A miniature triple hot-wire probe for wall bounded flows

 Four orthogonal and one non-orthogonal miniature triple hot-wire probes have been developed and tested in a two-dimensional turbulent boundary layer. The influence of the different wire configurations on measurements of the Reynolds stresses has been studied. A directional calibration with an analytical solution for the wire response equations was used for the measurements of the non-orthogonal probe and was tested for the orthogonal probes in order to correct their possible geometrical imperfections. It is shown that a directional calibration does not significantly improve the quality of the measurements for precisely manufactured orthogonal probes and that measuring errors are related rather to the measuring volume, the size of the domain of unique solutions for the instantaneous velocity vector and interference effects, i.e. the wire configuration itself. Received: 7 February 1997/Accepted: 18 November 1997     

An explicit transient algorithm for predicting incompressible viscous flows in Arbitrary Geometry

A numerical method for predicting viscous flows in complex geometries has been presented. Integral mass and momentum conservation equations are deploved and these are discretized into algebraic form through numerical quadrature. The physical domain is divided into a number of non-orthogonal control volumes which are isoparametrically mapped on to standard rectangular cells. Numerical integration for unsteady mementum equations is performed over such non-orthogonal cells. The explicitly advanced velocity components obtained from unsteady momentum equations may not necessarily satisfy the mass conservation condition in each cell. Compliance of the mass conservation equation and the consequent evolution of correct pressure distribution are accomplished through an iterative correction of pressure and velocity till divergence-free condition is obtained in each cell. The algorithm is applied on a few test problems, namely, lid-driven square and oblique cavities, developing flow in a rectangular channel and flow over square and circular cylinders placed in rectangular channels. The results exhibit good accuracy and justify the applicability of the algorithm. This Explicit Transient Algorithm for Flows in Arbitrary Geometry is given a generic name EXTRAFLAG.     

A numerical method for 3D viscous incompressible flows using non-orthogonal grids

This paper presents a numerical method for fluid flow in complex three-dimensional geometries using a body-fitted co-ordinate system. A new second-order-accurate scheme for the cross-derivative terms is proposed to describe the non-orthogonal components, allowing parts of these terms to be treated implicitly without increasing the number of computational molecules. The physical tangential velocity components resulting from the velocity expansion in the unit tangent vector basis are used as dependent variables in the momentum equations. A coupled equation solver is used in place of the complicated pressure correction equation associated with grid non-orthogonality. The co-ordinate-invariant conservation equations and the physical geometric quantities of control cells are used directly to formulate the numerical scheme, without reference to the co-ordinate derivatives of transformation. Several two- and three-dimensional laminar flows are computed and compared with other numerical, experimental and analytical results to validate the solution method. Good agreement is obtained in all cases.     

Simultaneous Measurement of Velocity and Fluctuating Pressure in a Turbulent Wing-tip Vortex Using Triple Hot-film Sensor and Miniature Total Pressure Probe

We have developed a probe-system for simultaneous measurement of three velocity components and pressure in turbulent flows. A miniature total pressure probe is placed adjacent to the sensors of a triple hot-film probe in order to achieve the spatial resolution which is equivalent to that of the triple hot-film probe itself. The instantaneous static pressure is calculated from measured velocity and total pressure by means of a newly developed processing method based on the Bernoulli equation for unsteady flows. The measurements were undertaken in a turbulent wing-tip vortex flow. The look-up table method is employed for the calibration of the hot-film probe so accurate velocity data could be obtained over a wide range of the flow-attack angles. It is also demonstrated that the present probe-system is capable of measuring fluctuations in both velocity and pressure in the 20?C650 Hz frequency range. The distribution of the fluctuating pressure obtained by this indirect method is in good agreement with the results from direct measurements of static pressure, demonstrating the promising performance of the present method. Furthermore, an improvement in the ability to make measurements of the velocity?Cpressure correlation across the wing-tip vortex is achieved. This improvement is possible because the effects of lateral velocity components are properly taken into account in the present formulation. The investigation regarding the transport equation budget for turbulent kinetic energy shows an anomalous structure of turbulence in this flow, mainly due to the meandering of the vortex, and the measurement of pressure diffusion is found to play an important role in the characterization of this kind of flow.     

