Velocity-temperature Correlations Research Articles

Modeling high-order statistics in the turbulent Ekman layer

ABSTRACTResults from a direct numerical simulation (DNS) of the neutral and unstable turbulent Ekman layer at a Reynolds number of 1000 were used to evaluate turbulence closure models. For the neutrally stratified Ekman layer, the higher-order moments of velocity were examined and the accuracy of a kurtosis model was assessed. For the unstable Ekman layer, the analysis of higher-order moments was extended to temperature-velocity correlations. Model coefficients were optimised using DNS data and it was shown that the optimised models accurately captured the distributions of all fourth-order moments. These low-Reynolds number results can be extrapolated to higher Reynolds numbers to parameterise turbulence in other flow fields with rotational effects such as the atmospheric boundary layer.

Large eddy simulation studies on the influence of turbulent inlet conditions on the flow behavior in a mixing tee

Mixing of coolant streams at significant temperature differences in a mixing tee occurs in the cooling systems (e.g. Residual Heat Removal System) of a nuclear power plant resulting in cyclical thermal fluctuations that may lead to high cycle thermal fatigue (HCTF) in the structure. The present study aims to numerically investigate such a scenario using the large-eddy simulation (LES) method. The LES is based on an experiment conducted at the fluid–structure interaction (FSI) test facility, University of Stuttgart. Hot and cold water streams flow in the main and branch pipes with a temperature difference (ΔT) of 117K. The mass flow rate ratio (main/branch) is 4:1.Two LESs with different inlet conditions are performed to study and compare the effect of each inlet condition on the flow behavior downstream of the mixing tee. They are (i) unperturbed inlet conditions and (ii) inlets with synthetic turbulence. The experimental inflow conditions result in an incompletely mixed thermally stratified flow marked by significant buoyancy effects. Assessment of parameters like mean temperature and velocity predicted by both LESs exhibit very little deviation with each other indicating the insignificant effect of inflow turbulence on the bulk flow. But the inclusion of inflow turbulence is seen to have a non-negligible effect in the assessment of parameters like temperature fluctuations, turbulent kinetic energy and temperature–velocity correlation. The prevailing flow conditions are not seen to induce any dominant frequency of near-wall temperature fluctuations, an important factor in thermal fatigue analysis. Energy content of these fluctuations mainly lies in the frequency range of 0.1–2Hz.

A new method for measuring turbulent heat fluxes using PIV and fast-response cold-wires

A new method for measuring turbulent heat fluxes using a combination of particle image velocimetry and a nanoscale fast-response cold-wire is tested by examining a rough-wall turbulent boundary layer subject to weakly stable stratification. The method has the advantages of simple calibration and setup, as well as providing spatial correlations of velocity and temperature and their associated integral length scales. The accuracy of using Taylor’s hypothesis when employing a large field of view is investigated. Heat flux, velocity–temperature correlation coefficients and turbulent Prandtl number profiles, as well as spatial velocity and temperature correlations, are presented.

Spectral calculations in stably stratified turbulence.

We perform a Leslie-type perturbative treatment on stably stratified turbulence with Boussinesq approximation, where the buoyancy terms in the corresponding dynamical equations are treated as perturbations against the isotropic background fields. Thus we calculate the anisotropic corrections to various correlation functions, namely, velocity-velocity, temperature-temperature, and velocity-temperature correlations, up to second order in this scheme. We find that the prefactors associated with the anisotropic corrections depend on the energy flux, scalar flux, Kolmogorov constant, Batchelor constant, and the eddy-damping amplitudes. The correlation functions further yield the anisotropic parts of the energy and mean-square temperature spectra as k(-3) and the anisotropic buoyancy spectrum as k(-7/3). The resulting angle-dependent energy density is found to be concentrated predominantly around the vertical wave vector signifying layered structures in the physical space.

