Exact solutions for the unsteady flow of a Burger’s fluid in a duct induced by time-dependent prescribed volume flow rate

In this investigation, some unsteady flows in a circular duct have been studied. The fluid obeys viscoelastic non-Newtonian model with the Burgers’ constitutive equation and all fluid properties are constant. The flows in a duct are due to the prescribed arbitrary time dependent inlet volume flow rates. Four types of flow situations are considered. The governing equations are first developed and then solved using Laplace transform technique. Results indicate the strong effect of Burgers’ fluid parameter on the velocity fields and pressure gradients.     

Flow of a Weakly Conducting Fluid in a Channel Filled with a Darcy–Brinkman–Forchheimer Porous Medium

We investigate in this article, the fully developed flow in a fluid-saturated channel filled with a Darcy–Brinkman–Forchheimer porous medium, which is conducted with an electrically varying parallel Lorentz force. The Lorentz force varies exponentially in the vertical direction due to low fluid electrical conductivity and the special arrangement of the magnetic and electric fields at the lower plate. With the homotopy analysis method (HAM), a particularly effective technique in solving nonlinear problems, analytical approximation series solutions with high accuracy are derived for fluid velocity and the results are illustrated in form of figures. All these flows are new and are presented for the first time in the literature.     

Dynamic measurement of temperature, velocity, and density in hot jets using Rayleigh scattering

A molecular Rayleigh scattering technique is utilized to measure gas temperature, velocity, and density in unseeded gas flows at sampling rates up to 10 kHz, providing fluctuation information up to 5 kHz based on the Nyquist theorem. A high-power continuous-wave laser beam is focused at a point in an air flow field and Rayleigh scattered light is collected and fiber-optically transmitted to a Fabry–Perot interferometer for spectral analysis. Photomultiplier tubes operated in the photon counting mode allow high-frequency sampling of the total signal level and the circular interference pattern to provide dynamic density, temperature, and velocity measurements. Mean and root mean square velocity, temperature, and density, as well as power spectral density calculations, are presented for measurements in a hydrogen-combustor heated jet facility with a 50.8-mm diameter nozzle at NASA John H. Glenn Research Center at Lewis Field. The Rayleigh measurements are compared with particle image velocimetry data and computational fluid dynamics predictions. This technique is aimed at aeronautics research related to identifying noise sources in free jets, as well as applications in supersonic and hypersonic flows where measurement of flow properties, including mass flux, is required in the presence of shocks and ionization occurrence.     

Viscous fluid velocity field between two cylinders which rotate and move translationally

Viscous fluid flow in the domain between circular cylinders is considered. The fluid flow is initiated by rotational and translational motions of the cylinders. A general analytic expression for the fluid velocity field is constructed using the conformal mapping method and the bipolar coordinates. The streamline structure is studied for the steady-state flows.     

Experimental study of simultaneous measurement of velocity and surface topography: in the wake of a circular cylinder at low Reynolds number

A technique to provide simultaneous measurement on both free surface topography and the velocity vector field of free surface flows is further developed and validated. Testing was performed on the topography measurement by imaging static plastic wave samples over a wide range of amplitudes. Analysis on the accuracy of the topography reconstruction, the sensitivity to noise and the dependence on spatial resolution are presented. The displacement of the free surface is insensitive to noisy input and the sensitivity shows a linear dependence with the sample spacing. Simultaneous measurements of the free surface and associated velocity field in the wake of a circular cylinder are presented for Reynolds numbers between 55 and 100.     

An anemometer for highly turbulent or recirculating flows

An anemometer which determines flow velocity by ionizing air and sensing the convective displacement of the ions is described. It is suited to measurement in low speed, highly unsteady gas flows. Comparisons to hot wire spectra suggest the corona anemometer has adequate frequency response to make it a useful tool for fluid dynamics measurement.     