非正交同位网格下压力与速度耦合算法

发展了一种在非正交同位网格下以笛卡儿速度分量作为动量方程的独立变量、压力与速度耦合的S IM-PLER算法。该算法的特点是显式处理界面速度中的压力交叉导数项,得出压力与压力修正方程,使得压力及压力修正值与界面逆变速度直接耦合。通过对分汊通道内的流动问题进行验证计算,结果表明该算法可以有效而准确地模拟复杂区域内的流动与换热问题。     

Ultrasound scattering from a turbulent round thermal pure plume

This research work brings about additional contribution to validate the ultrasound scattering technique as a nonintrusive probe in the Fourier space for measurements performed in unsteady flows. In particular, this work reports experimental evidence of scattering from a turbulent thermal plume utilized as a testing flow. This technique is based upon the scattering of an ultrasound wave hitting and interacting with an unstable flow. The coupling among the acoustic mode with vorticity and entropy modes is derived from nonlinear terms of Navier–Stokes and energy equations. Scattering mechanism occurs when characteristic length scales of flows are comparable with wavelength of sound. Thus, it is possible to probe the flow at different length scales by changing the incoming frequency. The results allow verifying some theoretical predictions, such as the existence of a nonscattering angle. It was also observed, that both the phase and the Doppler shift of the Fourier's signal are linear, respectively, with respect to the time and the frequency of the incident wave. The Doppler shift allowed us to determine the advection velocity and has proved to be sensitive to the direction of the wave vector, to the scattering angle and also, we show that it is possible to have both positive and negative angles. The advection velocity increases with temperature and its values are coherent with those obtained with traditional techniques. Broadening and Doppler shift of the scattering signal allowed us to define the turbulence intensity, whose values are in agreement with those found in thermal plumes, where well-known techniques are currently used. This study has shown that the turbulence intensity increases weakly with temperature, nevertheless it seems more sensitive to the size of the structure under observation.     

A study on the extension of a VOF/PLIC based method to a curvilinear co-ordinate system

The conventional volume-of-fluid method has the potential to deal with large free surface deformation on a fixed Cartesian grid. However, when free-surface flows are within or over complex geometries of industrial relevance, such as free-surface flows over offshore oil platforms, it is advantageous to extend the method originally written in Cartesian forms into non-Cartesian forms. In the present study, an algorithm similar to the algorithm described by Rudman in 1997 is proposed for use with curvilinear co-ordinates. This extension results in the ability to model complex geometries which could not be modelled using the original algorithm. Excellent agreement between the solutions obtained on both orthogonal and non-orthogonal meshes is achieved, although in general the L ₁ error, based on the exact solution, on the non-orthogonal mesh is slightly higher than that on the orthogonal mesh. The extended fluid flow solving capacity of the present method is demonstrated through its application to a non-orthogonal Rayleigh–Taylor instability problem.     

On general form of Navier-Stokes equations and implicit factored scheme

A general weak conservative form of Navier-Stokes equations expressed with respect to non-orthogonal Curvilinear coordinates and with primitive variables was obtained by using tensor analysis technique, where the contravariant and covariant velocity components were employed. Compared with the current coordinate transformation method, the established equations are concise and forthright, and they are more convenient to be used for solving problems in body-fitted curvilinear coordinate system. An implicit factored scheme for solving the equations is presented with detailed discussions in this paper. For n-dimensional flow the algorithm requires n-steps and for each step only a block tridiagonal matrix equation needs to be solved. It avoids inverting the matrix for large systems of equations and enhances the speed of arithmetic. In this study, the Beam- Warming’s implicit factored schceme is extended and developed in non-orthogonal curvilinear coordinate system.     

Multisensor Hot Wire Vorticity Probe Measurements of the Formation Field of Two Corotating Vortices

Experimental evidence is reported, regarding the formation of a pair of co-rotating tip vortices by a split wing configuration, consisting of two half wings at equal and opposite angles of attack. Simultaneous measurements of the three-dimensional vector fields of velocity and vorticity were conducted on a cross plane at a downstream distance corresponding to 0.3 cord lengths (near wake), using an in-house constructed 12-sensor hot wire anemometry vorticity probe. The probe consists of three closely separated orthogonal 4-wire velocity sensor arrays, measuring simultaneously the three-dimensional velocity vector at three closely spaced locations on a cross plane of the flow filed. This configuration makes possible the estimation of spatial velocity derivatives by means of a forward difference scheme of first order accuracy. Velocity measurements obtained with an X-wire are also presented for comparison. In this near wake location, the flow field is dictated by the pressure distribution established by the flow around the wings, mobilizing large masses of air and leading to the roll up of fluid sheets. Fluid streams penetrating between the wings collide, creating on the cross plane flow a stagnation point and an “impermeable” line joining the two vortex centres. Along this line fluid is directed towards the two vortices, expanding their cores and increasing their separation distance. This feeding process generates a dipole of opposite sign streamwise mean vorticity within each vortex. The rotational flow within the vortices obligates an adverse streamwise pressure gradient leading to a significant streamwise velocity deficit characterizing the vortices. The turbulent flow field is the result of temporal changes in the intensity of the vortex formation and changes in the position of the cores (wandering).     