Tracking of large-scale structures in turbulent channel with direct numerical simulation of low Prandtl number passive scalar

Channel flow DNS (Direct Numerical Simulation) at friction Reynolds number 180 and with passive scalars of Prandtl numbers 1 and 0.01 was performed in various computational domains. The “normal” size domain was ∼2300 wall units long and ∼750 wall units wide; size taken from the similar DNS of Moser et al. The “large” computational domain, which is supposed to be sufficient to describe the largest structures of the turbulent flows was 3 times longer and 3 times wider than the “normal” domain. The “very large” domain was 6 times longer and 6 times wider than the “normal” domain. All simulations were performed with the same spatial and temporal resolution. Comparison of the standard and large computational domains shows the velocity field statistics (mean velocity, root-mean-square (RMS) fluctuations, and turbulent Reynolds stresses) that are within 1%-2%. Similar agreement is observed for Pr = 1 temperature fields and can be observed also for the mean temperature profiles at Pr = 0.01. These differences can be attributed to the statistical uncertainties of the DNS. However, second-order moments, i.e., RMS temperature fluctuations of standard and large computational domains at Pr = 0.01 show significant differences of up to 20%. Stronger temperature fluctuations in the “large” and “very large” domains confirm the existence of the large-scale structures. Their influence is more or less invisible in the main velocity field statistics or in the statistics of the temperature fields at Prandtl numbers around 1. However, these structures play visible role in the temperature fluctuations at low Prandtl number, where high temperature diffusivity effectively smears the small-scale structures in the thermal field and enhances the relative contribution of large-scales. These large thermal structures represent some kind of an echo of the large scale velocity structures: the highest temperature-velocity correlations are not observed between the instantaneous temperatures and instantaneous streamwise velocities, but between the instantaneous temperatures and velocities averaged over certain time interval.

A generalized Reynolds analogy for compressible wall-bounded turbulent flows

AbstractA generalized Reynolds analogy (GRA) is proposed for compressible wall-bounded turbulent flows (CWTFs) and validated by direct numerical simulations. By introducing a general recovery factor, a similarity between the Reynolds-averaged momentum and energy equations is established for the canonical CWTFs (i.e. pipes, channels, and flat-plate boundary layers that meet the quasi-one-dimensional flow approximation), independent of Prandtl number, wall temperature, Mach number, Reynolds number, and pressure gradient. This similarity and the relationships between temperature and velocity fields constitute the GRA. The GRA relationship between the mean temperature and the mean velocity takes the same quadratic form as Walz’s equation, with the adiabatic recovery factor replaced by the general recovery factor, and extends the validity of the latter to diabatic compressible turbulent boundary layers and channel/pipe flows. It also derives Duan & Martín’s (J. Fluid Mech., vol. 684, 2011, pp. 25–59) empirical relation for flows at different physical conditions (wall temperature, Mach number, enthalpy condition, surface catalysis, etc.). Several key parameters besides the general recovery factor emerge in the GRA. An effective turbulent Prandtl number is shown to be the reason for the parabolic profile of mean temperature versus mean velocity, and it approximates unity in the fully turbulent region. A dimensionless wall temperature, that we call the diabatic parameter, characterizes the wall-temperature effects in diabatic flows. The GRA also extends the analysis to the fluctuation fields. It recovers the modified strong Reynolds analogy proposed by Huang, Coleman & Bradshaw (J. Fluid Mech., vol. 305, 1995, pp. 185–218) and explains the variation of the temperature–velocity correlation coefficient with wall temperature. Thus, the GRA unveils a generalized similarity principle behind the complex nonlinear coupling between the thermal and velocity fields of CWTFs.

Large-eddy simulation of particle-laden turbulent flow with heat transfer

The influence of solid particles on the heat transfer rate of a non-isothermal turbulent channel flow is studied using large-eddy simulation. An Eulerian–Lagrangian approach is adopted, and the backward effects of particles in both the momentum and energy equations are taken into account. It is shown that at a constant particle mass loading, the heat transfer rate increases proportionally with the particle specific heat. For a constant particle specific heat, however, depending on the value of the particle specific heat, the heat transfer rate may decrease, increase, or stay unchanged with the increase of the mass loading. To further clarify this issue, the total Nusselt number is split into a turbulence contribution and a particles contribution, and the relation of the Nusselt number with the fluid temperature–velocity correlation and the fluid-particles heat transfer is examined in details. In addition, the mean and fluctuating profiles for fluid and particles are reported, and the results are validated against the available data in the literature.

