The influence of probe resolution on the measurement of a passive scalar and its derivatives

The influence of probe resolution on the statistical measurement of a passive scalar is reported. A spectral method is employed to simulate degradation of the spatial resolution of a probe on the measured variances of a fluctuating scalar and its streamwise derivative by low-pass filtering a time-series of data at different cutoff frequencies. Direct measurements are also employed by varying probe sensor separation. The far field of a circular jet and the near wake of a circular cylinder are both investigated using air as the working fluid. The use of this low-Schmidt number working fluid and relatively low turbulence Reynolds numbers allows for good resolution of small scales of scalar fluctuations. By comparison, the same level of resolution is much more difficult to achieve when utilising a high-Schmidt number working fluid. A small temperature differential above ambient is used to mark the passive scalar, which is measured using a cold-wire anemometer. Taylor's hypothesis is employed to determine length scales. The present results are in good agreement with previous direct measurements using both optical techniques and cold-wire probes. It is found that the spatial resolution required for accurate measurement of the scalar dissipation rate is well described by the characteristic smallest scale of the scalar fluctuation, i.e. 'the Batchelor scale'. However, an order of magnitude less resolution is required for the scalar variance. The effect of degrading resolution on the variance measurements is more significant in the near wake than the far-field jet, suggesting that these requirements may be flow-dependent.     

The effect of cross-flow velocity on mean-square derivatives measured using hot wires

 It is well known that significant errors occur in the velocity derivative moments measured in turbulent flows when the measuring transducer is too large or Taylor's hypothesis is used in high-turbulence-intensity flows. An additional error occurs when velocity derivative moments are measured with hot wires in high-turbulence-intensity flows, because the wires cannot resolve the individual velocity components in these flows. Estimates of the error this causes in the derivative moments measured with single-, cross-, and parallel-wire probes are developed herein. The errors are significant in the derivative moments measured with cross-wire probes, but are smaller in derivative moments measured with single- and parallel-wire probes. For example, the relative errors in measured in the far field of the round jet are 30–50% smaller than predicted in previous analyses. Received: 10 March 1995/Accepted: 07 December 1999     

The effect of closed-loop feedback control on scalar mixing in a plane shear layer

The effect of feedback on mixing in a plane shear layer was studied using temperature as an analog to species concentration. Mixing was quantified using temperature measurements made by an array of cold-wire sensors. Upstream of the cold-wire sensors, a schlieren imager measured the cross-stream position of the temperature interface between the two streams before the primary vortical structures had formed. Surface heaters mounted on the flow partition were used as control actuators. Feeding the gained output from the interface position sensor back to the surface heaters closed the loop and created resonance and out-of-resonance conditions in the flow, both of which increased mixing. The feedback gains were adaptively modified in real time to maximize mixing at a given streamwise station. Finally, it was found that deliberately introducing streamwise vorticity, and then choosing feedback gains that strengthen these streamwise vortices, can greatly enhance mixing.     

An Experimental Study of the Near-Field Mixing Characteristics of a Swirling Jet

The present experimental investigation is devoted to the mixing characteristics of a passive scalar in the near-field region of a moderately swirling jet issuing from a fully developed axially rotating pipe flow. Instantaneous streamwise and azimuthal velocity components as well as the temperature were simultaneously accessed by means of a combined X-wire and cold-wire probe. The results indicate a modification of the turbulence structures to that effect that the swirling jet spreads, mixes and evolves faster compared to its non-swirling counterpart. The high correlation between streamwise velocity and temperature fluctuations as well as the streamwise passive scalar flux are even more enhanced due to the addition of swirl, which in turn shortens the distance and hence time needed to mix the jet with the ambient air.     

Calibration of a temperature dissipation probe in decaying grid turbulence

A four cold-wire probe, which allows all three components of the temperature dissipation rate ? _θ to be measured, is “calibrated” in decaying grid turbulence, where <? _θ >, the mean value of ? _θ , can be determined accurately from the decay of the temperature variance <θ ²>. The probe yields values of the three components of <? _θ > which are in reasonable agreement with local isotropy, in the range x ₁/M?50. The pdfs and spectra of the three temperature derivatives also satisfy local isotropy reasonably well.     

A calibration technique for a parallel-wire depth probe with conductivity compensation

A new technique of calibrating a parallel-wire depth probe is presented. The technique allows the effects of electric conductivity of liquids to be compensated. The advantage of the probe lies in its simple AC circuitry employed which consists of only a variable resistor together with one AC input and an AC output. The compensation technique employs a two-staging compensation method that allows only one calibration curve to be used for measuring the depth of various liquids with different electric conductivity values.     