A robust algorithm for computing fluid flows on highly non‐smooth staggered grids

A new method for computing the fluid flow in complex geometries using highly non‐smooth and non‐orthogonal staggered grid is presented. In a context of the SIMPLE algorithm, pressure and physical tangential velocity components are used as dependent variables in momentum equations. To reduce the sensitivity of the curvature terms in response to coordinate line orientation change, these terms are exclusively computed using Cartesian velocity components in momentum equations. The method is then used to solve some fairly complicated 2‐D and 3‐D flow field using highly non‐smooth grids. The accuracy of results on rough grids (with sharp grid line orientation change and non‐uniformity) was found to be high and the agreement with previous experimental and numerical results was quite good. Copyright © 2008 John Wiley & Sons, Ltd.     

A four-sensor hot-wire probe system for three-component velocity measurement

 A velocity measurement system based on a miniature four-sensor hot-wire probe capable of simultaneous three-component measurements throughout a wide range of flow angles has been developed. The calibration technique allows measurements to be made throughout the acceptance cone of the probe without being restricted by the errors associated with analytic angle response equations. This technique is based upon look-up tables with values which tend to vary slowly, allowing a simple interpolation scheme to be used. Measurements made in a turbulent pipe flow verify the accuracy of the technique. Received: 27 September 1996/Accepted: 20 October 1997     

River and reservoir flow modelling using the transformed shallow water equations

This paper describes a versatile finite difference scheme for the solution of the two-dimensional shallow water equations on boundary-fitted non-orthogonal curvilinear meshes. It is believed that this is the first non-orthogonal shallow water equation model incorporating the advective acceleration terms to have been developed in the United Kingdom. The numerical scheme has been validated against the severe condition of jet-forced flow in a circular reservoir with vertical side walls, where reflections of the initial free surface waves pose major problems in achieving a stable solution. Furthermore, the validation exercises are designed to test the computer model for artificial diffusion, which may be a consequence of the numerical scheme adopted to stabilize the shallow water equations. The model is shown to be capable of simulating the flow conditions in an irregularly shaped domain typical of the geometries frequently encountered in civil engineering river basin management.     

基于多层分块算法的激波干扰流场预测

激波-激波干扰流场预测是超声速乃至高超声速流动中最具挑战性的问题之一. 特别地, 第IV类激波干扰由于其在壁面驻点附近产生极高的热载荷而备受关注. 本文针对圆柱诱导的弓形激波和入射斜激波的干扰问题, 分别基于量热完全气体模型和考虑振动激发的热完全气体模型, 数值求解有黏二维可压缩NS方程, 分析了高温气体效应对激波干扰流场结构, 以及第IV类激波干扰流场状态参数的影响. 接着, 本文基于一种具有广义可分离特性的遗传算法 (多层分块算法), 给出能够预测不同气体模型下第IV类激波干扰流场三波点的坐标位置、超声速射流的几何形状等特征性几何结构的数学模型, 进一步获得高温气体效应对激波干扰类型转变准则影响的定量化评估. 激波干扰类型转变准则面上的多组临界工况的激波干扰流场结构以及壁面压力和壁面热流分布的对比结果表明, 不同气体模型下的激波干扰类型和流场结构差异较为显著, 获得的定量化预测模型对工程中气动热环境的预测具有一定的参考价值.      

Computer-aided calibration and measurements with a quadruple hotwire probe

A method for calibration and measurement with a four-wire probe is described. For each of the wires a three dimensional calibration field is determined, thus no assumption like King's law or the cosine law need to be made. The velocity vector can then be detected in a fairly large angular range (± 40°) with a numerical search algorithm. First measurements in a free jet and a confined, strongly swirling flow are presented.A version of this paper was presented at the 11th Symposium on Turbulence, University of Missouri-Rolla, Oct. 17–19, 1988     

Crossflow of viscoplastic materials through tube bundles

The flow of viscoplastic materials through staggered arrays of tubes is analyzed. The mechanical behavior of the materials is assumed to obey the generalized Newtonian liquid (GNL) model, with a viscosity function given by the biviscosity law. The governing equations of this flow are solved numerically using a finite-volume method with a non-orthogonal mesh. For a representative range of the relevant parameters, results are presented in the form of velocity, pressure and viscosity fields. The pressure drop is also given as a function of rheological and geometric parameters.     

