Spatial resolution effects on the measurement of scalar variance and scalar gradient in turbulent nonpremixed jet flames

The effect of spatial averaging is important for scalar gradient measurements in turbulent nonpremixed flames, especially when the local dissipation length scale is small. Line imaging of Raman, Rayleigh and CO-LIF is used to investigate the effects of experimental resolution on the scalar variance and radial gradient in the near field of turbulent nonpremixed CH₄/H₂/N₂ jet flames at Reynolds numbers of 15,200 and 22,800 (DLR-A and B) and in piloted CH₄/air jet flames at Reynolds numbers of 13,400, 22,400 and 33,600 (Sandia flames C/D/E). The finite spatial resolution effects are studied by applying the Box filter with varying filter widths. The resulting resolution curves for both scalar variance and mean squared-gradient follow nearly the same trends as theoretical curves calculated from the model turbulence kinetic energy spectrum of Pope. The observed collapse of resolution curves of mean squared-gradient for nearly all studied cases implies the shape of the dissipation spectrum is approximately universal. Fluid transport properties are shown to have no effect on the dissipation resolution curve, which implies that the dissipation length scale inferred from the square gradient is equivalent to the length scale for the scalar dissipation rate, which includes the diffusion coefficient. With the Box filter, the required spatial resolution to resolve 98% of the mean dissipation rate is about one−two times of the dissipation cutoff length scale (analogous to the Batchelor scale in turbulent isothermal flows). The effects of resolution on the variances of mixture fraction, temperature, and the inverted Rayleigh signal are also compared. The ratio of the filtered variance to the true variance is shown to depend nearly linearly on the probe resolution. The inverted Rayleigh scattering signal can be used to study the resolution effect on temperature variance even when the Rayleigh scattering cross section is not constant. The experimental results also indicate that these laboratory scale turbulent jet flames have small effective Reynolds numbers, such that there is some direct interaction of the large (energy containing) and small (dissipative) scalar length scales, especially for the near field case at x/d = 7.5 of the piloted Sandia flames C/D/E.     

Spatial resolution and noise considerations in determining scalar dissipation rate from passive scalar image data

The effects of photonic shot noise and finite spatial resolution on the scalar dissipation rate were investigated for the analytical profile of a passive scalar layer subjected to a compressive strain, and the results were applied to interpret measured data from spray mixing data from an internal combustion engine. A Monte Carlo approach was employed. The measured scalar dissipation rate is underestimated, and the layer width measured at 20% of the peak height is overestimated by the finite resolution. The ratio of the local scalar spread value to the noise level, the spread-noise ratio, was found to describe the noise effects, which principally results in an overestimation of the scalar dissipation rate, especially at high resolution levels. The Nyquist resolution provides a good compromise between the sampling bias at low resolution and the noise bias at high resolution. Top hat filtering the raw data prior to calculation of the scalar dissipation rate was found to, effectively, reduce spatial resolution, whereas median filtering preserved the resolution. Both filters had a comparable effect on noise reduction. The evaluation of experimental data showed that a significant fraction of data reside at low spread-noise ratio and are biased by noise. The peak scalar dissipation rate is, however, not biased by noise and a method of estimating spatial resolution based on the peak scalar dissipation rate is described.     

Conditional correlation between a passive scalar and its dissipation in a turbulent boundary layer

 A study of the conditional correlation between a passive scalar and its dissipation offers an interesting strategy for understanding turbulence properties associated with both large and small scales. This correlation is investigated with particular emphasis on the dominant coherent motions in turbulent boundary layers; namely, sweeps and ejections, using a local cross-correlation analysis based on the wavelet transform. Contributions to the three temperature derivatives show different features, reflecting clear “local” departures from isotropy. This property of coherent motions is investigated through the conditional cross-spectra inferred from the wavelet analysis, which provides localized scale decomposition of the quantity under consideration, and is translated in the spectral domain. These decompositions indicate the particular coherent motions of the flow which most contribute to the conditional correlation between temperature and its dissipation. Received: 27 November 1997/Accepted: 20 July 1998     

On high spatial resolution scalar measurement with LIF Part 2: The noise characteristic

A spatial resolution of about 4 (m)³ for scalar measurement in turbulent mixing with Laser-Induced-Fluorescence is realized in this experiment. It is shown that for the high spatial resolution the signal is weak because of the measuring volume is very fine. The corresponding main problem is that the signal to noise ratio is small, especially for the high frequency signal corresponding to small structures. It is shown that the dominating noise is the shot noise in the signal from the photomultiplier tube. The measurement results indicate that an increase of the signal level through the increase of dye concentration and/or laser power is limited, mainly due to thermal blooming and photobleaching.     

