Sublayer Region Research Articles

Non-dimensional energy dissipation rate near the turbulent/non-turbulent interfacial layer in free shear flows and shear free turbulence

The non-dimensional dissipation rate $C_{\unicode[STIX]{x1D700}}=\unicode[STIX]{x1D700}L/u^{\prime 3}$, where $\unicode[STIX]{x1D700}$, $L$ and $u^{\prime }$ are the viscous energy dissipation rate, integral length scale of turbulence and root-mean-square of the velocity fluctuations, respectively, is computed and analysed within the turbulent/non-turbulent interfacial (TNTI) layer using direct numerical simulations of a planar jet, mixing layer and shear free turbulence. The TNTI layer that separates the turbulent and non-turbulent regions exists at the edge of free shear turbulent flows and turbulent boundary layers, and comprises both the viscous superlayer and turbulent sublayer regions. The computation of $C_{\unicode[STIX]{x1D700}}$ is made possible by the introduction of an original procedure, based on local volume averages within spheres of radius $r$, combined with conditional sampling as a function of the location with respect to the TNTI layer. The new procedure allows for a detailed investigation of the scale dependence of several turbulent quantities near the TNTI layer. An important achievement of this procedure consists in permitting the computation of the turbulent integral scale within the TNTI layer, which is shown to be approximately constant. Both the non-dimensional dissipation rate and turbulent Reynolds number $Re_{\unicode[STIX]{x1D706}}$ vary in space within the TNTI layer, where two relations are observed: $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-1}$ and $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-2}$. Specifically, whereas the viscous superlayer and part of the turbulent sublayer display $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-2}$, the remaining of the turbulent sublayer exhibits $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-1}$, which is consistent with non-equilibrium turbulence (Vassilicos, Annu. Rev. Fluid Mech. vol. 47, 2015, pp. 95–114).

Entropy generation analysis of fully-developed turbulent heat transfer flow in inward helically corrugated tubes

The entropy generation analysis of fully-developed turbulent heat transfer flow in inward helically corrugated tubes was numerically performed by using a Reynolds stress model. The simulations were conducted for a smooth tube and five cases of corrugated tubes with Reynolds number (Re) ranging from 10,020 to 40,060 at a constant wall temperature condition. The effects of corrugation pitch and height on the flow patterns as well as local thermal and frictional entropy generation are detailed in the near wall region. The results indicate that the local heat transfer entropy generation is significantly evident at the sub-layer region and the detached vortex region, and the local thermal entropy is improved with increases in the secondary flow. Local friction entropy generation is mainly located at the windward of the corrugation and the severely turbulent fluctuation region and is mainly induced by the velocity gradient. The average friction entropy generation exhibits an exponential growth, while the average heat transfer and the total entropy generation display a linear growth trend with increased Re. The average Bejan number (Be) exhibits an exponential decline, and the minimum value can reach 0.69. From a comprehensive viewpoint, it is optimal for the Re to be lower than 30,050. When Re <20,030, higher and dense corrugations are beneficial. When 20,030 < Re <30,050, low and spare corrugations are more optimal. Besides, the case with Hl/D = 0.08 is not recommended.

Experimental and Numerical Investigation of Convective Heat Transfer of Supercritical Carbon Dioxide at Low Mass Fluxes

Significant differences in the heat transfer behaviors of supercritical carbon dioxide in a heated channel have been observed at different mass fluxes. At low mass fluxes, a unique heat transfer characteristic is accompanied by a monotonously smooth temperature variation without any temperature peak, even though the ratio of heat flux to mass flux (q/G) is high. In this study, experimental and numerical investigations explore the hidden mechanism of the peculiar heat transfer characteristics of supercritical carbon dioxide at low mass fluxes in vertically upward tubes with inside diameters (ID) of 5 mm. The range of operating conditions examined within the study include a mass flux (G) between 0–200 kg/m2s, and a heat flux (q) of up to 120 kW/m2. The parametric effects within these experimental conditions were analyzed on the basis of the obtained heat transfer data. Furthermore, a qualitative modeling force analysis and quantitative numerical simulation of vertical flow at low mass flux reveal the heat transfer mechanism for these temperature profiles. In addition, the distribution of flow parameters and thermo-physical properties (such as shear stress, density, and specific heat) in the near-wall region were also studied. It is found that the heat transfer behavior of supercritical CO2 at low mass flux is similar to “film boiling” at subcritical pressure, where “vapor-like” fluid occupies the sublayer region. Due to reduced buoyancy, the fluid does not cause enough mixing/instability to bring it to the bulk flow.