Simulation of angular velocity sensor measurements using telemetry data on the motion of an object

An algorithm for the formation of smooth trajectories corresponding to telemetry data on the coordinates and orientation angles of a flying object with a strapdown inertial navigation system is proposed. Another algorithm of forming the angular velocity sensor measurements corresponding to this trajectory is developed. These algorithms allow one to analyze the accuracy of various numerical methods of determining the orientation of such system using the information on motions close to the real motions with known telemetry data.     

Numerical Simulation of the 3D Laminar Viscous Flow on a Horizontal-axis Wind Turbine Blade

The aim of this paper is to describe the methodology followed in order to determine the viscous effects of a uniform wind on the blades of small horizontal-axis wind turbines that rotate at a constant angular speed. The numerical calculation of the development of the three-dimensional boundary layer on the surface of the blades is carried out under laminar conditions and considering flow rotation, airfoil curvature and blade twist effects. The adopted geometry for the twisted blades is given by cambered thin blade sections conformed by circular are airfoils with constant chords. The blade is working under stationary conditions at a given tip speed ratio, so that an extensive laminar boundary layer without flow separation is expected. The boundary layer growth is determined on a non-orthogonal curvilinear coordinate system related to the geometry of the blade surface. Since the thickness of the boundary layer grows from the leading edge of the blade and also from the tip to the blade root, a domain transformation is proposed in order to solve the discretized equations in a regular computational 3D domain. The non-linear system of partial differential coupled equations that governs the boundary layer development is numerically solved applying a finite difference technique using the Krause zig-zag scheme. The resulting coupled equations of motion are linearized, leading to a tridiagonal system of equations that is iteratively solved for the velocity components inside the viscous layer applying the Thomas algorithm, procedure that allows the subsequent numerical determination of the shear stress distribution on the blade surface.     

Effects of chemical reaction on mixed convection flow of a polar fluid through a porous medium in the presence of internal heat generation

This paper reports a detailed numerical investigation on mixed convection flow of a polar fluid through a porous medium due to the combined effects of thermal and mass diffusion. The energy equation accounts for heat generation or absorption, while the nth order homogeneous chemical reaction between the fluid and the diffusing species is included in the mass diffusion equation. The governing equations of the linear momentum, angular momentum, energy and concentration are obtained in a non-similar form by introducing a suitable group of transformations. The final set of non-similar coupled non-linear partial differential equations is solved using an implicit finite-difference scheme in combination with quasi-linearization technique. The effects of various parameters on the velocity, angular velocity, temperature and concentration fields are investigated. Numerical results for the skin friction coefficient, wall stress of angular velocity, Nusselt number and Sherwood number are also presented.     

Entry region of louvered fin heat exchangers

The dominant thermal resistance for most compact heat exchangers occurs on the gas side and as such an understanding of the gas side flowfield is needed before improving current designs. Louvered fins are commonly used in many compact heat exchangers to increase the surface area and initiate new boundary layer growth. For this study, detailed flowfield measurements were made in the entry region of several louvered fin geometries whereby the louver angle, ratio of fin pitch to louver pitch, and Reynolds number were all varied. In addition to mean velocity measurements, time-resolved velocity measurements were made to quantify unsteady effects.

The results indicated larger fin pitches resulted in lower average flow angles in the louver passages and longer development lengths. Larger louver angles with a constant ratio of fin pitch to louver pitch resulted in higher average flow angles and shorter development lengths. As the Reynolds number increased, longer development lengths were required and higher average flow angles occurred as compared with a lower Reynolds number case. Time-resolved velocity measurements indicated some flow periodicity behind the fully developed louver for a range of Reynolds numbers. The Strouhal number of these fluctuations was constant for a given louver geometry, but the value increased with increasing fin pitch.     

Numerical simulation of 2D lid‐driven cavity flow with CLEARER algorithm on extremely highly skewed grids at high Reynolds numbers

It is crucial to deal with the grid non‐orthogonality effectively in solving the flow in complex geometries, especially at high Reynolds numbers. In this study, the newly proposed Coupled and Linked Equations Algorithm Revised‐ER (CLEARER) algorithm is adopted to solve this problem successfully. In CLEARER algorithm the second relaxation factor is introduced in constructing the contravariant interface velocities, by setting it to a low value. CLEARER algorithm can overcome the severe grid non‐orthogonality and non‐linearity of equations effectively. After the numerical results with CLEARER are validated with the benchmark solutions, this algorithm is used to solve the lid‐driven flow in inclined cavity with inclination angles varying from 10 to 170^°, and Reynolds numbers varying from 5000 to 15 000. The streamlines and the centerline velocity distributions are provided in detail for all cases, which may offer some guidance for the study in this area. Copyright © 2010 John Wiley & Sons, Ltd.