A crossed hot-wire technique for complex turbulent flows

This paper describes a crossed hot-wire technique for the measurement of all components of mean velocity, Reynolds stresses, and triple products in a complex turbulent flow. The accuracy of various assumptions usually implicit in the use of crossed hot-wire anemometers is examined. It is shown that significant errors can result in flow with gradients in mean velocity or Reynolds stress, but that a first order correction for these errors can be made using available data. It is also shown how corrections can be made for high turbulence levels using available data.     

Turbulent Air-Flow Measurement with the Aid of 3-D Particle Tracking Velocimetry in a Curved Square Bend

A three-dimensional particle tracking velocimeter (3-D PTV) was applied to air-flow measurement in a strongly curved U-bend of a square cross-section. He-filled neutral-buoyant soap bubbles were employed as a flow tracer, and turbulent statistics including all Reynolds stress components were measured. The pressure-induced secondary flow, of which magnitude reached about 30% of the bulk mean velocity, was observed. The present experimental result is mostly in good agreement with the LDA data at higher bulk-mean Reynolds number taken by Chang et al. The effect of the secondary flow on the production mechanism of turbulent kinetic energy as well as on the distributions of the invariants of stress anisotropy tensor was examined in detail. This revised version was published online in July 2006 with corrections to the Cover Date.     

Numerical analysis of turbulent flow in a rotating U-bend with roughened walls

A numerical analysis has been performed for a developing turbulent flow in a rotating U-bend of strong curvature with rib-roughened walls using an anisotropic turbulent model. In this calculation, an algebraic Reynolds stress model is used to precisely predict Reynolds stresses, and a boundary-fitted coordinate system is introduced as a method of coordinate transformation to set the exact boundary conditions along the complicated shape of U-bend with rib-roughened walls. Calculated results for mean velocity and Reynolds stresses are compared to the experimental data in order to validate the proposed numerical method and the algebraic Reynolds stress model. Although agreement is certainly not perfect in all details, the present method can predict characteristic velocity profiles and reproduce the separated flow generated near the outer wall, which is located just downstream of the curved duct. The Reynolds stresses predicted by the proposed turbulent model agree well with the experimental data, except in regions of flow separation.     

Laser-Doppler measurements of laminar and turbulent flow in a pipe bend

Laser-Doppler measurements are reported for laminar and turbulent flow through a 90° bend of circular cross-section with mean radius of curvature equal to 2.8 times the diameter. The measurements were made in cross-stream planes 0.58 diameters upstream of the bend inlet plane, in 30, 60 and 75° planes in the bend and in planes one and six diameters downstream of the exit plane. Three sets of data were obtained: for laminar flow at Reynolds numbers of 500 and 1093 and for turbulent flow at the maximum obtainable Reynolds number of 43 000. The results show the development of strong pressure-driven secondary flows in the form of a pair of counter-rotating vortices in the streamwise direction. The strength and character of the secondary flows were found to depend on the thickness and nature of the inlet boundary layers, inlet conditions which could not be varied independently of Reynolds number. The quantitative anemometer measurements are supported by flow visualization studies. Refractive index matching at the fluid-wall interface was not used; the measurements consist, therefore, of streamwise components of mean and fluctuating velocities only, supplemented by wall pressure measurements for the turbulent flow. The displacement of the laser measurement volume due to refraction is allowed for in simple geometrical calculations. The results are intenden for use as benchmark data for calibrating flow calculation methods.     

Improvement of a pressure gradient method and its application to an unsteady flow problem

The pressure gradient method using velocity components and components of a pressure gradient as dependent variables has been modified to solve incompressible Newtonian fluid flow problems numerically. Applying this modified method to unsteady-state development of flow in a circular cavity shows that, at least for the case of a low Reynolds number flow, relative errors produced by the proposed method are smaller for most time intervals than those produced by the primitive velocity-pressure variable method and by the standard pressure gradient method. Also it is found that the modified and standard pressure gradient methods can be applied to the unsteady circular cavity flow at a moderate Reynolds number of at least up to 200.     

Nonlinear algebraic model of the Reynolds stresses for a disperse turbulent flow with low-inertia particles

The purpose of the study is to present an explicit self-consistent algebraic model of the Reynolds stresses (nonlinear turbulent viscosity) for calculating two-phase flows laden with small heavy particles. The model is tested by means of comparing with the results of the solution of a system of differential equations for all components of the Reynolds stresses and the data of direct numerical calculations in a homogeneous shear flow with particles.     

