Comparison of magnetic resonance concentration measurements in water to temperature measurements in compressible air flows

Magnetic resonance imaging (MRI) measurements in liquid flows provide highly detailed 3D mean velocity and concentration data in complex turbulent mixing flow applications. The scalar transport analogy is applied to infer the mean temperature distribution in high speed gas flows directly from the MRI concentration measurements in liquid. Compressibility effects on turbulent mixing are known to be weak for simple flows at high subsonic Mach number, and it was not known if this would hold in more complex flows characteristic of practical applications. Furthermore, the MRI measurements are often done at lower Reynolds number than the compressible application, although both are generally done in fully turbulent flows. The hypothesis is that the conclusions from MRI measurements performed in water are transferable to high subsonic Mach number applications. The present experiment is designed to compare stagnation temperature measurements in high speed airflow (M = 0.7) to concentration measurements in an identical water flow apparatus. The flow configuration was a low aspect ratio wall jet with a thick splitter plate producing a 3D complex downstream flow mixing the wall-jet fluid with the mainstream flow. The three-dimensional velocity field is documented using magnetic resonance velocimetry in the water experiment, and the mixing is quantified by measuring the mean concentration distribution of wall-jet fluid marked with dissolved copper sulfate. The airflow experiments are operated with a temperature difference between the main stream and the wall jet. Profiles of the stagnation temperature are measured with a shielded thermocouple probe. The results show excellent agreement between normalized temperature and concentration profiles after correction of the temperature measurements for the effects of energy separation. The agreement is within 1 % near the edges of the mixing layer, which suggests that the mixing characteristics of the large scale turbulence structures are the same in the two flows.     

Experimental study of stratified jet by simultaneous measurements of velocity and density fields

Stratified flows with small density difference commonly exist in geophysical and engineering applications, which often involve interaction of turbulence and buoyancy effect. A combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) system is developed to measure the velocity and density fields in a dense jet discharged horizontally into a tank filled with light fluid. The illumination of PIV particles and excitation of PLIF dye are achieved by a dual-head pulsed Nd:YAG laser and two CCD cameras with a set of optical filters. The procedure for matching refractive indexes of two fluids and calibration of the combined system are presented, as well as a quantitative analysis of the measurement uncertainties. The flow structures and mixing dynamics within the central vertical plane are studied by examining the averaged parameters, turbulent kinetic energy budget, and modeling of momentum flux and buoyancy flux. At downstream, profiles of velocity and density display strong asymmetry with respect to its center. This is attributed to the fact that stable stratification reduces mixing and unstable stratification enhances mixing. In stable stratification region, most of turbulence production is consumed by mean-flow convection, whereas in unstable stratification region, turbulence production is nearly balanced by viscous dissipation. Experimental data also indicate that at downstream locations, mixing length model performs better in mixing zone of stable stratification regions, whereas in other regions, eddy viscosity/diffusivity models with static model coefficients represent effectively momentum and buoyancy flux terms. The measured turbulent Prandtl number displays strong spatial variation in the stratified jet.     

A study of turbulent mixing in a turbine-agitated tank using a fluorescence technique

Two-dimensional images of (Plane) Laser Induced Fluorescence (PLIF) have been used to study the turbulent mixing process in a model stirred tank. A calibration procedure is presented and discussed in terms of its accuracy. Data from the literature are used for comparison. A pattern-recognition algorithm has been designed to identify and quantitatively describe large-scale structures in the flow. This methodology, called “structural analysis”, is based on a conditional analysis of the PLIF data and requires the definition of an appropriate structure-detector function which is calculated locally. The mathematical tools developed have been used to study the mixing in a Rushton turbine-agitated reactor. Particular attention is paid to two specific regions of the tank; namely the bulk and the impeller stream regions, at two measured power input (0.3 and 0.7 W kg⁻¹). The averaged concentration fields show a common two-dimensional steady circulation pattern. Concentration probability density functions reflect well the instability of the flow in the two regions investigated. The data reveal the non-isotropic distribution of these instabilities around a reference point when the feed port is situated in the bulk region only. In this case, the structural analysis quantitatively shows the presence of a folding of the concentration field. It was found that this phenomenon can last several seconds. Received: 16 June 1998/Accepted: 14 April 1999     