Measurement of instantaneous velocity and surface topography in the wake of a cylinder at low Reynolds number

A technique capable of simultaneous measurement of free-surface topography and velocity vector field data is presented. This technique offers substantial benefits of both reduced complexity and enhanced accuracy over all other techniques known to offer the same measurements. The flow behind a circular cylinder at low Reynolds numbers is measured using this technique. The velocity and vorticity fields as well as Strouhal number closely match the expected results. The free-surface topography, which can be related to the pressure field, exhibits an intimate relationship to the vorticity field.     

Gas-kinetic numerical method for solving mesoscopic velocity distribution function equation

A gas-kinetic numerical method for directly solving the mesoscopic velocity distribution function equation is presented and applied to the study of three-dimensional complex flows and micro-channel flows covering various flow regimes. The unified velocity distribution function equation describing gas transport phenomena from rarefied transition to continuum flow regimes can be presented on the basis of the kinetic Boltzmann–Shakhov model equation. The gas-kinetic finite-difference schemes for the velocity distribution function are constructed by developing a discrete velocity ordinate method of gas kinetic theory and an unsteady time-splitting technique from computational fluid dynamics. Gas-kinetic boundary conditions and numerical modeling can be established by directly manipulating on the mesoscopic velocity distribution function. A new Gauss-type discrete velocity numerical integration method can be developed and adopted to attack complex flows with different Mach numbers. HPF parallel strategy suitable for the gas-kinetic numerical method is investigated and adopted to solve three-dimensional complex problems. High Mach number flows around three-dimensional bodies are computed preliminarily with massive scale parallel. It is noteworthy and of practical importance that the HPF parallel algorithm for solving three-dimensional complex problems can be effectively developed to cover various flow regimes. On the other hand, the gas-kinetic numerical method is extended and used to study micro-channel gas flows including the classical Couette flow, the Poiseuille- channel flow and pressure-driven gas flows in two-dimensional short micro-channels. The numerical experience shows that the gas-kinetic algorithm may be a powerful tool in the numerical simulation of micro-scale gas flows occuring in the Micro-Electro-Mechanical System (MEMS). The project supported by the National Natural Science Foundation of China (90205009 and 10321002), and the National Parallel Computing Center in Beijing. The English text was polished by Yunming Chen.     

Natural convection in a bottom-heated top-cooled cubic cavity with a baffle at the median height: experiment and model validation

This paper presents an experimental and numerical investigation on the natural convection flow and heat transfer in an enclosure with a single-hole baffle at the median height. The temperature in the fluid is quantified by means of temperature sensitive thermo-chromic liquid crystal (TLC) particles. The fluid flow velocity is measured non-intrusively with a full field particle tracking technique. The three-dimensional numerical model, developed and validated with experimental data, provides a computational tool for further investigation of mass and energy transport through the baffle openings in these types of enclosures. The experimentally visualized and numerically simulated flow structures show a pair of streams across the baffle-hole. The two chambers communicate through this pair of streams which carry the fluid exchange and heat transfer between the two chambers. At the baffle opening, the two streams are aligned in a diagonal direction across of the enclosure. The streams are accelerated and form jet-like flows that drive the whole circulation in the chambers. The jet-like flows leave the baffle opening, approach the vertical centerline of the cavity, and finally impinge on the top/bottom walls.     

Measured Reynolds stress distributions and energy budgets of a fully pulsed round air jet

 Most particle-tracking velocimetry (PTV) algorithms are not suitable for calculating the velocity vectors of a fluid flow subjected to strong deformation, because these algorithms deal only with flows due to translation. Accordingly, it is necessary to develop a novel algorithm applicable to flows subjected to strong deformations such as rotation, shear, expansion and compression. This paper proposes a novel particle tracking algorithm using the velocity gradient tensor (VGT) which can deal with strong deformations and demonstrates that this algorithm is applicable to some basic fluid motions (rigidly rotating flow, Couette flow, and expansion flow). Furthermore, the performance of this algorithm is compared with the binary image cross-correlation method (BICC), the four-consecutive-time-step particle tracking method (4-PTV), and the spring model particle tracking algorithm (SPG) using simulations and experimental data. As a result, it is shown that this novel algorithm is useful and applicable for the highly accurate measurement and analysis of fluid flows subjected to strong deformations. Received: 9 February 1999/Accepted: 22 November 1999     