Comparison of summer chlorophyll a concentration in the South China Sea and the Arabian Sea using remote sensing data

The South China Sea (SCS) and the Arabian Sea (AS) are both located roughly in the north tropical zone with a range of similar latitude (0°–24°N). Monsoon winds play similar roles in the upper oceanic circulations of the both seas. But the distinct patterns of chlorophyll a (Chl a) concentration are observed between the SCS and the AS. The Chl a concentration in the SCS is generally lower than that in the AS in summer (June–August); the summer Chl a concentration in the AS shows stronger interannual variation, compared with that in the SCS; Moderate resolution imaging spectroradiometer (MODIS)-derived data present higher atmospheric aerosol deposition and stronger wind speed in the AS. And it has also been found that good correlations exist between the index of the dust precipitation indicated by aerosol optical thickness (AOT) and the Chl a concentration, or between wind and Chl a concentration. These imply that the wind and the dust precipitation bring more nutrients into the AS from the sky, the sub-layer or coast regions, inducing higher Chl a concentration. The results indicate that the wind velocity and the dust precipitation can play important roles in the Chl a concentration for the AS and the SCS in summer. However aerosol impact is weak on the biological productivity in the west SCS and wind-induced upwelling is the main source.

Rectangular ribs in turbulent boundary layer on the initially smooth surface

Results of experimental investigation of hydrodynamics and heat transfer in turbulent boundary layer before and after a rectangular rib with sharp corners and a rectangular rib with round top corners are presented. The rib is placed on the flat plate and heated by the law of qw=const. Experimental studies were conducted using hot-wire anemometry system by Dantec Dynamics and obtained are new experimental data on the mean and fluctuating characteristics in turbulent boundary layer in flow over ribs – in the laminar sublayer and transition region. A faster growth of the coefficient heat transfer is observed from the distribution features of drag and heat transfer coefficients..

Stabilization of gas transport properties of PTMSP with porous aromatic framework: Effect of annealing

This work was focused on the study of physical aging of PTSMP and preventing this effect via incorporation of porous aromatic frameworks (PAF-11). The dense PTMSP membranes with PAF-11 content of 0, 1, 5 and 10wt% were stepwise annealed in air at 100°C for up to 510h with constant monitoring of O2, N2 and CO2 permeability (measured at 30°C). As-cast and aged PTMSP samples were characterized by means of helium pycnometry, dynamic mechanical analysis and IR spectroscopy. Gas transport characteristics of the PTMSP sample containing 10wt% of PAF-11 became stable upon annealing at 100°С within the short time interval (100–200h). However, for all other samples containing 5wt% of PAF-11 or less, gas permeability gradually decreased with time. According to the IR analysis, upon high-temperature treatment, PAF-11 nanoparticles tended to migrate from the sub-layer region into the membrane matrix bulk. According to the helium pycnometry, the introduction of PAF-11 to the PTMSP matrix provided a loosened packaging of polymer chains, and the structure became more stabilized since the porous filler served as a “physical” cross-linker.