Planar laser induced fluorescence technique for measurements of concentration fields in continuous stirred tank reactors

 A new non-intrusive method based on laser sheet visualization and image processing has been developed to measure the instantaneous concentration fields of a non-reacting fluorescent dye in a continuous stirred tank reactor. The method consists of measuring the fluorescence intensity of a tracer excited by a thin planar laser sheet and in transforming it into an instantaneous concentration field of tracer by a calibration procedure. This allows the characterization of mixing in a plane defined as the cross section of the flow by the laser sheet. Flow visualization images have been recorded on video tape and subsequently digitized. The relationship between the intensity of the fluorescent light and the grey level of the images has been established. The first result is the instantaneous field of dye concentration. A contacting parameter between the fluids coming from the two inlet sources, and emphasizing the average state of the mixing, has been defined and its field has been determined. The field of temporal variance, which characterizes the segregation of the investigated zone, has also been computed. Received: 15 December 1995/Accepted: 28 April 1996     

A microtube viscometer with a thermostat

The viscometer presented in this paper is suitable for measuring the viscosity of liquids in micro-litre quantities. It consists of a micro-flow experimental system with a thermostat. Using the measurements of the flow rates and pressure drops of a liquid passing through a microtube, the liquids viscosity can be calculated from on Hagen-Poiseuille theory. After calibration, the viscometer was used to measure viscosities of deionized water and ethyl alcohol at temperatures ranging from 0 to 40 °C. For both test liquids, the relative deviation of the measured values from those quoted in the literature (obtained using other viscometers) was less than 2.6%. The relative uncertainty of the experimental system was reduced to ±1.8% using the relative measuring method. Due to the micro-scale of the test section, only a micro-litre quantity of liquid is needed for a test; this is a potential advantage for measurement of bio-liquid viscosities.     

Theory of turbulent mixing at the interface of fluids in a gravity field

The theory of turbulent mixing at the interface of two media in accelerated motion was constructed in [1], and an approximate solution was given for incompressible fluids. The time variation of kinetic energy was neglected in the equation of balance for the kinetic energy of the turbulent motion. In [2] the characteristic turbulent velocity is averaged over the mixing region. This allows the initial equations to be solved allowing for the time variation of kinetic energy. It turns out that the resulting density profile roughly coincides with the profile of [1] within a wide range of variation of the initial density differential. In the present paper the equations for the mixing of incompressible fluids are studied in their complete form. It is established that the solutions of [1, 2] are applicable within a limited region, valid for small density ratios. The resulting solution is analyzed qualitatively, and it is shown that the density gradient at the mixing front is discontinuous. The dependence of the solution on two empirical constants is investigated. An approximate choice of the values of these constants is made on the basis of the theoretical considerations of [2, 3], and by comparison with the solution of [1]. The mixing asymmetry is found numerically as a function of the initial density differential. Quantitative characteristics of the solution are illustrated in graphs.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 74–81, July–August, 1976.     

Mixing in a confined turbulent impinging jet using planar laser-induced fluorescence

 The non-intrusive Planar Laser-Induced Fluorescence (PLIF) technique was applied to the study of the mixing of a turbulent water jet impinging orthogonally onto a flat surface. A procedure for calibrating the system at each pixel of a CCD camera array was first developed and tested. Post-processing of the PLIF data gave quantitative results of good quality. The mixing at the entrance of the deflection zone was also investigated. Average concentration fields in the centre plane of the jet were calculated and compared with Large Eddy Simulations (LES) and also with data from the literature. Probability density functions, space coefficients of correlation and radial concentration fluctuation profiles were calculated to further quantify the spreading of the jet, both in the free and deflection zones. Inside the deflection region, a slight tendency towards intensified mixing at the outer edge of the jet was found. This was attributed to a deceleration of the fluid which resulted in accelerated diffusion. Received: 11 July 1997 / Accepted: 9 January 1998     