Thermal Spray Maps: Material Genomics of Processing Technologies

There is currently no method whereby material properties of thermal spray coatings may be predicted from fundamental processing inputs such as temperature-velocity correlations. The first step in such an important understanding would involve establishing a foundation that consolidates the thermal spray literature so that known relationships could be documented and any trends identified. This paper presents a method to classify and reorder thermal spray data so that relationships and correlations between competing processes and materials can be identified. Extensive data mining of published experimental work was performed to create thermal spray property-performance maps, known as “TS maps” in this work. Six TS maps will be presented. The maps are based on coating characteristics of major importance; i.e., porosity, microhardness, adhesion strength, and the elastic modulus of thermal spray coatings.

Simultaneous PIV/LIF measurements of a transitional buoyant plume above a horizontal cylinder

Results from an experimental investigation of the simultaneous temperature and velocity fields above an evenly heated horizontal cylinder with a Rayleigh number of 9.4E7 is presented. Ensemble averaged two-dimensional velocity and temperature fields, velocity fluctuations, temperature variance, and velocity–temperature correlations are computed from 2700 instantaneous data sets from simultaneous laser-induced fluorescence (LIF) and particle image velocimetry (PIV). The vertical velocity and temperature field in the plume are compared with similarity solutions from turbulent planar plumes. The production of turbulent kinetic energy (TKE) due to mean shear and buoyancy is evaluated and shows that the production of TKE is dominated by velocity shear.

Large eddy simulation of a confined square cavity with natural convection based on compressible flow equations

Large eddy simulation of natural convection in a confined square cavity is described. The use of a complex compressible code with an artificial acoustic stiffness correction method, allows the use of higher time steps for a faster time and statistical convergence. We consider a broadly studied experimental case, consisting of a natural convective flow in a confined square cavity, with vertical walls heated at different rates (active walls), set at Ra = 1.58 × 10 9. Turbulent boundary layers developing on the active walls and a vertical stable stratification characterize the mean flow. It is shown here that the results of this study match the experimental results reported in literature; for instance, mean velocity results. Although results for rms velocity fluctuations are barely over-predicted, the peak region is properly represented, while the greatest disagreements are found in the turbulent heat flow rate (velocity–temperature correlations). Turbulent structures were identified using different visualization methods and statistical studies. The authors found that the boundary layers on the active walls almost reach the fully turbulent regime, tending toward the laminar regime along the horizontal walls.

Turbulent flow and heat transfer in eccentric annulus

A detailed statistical analysis of turbulent flow and heat transfer in eccentric annular duct was performed via direct numerical simulations (DNS) with particular emphasis on the needs of turbulence closure models. A large number of flow characteristics such as components of the Reynolds stress tensor, temperature–velocity correlations and some others were obtained for the first time for such kind of a flow. The results of the paper will serve as a benchmark test case for turbulence modelling, specifically for models intended to be used for flows with partly turbulent regimes.

Modeling the effect of upstream temperature fluctuations on shock/homogeneous turbulence interaction

Reynolds-averaged Navier–Stokes (RANS) equations can yield significant error when applied to the interaction of turbulence with shock waves. This is often due to the fact that RANS turbulence models do not account for the underlying physical phenomena correctly. For example, in the presence of appreciable temperature fluctuations in the upstream flow, turbulence amplification across a shock is significantly affected by the magnitude of the temperature fluctuations and the sign of the upstream velocity-temperature correlation [Mahesh et al., J. Fluid Mech. 334, 353 (1997)]. Standard two-equation models with compressibility correction do not reproduce this effect. We use the interaction of homogeneous isotropic turbulence with a normal shock to suggest improvements to the k-ϵ model. The approach is similar to that presented in an earlier work [Sinha et al., Phys. Fluids 15, 2290 (2003)]. Linear inviscid analysis is used to study the effect of upstream temperature fluctuations on the evolution of turbulent kinetic energy k across the shock. The dominant mechanisms contributing to the k amplification are identified and then modeled in a physically consistent way. The dissipation rate equation is also altered based on linear analysis results. The modifications yield significant improvement over existing two-equation models and the new model predictions are found to match linear theory and direct numerical simulation data well.

How to define the boundaries of a convective zone, and how extended is overshooting?