Simulation of inertial fibre orientation in turbulent flow

The spatial and orientational behaviour of fibres within a suspension influences the rheological and mechanical properties of that suspension. An Eulerian-Lagrangian framework to simulate the behaviour of fibres in turbulent flows is presented. The framework is intended for use in simulations of non-spherical particles with high Reynolds numbers, beyond the Stokesian regime, and is a computationally efficient alternative to existing Stokesian models for fibre suspensions in turbulent flow. It is based on modifying available empirical drag correlations for the translation of non-spherical particles to be orientation dependent, accounting for the departure in shape from a sphere. The orientational dynamics of a particle is based on the framework of quaternions, while its rotational dynamics is obtained from the solution of the Euler equation of rotation subject to external torques on the particle. The fluid velocity and turbulence quantities are obtained using a very high-resolution large eddy simulation with dynamic calibration of the sub-grid scale energy containing fluid motions. The simulation matrix consists of four different fibre Stokes numbers (St = 1, 5, 25, and 125) and five different fibre aspect ratios (λ = 1.001, 3, 10, 30, and 50), with results considered at four distances from a channel wall (in the viscous sub-layer, buffer, and fully turbulent regions), which are taken as a measure of the flow velocity gradient, all at a constant fibre to fluid density ratio (ρp/ρ = 760) and shear Reynolds number Reτ = 150. The simulated fibre orientation, concentration, and streakiness confirm previous experimentally observed characteristics of fibre behaviour in turbulence, and that of direct numerical simulations of fibres in Stokesian, or creeping flow, regimes. The fibres exhibit translational motion similar to spheres, where they tend to accumulate in the near-wall (viscous sub-layer and buffer) region and preferentially concentrate in regions of low-speed streaks. The current results further demonstrate that the fibres’ translational dynamics, in terms of preferential concentration, is strongly dependent on their inertia and less so on their aspect ratio. However, the contrary is the case for the fibre alignment distribution as this is strongly dependent on the fibre aspect ratio and velocity gradient, and only moderately dependent on particle inertia. The fibre alignment with the flow direction is found to be mostly anisotropic where the velocity gradient is large (i.e., viscous sub-layer and buffer regions), but is virtually non-existent and isotropic where the turbulence is near-isotropic (i.e., channel centre). The present investigation highlights that the level of fibre alignment with the flow direction reduces as a fibre’s inertia decreases, and as the shape of the fibre approaches that of a sphere. Short fibres, and especially near-spherical λ = 1.001 particles, are found to exhibit isotropic orientation with respect to all directions, whilst sufficiently long fibres align themselves parallel to the flow direction, and orthogonal to the other two co-ordinate directions, and the vorticity and flow velocity gradient directions.

Analysis of Turbulence Characteristics in the Laminar Sub-Layer Region of a Perturbed Turbulent Boundary Layer

Turbulent boundary layer plays an important role for generation of aerodynamic drag. Shear force and pressure force due to the presence of boundary layer separation from the body surface contribute to the total drag. Studies of drag reduction due the the boundary layer effect are continuously performed by many researchers. Present study is intended to evaluate the behaviour of the laminar sub-layer in a turbulent boundary layer using a hot-wire anemometer system. The study was conducted in a low-speed wind tunnel at a Reynolds number based on the momentum thickness of approximately Reθ = 1000. A smooth-flat plate and a plate with a single transverse square groove was used in the study of the boundary layer characteristics. The groove size of 10 mm x 10 mm was cut transversally across the test plate. The results show that no significant differences in the streamwise mean velocity, steamwise turbulence intensity, and velocity signals for the smooth-and grooved-wall cases. For the the energy spectra for the two cases, however, show significant differences.

Direct numerical simulation of turbulent boundary layer with heat transfer

A direct numerical simulation was conducted of an incompressible, nominally zero-pressure-gradient flat-plate boundary layer from momentum thickness Reynolds numbers 80–1150. Heat transfer was considered with a constant-temperature solid boundary and the Prandtl number Pr=0.71. Both the temperature boundary layer thickness and the Stanton number compared well to experimental data. The mean temperature distributions, the root-mean-square of the temperature fluctuations and the correlations between the velocity fluctuations and the temperature fluctuations have good agreements with previous investigations. One of the main focuses of the present paper is the statistical behavior of the velocity and temperature fluctuations in the wall-normal direction from the sub-layer region to the outer region of the boundary layer. Probability density functions (PDF) are presented to investigate the statistical characteristics near the wall. In addition, the near-wall temperature streaky structures are presented, and the coherence of the turbulent structures between the velocity and the temperature fields is discussed.

Effect of rib roughness pitch on thermal and thermo-hydraulic performance of a solar air heater roughened artificially with arc rib having gap

This experimental study on a solar air heater having absorber plate roughened artificially by providing roughness in the form of arc ribs having gap was carried out in the Department of Mechanical Engineering, Punjab Agricultural University, Ludhiana, India to study the effect of relative roughness pitch on thermal and thermohydraulic performance as well as to compare the performance of arc rib with gap roughened solar air heater with that of continuous arc rib roughened solar air heater. The roughness geometry parameters included relative roughness height of 0.043, angle of attack of 30 degree, relative gap position of 0.80, gap-width equal to the width of the rib and five values of relative roughness pitch ranging from 4 to 12 for flow Reynolds number range of 2000 to 16,000. The Nusselt number and friction factor were found to be more for relative roughness pitch value of 10 as compared to other values of relative roughness pitch. Thermo-hydraulic performance of solar air heaters roughened by arc with gap and continuous arc roughness geometries were found to be 1.91 times and 1.78 times respectively as compared to that of solar air heater having smooth absorber plate due to generation of turbulence in laminar sublayer region. However, improvement in thermo-hydraulic performance of solar air heater roughened by arc with gap geometry over continuous arc rib roughened solar air heater was attributed to generation of a region of turbulence on downstream side of the gap.

