Speckle tomography of turbulent flows with density fluctuations

The speckle tomography technique is used for reconstructing both large-scale structures in turbulent flows and the microstructure of turbulence. The technique is based on multi-projectional line-of-sight speckle photography measurements with a subsequent computer-assisted tomographic reconstruction of the interior structure of the flowfield. The large-scale structure is reconstructed using the Radon integral equation, and the microstructure is analysed using a statistical approach and a novel Erbeck-Merzkirch integral transform. Digital speckle photography and speckle tomography methods are described. Numerical simulation of the optical technique is performed using digital ray tracing through a turbulent flowfield. The methods are illustrated by the 3D "averaged" temperature fields in turbulent convective flows obtained earlier and by the recent reconstruction of 3D correlation functions of density variations in turbulent flows. Local values of turbulence (Kolmogorov) microscale are evaluated using these correlation functions and the Erbeck-Merzkirch integral transform The precision of the reconstruction and the spatial resolution achieved are analysed.     

A low cost laser-speckle photographic technique for velocity measurement in slow flows

A low cost, low power laser-speckle photographic technique has been developed and is duscussed for the measurement of point velocities in slow laminar flows. The technique is particularly suitable for axisymmetric flows where the two velocity components can be easily measured. The accuracy of the technique is established by measurement of the velocity distribution for Poiseuille flow and from data obtained for acceleration of an inelastic Newtonian fluid through a four-to-one circular contraction. Preliminary results are also presented in the contracting flow field for a non shear-thinning highly elastic fluid. These data are particularly significant for verification of finite element numerical solutions currently being developed for viscoelastic fluids in circular entry flows.     

An extended algebraic reconstruction technique (ART) for density-gradient projections: laser speckle photographic tomography

An extended algebraic reconstruction technique (ART) is presented for tomographic image reconstruction from the density-gradient projections, such as laser speckle photography. The essence of the extended ART is that the density-gradient projection data of speckle photography (Eq. (1)) are first numerically integrated to the algebraic representation of interferometric fringe number data (Eq. (12)), which ART can readily reconstruct into the cross-sectional field. The extended ART is numerically examined by using two computer synthesized phantom fields, and experimentally by using asymmetric single and double helium jets in air. The experimentally reconstructed images were also compared with the direct measurements of helium concentration using an oxygen analyzing probe. The extended ART method shows an improved accuracy and is proposed to use to tomographically reconstruct the density-gradient projections over the previous Fourier convolution (FC) method (Liu et al. 1989). Received: 26 June 1998/Accepted: 18 March 1999     

A variant of the low-Reynolds-number two-equation turbulence model applied to variable property mixed convection flows

Previous work has demonstrated that the low-Reynolds-number model of Launder and Sharma (1974) offers significant advantages over other two-equation turbulence models in the computation of highly non-universal buoyancy-influenced (or “mixed convection”) pipe flows. It is known, however, that the Launder and Sharma model does not possess high quantitative accuracy in regard to simpler forced convection flows. A variant of the low-Reynolds-number scheme is developed here by reference to data for constant property forced convection flows. The re-optimized model and the Launder and Sharma formulation are then examined against experimental measurements for mixed convection flows, including cases in which variable property effects are significant.     

Optical density and velocity measurements in cryogenic gas flows

This paper presents the application of optical measurement techniques in dense-gas flows in a heavy-gas channel to determine planar two-component (2C) velocity profiles and two-dimensional (2D) temperature profiles. The experimental approach is rather new in this area, and represents progress compared with the traditional techniques based on thermocouple measurements. The dense-gas flows are generated by the evaporation of liquid nitrogen. The optical measurement of both the velocity and density profiles is accomplished by the implementation of particle image velocimetry (PIV) and background-oriented schlieren (BOS) systems. Supplemental thermocouple measurements are used as independent calibrations to derive temperatures from the density data measured with the BOS system. The results obtained with both systems are used to quantify the dilution behavior of the propagating cloud through a global entrainment parameter . Its value agrees well with the results obtained by earlier studies.     