A device to achieve low Reynolds numbers in an open surface water channel

When investigating flow structures, and especially flow transitions, research projects often seek to increase insight using complementary numerical and physical experiments. Obtaining exact Reynolds number correspondence can frequently be difficult in experiments, particularly when relatively low values are required. Often, available test facilities were designed and optimised for a specific velocity range, meaning they have restrictions on the minimum flow velocity. This study describes a device to reduce the flow velocity locally in an open surface water channel. The underlying idea is to divert a controlled fraction of the incoming flow from the working section by increasing the pressure there, resulting in reduced velocity. This idea is realised using a ‘sub-channel’ that can be inserted into the main test chamber, with a variable porosity perforated screen at its downstream end. This study assesses and optimises the flow quality inside this structure, such as usable test section length, uniformity of the velocity profiles and turbulence intensity. The results demonstrate that the device creates high quality low Reynolds number flows, which is exemplified with the canonical circular cylinder in cross-flow.     

NMR flow imaging of Newtonian liquids and a concentrated suspension through an axisymmetric sudden contraction

Using nuclear magnetic resonance (NMR) flow imaging to examine fluid motions at constant velocities or flows that change relatively slowly has been well-documented in the literature. Application of this technique to accelerative flows, on the other hand, has been limited. This study reports the use of an NMR flow imaging method, for which acceleration is not explicitly compensated in the NMR pulse sequence, to measure axial and radial fluid motions during flow through an axisymmetric sudden contraction. In this flow geometry, both velocity and acceleration are spatially dependent. The flow contraction ratio was 2:1. The method was first applied to examine Newtonian liquids at low and high Reynolds numbers under laminar flow conditions. The measured axial and radial velocity profiles, without accounting for acceleration effects in the data analysis, across the contraction are in excellent qualitative agreement with previous experimental data and theoretical calculations reported in the literature. Quantitative comparison of the axial and radial velocities with numerical results indicates that the maximum error from acceleration effects is about 10%. The method has also been used to examine the flow of a concentrated suspension (50% by volume of solid particles) through the contraction. The flow kinematics of the suspension at creeping flow conditions appear to mimic those of the Newtonian fluid with some slight differences. NMR images taken immediately following the cessation of flow suggest a slight degree of particle migration toward the center of the pipe downstream of the contraction.     

基于Boltzmann模型方程的气体运动论统一算法研究

模型方程出发,研究确立含流态控制参数可描述不同流域气体流动特征的气体分子速度分布函数方程; 研究发展气体运动论离散速度坐标法, 借助非定常时间分裂数值计算方法和NND差分格式, 结合DSMC方法关于分子运动与碰撞去耦技术, 发展直接求解速度分布函数的气体运动论耦合迭代数值格式; 研制可用于物理空间各点宏观流动取矩的离散速度数值积分方法, 由此提出一套能有效模拟稀薄流到连续流不同流域气体流动问题统一算法. 通过对不同Knudsen数下一维激波内流动、二维圆柱、三维球体绕流数值计算表明, 计算结果与有关实验数据及其它途径研究结果(如DSMC模拟值、N-S数值解)吻合较好, 证实气体运动论统一算法求解各流域气体流动问题的可行性. 尝试将统一算法进行HPF并行化程序设计, 基于对球体绕流及类``神舟'返回舱外形绕流问题进行HPF初步并行试算, 显示出统一算法具有很好的并行可扩展性, 可望建立起新型的能有效模拟各流域飞行器绕流HPF并行算法研究方向. 通过将气体运动论统一算法推广应用于微槽道流动计算研究, 已初步发展起可靠模拟二维短微槽道流动数值算法; 通过对Couette流、Poiseuille流、压力驱动的二维短槽道流数值模拟, 证实该算法对微槽道气体流动问题具有较强的模拟能力, 可望发展起基于Boltzmann模型方程能可靠模拟MEMS微流动问题气体运动论数值计算方法研究途径.      

