On the application of LDA to bubbly flow in the wobbling regime

 Considerations for applying LDA to bubbly flows with bubbles about 3 to 4 mm in diameter were investigated by means of detailed experiments in the model geometry of a train of bubbles. Both forward scatter and backscatter LDA were studied. The validity of phase discrimination via burst amplitude was tested and special attention was paid to the impact of bubble interface response to the laser beams. Forward and backscatter measurements can be compared well. In both configurations, predominantly the liquid phase is “seen” by LDA. A bubble itself only leads to a velocity realization in special conditions. In those cases the Doppler shift is determined by the motion of the bubble interface which consists of the motion of the center of gravity of the bubble as well as shape oscillations. In backscatter bubbles only give velocity realizations when their “cheeks” pass through the measuring volume virtually perpendicularly. It is shown that the bubble-caused velocity realization frequency is very low for bubbles of the size used. Phase discrimination on burst amplitude does not hold. In ambient cases such as bubble columns one can assume that only the liquid phase is being studied. Received: 4 May 1998/Accepted: 30 September 1998     

The effect of astigmatism due to beam refractions on the formation of the measurement volume in LDA measurements

The accuracy of LDA measurements depends on the optical alignment of the laser beams. Improperly designed optical systems lead to fringe distortion in the measurement volume and in earlier investigations this effect has always been taken as the main cause of optical inaccuracy in LDA measurements. In the present work a different cause of fringe distortion is considered: astigmatism due to beam refractions. A quantitative theory for the astigmatism of laser beams is derived for both single and multiple refractions. Parameter calculations with regard to the size of the astigmatism effect have been carried out. It is shown that astigmatism is a relevant parameter which influences the fringe uniformity and fringe distortion in an LDA measurement volume and affects the measurement accuracy of measurements in internal flow. The equations derived enable the change in cross sections of the refracted laser beams to be determined. The spatial deviations of the diverse focusing points of refracted laser beams relative to the position of the LDA measurement volume are found to depend strongly on the incident angle of the beams and therefore on the off-axis alignment angle of the LDA probe (off-axis from the normal to the flow-wall-interface).     

Approach to the investigation of the occurrence of turbulence in the flow of a viscous fluid in closed volumes

Moscow. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 64–72, January–February, 1995.     

Subharmonic transition to turbulence in channel flow

A direct numerical simulation of subharmonic transition to turbulence in channel flow has been performed. The stages of primary and secondary instability have been identified in the results leading to a staggered pattern of A-shaped vortices. The associated staggered symmetry has been found to persist up to rather late stages of the breakdown process. This symmetry rapidly disappears in the final stage of transition and a developed turbulent flow is attained. A pronounced difference in the development between the two channel halves is observed which is consistent with the predictions of secondary instability theory.     

Transition to turbulence in a plane plume above a horizontal heat source: measurement of flow properties and flow visualization

Flow properties and flow visualization are measured during the process of transition to turbulence in a natural convection plume above a horizontal line heat source. Streamwise variations of time-mean vertical velocity and temperature on the center plane of the plume suggest the beginning and the end of the transition. Smoke photographs show that a pair of vortices are formed at a certain distance from the source as a result of growth of an anti-symmetric disturbance and break down a short distance downstream. The experimentally obtained profiles of mean temperature show that no similarity holds among them all through the process observed, but that there seems to be a similarity in the final stage, when the scaling law for turbulent profiles is adopted. However, this similarity profile is quite different from those given previously by other investigators, whose turbulent plumes were established without passing through such a gradual process of transition as was observed in the present experiment. Our flow visualization, on the other hand, supports the validity of our profile. Hence, there remains the question of whether our similarity profile is self-preserved in a fully-developed turbulent state or whether it will conform to others further downstream.     

How to get spatial resolution inside probe volumes of commercial 3D LDA systems

In laser Doppler anemometry (LDA) it is often the aim to determine the velocity profile for a given fluid flow. The spatial resolution of such velocity profiles is limited in principal by the size of the probe volume. The method of using time of flight data from two probe volumes allows improvements of the spatial resolution by at least one order of magnitude and measurements of small-scale velocity profiles inside the measuring volume along the optical axis of commercial available 3D anemometers without moving the probe. No change of the optical set-up is necessary. An increased spatial resolution helps to acquire more precise data in areas where the flow velocity changes rapidly as shown in the vicinity of the stagnation point of a cuboid. In the overlapping region of three measuring volumes a spatially resolved 3D velocity vector profile is obtained in the direction of the optical axis in near plane flow conditions. In plane laminar flows the probe volume is extended by a few millimetres. The limitation of the method to a plane flow is that it would require a two-component LDA in a very special off-axis arrangement, but this arrangement is available in most commercial 3D systems.     