High spatial range velocity measurements in a high Reynolds number turbulent boundary layer

Here, we detail and analyse a multi-resolution particle image velocity measurement that resolves the wide range of scales prevalent in a zero pressure gradient turbulent boundary layer at high Reynolds numbers (up to Reτ ≈ 20 000). A unique configuration is utilised, where an array of eight high resolution cameras at two magnification levels are used simultaneously to obtain a large field of view, while still resolving the smaller scales prevalent in the flow. Additionally, a highly magnified field of view targeted at the near wall region is employed to capture the viscous sublayer and logarithmic region, with a spatial resolution of a few viscous length scales. Flow statistics from these measurements show good agreement with prior, well resolved hot-wire anemometry measurements. Analysis shows that the instantaneous wall shear stress can be reliably computed, which is historically known to be challenging in boundary layers. A statistical assessment of the wall shear stress shows good agreement with existing correlations, prior experimental and direct numerical simulation data, extending this view to much higher Reynolds numbers. Furthermore, conditional analysis using multiple magnification levels is detailed, to study near-wall events associated with high skin friction fluctuations and their associated overlaying structures in the log region. Results definitively show that the passage of very large-scale positive (or negative) velocity fluctuations are associated with increased (or reduced) small-scale variance in wall shear stress fluctuations.

Studies on gain medium inhomogeneity and spectral fluctuations coupled with a high repetition rate dye laser

Gain medium inhomogeneity is inevitable in a high repetition rate dye laser. In this paper, gain medium inhomogeneity coupled with a high repetition rate dye laser and their influences on the spectral fluctuations are investigated. The wavelength fluctuates within ±0.025 nm while the bandwidth fluctuates within ±1.108 GHz by reducing the flow Reynolds number from 1012 to 221 in the laminar region of flow. The wavelength fluctuations increase from 0.0110 to 0.0200 nm while the bandwidth fluctuations increase from 0.296 to 0.509 GHz by increasing the Reynolds number from 5645 to 6774 in the turbulent region. The heat deposition as a function of distance from the window wall in the gain medium and heat transfer coefficients as a function of Reynolds numbers in laminar and turbulent flow were estimated. Enlargement of the turbulent attribute (through a laminar sub-layer and buffer region) in the gain medium as a function of the Reynolds number was used to illustrate the observed spectral fluctuation trends of the dye laser.

Bending mechanics of the red-eared slider turtle carapace

The turtle shell is a natural shield that possesses complex hierarchical structure, giving rise to superior mechanical properties. The keratin-covered boney top (dorsal) part of the shell, termed carapace, is composed of rigid sandwich-like ribs made of a central foam-like interior flanked by two external cortices. The ribs are attached to one another in a 3-D interdigitated manner at soft unmineralized collagenous sutures. This unique structural combination promotes sophisticated mechanical response upon predator attacks.In the present study mechanical bending tests were performed to examine the static behavior of the red-eared slider turtle carapace, in different orientations and from various locations, as well as from whole-rib and sub-layer regions. In addition, the suture properties were evaluated as well and compared with those of the rib. A simplified classical analysis was used here to rationalize the experimental results of the whole rib viewed as a laminated composite.The measured strength (~300MPa) and bending modulus (~7–8.5GPa) of the rib were found to be of the same order of magnitude as the strength and modulus of the cortices. The theoretical prediction of the ribs' moduli, predicted in terms of the individual sub-layers moduli, agreed well with the experimental results. The suture regions were found to be more compliant and weaker than the ribs, but comparatively tough, likely due to the interlocking design of the boney zigzag elements.

Monte Carlo simulation of micron size spherical particle removal and resuspension from substrate under fluid flows

Particle detachment from surfaces and subsequent entrainment into fluid flow occurs in many natural and industrial applications. In this study, a Monte Carlo model for particle resuspension from substrate under turbulent flow conditions was developed. The forces and torque acting on a particle were evaluated and the criteria for the rolling detachment of rough spherical and nearly spherical particles from substrate under turbulent flow conditions were used in the analysis. The statistical variations of physical parameters that were relevant to particle resuspension as well as occurrence of turbulence bursts in the viscous sublayer region were included in the model through a series of Monte Carlo simulations. The fluctuating velocities were assumed to follow a Gaussian distribution and the resuspension fractions were evaluated for a range of conditions. The effects of surface roughness, particle and substrate material properties including Hamaker constant and particle sizes were studied. The model predictions were compared with the available experimental data and good agreement was found.