In non-local convection theory, convection extends without limit and therefore an apparent boundary cannot be defined clearly, as in local theory. From the requirement that a similar structure for both local and non-local models has the same depth of convection zone, and taking into account the driving mechanism of turbulent convection, we argue that a proper definition of the boundary of a convective zone should be the place where the convective energy flux (i.e. the correlation of turbulent velocity and temperature) changes its sign. Therefore, it is a convectively unstable region when the flux is positive, and it is a convective overshooting zone when the flux becomes negative. The physical picture of the overshooting zone drawn by the usual non-local mixing-length theory is incorrect. In fact, convection is already subadiabatic (del < del(ad)) long before reaching the unstable boundary, while in the overshooting zone below the convective zone, convection is subadiabatic and superradiative (del(rad) < del < del(ad)). The transition between the adiabatic and radiative temperature gradients is continuous and smooth instead of being a sudden switch. In the unstable zone, the temperature gradient approaches a radiative temperature gradient rather than an adiabatic temperature gradient. We would like to note again that the overshooting distance is different for different physical quantities. In an overshooting zone at deep stellar interiors, the e-folding lengths of turbulent velocity and temperature are about 0.3H(P), whereas that of the velocity-temperature correlation is much shorter, about 0.09H(P). The overshooting distance in the context of stellar evolution, measured by the extent of the mixing of stellar matter, should be more extended. It is estimated to be as large as 0.25-1.7H(P) depending on the evolutionary time-scale. The larger the overshooting distance, the longer the time-scales. This is because of the participation of the extended overshooting tail in the mixing process.

Experimental study of the blowing impact on a hot turbulent boundary layer

We present an experimental study of non-isothermal blowing through a porous flat plate using hot and cold wires anemometry. The calibration procedure is presented, taking into account the influence of the temperature. King’s law coefficients are determined and a cosinus method is employed to calibrate the angle of the cross wires. A first set of measurements permits to investigate the influence of the temperature on the hot wire and the Seebeck effect on the cold wire. The experimental results are presented. We observe that blowing has a strong influence on the velocity and temperature profiles as well as on the velocity–velocity and velocity–temperature correlations and on the flow statistics. The velocity and temperature spectra are also given, showing that their slopes are modified by the blowing.

Scalar mixing from a concentrated source in turbulent channel flow

The mixing of a scalar (temperature) emitted from a concentrated line source in fully developed high-aspect-ratio turbulent channel flow is studied. The motivation for the work is to study the effect of the inhomogeneity on the scalar dispersion. It is most readily carried out in a flow that is inhomogeneous in only one direction, i.e. channel flow. Experiments were performed at two Reynolds numbers (). Both the mean and r.m.s. temperature profiles were found to be described well by truncated Gaussian distributions. In contrast to homogeneous flows, (i) the growth rates of the mean profile widths did not exhibit power law behaviours, (ii) the centres of the r.m.s. profiles were found to drift towards the centre of the channel for plumes emanating from off-centreline source locations and (iii) the r.m.s. profiles showed no tendency towards double peaks far downstream, as are observed in homogeneous flows. For near-wall source locations, the probability density function (PDF) of the scalar fluctuations evolved from a quasi-Gaussian distribution near the wall to a strongly positively skewed PDF (with a large spike at the cold-fluid temperature) for transverse locations away from the wall. Increasing the Reynolds number was found to improve the mixing, even though this decreases the amount of time for which the scalar can mix (owing to the more rapid advection). For the centreline source location, the PDF shape was, in general, more spiked, indicating the importance of the flapping of the plume in this case. The effect of the meandering of the plume was less significant when the plume was bounded by the wall. Second- and third-order velocity–temperature correlations were presented. The differences in their profiles for the near-wall and centreline source locations were distinct.

Measurement of velocity-temperature correlations in a turbulent diffusion flame

The paper reports on the nonintrusive, simultaneous measurement of velocity and temperature fluctuations in a turbulent jet diffusion flame. Velocity fluctuations were measured using laser Doppler anemometry (LDA), whereas coherent anti-Stokes Raman spectroscopy (CARS) was used for temperature measurements. The simultaneous measurements were affected by both density bias and velocity bias because the LDA imposed a form of biased sampling on the CARS. The measured velocity-temperature correlation coefficients indicated that the gradient-diffusion hypothesis is reasonably accurate for the radial direction. However, for the axial direction the gradient diffusion hypothesis is accurate only in the central region of the flame, while countergradient diffusion is found in the outer region.