Velocity profile measurement by ultrasonic doppler method

The ultrasonic velocity profile measuring method has been developed at PSI for application in fluid mechanics and fluid flow measurement. It uses pulsed ultrasonic echography together with the detection of the instantaneous Doppler shift frequency. This method has the following advantages over the conventional techniques: (1) an efficient flow mapping process, (2) applicability to opaque liquids, and (3) a record of the spatiotemporal velocity field. After a brief introduction of its principle, the characteristics and specifications of the present system are given. Then examples in fluid engineering for oscillating pipe flow, T-branching flow of mercury, and recirculating flow in a square cavity are described that confirm the method's advantages. Several other works under way by other investigators are introduced. A potential for in-depth study of fluid dynamics is demonstrated by several examples from an investigation of modulated wavy flows in a rotating Couette system. The position-averaged power spectrum and the time-averaged energy spectral density were used to study the dynamic characteristics of the flow, and subsequently the velocity field was decomposed into its intrinsic wave structure based on two-dimensional Fourier analysis.     

Lagrangian finite element method for the analysis of two-dimensional sloshing problems

A new version of a numerical algorithm for the Lagrangian treatment of incompressible fluid flows with free surfaces is developed. The novel features of the present method are the adoptions of the Lagrangian finite element method and the velocity correction technique. The use of the velocity correction approach makes the computational scheme extremely simple in algorithmic structure. Hence, the present method is particularly attractive for large-scale problems. The techniques discussed here are applied to some two-dimensional sloshing problems, which may indicate the versatility and effectiveness of the present method.     

Pulsed-wire anemometry

Pulsed-wire anemometry was first developed as a tool for making velocity and turbulence measurements in the late 1960s. It has been continuously refined and its potential exploited by a number of groups who have obtained reliable data in situations where the use of other techniques would have been extremely difficult. The technique is particularly useful in flows of high turbulence intensity and has therefore been used to greatest effect in separated flows. Although its range of applicability is much more restricted than that of laser-Doppler anemometry, it is an order of magnitude cheaper, and it does not require seeding of the flow, with all the attendant uncertainties.

First the physical basis of pulsed-wire anemometry is briefly described, and the major sources of experimental error are outlined for cases in which the technique is used both remote from and close to walls. Progress in the design of probes, which have been improved in a number of ways since the early days to reduce errors, is also outlined. The author then reviews the kinds of measurements that have been successfully made and the consequent improvements in the understanding of the physics of complex flows. Examples are drawn from a wide range of work, including some unusual applications like measurements in very low velocity gas mixtures. The paper closes with a summary of the limitations of the technique and an overall assessment of the likely potential for its use in future turbulence research.     

Numerical investigation from rarefied flow to continuum by solving the Boltzmann model equation

Based on the Bhatnagar–Gross–Krook (BGK) Boltzmann model equation, the unified simplified velocity distribution function equation adapted to various flow regimes can be presented. The reduced velocity distribution functions and the discrete velocity ordinate method are developed and applied to remove the velocity space dependency of the distribution function, and then the distribution function equations will be cast into hyperbolic conservation laws form with non‐linear source terms. Based on the unsteady time‐splitting technique and the non‐oscillatory, containing no free parameters, and dissipative (NND) finite‐difference method, the gas kinetic finite‐difference second‐order scheme is constructed for the computation of the discrete velocity distribution functions. The discrete velocity numerical quadrature methods are developed to evaluate the macroscopic flow parameters at each point in the physical space. As a result, a unified simplified gas kinetic algorithm for the gas dynamical problems from various flow regimes is developed. To test the reliability of the present numerical method, the one‐dimensional shock‐tube problems and the flows past two‐dimensional circular cylinder with various Knudsen numbers are simulated. The computations of the related flows indicate that both high resolution of the flow fields and good qualitative agreement with the theoretical, DSMC and experimental results can be obtained. Copyright © 2003 John Wiley & Sons, Ltd.     

