points. By increasing the number of processors, slower than linear speedups are achieved with optimized (machine-dependent library) routines. This slower than linear speedup results because the computational cost is dominated by FFT routine, which yields less than ideal speedups. By using appropriate compile options and optimized library routines on the SP1, the serial code achieves 52–56 Mflops on a single node of the SP1 (45 percent of theoretical peak performance). The actual performance of the PSDNS code on the SP1 is evaluated with a real world simulation that consists of 1.7 million grid points. One time step of this simulation is calculated on eight nodes of the SP1 in the same time as required by a Cray Y/MP supercomputer. For the same simulation, 32-nodes of the SP1 and SP2 are required to reach the performance of a Cray C-90. A 32 node SP1 (SP2) configuration is 2.9 (4.6) times faster than a Cray Y/MP for this simulation, while the hypercube is roughly 2 times slower than the Y/MP for this application.     

A numerical and experimental study on gap compensation and wavelength selection in UV-lithography of ultra-high aspect ratio SU-8 microstructures

This paper presents a study on UV-lithography of thick SU-8 resist using air gap compensation and optimal wavelength selection for ultra-high aspect ratio microstructures. Both numerical simulations and experiments were conducted to study effects of different lithography conditions: broadband light source with and without air gap compensation, filtered light source with glycerol liquid, and filtered light source with Cargille refractive index matching liquid. A thick PMMA sheet was used as an optical filter to eliminate most of the i-line components of a broadband light source. Using the filtered light source and gap compensation with the Cargille refractive index liquid perfectly matching that of SU-8, patterns with feature sizes of 6 μm thick, 1150 μm tall (aspect ratio of more than 190:1) and high quality sidewalls were obtained. Microstructures with height up to 2 mm and good sidewall quality were also obtained and presented. The study also proved that Cargille refractive index matching liquid is compatible with UV-lithography of SU-8 and may be used as an effective air gap compensation solution.     

Thermo-flow characteristics and air flow field leading of the air-cooled condenser cell in a power plant

Special A-frame geometry of the air-cooled condenser cell and the complicated flow field at the exit of the axial flow fan bring on the air mal-distribution on the surface of the finned tube bundles and the deteriorated thermo-flow performances of a condenser cell.It is of benefit to the design and operation optimization of the direct dry cooling system in a power plant to investigate the thermo-flow characteristics of the condenser cell and propose the flow leading measures of cooling air.On the basis of t...     

A型地铁空调系统及客室内流场数值分析

为给目前国内A型地铁车辆的舒适度设计提供理论参考,针对地铁车辆静压风道结构特点,基于k-ε两方程湍流模型和SIMPLE算法,建立包含空调送风风道和客室的三维计算模型.对计算模型的空气流动和传热状况进行CFD数值计算.计算过程综合考虑车体壁面传热和人体散热等多种传热.分析计算结果得到客室内温度场和速度场的分布规律,并对空调通风设计方案进行量化评估.计算结果表明:客室内人体头部区域温度场分布均匀,平均温度为26.6℃,最大温差为6℃;车厢内有较理想的气流组织形式,速度分布范围为0.50~0.79 m/s,而且客室端部和中部区域人体头部周围速度较大.将计算结果与欧洲EN 14750-1标准进行对比分析,认为乘客的舒适性较好.     

The numerical study on the unsteady flow of gas in a semi-infinite porous medium using an RBF collocation method

In this paper, we study a nonlinear two-point boundary value problem on semi-infinite interval that describes the unsteady gas equation. The solution of the mentioned ordinary differential equation (ODE) is investigated by means of the radial basis function (RBF) collocation method. The RBF reduces the solution of the above-mentioned problem to the solution of a system of algebraic equations and finds its numerical solution. To examine the accuracy and stability of the approach, we transform the mentioned problem into another nonlinear ODE which simplifies the original problem. The comparisons are made between the results of the present work and the numerical method by shooting method combined with the Runge–Kutta technique. It is found that our results agree well with those by the numerical method, which verifies the validity of the present work.