1‐D numerical modelling of shallow flows with variable horizontal density

A1‐D numerical model is presented for vertically homogeneous shallow flows with variable horizontal density. The governing equations represent depth‐averaged mass and momentum conservation of a liquid–species mixture, and mass conservation of the species in the horizontal direction. Here, the term ‘species’ refers to material transported with the liquid flow. For example, when the species is taken to be suspended sediment, the model provides an idealized simulation of hyper‐concentrated sediment‐laden flows. The volumetric species concentration acts as an active scalar, allowing the species dynamics to modify the flow structure. A Godunov‐type finite volume scheme is implemented to solve the conservation laws written in a deviatoric, hyperbolic form. The model is verified for variable‐density flows, where analytical steady‐state solutions are derived. The agreement between the numerical predictions and benchmark test solutions illustrates the ability of the model to capture rapidly varying flow features over uniform and non‐uniform bed topography. A parameter study examines the effects of varying the initial density and depth in different regions. Copyright © 2009 John Wiley & Sons, Ltd.     

High data density temperature measurement for quasi steady-state flows

A new optical instrument, the liquid crystal point diffraction interferometer (LCPDI), is used to measure the temperature distribution across a heated chamber filled with silicone oil. Data taken using the LCPDI are compared to equivalent measurements made with a traversing thermocouple and the two data sets show excellent agreement. This instrument maintains the compact, robust design of Linnik's point diffraction interferometer and adds to it phase stepping capability for quantitative interferogram analysis. The result is a compact, simple to align, environmentally insensitive interferometer capable of accurately measuring optical wavefronts with very high data density and with automated data reduction.     

Diffraction efficiencies of speckle patterns recorded on photographic film

Optical Fourier transform processing of double-exposure speckle patterns creates a fringe pattern with a central bright spike. The relation between mean transmittance of the double-exposure and the strength and quality of the fringe pattern is examined. A simple model serves to quantify the diffraction, and agrees well with measured quantities. The ratio of diffracted power to incident power is the diffraction efficiency, and the ratio of the diffracted power to transmitted power is termed the transmitted diffraction efficiency. The different characteristics of the signal described by the two efficiencies are discussed. It is shown that the cleanest signal and the most powerful signal occur for different exposures.     

Cubic eddy‐viscosity turbulence models for strongly swirling confined flows with variable density

An investigation on the predictive performance of cubic eddy‐viscosity turbulence models for strongly swirling confined flows with variable density is presented. Comparisons of the prediction with the experiments show some improvements of cubic models over the linear k–ε model. The linear k–ε model does not contain any mechanism to represent the interaction of swirl and density variation and as a consequence it performs poorly. With appropriate modelling, two‐equation cubic turbulence models can capture the subcritical nature of the flow, represent the azimuthal velocity profiles of combined forced‐free vortex motion, and predict the combined effects of swirl and density variation fairly well. However, the calibration of model coefficients is still a topic of investigation. Further amendments are also needed for the equations of k and ε to take into account the effects of swirl and density gradients correctly. Copyright © 2004 John Wiley & Sons, Ltd.     

Adaptive mesh strategy applied to turbulent flows

An adaptive mesh procedure controlled by an error estimate for the Navier–Stokes equations is developed. The mesh can be refined but also coarsened by the mean of an agglomeration algorithm. The error estimation is based on an equation for the discretization error with a source term approximated by the use of a higher order discretized operator. The whole procedure is applied to a turbulent flow around a square-cross section cylinder. The efficiency of the method, evaluated in terms of CPU time and number of cells, shows interesting gains compared to single mesh computations. To cite this article: A. Hay, M. Visonneau, C. R. Mecanique 333 (2005).     

Interferometric measurement and tomography of the density field of supersonic jets

 The density field of cylindrical supersonic jets is investigated by Mach-Zehnder interferometry. The optical phase shift is extracted from the interferograms by digital image processing. Disturbing turbulence effects in the free shear layer are eliminated by sequential averaging of the phase shifts of several experimental images. The resulting steady state phase shift is used to calculate time-averaged interferograms and to reconstruct the density field by computerized tomography. The obtained results are compared with theoretical predictions and good quantitative agreement is found. Received: 3 March 1997/Accepted: 3 October 1997     

Stereoscopic particle image velocimetry applied to liquid flows

A twin-camera stereoscopic system has been developed to extend conventional high image-density Particle Image Velocimetry (PIV) to three-dimensional vectors on planar domains. The stereoscopic velocimeter performs with extremely high accuracy. Translation tests have yielded errors (rms) of 0.2% of full-scale for the in-plane displacement, and 0.8% of full-scale for the out-of-plane component, both of which agree with the errors predicted by an uncertainty analysis. In addition, modified techniques in hardware and software have enabled the stereoscopic system to perform successfully when acquiring images through a thick liquid layer, wherein previously the aberrations arising due to the liquid-air interface have restricted the use of such systems. With these techniques, the stereoscopic system, in combination with a simple method for image-shifting, is able to accurately measure threedimensional velocity fields in liquids. This is demonstrated by measurements of the helical, three-dimensional flow induced by a rotating disk in glycerine.     