A single-camera coupled PTV–LIF technique

 A single-camera coupled particle tracking velocimetry–laser-induced fluorescence (PTV–LIF) technique and validation results from an experiment in a neutrally buoyant turbulent round jet are presented. The single-camera implementation allows the use of a 12-bit 60 frame-per-second 1024 × 1024 pixel digital CCD camera capable of streaming images in real time to hard disk resulting in very accurate PTV and LIF with excellent spatial and temporal resolution. The technique is capable of determining the turbulent scalar flux, as well as the Reynolds stress and mean and fluctuating velocity and concentration fields. Details of dye choice, corrections for attenuation due to dye, particles and water, photobleaching, vignetting, CCD calibration, and illumination power and geometry corrections are presented. Detailed results from the validation experiment confirm the accuracy and resolution of the technique, and in particular, the ability to measure . Bootstrap 95% uncertainty intervals are presented for the calculated statistics. Received: 28 July 2000/Accepted: 8 November 2000     

The concentration field in a turbulent channel flow with polymer injection at the wall

Instantaneous concentration profiles have been measured in turbulent water channel flows at 5 axial locations immediately downstream of a line, wall injection of a dyed 700 ppm polymer solution and for comparison, dyed water. Concentration was deduced from a line of fluoresced radiation that was stimulated by a laser beam directed through the dyed injectant and normal to the channel wall. Both statistical and time-resolved results show how the turbulent mixing is modified and damped when the injectant is a polymer solution. A version of this paper was presented at the 11th Symposium on Turbulence, University of Missouri-Rolla, Oct. 17–19, 1988     

Stereoscopic micro particle image velocimetry

A stereoscopic micro-PIV (stereo-μPIV) system for the simultaneous measurement of all three components of the velocity vector in a measurement plane (2D–3C) in a closed microchannel has been developed and first test measurements were performed on the 3D laminar flow in a T-shaped micromixer. Stereomicroscopy is used to capture PIV images of the flow in a microchannel from two different angles. Stereoscopic viewing is achieved by the use of a large diameter stereo objective lens with two off-axis beam paths. Additional floating lenses in the beam paths in the microscope body allow a magnification up to 23×. The stereo-PIV images are captured simultaneously by two CCD cameras. Due to the very small confinement, a standard calibration procedure for the stereoscopic imaging by means of a calibration target is not feasible, and therefore stereo-μPIV measurements in closed microchannels require a calibration based on the self-calibration of the tracer particle images. In order to include the effects of different refractive indices (of the fluid in the microchannel, the entrance window and the surrounding air) a three-media-model is included in the triangulation procedure of the self-calibration. Test measurement in both an aligned and a tilted channel serve as an accuracy assessment of the proposed method. This shows that the stereo-μPIV results have an RMS error of less than 10% of the expected value of the in-plane velocity component. First measurements in the mixing region of a T-shaped micromixer at Re = 120 show that 3D flow in a microchannel with dimensions of 800 × 200 μm² can be measured with a spatial resolution of 44 × 44 × 15 μm³. The stationary flow in the 200 μm deep channel was scanned in multiple planes at 22 μm separation, providing a full 3D measurement of the averaged velocity distribution in the mixing region of the T-mixer. A limitation is that this approach requires a stereo-objective that typically has a low NA (0.14–0.28) and large depth-of-focus as opposed to high NA lenses (up to 0.95 without immersion) for standard μPIV.     

Numerical simulation of a developed shear turbulence

Results of two-dimensional numerical studies of turbulence that arises at the interface of two flows of poorly compressible gases are described. The results were obtained using a MAKh software system. The interrelation between spatial and time problems on the development of a turbulent zone induced by shear instability is analyzed. A constant that characterizes the degree of turbulent shear mixing is calculated. The effect of the density difference of the mixing fluids on the growth rate of the turbulence zone is studied. For all density differences considered, the coefficient of heterogeneity of the resultant mixture is evaluated. Institute for Technical Physics, Snezhinsk 456770. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 77–83, January–February, 2000.     