A Bayesian Calibration–Prediction Method for Reducing Model-Form Uncertainties with Application in RANS Simulations

Model-form uncertainties in complex mechanics systems are a major obstacle for predictive simulations. Reducing these uncertainties is critical for stake-holders to make risk-informed decisions based on numerical simulations. For example, Reynolds-Averaged Navier-Stokes (RANS) simulations are increasingly used in the design, analysis, and safety assessment of mission-critical systems involving turbulent flows. However, for many practical flows the RANS predictions have large model-form uncertainties originating from the uncertainty in the modeled Reynolds stresses. Recently, a physics-informed Bayesian framework has been proposed to quantify and reduce model-form uncertainties in RANS simulations for flows by utilizing sparse observation data. However, in the design stage of engineering systems, when the system or device has not been built yet, measurement data are usually not available. In the present work we extend the original framework to scenarios where there are no available data on the flow to be predicted. In the proposed method, we first calibrate the model discrepancy on a related flow with available data, leading to a statistical model for the uncertainty distribution of the Reynolds stress discrepancy. The obtained distribution is then sampled to correct the RANS-modeled Reynolds stresses for the flow to be predicted. The extended framework is a Bayesian calibration–prediction method for reducing model-form uncertainties. The merits of the proposed method are demonstrated on two flows that are challenging to standard RANS models. By not requiring observation data on the flow to be predicted, the present calibration–prediction method will gain wider acceptance in practical engineering design and analysis compared to the original framework. While RANS modeling is chosen to demonstrate the merits of the proposed framework, the methodology is generally applicable to other complex mechanics models involving solids, fluids flows, or the coupling between the two (e.g., mechanics models for the cardiovascular systems), where model-form uncertainties are present in the constitutive relations.     

Reynolds stress modelling of rectangular open‐channel flow

A Reynolds stress model for the numerical simulation of uniform 3D turbulent open‐channel flows is described. The finite volume method is used for the numerical solution of the flow equations and transport equations of the Reynolds stress components. The overall solution strategy is the SIMPLER algorithm, and the power‐law scheme is used to discretize the convection and diffusion terms in the governing equations. The developed model is applied to a flow at a Reynolds number of 77000 in a rectangular channel with a width to depth ratio of 2. The simulated mean flow and turbulence structures are compared with measured and computed data from the literature. The computed flow vectors in the plane normal to the streamwise direction show a small vortex, called inner secondary currents, located at the juncture of the sidewall and the free surface as well as the free surface and bottom vortices. This small vortex causes a significant increase in the wall shear stress in the vicinity of the free surface. A budget analysis of the streamwise vorticity is carried out. It is found that both production terms by anisotropy of Reynolds normal stress and by Reynolds shear stress contribute to the generation of secondary currents. Copyright © 2006 John Wiley & Sons, Ltd.     

Aerodynamic drag of bodies in transonic flow. Theory and applications to computational aerodynamics

Formulas for all the components of the aerodynamic drag (total, friction, inductive, wave, pressure, and heat-transfer) are uniformly derived as applied to flows governed by the Navier-Stokes and Reynolds equations. For flows of this type the definition of the aerodynamic drag components is refined and the physical basis of the chosen method of breaking up the total drag into components is discussed. Ways of calculating the aerodynamic drag components using the methods of computational aerodynamics are considered. On the basis of the refined formulas the drag components are calculated for flows around airfoils and a high-aspect-ratio wing in transonic flow.     

亚临界雷诺数下圆柱绕流的大涡模拟

本文应用Smagorinsky涡粘性模式和二阶精度的有限体积法对圆柱绕流的流场进行大涡模拟．求解了非正交曲线坐标系下的N-S方程,对雷诺数为100和20000的工况进行了计算．计算结果与实验及动力涡粘性模式的结果进行了比较,表明计算对于层流及高亚临界雷诺数的湍流流动是合理的     

Effect of the measurement volume in turbulent pipe flow measurement by the ultrasonic velocity profile method (mean velocity profile and Reynolds stress measurement)

 The ultrasonic velocity profile measurement method has some favorable advantages over the conventional flow measurement methods, such as measurement of the instantaneous velocity profile over the measuring line and its applicability to opaque liquids. The method has another advantage of being non-intrusive. Hence, it is applicable to various flow conditions, although it requires a relatively large measurement volume. In this paper, the effects of the measurement volume on the mean velocity profile and the Reynolds stress measurement have been investigated for fully developed turbulent flows in a vertical pipe. The results were then compared with data obtained by direct numerical simulation. Received: 9 March 2000 / Accepted: 27 March 2001 Published online: 29 November 2001     