On high spatial resolution scalar measurement with LIF Part 1: Photobleaching and thermal blooming

A spatial resolution of about 4 (m)³ of LIF is done in the present work. For such measurements, the photobleaching and possible thermal blooming become important because of the very high laser intensity at measuring volume. The corresponding problems for the scalar measurement, calibration, the influence of laser power and laser dye concentration on photobleaching, and the measurement of photobleaching are investigated. A simple photobleaching model is proposed. Received: 18 September 1998/Accepted: 20 October 1999     

Streamwise evolution of a high-Schmidt-number passive scalar in a turbulent plane wake

The concentration fluctuation c of diluted fluorescein dye, a high-Schmidt-number passive scalar (Sc=ν/D ≈ 2000, ν and D are the fluid momentum and dye diffusivities, respectively), is measured in the wake of a circular cylinder using a single-point laser-induced fluorescence (SPLIF) technique. The streamwise decay rate of the mean and rms values of c is slow in comparison to that of θ, the temperature fluctuation for which the molecular Prandtl number Pr=ν/κ is about 0.7 (κ is the thermal diffusivity). The comparison between mean and rms distributions of c and θ highlights the combined role the Reynolds and Schmidt numbers play in terms of dispersing the scalar. The streamwise evolution of the probability density functions (pdfs) of c and θ suggest that while p(θ) is approximately Gaussian in the intermediate wake (x/d ≈ 80), p(c) is strongly non-Gaussian, and depends on both x/d and Re. The skewness of c is larger than that of θ along the wake centreline. Arguably, the asymmetry of p(c) reflects the relatively strong organisation of the large-scale motion in the far-wake. Received: 27 July 2000/Accepted: 22 December 2000     

Multipoint correlations of concentration fluctuations in a turbulent passive scalar field

This study experimentally analyzes a turbulent passive scalar field using two-point and three-point correlation functions of the concentration fluctuations. The scalar field was created by the iso-kinetic release of a high Schmidt number dye into a fully developed turbulent boundary layer of an open channel flow. Concentration data at spatially separated measurement points were collected via the planar laser induced fluorescence (PLIF) technique. The current study complements previous research efforts by examining three-point correlations for several configurations in a turbulent shear flow. In the case of two streamwise-aligned points combined with one transversely separated point, contours of the three-point correlation function exhibit the symmetric properties reported in an earlier study of non-shear flow. In a second set of three-point configurations consisting of isosceles and collinear geometries, the influence of the orientation angle between the three-point configuration and the mean concentration gradient varies depending on the specified three-point geometry. The results also suggest that the scaling exponent in the inertial-convective regime is dependent on the injection length scale with weak dependence on the Reynolds number.     

DNS of a spatially developing turbulent boundary layer with passive scalar transport

A direct numerical simulation (DNS) of a spatially developing turbulent boundary layer over a flat plate under zero pressure gradient (ZPG) has been carried out. The evolution of several passive scalars with both isoscalar and isoflux wall boundary condition are computed during the simulation. The Navier–Stokes equations as well as the scalar transport equation are solved using a fully spectral method. The highest Reynolds number based on the free-stream velocity U_∞ and momentum thickness θ is Re_θ=830, and the molecular Prandtl numbers are 0.2, 0.71 and 2. To the authors’ knowledge, this Reynolds number is to date the highest with such a variety of scalars. A large number of turbulence statistics for both flow and scalar fields are obtained and compared when possible to existing experimental and numerical simulations at comparable Reynolds number. The main focus of the present paper is on the statistical behaviour of the scalars in the outer region of the boundary layer, distinctly different from the channel-flow simulations. Agreements as well as discrepancies are discussed while the influence of the molecular Prandtl number and wall boundary conditions is also highlighted. A Pr scaling for various quantities is proposed in outer scalings. In addition, spanwise two-point correlation and instantaneous fields are employed to investigate the near-wall streak spacing and the coherence between the velocity and the scalar fields. Probability density functions (PDF) and joint probability density functions (JPDF) are shown to identify the intermittency both near the wall and in the outer region of the boundary layer. The present simulation data will be available online for the research community.     

