A high-resolution laser Doppler anemometer: design, qualification, and uncertainty

A new high-resolution laser Doppler anemometer (LDA) has been developed with a working distance of 350 mm, allowing operation in lab-scale wind tunnels. The measurement volume size is 35 μm in diameter by 60 μm in length, allowing resolution of the smallest turbulence scales even at fairly high Reynolds numbers. The controversial question of velocity and validation bias in LDA data is resolved with an experimental method for measuring and removing those effects. Uncertainty estimates are also derived for all the mean and Reynolds stress measurements. Received: 27 June 1999/Accepted: 30 August 2000     

Near-wall structure of three-dimensional turbulent boundary layers

 Modifications to near-wall turbulent boundary layer structure with increased three-dimensionality have been investigated through the use of hydrogen bubble wire flow visualization. Results indicate that three-dimensionality does not influence the strength or sign of near-wall streamwise vortices. Increased three-dimensionality does stabilize the near-wall structure resulting in less ejection type activity. The spanwise spacing between low-speed streaks also decreased slightly with increased cross-flow. Received: 15 October 1996/Accepted: 2 April 1997     

Multi-mode fibre laser Doppler anemometer (LDA) with high spatial resolution for the investigation of boundary layers

A novel LDA system using laser diode arrays and multi-mode fibers in the transmitting optics is presented. The use of high numerical aperture multi-mode step-index fibres results in measurement volumes with, for example, 80 µm length and minimal speckle effects. Because of the high spatial resolution and low relative fringe spacing variation of d/d5×10^–4 the multi-mode fibre LDA is predestined for investigating turbulent flows. Boundary layer measurements carried out show excellent agreement with theoretical velocity profiles.     

Wall shear stress prediction in three-dimensional turbulent boundary layers

A method is developed to infer the wall shear stress for three-dimensional turbulent boundary layers based on the assumption that the resultant surface shear stress and the effective velocity based on Prahlad's model correlates the velocity profile into its two-dimensional form. Existence of the near wall region similarity has been demonstrated for three-dimensional turbulent boundary layers.     

A model for adiabatic supersonic turbulent boundary layers

An asymptotic analysis of the equations describing supersonic turbulent flow over an adiabatic wall is carried out for high Reynolds numbers, Re, and mainstream Mach numbers, M _e=O(1). A general expression for the adiabatic-wall temperature is derived. The asymptotic theory constrains the types of turbulence models that are suitable to represent the effects of viscous dissipation. A simple algebraic turbulence model is proposed and comparisons with measured total enthalpy profile data show good agreement, capturing the overshoot observed in total enthalpy near the boundarylayer edge.This work was supported by NASA Langley Research Center under Grant NAG-1-832 and the Air Force Office of Scientific Research under Grants AFOSR-91-0069 and F49620-93-0130; Dr. Ruban was supported by a grant from United Technologies Corporation.     

Shock-induced turbulent boundary layers

Experimental data for an incompressible turbulent moving surface boundary layer are reviewed and a theoretical extension of their predictions is suggested for the case of finite free stream velocities. It is argued that such a boundary layer provides an incompressible analogue for shock-induced turbulent boundary layers. Coles's transformation is used to predict the behaviour of the shock-induced case from the incompressible analogue. These predictions are used to attempt to correlate the available experimental shock-induced turbulent boundary layer data. It is felt that the correlations are reasonably successful for some of the data. It is suggested that the remaining data have been affected by the premature arrival of the contact region and reflected rarefaction wave.     

Auto-correlation measurements and integral time scales in three-dimensional turbulent boundary layers

Auto-correlation, time and length scales of the three components of turbulence and power spectra in a three-dimensional turbulent boundary layer developing on a yawed flat plate have been obtained. The measurements indicate that close to the wall, in the region of turbulence production, there is a marked disparity among the time scales but as the outer edge of the boundary layer is approached, the scales become comparable to one another. Also, the behaviour of the length scales and the power spectra across the boundary layer is presented.Nomenclature Boundary layer thickness where Q/Q _e=0.995 - E _u(f) one dimensional frequency spectra - f frequency in Hz - k ₁ wave number defined as k ₁=2f/Q - L length scale defined as: time scale times local mean velocity - Q local mean velocity - Q _e free stream velocity - R _u, R _v, R _w Auto-correlation coefficients of u, v and w respectively as defined in equation (1) - T _u, T _v, T _w the time scales of u, v and w fluctuations as defined in equation (2) - delay time - u fluctuating velocity component in x-direction - v fluctuation velocity component in y-direction - w fluctuation velocity component in z-direction - x coordinate axis in the streamwise direction - y coordinate axis normal to the surface - z coordinate axis normal to the x-direction and parallel to the wall     

Some Reynolds number effects on two- and three-dimensional turbulent boundary layers