A laboratory study of irregular shoaling waves

The present research aims to investigate the dynamics of a single laboratory irregular wave, characterized by a narrow-banded spectrum and developing on a sloping sand bottom, in intermediate waters up to the surf zone. Experiments focused on the wave shoaling region, in order to examine how the wave is affected by breaking induced turbulence offshore the surf zone. A 3D acoustic Doppler velocimeter was used to measure the three wave velocity components, which were all processed to evaluate the time-averaged vertical distributions of orbital velocities, wave and turbulent Reynolds shear stresses and turbulent intensities. The vertical distributions of the phase-averaged velocity components, turbulent kinetic energy and transport of turbulence were also analysed. The adopted phase-averaging technique was applied to each investigated measurement point. Therefore, the crucial element of the study is that all the analysed values derive directly from real measurements and are not approximated by any kind of interpolation. The study confirmed some dynamic behaviour in the shoaling zone already known in the literature, such as the typical cell-type flow pattern of the mean flow and the necessity to evaluate the turbulent kinetic energy with all the three velocity components, when available, which would otherwise be underestimated. Referring to the time-averaged wave and Reynolds shear stresses, a contribution was added to the open debate on their order of magnitude. The measured wave Reynolds shear stresses were also compared with the results of the model by Zou et al. (J Geophys Res 111:C09032, 2006), confirming the behaviour typical of dissipative breaking waves. The analysis of turbulence transport in the shoaling zone revealed that it is seaward directed close to the surface and landward directed close to the bottom. The results presented in the paper can be extended only to other analogous flow conditions.     

Study of the Turbulent Velocity Field in the Near Wake of a Bluff Body

An experimental characterization of the turbulent flow structure formed downstream of a vertically mounted circular bluff body is performed. Three components of an instantaneous velocity field are measured using the stereo particle image velocimetry technique at the symmetry plane. The average velocity and the turbulent properties are analyzed. The results indicate a recirculation zone consisting of a toroidal vortex with similar dimensions for all Reynolds numbers. The largest turbulent fluctuations are found at the stagnation point region. The observed anisotropy of the normal Reynolds stress components is associated with the stagnation point flow, whereas the cross-correlation component extreme occurs in high strain rate regions. An analysis of the Reynolds tensor anisotropy using the Lumley triangle is performed, revealing that the largest departures from isotropy occur at high shear regions and also within the vortex.     

3D pressure imaging of an aircraft propeller blade-tip flow by phase-locked stereoscopic PIV

The flow field at the tip region of a scaled DHC Beaver aircraft propeller, running at transonic speed, has been investigated by means of a multi-plane stereoscopic particle image velocimetry setup. Velocity fields, phase-locked with the blade rotational motion, are acquired across several planes perpendicular to the blade axis and merged to form a 3D measurement volume. Transonic conditions have been reached at the tip region, with a revolution frequency of 19,800 rpm and a relative free-stream Mach number of 0.73 at the tip. The pressure field and the surface pressure distribution are inferred from the 3D velocity data through integration of the momentum Navier-Stokes equation in differential form, allowing for the simultaneous flow visualization and the aerodynamic loads computation, with respect to a reference frame moving with the blade. The momentum and pressure data are further integrated by means of a contour-approach to yield the aerodynamic sectional force components as well as the blade torsional moment. A steady Reynolds averaged Navier-Stokes numerical simulation of the entire propeller model has been used for comparison to the measurement data.     

Laser Doppler anemometry measurements of laminar flow in helical pipes

Three-dimensional laser Doppler anemometry measurements are performed on developed laminar flow in three helical pipes. The experimental observations are compared to results of numerical calculations employing the fully elliptic numerical method. Good agreement is found between measured data and numerical results. The three helical pipes, with curvature ratios of 0.0734 and 0.1374 and non-dimensional pitches of 0.0793 and 0.193, are adopted to study the effects of curvature and pitch on laminar flow in the experimental approach. The range of Reynolds numbers is 500–2000 to ensure laminar flow in the entire helical pipe. Both the profile shapes of the normal components of the secondary flow and those of the axial flow along the same centerline present not only similar patterns but also similar change when pitch, curvature ratio, and Reynolds number vary. The results demonstrate comprehensive relationships between the axial flow and the secondary flow.     