Optical measurement of liquid film thickness and wave velocity in liquid film flows

Two optical techniques are described for measurement of a liquid film's surface. Both techniques make use of the total internal reflection which occurs at a liquid-vapor interface due to the refractive index difference between a liquid and a vapor. The first technique is used for film thickness determination. A video camera records the distance between a light source and the rays which are reflected back from the liquid-vapor interface. This distance can be shown to be linearly proportional to film thickness. The second technique measures surface wave velocities. Two photo sensors, spaced a fixed distance apart, are used to record the time varying intensity of light reflected from the liquid-vapor interface. The velocity is then deduced from the time lag between the two signals.The authors appreciate the support of the Air Conditioning and Refrigeration Center at the University of Illinois at Urbana-Champaign under project 45.     

The MLPG applied to porous materials with variable stiffness and permeability

Two-dimensional (2-d) and axisymmetric consolidation problems are treated with a meshless local Petrov–Galerkin approach. The porous continuum is modeled with Biot’s theory, where the solid displacements and the pore pressure are chosen as unknowns (u-p-formulation). These unknowns are approximated with independent spatial discretizations using the moving least-squares scheme. The method is validated by a comparison with an 1-d analytical solution. Studies with graded material data show that a variable permeability has a strong influence on the consolidation process. The example of a disturbed zone around a borehole shows as well the importance of graded material data.     

Quantitative measurement of solids distribution in gas–solid riser flows using electrical impedance tomography and gamma densitometry tomography

An electrical impedance tomography (EIT) system has been developed to non-invasively measure particle distributions in the riser of a pilot-scale circulating fluidized bed (CFB). Although EIT systems have often been applied to yield qualitative information about gas–solid flows, the present EIT system yields quantitative information that is validated by comparison to a gamma densitometry tomography (GDT) system. EIT and GDT were applied to the CFB riser (14-cm inner diameter, 5.77-m height) containing fluid catalytic cracking particles in air. The flows examined were annular with a dilute core and had average and near-wall solids volume fractions up to 0.25 and 0.66, respectively. For all cases, the average and near-wall solids volume fractions from EIT and GDT agreed to within 0.03 and 0.07, respectively. This good agreement suggests that, where feasible, EIT can be used in place of GDT, which is advantageous since EIT systems are often safer, less expensive, and faster than GDT systems.     

Simultaneous measurement of temperature,density and velocity in gas flows by modulated photoluminescence

A novel possibility to determine the temperature, density and velocity simultaneously in gas flows by measuring the average value, amplitude of modulation and phase shift of the photoluminescence excited by a temporally or spatially modulated light source is investigated. Time-dependent equations taking the flow, diffusion, excitation and decay into account are solved analytically. Different experimental arrangements are proposed. Measurements of velocity with two components, and temporal and spatial resolutions in the measurements are investigated. Numerical examples are given for N ₂with biacetyl as the seed gas. Practical considerations for the measurements and the relation between this method and some existing methods of lifetime measurement are discussed.     

Speckle photographic measurement of turbulence in an air stream with fluctuating temperature

The deflection of laser light passing through the mildy heated, turbulent air stream in a lowspeed wind tunnel is measured by means of speckle photography. This optical wholefield method provides a dense distribution of data values of the deflection angle in the field of view. When isotropic turbulence is assumed, it becomes possible to calculate the correlation function of the three-dimensional, turbulent temperature (or density) field from the correlation function of the plane distribution of measured deflection angles. Spectra and characteristic length scales are determined and compared with cold-wire data reported in the literature.A version of this paper was presented at the 10th Symposium on Turbulence, University of Missouri-Rolla, Sept. 22–24, 1986To Professor R. J. Emrich on the occasion of his 70th birthday     

Short wave stability of homogeneous shear flows with variable topography

For the stability problem of homogeneous shear flows in sea straits of arbitrary cross section, a sufficient condition for stability is derived under the condition of inviscid flow. It is shown that there is a critical wave number, and if the wave number of a normal mode is greater than this critical wave number, the mode is stable.