Experimental data for a two-dimensional (2-D) turbulent boundary layer (TBL) flow and a three-dimensional (3-D) pressure-driven TBL flow outside of a wing/body junction were obtained for an approach Reynolds number based on momentum thickness of Re _θ =23,200. The wing shape had a 3:2 elliptical nose, NACA 0020 profiled tail, and was mounted on a flat wall. Some Reynolds number effects are examined using fine spatial resolution (Δy ⁺=1.8) three-velocity-component laser-Doppler velocimeter measurements of mean velocities and Reynolds stresses at nine stations for Re _θ =23,200 and previously reported data for a much thinner boundary layer at Re _θ =5,940 for the same wing shape. In the 3-D boundary layers, while the stress profiles vary considerably along the flow due to deceleration, acceleration, and skewing, profiles of the parameter correlate well and over available Reynolds numbers. The measured static pressure variations on the flat wall are similar for the two Reynolds numbers, so the vorticity flux and the measured mean velocities scaled on wall variables agree closely near the wall. The stresses vary similarly for both cases, but with higher values in the outer region of the higher Re _θ case. The outer layer turbulence in the thicker high Reynolds number case behaves similarly to a rapid distortion of the flow, since stream-wise vortical effects from the wall have not diffused completely through the boundary layer at all measurement stations. Received: 9 June 2000/Accepted: 26 January 2001     

Investigation of a compressible turbulent boundary layer and a region of separation at M=5 by a laser Doppler anemometer

Results are cited of an experimental investigation of the structure of a compressible turbulent boundary layer on a thermally insulated cylinder placed longitudinally in the flow. The experiments were conducted at M=5 and Re_x10⁷. In order to establish a longitudinal positive pressure gradient and a region of separation at the end of the cylinder, a tailpiece in the shape of an axisymmetric isentropic compression surface, or conical flaps with various half angles, were mounted. Profiles of the longitudinal velocity component were measured using p_o' and t_o probes, and also using a laser Doppler anemometer (LDA) with a Fabry-Perot interferometer. In the absence of a longitudinal pressure gradient the velocity profiles measured by the different methods were in satisfactory agreement among themselves and with the results of calculations. In the presence of a longitudinal positive pressure gradient, the velocity profiles become less filled and the static pressure, calculated according to the results of measurements of the velocity with the aid of the LDA and the pressure p_o', varied across the thickness of the boundary layer. In the separated region, the recirculating velocity of the flow was measured with the aid of the LDA.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 175–178, March–April, 1976.     

A numerical technique for three-dimensional compressible boundary layers

The non-linear two-point boundary value problem for three-dimensional compressible boundary layers is solved through the application of a boundary value technique for a range of parameters characterizing the nature of stagnation point flows. The analytical boundary conditions, at infinity, are applied at the edge of the computational mesh with iterations on the size of the domain. The solutions obtained show excellent agreement with the established similarity solutions for three-dimensional flows. The present method has the potential advantage of yielding the wall values of f″_w, g″_w and θ′_w as a part of the solution, contrary to the previously used ‘shooting’ methods. The algorithm is computationally simple and numerically stable and extremely suitable for engineering design applications.     

Some equilibrium turbulent boundary layers

Using the Coles additive law of the wall and law of the wake for the mean velocity profile of a two-dimensional turbulent boundary layer, a differential equation for the friction and wake parameters is derived from the momentum integral equation with a view to finding out the conditions under which the boundary layer can exhibit equilibrium. It is predicted that equilibrium is possible for boundary layers in favorable pressure gradient over smooth as well as k-type rough walls. When the roughness height is allowed to increase linearly with the streamwise distance, equilibrium exists also in zero pressure gradient. For a d-type rough wall, equilibrium is possible for a certain range of pressure gradients, from favorable to adverse. Most of the predictions are verified by evaluating the friction and wake parameters from the available experimental data on mean velocity measurements.     

A technique for evaluation of three-dimensional behavior in turbulent boundary layers using computer augmented hydrogen bubble-wire flow visualization

A system is described which allows the recreation of the three-dimensional motion and deformation of a single hydrogen bubble time-line in time and space. By digitally interfacing dualview video sequences of a bubble time-line with a computer-aided display system, the Lagrangian motion of the bubble-line can be displayed in any viewing perspective desired. The u and v velocity history of the bubble-line can be rapidly established and displayed for any spanwise location on the recreated pattern. The application of the system to the study of turbulent boundary layer structure in the near-wall region is demonstrated.List of Symbols Reynolds number based on momentum thickness u /v - t⁺ nondimensional time - u shear velocity - u local streamwise velocity, x-direction - u ⁺ nondimensional streamwise velocity - v local normal velocity, -direction - x ⁺ nondimensional coordinate in streamwise direction - ⁺ nondimensional coordinate normal to wall - ₊ ^wire wire nondimensional location of hydrogen bubble-wire normal to wall - z ⁺ nondimensional spanwise coordinate - momentum thickness - v kinematic viscosity - _W wall shear stress     