Eine Metallfilmsonde zur Messung von kleinen und schnellen Strömungstemperaturschwankungen

Measurements of the temperature fluctuations in flows are restricted to low fluctuation frequencies, if the temperature probes which have been available and which have a relative high thermal inertia are used. A newly constructed metalfilm probe, which works in principle as a resistance thermometer, overcomes this restriction to a large degree so that temperature fluctuations in the order of 0.01 °C can be measured up to fluctuation frequencies of about 5 kHz. The construction, the procedure of manufacture, and a method of calibration are presented for the newly developed probe, and its applicability for the measurement of temperature fluctuations in flows is demonstrated by some examples (measurements of the natural temperature fluctuations in the wake of a circular rod in air flow at a Reynolds number of about 5 · 10⁴). Some further applications of the probe are mentioned, in which its high sensitivity and its low thermal inertia is especially advantageous (measurement of flow velocities and measurement of fast temperature variations by infra-red detectors).     

Performance of a combined three-hole conductivity probe for void fraction and velocity measurement in air–water flows

The development of a three-hole pressure probe with back-flushing combined with a conductivity probe, used for measuring simultaneously the magnitude and direction of the velocity vector in complex air–water flows, is described in this paper. The air–water flows envisaged in the current work are typically those occurring around the rotors of impulse hydraulic turbines (like the Pelton and Cross-Flow turbines), where the flow direction is not known prior to the data acquisition. The calibration of both the conductivity and three-hole pressure components of the combined probe in a rig built for the purpose, where the probe was placed in a position similar to that adopted for the flow measurements, will be reported. After concluding the calibration procedure, the probe was utilized in the outside region of a Cross-Flow turbine rotor. The experimental results obtained in the present study illustrate the satisfactory performance of the combined probe, and are encouraging toward its use for characterizing the velocity field of other complex air–water flows.     

Turbulent Heat and Fluid Flow over a Two-Dimensional Hill

Experimental investigation has been made on the flow and thermal fields over a heated two-dimensional hill with a cosine-squared shape. The detailed turbulent characteristics are measured by a backscatter-type two-component LDV, a PIV system, a fine thermocouple and a cold-wire probe. In the reverse-flow region on the leeward side of the hill, the turbulence intensities and the Reynolds shear stress show much larger values than in a canonical wall-bounded shear flow. The mean temperature maintains a relatively high value below the location where the horizontal mean velocity rapidly decreases. At the outer edge of the reverse-flow region, there exists a second maximum intensity of temperature fluctuations. The instantaneous temperature waveforms near the heated surface show very large amplitude consisting of high-frequency fluctuations superimposed on the low-frequency motions. Simultaneous measurement of velocity and temperature is also done using a combination of a two-component LDV and a fine-wire thermocouple together with digital response compensation. In the downstream region of the hill, the horizontal and vertical turbulent heat fluxes become maximum at the hill-top height, and tend to diffuse in the vertical direction. On the other hand, in the reverse-flow region formed behind the hill, both of the heat fluxes decrease remarkably. In particular, it is worth noting that the horizontal turbulent heat flux near the surface becomes opposite in sign to that in the forward flow region. This is mainly due to the reversal of the mean flow direction.     

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.     

The nonlinear analysis of horizontal oil-water two-phase flow in a small diameter pipe

Horizontal oil-water two-phase flows are frequently encountered in many industrial processes but the understanding of the dynamic behavior underlying the different flow patterns is still a challenge. In this study, we first conduct experiments of horizontal oil-water flows in a small diameter pipe, and collect the fluctuation signals from conductance probes. The multi-scale power-law correlations of the oil-water flow structures are investigated using detrended fluctuation analysis (DFA) based on the magnitude and sign decomposition of the raw signals. The analysis reveals the scaling behavior of different flow structures; five conductive flow patterns are indentified based on the magnitude and sign scaling exponents at different time scales. In addition, the transfer entropy (TE) in a state space is used to study the information transferring characteristics of the oil-water mixture flowing past a conductance cross-correlation velocity probe. The results of TE indicate that the transferring information depends on the flow conditions and can be used to show changes in the flow patterns.     

Spatio-temporal chaos in colloid convection

The gravity convection in a plane horizontal colloid layer heated from below has been investigated experimentally and numerically. The temperatures and heat fluxes were measured using thermocouples. The flows were visualized using a thermosensitive liquid-crystal film. The Fourier and wavelet spectra of the thermal signals have been calculated. The numerical calculations were based on the model of a two-phase mixture of rigid particles with a carrier fluid. It was found that in colloids the branching-off of convective flows from mechanical equilibrium is hard and has an hysteresis. On the investigated interval up to four supercriticalities the spatio-temporal structures are irregular and wavy, which can be attributed to the competition between thermally and barometrically induced density drops.     

Thermal gravitational convection of a side-heated supercritical fluid with variable physical properties

Thermal gravitational convection in a supercritical medium is studied at parameter values higher than those corresponding the liquid-gas phase transition point. Steady convective flow and heat transfer are modeled in an extended region with a square cross-section, the temperatures on the lateral boundaries being constant and different. Both Boussinesq flows, in which spatial variations of the density and the thermodynamic parameters are small, and non-Boussinesq flows with considerably spatially-variable physical properties are considered. The effect of the temperature inhomogeneity parameter on the distinctive features of the flow and the heat transfer is determined.     