A Study of Physical and Numerical Effects of Dissipation on Turbulent Flow Simulations

ABSTRACT: The present work is primarily concerned with studying the effects of artificial dissipation and of certain diffusive terms in the turbulence model formulation on the capability of representing turbulent boundary layer flows. The flows of interest in the present case are assumed to be adequately represented by the compressible Reynolds-averaged Navier-Stokes equations, and the Spalart-Allmaras eddy viscosity model is used for turbulence closure. The equations are discretized in the context of a general purpose, density-based, unstructured grid finite volume method. Spatial discretization is based on the Steger-Warming flux vector splitting scheme and temporal discretization uses a backward Euler point-implicit integration. The work discusses in detail the theoretical and numerical formulations of the selected model. The computational studies consider the turbulent flow over a flat plate at 0.3 freestream Mach number. The paper demonstrates that the excessive artificial dissipation automatically generated by the original spatial discretization scheme can deteriorate boundary layer predictions. Moreover, the results also show that the inclusion of Spalart-Allmaras model cross-diffusion terms is primarily important in the viscous sublayer region of the boundary layer. Finally, the paper also demonstrates how the spatial discretization scheme can be selectively modified to correctly control the artificial dissipation such that the flow simulation tool remains robust for high-speed applications at the same time that it can accurately compute turbulent boundary layers.

Reynolds number effects on scale energy balance in wall turbulence

The scale energy budget utilizes a modified version of the classical Kolmogorov equation of wall turbulence to develop an evolution equation for the second order structure function [R. J. Hill, “Exact second-order structure-function relationships,” J. Fluid Mech. 468, 317 (2002)]. This methodology allows for the simultaneous characterization of the energy cascade and spatial fluxes in turbulent shear flows across the entire physical domain as well as the range of scales. The present study utilizes this methodology to characterize the effects of Reynolds number on the balance of energy fluxes in turbulent channel flows. Direct numerical simulation data in the range Reτ = 300–934 are compared to previously published results at Reτ = 180 [N. Marati, C. M. Casciola, and R. Piva, “Energy cascade and spatial fluxes in wall turbulence,” J. Fluid Mech. 521, 191 (2004)]. The present results show no Reynolds number effects in the terms of the scale energy budget in either the viscous sublayer or buffer regions of the channel. In the logarithmic layer, the transfer of energy across scales clearly varies with Reynolds number, while the production of turbulent kinetic energy is not dependent on Reynolds number. An envelope of inverse energy cascade is quantified in the buffer region within which energy is transferred from small to larger scales. This envelope is observed in the range 6 &amp;lt; y+ &amp;lt; 37, where all scales except the smallest scales display characteristics of an inverse energy cascade. The cross-over scale lc+, which indicates the transition between production dominated and scale transfer dominated regimes, increases with Reynolds number, implying a larger range of transfer dominated scales, before the dominant mechanism switches to production. At higher Reynolds numbers, two distinct regimes of lc+ as a function of wall-normal location are observed, which was not captured at Reτ = 180. The variations of lc+ match the trends of the shear scale, which is a representation of the mean shear in the flow. Thus, this study demonstrates the utility and importance of the use of higher Reynolds number data in order to accurately characterize and understand the energy dynamics of various scales across the entire boundary layer.

A robust k − ε − [formula omitted]/k elliptic blending turbulence model applied to near-wall, separated and buoyant flows