Bursting frequency in turbulent boundary layers

Employing laser Doppler anemometry and VITA techniques, the bursting frequency in turbulent boundary layers has been measured over the Reynolds-number range 320 to 1470. The result indicates that the mean and non-dimensional bursting frequency scaled with the variables appropriate for the wall region was constant and independent of Reynoids number. When the same data are plotted using the outer variables of boundary layer to normalize the bursting frequency, the non-dimensional frequency increases as the Reynolds number increases. This is in agreement with the results of Blackwelder et al. (1983) who used hot wire anemometry and VITA technique. The project is supported by the National Natural Science Foundation of China     

Self-preservation of rough-wall turbulent boundary layers

It is proposed that all fully rough-wall boundary layers should satisfy self-preservation more closely than a smooth-wall boundary layer. Previous work has shown that the self-preserving forms of the momentum and turbulent kinetic energy equations for a zero pressure gradient turbulent boundary layer, at sufficiently high Reynolds number, require that the wall shear stress is constant with x, and the layer thickness increases linearly with x. Measurements in two rough wall boundary layers suggest these conditions are met without assuming a form for the mean velocity distribution, and are more likely to exist in a fully rough wall layer than a smooth wall layer.     

Interactive boundary layers in turbulent flow

An asymptotic analysis of the structure of the flow at high Reynolds number around a streamlined body is presented. The boundary layer is turbulent. This question is studied with the successive complementary expansion method, SCEM. The starting point is to look for a uniformly valid approximation (UVA) of the velocity field, including the boundary layer and the external flow. Thanks to the use of generalized expansions, SCEM leads to the theory of interactive boundary layer, IBL. For many years, IBL model has been used successfully to calculate aerodynamic flows. Here, the IBL model is fully justified with rational mathematical arguments. The construction of a UVA of the velocity profile in the boundary layer is also studied. To cite this article: J. Cousteix, J. Mauss, C. R. Mecanique 335 (2007).     

A new method to measure particle turbulent dispersion using laser doppler anemometer

A laser doppler anemometer (LDA) was used to measure local dispersion coefficients of particles in turbulent flow. The experimental set-up is described along with the data acquisition equipment and processing procedures. Results for 5 particles dispersing from a point source in pipe flow are shown. A second estimate for the diffusivity was obtained from mean square dispersion measurements.List of symbols A projected area of LDA measuring volume, normal to pipe axis - B ₀ – B ₂ coefficients used in concentration curve fits - C particle number density, concentration - d _f fringe spacing - f _B Bragg cell frequency shift - f _D frequency of Doppler signal - H LDA measuring volume dimension in pipe axial direction - h random variation in H - J particle flux - J ₀, J ₁ bessel function of zeroth and first order - r radial location - t time - U axial velocity - u fluctuating component of axial velocity - v_p average particle radial velocity - x axial coordinate - y position of particle in the direction normal to the mean flow relative to the centerline - mean square dispersion Greek Symbols _2,3 roots of Bessel functions - _p turbulent diffusivity of particles - laser wave length - laser beam intersection angle     

Vortex reynolds number in turbulent boundary layers

The effects of vortex Reynolds number on the statistics of turbulence in a turbulent boundary layer have been investigated. Vortex Reynolds number is defined as the ratio of circulation around the vortex structure to the fluid viscosity. The vortex structure of the outer region was modeled and a full numerical simulation was then conducted using a high-order spectral method. A unit domain of the outer region of a turbulent boundary layer was assumed to be composed of essentially three elements: a wall, a Blasius mean shear, and an elliptic vortex inclined at 45° to the flow direction. The laminar base-flow Reynolds number is roughly in the same range as that of a turbulent boundary layer based on eddy viscosity, and the vortex-core diameter based on the boundary-layer thickness is nearly the same as the maximum mixing length in a turbulent boundary layer. The computational box size, namely, 500, 150, and 250 wall units in the streamwise, surface-normal, and spanwise directions, respectively, is approximately the same as the measured quasi-periodic spacings of the near-wall turbulence-producing events in a turbulent boundary layer. The effects of vortex Reynolds number and the signs of the circulation on the moments of turbulence were examined. The signs mimic the ejection and sweep types of organized motions of a turbulent boundary layer. A vortex Reynolds number of 200 describes the turbulence moments in the outer layer reasonably well.     

Hydrodynamic structure of accelerated turbulent boundary layers

The aim of the paper is to determine the velocity profile and friction law in turbulent boundary layers that develop under conditions of a negative longitudinal pressure gradient (dP/dx < 0). In contrast to the numerous studies devoted to this problem and based on semi-empirical closure of the hydrodynamic equations, general expressions (containing, of course, some empirical coefficients) will be obtained on the basis of dimensional and similarity arguments alone. In this sense, the results of the paper are a natural continuation of the analysis of decelerated turbulent wall flows by Kader and Yaglom [1, 2]. It is shown that the general dependences found in this manner agree well with numerous experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 29–37, May–June, 1983.I thank A. M. Yaglom for his interest in the work and valuable advice during it.