An efficient algorithm for strain history tracking in finite element computations of non-Newtonian fluids with integral constitutive equations

A new finite element technique has been developed for employing integral-type constitutive equations in non-Newtonian flow simulations. The present method uses conventional quadrilateral elements for the interpolation of velocity components, so that it can conveniently handle viscoelastic flows with both open and closed streamlines (recirculating regions). A Picard iteration scheme with either flow rate or elasticity increment is used to treat the non-Newtonian stresses as pseudo-body forces, and an efficient and consistent predictor-corrector scheme is adopted for both the particle-tracking and strain tensor calculations. The new method has been used to simulate entry flows of polymer melts in circular abrupt contractions using the K-BKZ integral constitutive model. Results are in very good agreement with existing numerical data. The important question of mesh refinement and convergence for integral models in complex flow at high flow rate has also been addressed, and satisfactory convergence and mesh-independent results are obtained. In addition, the present method is relatively inexpensive and in the meantime can reach higher elasticity levels without numerical instability, compared with the best available similar calculations in the literature.     

Lattice Boltzmann simulations of viscoplastic fluid flows through complex flow channels

We present the results of lattice Boltzmann (LB) simulations for the planar-flow of viscoplastic fluids through complex flow channels. In this study, the Bingham and Casson model fluids are covered as viscoplastic fluid. The Papanastasiou (modified Bingham) model and the modified Casson model are employed in our LB simulations. The Bingham number is an essential physical parameter when considering viscoplastic fluid flows and the modified Bingham number is proposed for modified viscoplastic models. When the value of the modified Bingham number agrees with that of the “normal” Bingham number, viscoplastic fluid flows formulated by modified viscoplastic models strictly reproduce the flow behavior of the ideal viscoplastic fluids. LB simulations are extensively performed for viscoplastic fluid flows through complex flow channels with rectangular and circular obstacles. It is shown that the LB method (LBM) allows us to successfully compute the flow behavior of viscoplastic fluids in various complicated-flow channels with rectangular and circular obstacles. For even low Re and high Bn numbers corresponding to plastic-property dominant condition, it is clearly manifested that the viscosity for both the viscoplastic fluids is largely decreased around solid obstacles. Also, it is shown that the viscosity profile is quite different between both the viscoplastic fluids due to the inherent nature of the models. The viscosity of the Bingham fluid sharply drops down close to the plastic viscosity, whereas the viscosity of the Casson fluid does not rapidly fall. From this study, it is demonstrated that the LBM can be also an effective methodology for computing viscoplastic fluid flows through complex channels including circular obstacles.     

Measurement of mean rotation and strain-rate tensors by using stereoscopic PIV

A technique is described for measuring the mean velocity gradient (rate-of-displacement) tensor by using a conventional stereoscopic particle image velocimetry (SPIV) system. Planar measurement of the mean vorticity vector, rate-of-rotation and rate-of-strain tensors and the production of turbulent kinetic energy can be accomplished. Parameters of the Q criterion and negative λ₂ techniques used for vortex identification can be evaluated in the mean flow field. Experimental data obtained for a circular turbulent jet issuing normal to a crossflow in a low speed wind tunnel for a jet-to-crossflow velocity ratio of 3.3 are presented to show the applicability of the proposed technique. The results reveal the presence of a secondary counter-rotating vortex pair (SCVP) which is located within the jet core and has a sense of rotation opposite to that of the primary one (PCVP). Consistency of the measurements is verified by the agreement of data obtained in two perpendicular planes. Accuracy of the data is discussed and algebraic relations for some measurement uncertainties are presented.