Gas/shear-thinning liquid flows through pipes: Modeling and experiments

In chemical and oil industry gas/shear-thinning liquid two-phase flows are frequently encountered. In this work, we investigate experimentally the flow characteristics of air/shear-thinning liquid systems in horizontal and slightly inclined smooth pipes. The experiments are performed in a 9-m-long glass pipe using air and three different carboxymethyl cellulose (CMC) solutions as test fluids. Flow pattern maps are built by visual observation using a high-speed camera. The observed flow patterns are stratified, plug, and slug flow. The effects of the pipe inclination and the rheology of the shear-thinning fluid in terms of flow pattern maps are presented. The predicted existence region of the stratified flow regime is compared with the experimental observation showing a good agreement. A mechanistic model valid for air/power-law slug flow is proposed and model predictions are compared to the experimental data showing a good agreement. Slug flow characteristics are investigated by the analysis of the signals of a capacitance probe: slug velocity, slug frequency, and slug lengths are measured. A new correlation for the slug frequency is proposed and the results are promising.     

Experimental determination of the speed of sound in cavitating flows

This paper presents measurements of the speed of sound in two-phase flows characterized by high void fraction. The main objective of the work is the characterization of wave propagation in cavitating flows. The experimental determination of the speed of sound is derived from measurements performed with three pressure transducers, while the void fraction is obtained from analysis of a signal obtained with an optical probe. Experiments are first conducted in air/water mixtures, for a void fraction varying in the range 0–11%, in order to discuss and validate the methods of measurement and analysis. These results are compared to existing theoretical models, and a nice agreement is obtained. Then, the methods are applied to various cavitating flows. The evolution of the speed of sound according to the void fraction α is determined for α varying in the range 0–55%. In this second configuration, the effect of the Mach number is included in the spectral analysis of the pressure transducers’ signals, in order to take into account the possible high flow compressibility. The experimental data are compared to existing theoretical models, and the results are then discussed.     

Measurement and decomposition of periodic flow structures downstream of a test turbine

The temperature dissipation rate inferred from the balance of $\overline{\theta^{2}}/2$ budget is used for the purpose of studying different methods employed to directly measure dissipation. The terms involved in the budget equation of temperature variance are measured with laser Doppler velocimetry and cold-wire thermometry used simultaneously. This study focuses on the centerline of a turbulent round jet, in the far field, at high Reynolds number (x/D = 30, Re _D  = 1.5 × 10⁵ and Re _λ  = 548). Particular attention is devoted to statistical convergence of second- and third-order moments of velocity and temperature fluctuations. Temperature dissipation obtained by Taylor’s hypothesis and radial temperature derivative spectra confirm local isotropy. A high level of low wave number content is reported for the longitudinal derivative spectra, probably due to transverse mode spectral aliasing and noise contamination for small wire separation. A parallel is drawn between finite difference formulations and the behavior of the autocorrelation coefficient for small wire separations. The temperature dissipation estimates found are close to the budget reference value, but spectral analysis cast doubts on the validity of the streamwise derivative obtained with a pair of probes.     

The calibration of (multi-) hot-wire probes. 1. Temperature calibration

We study the performance of the classical relation for the correction for ambient temperature drift of the signal of a hot-wire anemometer and the influence of practical assumptions. It is shown that most methods to estimate the operational temperature via the temperature/resistance coefficient lead to underestimation of the operational temperature and thus to overcorrection of signals for temperature drift. We found that, in the presence of a sensible heat flow, temperature fluctuations cannot be sufficiently removed from the hot-wire signal when one relies on temperature/resistance coefficients from literature. When only slow temperature drift is involved, most literature values give a satisfactory temperature correction, but this depends on the specific combination of a probe and a literature reference. Therefore it is generally advisable to calibrate the value. A method that uses a ratio of (measured) resistances as a function of temperature, which does not require estimation of the operational temperature of the wire, is shown to depend crucially on a parasitic resistance of a few tenths of an ohm. This parameter can be found by optimizing its value using data from a collection of velocity calibrations at different temperatures. This additional calibration alone suffices to estimate the operational temperature of the wire via optimization. A quick calibration procedure (15 min) is proposed and tested.     

Simultaneous velocity and temperature measurements in a premixed flame

Procedures which allow the correlation of velocity signals from a laser anemometer and temperature signals from a compensated, small-diameter thermocouple are described together with the error sources associated with the use of the technique in premixed flames. The digital compensation procedure includes the effect of velocity and temperature on the time constant of the thermocouple and the influence of its exposure to the solid particles required by the laser anemometer are quantified and shown to be able to cause large differences in the measured probability-density-distribution of the reaction progress variable. The technique has been used to measure the probability-density-distribution of temperatures, conditioned by the arrival of velocity signals and velocity conditioned by the temperature signal and sample results are presented to help quantify the accuracy of the measurements.     

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.     

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