Investigation of scalar measurement error in diffusion and mixing processes

In variable density, multi-fluid and reacting flows, the degree of molecular mixing is a critical component of turbulent transfer and mixing models. Also, in many microflows and low Reynolds number flows, scalar diffusion length- and time-scales play a significant role in the mixing dynamics. Characterization of such molecular mixing processes requires scalar measurement devices with a small probe volume size. Spatial averaging, which occurs due to finite probe volume size, can lead to errors in resolving the density or scalar gradients between pockets of unmixed fluids. Given a probe volume size and a priori knowledge of the functional profile of the diffusion layer being measured, we obtain an estimate for the measurement error due to spatial averaging and make the corrections accordingly. An analytical model for the measure of scalar mixing is developed as a predictor for the growth of scalar gradients in a variable scalar flow. The model is applied to a buoyancy-driven mixing layer with a Prandtl number of 7. Measurements within the mixing layer have shown that initial entrainment of unmixed fluid causes a decrease in the measured amount of molecular mixing at the centerplane. Following this period of initial entrainment, the fluids within the mixing layer exhibit an increase in the degree of molecular mixing.     

Laminar,transitional and turbulent annular flow of drag-reducing polymer solutions

Mean and rms axial velocity-profile data obtained using laser Doppler anemometry are presented together with pressure-drop data for the flow through a concentric annulus (radius ratio κ = 0.506) of a Newtonian (a glycerine–water mixture) and non-Newtonian fluids—a semi-rigid shear-thinning polymer (a xanthan gum) and a polymer known to exhibit a yield stress (carbopol). A wider range of Reynolds numbers for the transitional flow regime is observed for the more shear-thinning fluids. In marked contrast to the Newtonian fluid, the higher shear stress on the inner wall compared to the outer wall does not lead to earlier transition for the non-Newtonian fluids where more turbulent activity is observed in the outer wall region. The mean axial velocity profiles show a slight shift (～5%) of the location of the maximum velocity towards the outer pipe wall within the transitional regime only for the Newtonian fluid.     

Turbulent Scalar Mixing in a Skewed Jet in Crossflow: Experiments and Modeling

Turbulent mixing of an inclined, skewed jet injected into a crossflow is investigated using MRI-based experiments and a high-fidelity LES of the same configuration. The MRI technique provides three-dimensional fields of mean velocity and mean jet concentration. The 30° skew of the jet relative to the crossflow produces a single dominant vortex which introduces spanwise asymmetries to the velocity and concentration fields. The turbulent scalar transport of the skewed jet is investigated in further detail using the LES, which is validated against the experimental measurements. Mixing is found to be highly anisotropic throughout the jet region. Isotropic turbulent diffusivity and viscosity are used to calculate an optimal value of the turbulent Schmidt number, which varies widely over the jet region and lies mostly outside of the typically accepted range 0.7 ≤ S c _t ≤ 0.9. Finally, three common scalar flux models of increasing complexity are evaluated based on their ability to capture the anisotropy and predict the scalar concentration field of the present configuration. The higher order models are shown to better represent the turbulent scalar flux vector, leading to more accurate calculations of the concentration field. While more complex models are better able to capture the turbulent mixing, optimization of model constants is shown to significantly affect the results.     

Measurement of the turbulent kinetic energy budget of a planar wake flow in pressure gradients

Turbulent kinetic energy (TKE) budget measurements were conducted for a symmetric turbulent planar wake flow subjected to constant zero, favorable, and adverse pressure gradients. The purpose of this study is to clarify the flow physics issues underlying the demonstrated influence of pressure gradient on wake development, and provide experimental support for turbulence modeling. To ensure the reliability of these notoriously difficult measurements, the experimental procedure was carefully designed on the basis of an uncertainty analysis. Three different approaches were applied for the estimate of the dissipation term. An approach for the determination of the pressure diffusion term together with correction of the bias error associated with the dissipation estimate is proposed and validated with the DNS results of Moser et al (J Fluid Mech (1998) 367:255–289). This paper presents the results of the turbulent kinetic energy budget measurement and discusses their implications for the development of strained turbulent wakes.An erratum to this article can be found at     