Temperature fluctuations of discrete particles in a homogeneous turbulent flow: a Lagrangian model

Within the frame of Lagrangian approaches for the prediction of heat transfer in dispersed two-phase flows, a new dispersion model is proposed which involves correlated stochastic processes to predict the velocity and temperature of a discrete particle along its path in terms of the instantaneous velocity and temperature of the surrounding fluid element. The dispersion problem is carefully addressed in taking into account the anisotropy of the flow and the turbulent heat flux resulting from velocity–temperature correlations. The model is used to simulate the behavior of particles suspended in a homogeneous turbulent shear flow. The numerically predicted correlations between the fluctuating quantities are in perfect agreement with the results of an analytical study by Zaichik (Phys. Fluids 11 (1999) 1521–1534). A supplementary investigation of the associated effects of non-linear drag and heat transfer is then proposed.

Heat transfer in a rotor–stator system with a radial inflow

The object of the present work is to produce a better understanding of the flow and heat transfer process occurring in a rotor-stator system, with a low aspect ratio and subjected to a superposed radial inflow. The theoretical approach presented in a previous paper (Debuchy et al., Eur. J. Mech. B-Fluids 17 (6) (1998) 791–810) in the framework of laminar, steady, axisymmetric flow is extended to heat transfer effects. The asymptotic model is simplified and new integral relations including temperature are indicated. The experiments, made in a rotor–stator system with a heated stationary disc, are in agreement with the features of the model in the explored range of the gap ratio, Ekman and Rossby numbers. The data include radial and circumferential mean velocity components, air temperature inside the cavity, temperature and temperature-velocity correlations, and also local Nusselt numbers measured on the stationary disc. The flow structure near the axis is found to be strongly affected by the presence of a superposed inflow, as already observed under isothermal conditions. By contrast, the mean temperature, as well as the correlations concerning velocity and temperature are smaller when a radial inflow is assigned.

Digital particle image velocimetry/thermometry and application to the wake of a heated circular cylinder

Digital particle image velocimetry/thermometry (DPIV/T) is a technique whereby the velocity and temperature fields are obtained using thermochromic liquid crystal (TLC) seeding particles in water. In this paper, the uncertainty levels associated with temperature and velocity measurements using DPIV/T are studied. The study shows that large uncertainties are encountered when the temperature is measured from individual TLC particles. Therefore, an averaging procedure is presented which can reduce the temperature uncertainties. The uncertainty is reduced by computing the average temperature of the particles within the common specified sampling window used for standard DPIV. Using this procedure, the velocity and temperature distributions of an unsteady wake behind a heated circular cylinder are measured experimentally at Re=610. The instantaneous DPIV/T measurements are shown to be useful for computing statistical flow quantities, such as mean and velocity-temperature correlations.

Three-dimensional flow field downstream of an embedded stator in a multistage axial flow compressor: Part 1: Steady and unsteady flow fields

A comprehensive investigation of the three-dimensional unsteady flow and thermal field downstream of an embedded stator in a multistage compressor, acquired with a high-response hot-film probe and aspirating probe, is presented and analysed. Some of the earlier data (from a five-hole probe and a high-response Kulite probe) from the same compressor is used with the present data to provide an integrated interpretation of the flow and thermal fields. Part 1 includes a brief description of the facility, the development of the hot-film technique for the multistage flow field measurement and an interpretation of the various flow field features, such as the hub clearance flow and the suction surface-casing end-wall corner region. Part 2 covers velocity-velocity and velocity-temperature correlations and the assessment of their magnitudes in the average-passage equations. The results presented in this part of the paper (Part 1) indicate that major blockage in the stator hub end wall is caused by leakage flow and its possible subsequent roll-up into a vortex. Similar features exist in the suction surface casing end-wall corner due to secondary flow and its interaction with the upstream rotor end-wall flow. These are also the regions with the highest levels of unsteadiness. The transport of rotor wake towards the pressure side of the stator is confirmed. Both the revolution and the blade periodic velocity fluctuations are found to be significantly greater than the aperiodic fluctuations.