On the role of the smallest scales of a passive scalar field in a near-wall turbulent flow

Role of the smallest diffusive scales of a passive scalar field in the near-wall turbulent flow was examined with pseudo-spectral numerical simulations. Temperature fields were analyzed at friction Reynolds number Re _τ=171 and at Prandtl numbers, Pr=1 and Pr=5.4. Results of direct numerical simulations (DNS) were compared with the under-resolved simulations where the velocity field was still resolved with the DNS accuracy, while a coarser grid was used to describe the temperature fields. Since the smallest temperature scales remained unresolved in these simulations, an appropriate spectral turbulent thermal diffusivity was applied to avoid pile-up at the higher wave numbers. In spite of coarser numerical grids, the temperature fields are still highly correlated with the DNS results, including instantaneous temperature fields. Results point to practically negligible role of the diffusive temperature scales on the macroscopic behavior of the turbulent heat transfer.     

Direct numerical simulation of turbulent mixing of a passive scalar in pipe flow

Turbulent mixing of a passive scalar in fully developed turbulent pipe flow has been investigated by means of a Direct Numerical Simulation (DNS). The scalar is released from a point source located on the centreline of the pipe. The domain size of the concentration field has been chosen large enough to capture the different stages of turbulent mixing. Results are presented for mean concentration profiles, turbulent fluxes, concentration fluctuations, probability density functions and higher-order moments. To validate the numerical simulations the results are compared with experimental data on mixing in grid-turbulence that have been reported in the literature. The agreement between the experimental measurements and the computations is satisfactory. We have also considered the Probability Density Function (PDF). For small diffusion times and positions not on the plume centreline, our results lead to a PDF of an exponential form with a large peak at zero concentration. When the diffusion time increases, the PDF shifts from a exponential to a more Gaussian form.     

Numerical analysis and modeling of plume meandering in passive scalar dispersion downstream of a wall-mounted cube

A DNS database is employed to examine the onset of plume meandering downstream of a wall-mounted cube and to address the impact of large-scale unsteadiness in modeling dispersion using the RANS equations. The cube is immersed in a uniform stream where the thin boundary-layer developing over the flat plate is responsible for the onset of vortex-shedding in the wake of the bluff-body. Spectra of velocity and concentration fluctuations exhibit a prominent peak in the energy content at the same frequency, showing that the plume meandering is established by the action of the vortex-shedding. The vortex-shedding and plume meandering display a low-frequency modulation where coherent fluctuations are suppressed at times with a quasi-regular period. The onset of the low-frequency modulation is indicated by a secondary peak in the energy spectrum and confirmed by the autocorrelation of velocity and scalar fluctuations. Unsteady RANS simulations performed with the v² − f model are able to detect the onset of the plume meandering and show remarkable improvement of the predicted decay rate and rate of spread of the scalar plume when compared to steady RANS solutions. By computing explicitly the periodic component of velocity and scalar fluctuations, the unsteady v² − f model is able to provide a representation of scalar flux components consistent with DNS statistics, where the counter-gradient transport mechanism that takes place in the streamwise component is also captured by URANS results. Nonetheless, the agreement with DNS statistics for the mean concentration and the plume width is limited by the onset of the low-frequency modulation in the vortex-shedding and plume meandering, giving a challenging modeling issue in the simulation of dispersion using the RANS equations.     

Use of caged fluorescent dyes for the study of turbulent passive scalar mixing

The non-intrusive initialization of a flow field with distinct and spatially segregated scalar components represents a significant experimental difficulty. Here a new technique is described which makes possible the non-intrusive initialization of a spatially binary passive scalar field in a laminar or turbulent flow field. This technique uses photoactivatable (caged) fluorescent dyes dissolved in the flow medium. The scalar field within the flow field is tagged or initialized by uncaging the appropriate regions with an ultraviolet excimer laser. Mixing between the tagged and untagged regions is quantified using standard laser induced fluorescence techniques. The method is currently being used to study mixing in a turbulent pipe flow.     

Speckle optical measurement of a turbulent scalar field with high fluctuation amplitudes

A turbulent temperature field is produced in the gas flow downstream of a turbulence grid by passing the flow through a plane combustion front at the grid that serves as a flame holder. RMS values of the temperature fluctuations of up to 33 K are generated thereby. Properties of the turbulent scalar are measured with an optical speckle technique. The experimental results are compared with theoretical models described by Rotta (1972) and Driscoll and Kennedy (1985). From this comparison it is evident that, even at these high fluctuation amplitudes, the turbulent temperature field still behaves as a passive scalar.     