An experimental and theoretical study of particle deposition due to thermophoresis and turbulence in an annular flow

The paper describes an experimental and theoretical study of the deposition of small particles from a turbulent annular-flow with cross-stream temperature variation, focusing on the effects of thermophoresis. Various expressions for the thermophoretic force on a spherical particle are critically discussed. The well-known composite formula of Talbot et al. (1980) does not include the ‘second mechanism of thermophoresis’ and it is concluded that the more recent theoretical approach of Beresnev and Chernyak (1995) is probably more reliable. New experimental measurements of particle deposition from a turbulent flow with cross-stream temperature gradients are then presented. The measurement technique is similar to the method of Liu and Agarwal (1974) but in the test section the aerosol flows vertically downwards in an annular gap between two concentric pipes. By heating the outer pipe and cooling the inner it is possible to establish a substantial, near-constant temperature difference between the two walls and hence a thermophoretic force which varies only with radius. Numerical calculations provide a comparison of theory with experiment. The theory is based on the turbulent deposition models of Young and Leeming (1997) and Slater et al. (2003) modified to include thermophoresis and the annular geometry. The theory of Beresnev and Chernyak gives good agreement with the experimental measurements.     

Errors in particle sizing by LDA due to turbidity in the incident laser beams

Measurements have been made of the effect of flow turbidity on the visibility and pedestal amplitude of an anemometer signal when incident laser beams are interrupted by particulate flow. The purpose is to assess the likely accuracy of particle sizing and the reliability of discrimination between continuous and particulate phase velocities. Optical depths of field were varied between 2.5 × 10^–2 and 14 × 10^–2 mm the diameter of the interrupting particles ranged between 14 and 800 m in six discrete ranges and the corresponding void fractions lay between 0.003% and 0.378%. The incident beam diameter was approximately 400 m.The measured size is subject to both systematic and random errors when inferred from measurements of pedestal amplitude: the random error increases as the ratio of the incident beam diameter to that of the particulate phase decreases. Systematic errors corresponding to a 10% underestimation of diameter occur at void fractions of 0.003%, 0.01% and 0.018% for particles below 40 m 75 m and 105 m respectively over a 5 cm depth of field. The r.m.s. error is smaller than 7% for particles below 40 m for all conditions studied but increases with increasing diameter and exceeds 10% at void fractions greater than 0.1% for particles above about 100 m. The random error in measured diameter derived from measurements of visibility is influenced mostly by the flow turbidity over the 5 cm of the incident beams closest to the measuring volume. For interrupting particles smaller than about 100 m the r.m.s. error is similar to that for measurements based on the pedestal amplitude.Discrimination of the velocity signal between the particulate and dispersed phase, based on the separation of pedestal amplitudes, is likely to be unreliable if the particle diameter is comparable to the diameter of the incident beams and if the probability of two particles simultaneously present in each beam is not negligible. A method for estimating the level of turbidity at which discrimination is no longer possible is described.List of symbols b beam diameter - d particle diameter - D amplitude of high passed Doppler signal (equation 7) - D ₁ depth of field of water tank - E particle extinction coefficient (= 2) - I _1,2 instantaneous light intensity at LDA measuring volume of each incident beam - n particle concentration (number per unit volume) - N number of particles in the incident beam - P maximum amplitude of pedestal component of Doppler signal - T Transmittance of beam {(attenuated/unattenuated) beam intensity} - V signal visibility (equation 8) - relative error in measured particle diameter {(truemeasured)/true)} - wavelength of laser beam (632.8 nm)     

Optical measurement uncertainties due to refractive index mismatch for flow in porous media

Application of optical techniques such as PIV, PTV, and LDA for velocity field estimation in porous media requires matching of refractive indices of the liquid phase to that of the solid matrix, including the channel walls. The methods most commonly employed to match the refractive indices have been to maximize the transmitted intensity through the bed or to rely on direct refractometer measurements of the indices of the two phases. Mismatch of refractive indices leads to error in estimation of particle position, ε _PD, due to refraction at solid–liquid interfaces. Analytical ray tracing applied to a model of solid beads placed randomly along the optical path is used to estimate ε _PD. The model, after validating against experimental results, is used to generate expression for ε _PD as a function of refractive index mismatch for a range of bead diameters, bed widths, bed porosity, and optical magnification. The estimate of ε _PD, which is found to be unbiased, is connected to errors in PIV measurement using the central limit theorem. Mismatch in refractive indices can also lead to reduction in particle density, N _s, detected light flux, J, and degrade the particle image. The model, verified through experiments, is used to predict the reduction in N _s and J, where it is found that particle defocusing caused by spherical beads in refractive index mismatched porous bed is the primary contributor to reductions of N _s and J. In addition, the magnitude of ε _PD is determined for the use of fluorescent dye emission for particle detection due to wavelength-dependent index of refraction.     