This paper first reconsiders evolution over 20years of the k−ε−v2¯−f strand of eddy-viscosity models, developed since Durbin’s (1991)original proposal for a near-wall eddy viscosity model based on the physics of the full Reynolds stress transport models, but retaining only the wall-normal fluctuating velocity variance, v2¯, and its source, f, the redistribution by pressure fluctuations. Added to the classical k−ε (turbulent kinetic energy and dissipation) model, this resulted in three transport equations f or k, epsilon and v2¯, and one elliptic equation for f, which accurately reproduced the parabolic decay of v2¯/k down to the solid wall without introducing wall-distance or low-Reynolds number related damping functions in the eddy viscosity and k−ε equations. However, most v2¯−f variants have suffered from numerical stiffness making them unpractical for industrial or unsteady RANS applications, while the one version available in major commercial codes tends to lead to degraded and sometimes unrealistic solutions. After considering the rationale behind a dozen variants and asymptotic behaviour of the variables in a number of zones (balance of terms in the channel flow viscous sublayer, logarithmic layer, and wake region, homogenous flows and high Reynolds number limits), a new robust version is proposed, which is applied to a number of cases involving flow separation and heat transfer. This k−ε type of model with v2¯/k anisotropy blends high Reynolds number and near-wall forms using two dimensionless parameters: the wall-normal anisotropy v2¯/k and a dimensionless parameter alpha resulting from an elliptic equation to blend the homogeneous and near-wall limiting expressions of f. The review of variants and asymptotic cases has also led to modifications of the epsilon equation: the second derivative of mean velocity is reintroduced as an extra sink term to retard turbulence growth in the transition layer (i.e. embracing the E term of the Jones and Launder (1972)k−ε model), the homogeneous part of epsilon is now adopted as main transported variable (as it is less sensitive to the Reynolds number effects), and the excessive growth of the turbulent length-scale in the absence of production is corrected (leading to a better distinction between log layer and wake region of a channel flow). For each modification numerical stability implications are carefully considered and, after implementation in an industrial finite-volume code, the final model proved to be significantly more robust than any of the previous variants.

A new approach to investigate hydrate deposition in gas-dominated flowlines

A new model describing the mechanism of the hydrate deposition based on the most recent particle dynamics theories is developed. The model splits the motion of the particle into two main regions: the turbulent and the sublayer regions. A novel approach is used to define the particle migration and attachment in the sublayer region. Depending on the ratio of the particle diameter relative to the thickness of the sublayer, the particle will either travel as a result of the force balance acting on the particle (lift, adhesion, gravity, and drag) or as it may experience bouncing process. The proposed model employs the following three main components to simulate the hydrate deposition: (a) computational fluid dynamics (CFD) technique is used to configure the flow field; (b) nucleation and growth models are incorporated in the simulation to predict the incipient hydrate particles size and growth rate; and finally (c) a novel approach of particle migration and deposition is used to determine how particles deposit and adhere to the walls of flow conduit. The results predicted by the model show that the distance of the deposition decreases as the particle size increases. However, after certain size of particle, there is no impact on the deposition distance. This critical particle size is called “ deposition critical size”. The experimental tests are shown to be in good agreement with the model predictions in terms of the following criteria: 1) Formation of hydrate particles are observed to be poly-dispersed since different sizes of particles are formed; 2) Studying the influence of the Reynolds number and pipe diameter, the deposition distance is found to be linearly corresponded to both.

A study on turbulence modulation via an analysis of turbulence anisotropy-invariants

We investigate the turbulence modulation by particles in a turbulent two-phase channel flow via an analysis of turbulence anisotropy-invariants. The fluid turbulence is calculated by a large eddy simulation with a point-force two-way coupling model and particles are tracked by the Lagrangian trajectory method. The channel turbulence follows the two-component turbulence state within the viscous sub-layer region and outside the region the turbulence tends to follow the right curve of the anisotropy-invariant. The channel turbulence, interacting with heavy particles, is modulated to the two-component turbulence limit state near the wall and is separate from the axisymmetric turbulence state in the turbulence anisotropy-invariants map. The fluctuations of streamwise component are transferred to the other two components and hence the anisotropy decreases due to particle modulation. The study has deepened the understanding of the turbulence modulation mechanism in two-phase turbulent flows.

Velocity Distributions in Spatially Varied Flow with Increasing Discharge

The experimental study presented in this paper explores the distribution of the mean velocities for a channel receiving spatially varied (SV) inflow from directly above the centerline of the channel via sets of nozzles. The velocity components u , v , and w have been measured using a laser Doppler velocimeter. Initially the validity of the law of the wall in the channel receiving SV inflow was investigated. It was found that the measured velocity profile within the inertial sublayer region near the channel bed falls below the line representing the log law. Further, if the SV inflow enters at the center of the channel, the degree that the data depart from the log law increases from the sidewall toward the center of the channel. The structures of the velocity distributions are also presented in detail. The results include both near field, that is the area close to where the flow enters the channel, and far field measurements. It was found that the influence of the SV inflow on velocity profiles is largely c...