Laser Doppler velocimetry measurements in an interior flow test facility: A database for CFD-code evaluation

Measurements in a test facility for a complex interior flow are provided as a database for CFD code evaluation. For pure forced convection as well as to a minor extent also for mixed convection flows, the three time-averaged components of the velocity vector and all components of the Reynolds stress tensor are measured in selected cross sections. Special attention is given to the inflow into the main flow section, since it is the important part of the boundary condition for a numerical solution.     

An experimental contribution to near-wall measurements by means of a special laser Doppler anemometry technique

 A new experimental technique for the investigation of near-wall turbulence using laser Doppler anemometry is presented, which allows an accurate measurement of the flow field very close to the wall, with good resolution and a high data rate. Such a technique is tested in a fully developed turbulent flow (with Reynolds numbers between 4,300 and 67,000) by carrying out a careful statistical analysis of the streamwise and wall-normal velocity components within the near-wall region, at distances from the wall ranging from approximately y ⁺ = 1 to y ⁺ = 100. The velocity profiles, Reynolds stresses and higher-order moments of the two-dimensional boundary layer are presented. The results, which are in agreement with the most recent data in the literature, testify the validity of the proposed experimental solution. Moreover, the accuracy of the results allows the friction velocity to be calculated as the intercept at the wall of the best linear fit of the total stress profile; in this way, an unambiguous examination of the normalized statistics is possible. Received: 17 April 2001 / Accepted: 15 August 2001     

PIV–LES analysis of channel flow rotating about the streamwise axis

The flow field of a channel rotating about the streamwise axis is analyzed experimentally and numerically. The current investigations were carried out at a bulk velocity based Reynolds number of Re_m = 2850 and a friction velocity based Reynolds number of Re_τ = 180, respectively. Particle-image velocimetry (PIV) measurements are compared with large-eddy simulation data to show earlier direct numerical simulation findings to generate too large a reverse flow region in the center region of the spanwise flow. The development of the mean spanwise velocity distribution and the influence of the rotation on the turbulent properties, i.e., the Reynolds stresses and the two-point correlations of the flow, are confirmed in both investigations. The rotation primarily influences those components of the Reynolds shear stresses, which contain the spanwise velocity component. The size of the correlation areas and thus the length scales of the flow generally grow in all three coordinate directions leading to longer structures. Furthermore, experimental results of the same channel flow at a significantly lower bulk Reynolds number of Re_{m, l} = 665, i.e., a laminar flow in a non-rotating channel, are introduced. The experiments show the low Reynolds number flow to become turbulent under rotation and to develop the same characteristics as the high Reynolds number flow.     

Effect of measurement volume size on turbulent flow measurement using ultrasonic Doppler method

This paper presents the results of an investigation on the effects of measurement volume size on the mean velocity profile and the Reynolds stress for fully developed turbulent pipe flows. The study employs the ultrasonic velocity profile method, which is based on the ultrasonic Doppler method. The ultrasonic Doppler method offers many advantages over conventional methods for flow rate measurement in the nuclear power plant piping system. This method is capable of measuring the instantaneous velocity profile along the measuring line and is applicable for opaque liquids and opaque pipe wall materials. Furthermore, the method has the characteristic of being non-intrusive. Although it is applicable to various flow conditions, it requires a relatively large measurement volume. The measurement volume of the present method has a disk-shape determined by the effective diameter of the piezoelectric element and the number of the wave cycles of the ultrasonic pulse. Considering this disk-shaped measurement volume and expressing the time-averaged velocity in a truncated Taylor series expansion around the value at the center of the measuring control volume, the value of the velocity can be obtained. The results are then compared with the data obtained from DNS and LDA measurements. The result shows that the effect of the measurement volume size appears in the buffer region and viscous sublayer.     

Distribution of the velocity profiles of the liquid phase in a gas-liquid flow with small gas contents

Artilce [1] gives the results of measurement of the friction at the wall of a channel under bubble conditions, in a wide range of Reynolds numbers. It is shown that the concept of laminar flow conditions has no meaning when it is applied to the flow of a two-phase mixture, since, even with very small Reynolds numbers, the level of the pulsations of the friction is high, and the spectrum of the pulsations of the friction is continuous. In this case, the mean friction is much greater than the calculated; here the value of the resistance coefficient is not a single-valued function of the Reynolds number. The present article gives the results of measurement of the velocity profiles of the liquid phase, carried out using an electro diffusion method. It is shown that, with Reynolds numbers corresponding to turbulent flow conditions, the profile of the velocity in a two-phase mixture is close to turbulent and does not depend on the gas content.