Growth of boundary-layer streaks due to free-stream turbulence

The growth of laminar boundary-layer streaks caused by free-stream turbulence encountering a flat plate in zero-pressure-gradient conditions is investigated experimentally in a wind tunnel and numerically by solving the unsteady boundary-region equations. A comparative discussion amongst the most relevant theoretical frameworks, such as the Goldstein theory, the Taylor–Stewartson theory, the optimal-growth theory and the Orr-Sommerfeld theory, is first presented and parallels and complimentary aspects of the theories are pointed out to justify the use of the Goldstein theory in our study. The statistical properties of the positive and negative fluctuations of the laminar streaks are discussed, showing how the total time average of the boundary-layer fluctuations masks the true character of the disturbance flow and revealing that the maximum values and the root-mean-square of positive and negative fluctuations grow downstream at the same rate. The downstream growth rate of the low-frequency disturbances and the decay rate of the high-frequency disturbances are also computed for the first time. The numerical solutions of the unsteady boundary-region equations are compared successfully with the streak profiles measured in the wind tunnel and with direct numerical simulation results available in the literature.     

Mechanism of flow instability and transition to turbulence

In this paper, a new mechanism of flow instability and turbulence transition is proposed for wall bounded shear flows. It is stated that the total energy gradient in the transverse direction and that in the streamwise direction of the main flow dominate the disturbance amplification or decay. Thus, they determine the critical condition of instability initiation and flow transition under given initial disturbance. A new dimensionless parameter K for characterizing flow instability is proposed which is expressed as the ratio of the energy gradients in the two directions for the flow without energy input or output. It is suggested that flow instability should first occur at the position of K_max which may be the most dangerous position. This speculation is confirmed by Nishioka et al.'s experimental data. Comparison with experimental data for plane Poiseuille flow and pipe Poiseuille flow indicates that the proposed idea is really valid. It is found that the turbulence transition takes place at a critical value of K_max of about 385 for both plane Poiseuille flow and pipe Poiseuille flow, below which no turbulence will occur regardless the disturbance. More studies show that the theory is also valid for plane Couette flows which holds a critical value of K_max of about 370.     

On numerical errors and turbulence modeling in tip vortex flow prediction

The accuracy of tip vortex flow prediction in the near‐field region is investigated numerically by attempting to quantify the shortcomings of the turbulence models and the flow solver. In particular, some turbulence models can produce a ‘numerical diffusion’ that artificially smears the vortex core. Low‐order finite differencing techniques of the convective and pressure terms of the Navier–Stokes equations and inadequate grid density and distribution can also produce the same adverse effect. The flow over a wing and the near‐wake with the wind tunnel walls included was simulated using 2.5 million grid points. Two subset problems, one using a steady, three‐dimensional analytical vortex, and the other, a vortex obtained from experiment and propagated downstream, were also devised in order to make the study of vortex preservation more tractable. The method of artificial compressibility is used to solve the steady, three‐dimensional, incompressible Navier–Stokes equations. Two one‐equation turbulence models (Baldwin–Barth and Spalart–Allmaras turbulence models), have been used with the production term modified to account for the stabilizing effect of the nearly solid body rotation in the vortex core. Finally, a comparison between the computed results and experiment is presented. Published in 1999 by John Wiley & Sons, Ltd.     

Quasilinear system of equations for parameters of developed turbulence. Calculation of irrotational flow distortion behind a grid

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 3, pp. 90–96, May–June, 1992.     

Analysis of errors in the measurement of energy dissipation with two-point LDA

In the present study, an attempt has been made to identify and quantify, with a rigorous analytical approach, all possible sources of error involved in the estimation of the fluctuating velocity gradients when a two-point laser Doppler velocimetry (LDV) technique is employed. Measurements were carried out in a grid-generated turbulence flow where the local dissipation rate can be calculated from the decay of kinetic energy. An assessment of the cumulative error determined through the analysis has been made by comparing the values of the spatial gradients directly measured with the gradient estimated from the decay of kinetic energy. The main sources of error were found to be related to the length of the two control volumes and to the fitting range, as well as the function used to interpolate the correlation coefficient when the Taylor length scale are estimated.

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Three-dimensional particle-tracking velocimetry measurement of turbulence statistics and energy budget in a backward-facing step flow

Using a three-dimensional (3-D) particle-tracking velocimeter, detailed turbulent flow measurements were made in a plane channel with a one-sided 50% abrupt expansion, which acted as a backward-facing step. The turbulent channel flow reached a fully developed state well upstream of the step. The Reynolds number based on the upstream centerline velocity and the step height H was 5540. With the mean reattachment point located at 6.51H downstream of the step, the measurement region ranged from −2H upstream to 12H downstream of the step. Various turbulent statistics and the energy budget were calculated from numerous instantaneous vector distributions. As in previous experimental investigations, the Reynolds normal and shear stresses had maximum values upstream of the reattachment. The stress anisotropy tensor revealed a peculiar phenomenon near the reattachment wall, wherein the spanwise normal stress was the largest among the three normal stresses. The triple velocity correlations indicated large values in the separating shear layer, and hence the turbulent diffusion was a major term in the energy budget. Comparison was made between the present results and those of the direct numerical simulation (DNS) of Le et al. (1993), and it was found that the mean and fluctuating velocities, the Reynolds shear stress, and the turbulent energy budget were in excellent agreement, although there was a considerable difference in the inflow conditions.