Dilution and mixing in an unsteady jet

 The mixing characteristics of a round, turbulent, unsteady jet were studied experimentally. A gravity-driven flow was created by releasing dyed fluid from a vertical tube into a large water tank. The jet velocity increased from zero to a maximum and then decreased continuously such that each run lasted about  s. The jet dilution was examined by an optical absorption technique that measured the line integral of concentration across the jet diameter. These measurements revealed that the portion of the unsteady jet corresponding to the deceleration phase dilutes more than the steady jet. The molecular scale mixing, as deduced from an acid-base neutralization reaction, corroborated the finding that the jet mixes in a shorter distance than the steady jet. Received: 22 August 1996/Accepted: 4 February 1997     

An insitu borescopic quantitative imaging profiler for the measurement of high concentration sediment velocity

The design, calibration, and testing of a borescopic quantitative imaging profiler (BQuIP) system, suitable for the insitu measurement of two components of the instantaneous velocity in high sediment concentration flows, are presented. Unlike planar quantitative imaging techniques, BQuIP has a concentration-dependent field of view, requiring detailed calibration. BQuIP is demonstrated in unidirectional sheet flow in an open channel flume with a narrow-graded sand with median diameter 0.25 mm. Acoustic velocity measurements are made in the suspension region above the BQuIP measured region yielding a continuous measurement of velocity and turbulent stress from the immobile bed to just below the free surface. The temporal history at a point reveals the sheet flow sediment velocities to be highly intermittent, and the spectra reveal a broad range of temporal scales close to −5/3 in slope for the streamwise velocity component. At its core BQuIP is a quantitative imaging technique giving it significant flexibility in terms of both the spatial and temporal analysis parameters (e.g., interrogation subwindow size and Δt, the time between images in a pair to be analyzed), allowing it to have tremendous dynamic range in terms of the velocities that can be measured.     

PLIF and PIV measurements of the self-preserving structure of steady round buoyant turbulent plumes in crossflow

Measurements of the mean concentration of source fluid and mean velocity fields were obtained for the first time in the self-preserving region of steady round buoyant turbulent plumes in uniform crossflows using Planar-Laser-Induced-Fluorescence (PLIF) and Particle-Image-Velocimetry (PIV), respectively. The experiments involved salt water sources injected into water/ethanol crossflows within a water channel. Matching the index of refraction of the source and ambient fluids was required in order to avoid image distortion and laser intensity nonuniformities. Further experimental methods and procedures are explained in detail. The self-preserving structure properties of the flow were correlated successfully based on the scaling analysis of [Fischer, H.B., List, E.J., Koh, R.C., Imberger, J., Brooks, N.H., 1979. Mixing in Inland and Coastal Waters, Academic Press, New York, pp. 315–389]. The resulting self-preserving structure consisted of two counter-rotating vortices having their axes nearly aligned with the crossflow direction that move away from the source in the streamwise (vertical) direction due to the action of buoyancy. This alignment, was a strong function of the source/crossflow velocity ratio, u₀/v_∞. Finally, the counter-rotating vortex system was responsible for substantial increases in the rate of mixing of the source fluid with the ambient fluid compared to axisymmetric round buoyant turbulent plumes in still environments, e.g., transverse dimensions in the presence of the self-preserving counter-rotating vortex system were 2–3 times larger than the transverse dimensions of self-preserving axisymmetric plumes at similar streamwise distances from the source.     

Instantaneous concentration field measurement technique from flow visualization photographs

A method of measuring the instantaneous concentration field in a planar section of a dyed turbulent flow is described. Negatives of photographed laser-sheet induced fluorescence are digitized and then computer processed to give the concentration distribution of the dye. A simple calibration procedure to account for the film characteristics is presented. This calibration also compensates for non-uniformities in the illumination of the flow field, irregularities in the illumination of the photographic negative and differences between characteristics of the individual digitizing light sensors of the digitizer. The method is illustrated with a cross-section containing the jet axis of the instantaneous concentration field of the entrained fluid from a small source outside of a circular turbulent jet.