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.     

Bubble aspect ratio and velocity measurement using a four-point fiber-optical probe

We propose a new algorithm to estimate the bubbles aspect ratio and its velocity from the time series obtained by a four-point fiber-optical probe. The accuracy and the robustness of the algorithm is analyzed for bubbles with an equivalent diameter of 2–4 mm using both synthetic and experimental data. The experimental data is obtained by means of stereoscopic high-speed imaging. The three dimensional shape of the bubble is reconstructed from a set of stereoscopic contour lines.     

Time-resolved, 3D, laser-induced fluorescence measurements of fine-structure passive scalar mixing in a tubular reactor

A three-dimensional, time-resolved, laser-induced fluorescence (3D-LIF) technique was developed to measure the turbulent (liquid-liquid) mixing of a conserved passive scalar in the wake of an injector inserted perpendicularly into a tubular reactor with Re=4,000. In this technique, a horizontal laser sheet was traversed in its normal direction through the measurement section. Three-dimensional scalar fields were reconstructed from the 2D images captured at consecutive, closely spaced levels by means of a high-speed CCD camera. The ultimate goal of the measurements was to assess the downstream development of the 3D scalar fields (in terms of the full scalar gradient vector field and its associated scalar energy dissipation rate) in an industrial flow with significant advection velocity. As a result of this advection velocity, the measured 3D scalar field is artificially skewed during a scan period. A method to correct for this skewing was developed, tested and applied. Analysis of the results show consistent physical behaviour.List of symbols  A  Deformation tensor - D_t, D_f  Reactor and injector diameter - L_x, L_y, L_z  Dimensions of the 3D-LIF measurement volume - N_x, N_y, N_z  Number of data samples per measurement volume - Re_m  Reynolds number based on mean velocity - Sc  Schmidt number - f  Focal length - f_c,lens, f_c,array  Cut-off frequency for camera lens and sensor array - f, f  Marginal probability density function for and - f  Joint probability density function of and -  Temporal separation of the 2D data planes -  Temporal resolution of the measurement volume -  Spatial resolution of the measurement volume - ,  Deformation angle and deformation, where =tan -  Fluid energy dissipation rate - ,  Strain limited vorticity and scalar diffusion layers -  Scalar concentration - , _B Kolmogorov and Batchelor length scale - ,  Spherical angles of the scalar gradient vector, -  Kinematic viscosity - _e^–2 Half-thickness (1/e²) of the laser sheet - , _a Kolmogorov and Kolmogorov advection time scales -  Scalar energy dissipation rate -  Scalar diffusivity - 2D, 3D Two- and three-dimensional - DNS Direct numerical simulation - LIF Laser-induced fluorescence - SED Scalar energy dissipation rate - TR Tubular reactor

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The measurement of bubble flows in fluidized beds by electrical probe

Measurements of bubble velocities, dimensions and flow rates in a two-dimensional fluidized bed by a dual electrical capacitive probe are compared with measurements from cine photography; the cine photographs and electric measurements were taken at the same point in a fluidized bed and at the same time. It was found that both sets of measurements were in agreement only when the conditions of electrical measurement were arranged to exclude spurious signals, while still retaining sensitivity, and when the theory of measurement included the effects of bubble retardation and distortion, and allowed for the stochastic incidence between the bubble front and the probes.     

Spatial resolution of PIV for the measurement of turbulence

Recent technological advancements have made the use of particle image velocimetry (PIV) more widespread for studying turbulent flows over a wide range of scales. Although PIV does not threaten to make obsolete more mature techniques, such as hot-wire anemometry (HWA), it is justifiably becoming an increasingly important tool for turbulence research. This paper assesses the ability of PIV to resolve all relevant scales in a classical turbulent flow, namely grid turbulence, via a comparison with theoretical predictions as well as HWA measurements. Particular attention is given to the statistical convergence of mean turbulent quantities and the spatial resolution of PIV. An analytical method is developed to quantify and correct for the effect of the finite spatial resolution of PIV measurements. While the present uncorrected PIV results largely underestimate the mean turbulent kinetic energy and energy dissipation rate, the corrected measurements agree to a close approximation with the HWA data. The transport equation for the second-order structure function in grid turbulence is used to establish the range of scales affected by the limited resolution. The results show that PIV, due to the geometry of its sensing domain, must meet slightly more stringent requirements in terms of resolution, compared with HWA, in order to provide reliable measurements in turbulence.

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