Turbulent transport dissimilarity with modulated turbulence structure in channel flow of viscoelastic fluid

This experimental study investigated the turbulent transport dissimilarity with a modulated turbulence structure in a channel flow of a viscoelastic fluid using simultaneous particle image velocimetry and planar laser-induced fluorescence measurements. An instantaneous dye concentration field with fluctuating velocity vectors showed that mass was transferred by hierarchically large-scale wavy motions with inclination. A co-spectral analysis showed that the spatial phase modulation of the streamwise velocity and dye concentration fluctuations for the wall-normal velocity fluctuation corresponded to the relaxation time. The occurrence of intense dye concentration fluctuation and small streamwise velocity fluctuation in a thin boundary layer caused dissimilar turbulent transport because of the non-zero negative correlation of the streamwise velocity and dye concentration fluctuations for the wall-normal velocity fluctuation only on large scales. This explains the turbulent transport dissimilarity which leads to the zero averaged Reynolds shear stress and non-zero wall-normal turbulent mass flux.     

Influence of a wavy boundary on turbulence.

Measurements of turbulence with laser Doppler velocimetry (LDV) are compared for turbulent flows over a flat surface and a surface with sinusoidal waves of small wavelength. The wavy boundary was highly rough in that the flow separated. The Reynolds number based on the half-height of the channel and the bulk velocity was 46,000. The wavelength was 5 mm and the height to wavelength ratio was 0.1. The root-mean-squares of the velocity fluctuations are approximately equal if normalized with the friction velocity. This can be explained as a consequence of the approximate equality of the correlation coefficients of the Reynolds shear stress. Calculations with a direct numerical simulation (DNS) are used to show that the fluid interacts with the wall in quite different ways for flat and wavy surfaces. They show similarity in that large quadrant 2 events in the outer flow, for both cases, are associated with plumes that emerge from the wall region and extend over large distances. Measurements of skewness of the streamwise and wall-normal velocity fluctuations and quadrant analyses of the Reynolds shear stresses are qualitatively similar for flat and wavy surfaces. However, the skewness magnitudes and the ratio of the quadrant 2 to quadrant 4 contributions are larger for the wavy surface. Thus, there is evidence that turbulent structures are universal in the outer flow and for quantitative differences in the statistics that reflect differences in the way in which the fluid interacts with the wall.     

Intense Reynolds-stress events in turbulent ducts

The aim of the present work is to investigate the role of intense Reynolds shear-stress events in the generation of the secondary flow in turbulent ducts. We consider the connected regions of flow where the product of the instantaneous fluctuations of two velocity components is higher than a threshold based on the long-time turbulence statistics, in the spirit of the three-dimensional quadrant analysis proposed by Lozano-Durán et al. (J. Fluid Mech., vol. 694, 2012, pp. 100–130). We examine both the geometrical properties of these structures and their contribution to the mean in-plane velocity components, and we perfom a comparison with turbulent channel flow at similar Reynolds number. The contribution to a certain mean quantity is defined as the ensemble average over the detected coherent structures, weighted with their own occupied volume fraction. In the core region of the duct, the contribution of intense events to the wall-normal component of the mean velocity is in very good agreement with that in the channel, despite the presence of the secondary flow in the former. Additionally, the shapes of the three-dimensional objects do not differ significantly in both flows. In the corner region of the duct, the proximity of the walls affects both the geometrical properties of the coherent structures and the contribution to the mean component of the vertical velocity. However, such contribution is less relevant than that of the complementary portion of the flow not included in such objects. Our results show that strong Reynolds shear-stress events are affected by the presence of a corner but, despite the important role of these structures in the dynamics of wall-bounded turbulent flows, their contribution to the secondary flow is relatively low, both in the core and in the corner.     

Evidences of persisting thermal structures in Couette flows

DNS of passive thermal turbulent Couette flow at several friction Reynolds numbers (180, 250, and 500), and the Prandtl number of air are presented. The time averaged thermal flow shows the existence of long and wide thermal structures never described before in Couette flows. These thermal structures, named CTFS (Couette Thermal Flow Superstructures), are defined as coherent regions of hot and cold temperature fluctuations. They are intrinsically linked to the velocity structures present in Couette flows. Two different 2D symmetries can be recognized, which get stronger with the Reynolds number. These structures do not affect the mean flow or mean quantities as the Nusselt number. However, turbulent intensities and thermal fluxes depend on the width of the structures, mainly far from the walls. Since the width of the structures is related to the channel width, the statistics of thermal Couette flow are to some point box-dependent.     

DNS of turbulent channel flow with conjugate heat transfer: Effect of thermal boundary conditions on the second moments and budgets

Budgets of turbulent heat fluxes and temperature variance obtained from the Direct Numerical Simulation of an incompressible periodic channel flow with a Reynolds number of 150 (based on friction velocity) and a Prandtl number of 0.71 are presented and analysed for four cases: locally imposed temperature at the wall (constant Dirichlet), locally imposed heat flux (constant Neumann), heat exchange coefficient (Robin) and 3D conjugate heat transfer. The dissipation rate associated with the temperature variance is strongly impacted by the thermal boundary condition. For non-conjugate cases, a straightforward analytical analysis establishes the connection between the boundary condition, the temperature variance and the wall-normal part of the thermal dissipation rate at the wall. For the conjugate case, the two-point correlations of the thermal field in the solid domain confirms the existence of very large scale thermal structures.     

Direct numerical simulation of turbulent heat transfer over fully resolved anisotropic porous structures

Lattice Boltzmann direct numerical simulations of turbulent heat transfer over and inside anisotropic porous media are performed. This study considers turbulent plane channel flows whose bottom walls are made from the porous media at the bulk Reynolds number of 2900 with isothermal and conjugate heat transfer wall conditions. Four different porous walls are considered. They are walls with only the wall-normal permeability, with the wall-normal and spanwise permeabilities, with the wall-normal and streamwise permeabilities, and with the isotropic wall-normal, spanwise and streamwise permeabilities. The porosity of the porous walls ranges from 0.6 to 0.8. Discussions on the effects of the anisotropic permeability on turbulent thermal fields are carried out by the instantaneous flow visualizations and the statistical quantities. In particular, temperature fluctuations, turbulent and dispersion heat fluxes are examined both inside and outside the porous walls. Finally, the heat transfer performance is discussed considering the effects of the anisotropic permeability.     

Spatio-temporal analysis of the turbulent flow in a ribbed channel

The turbulent flow in a channel with transverse ribs over one wall is studied experimentally. The height of the obstacles is about one tenth of the channel height, and the spacing is 10 times their height. The Reynolds number based on the channel hydraulic diameter and bulk flow velocity is 15,000. Velocity fields are obtained with high spatial and temporal resolution along the streamwise/wall-normal plane by means of time-resolved particle image velocimetry. Beside mean velocity and Reynolds stresses, the flow is investigated through two-point correlations, distributions of spanwise-swirling events, space–time velocity diagrams and power spectral density. Although the separated flow reattaches before the following obstacle is approached, a strong rib-to-rib interaction occurs. Spanwise vortices, 0.2 rib heights in size, are generated in the free shear layer, travel across the whole pitch, and may impact on the next rib. The large scale motions triggered by the separation grow in size until they reach the following obstacle. Flapping of the separated shear layer is observed at frequencies consistent with previous studies, causing the instantaneous reattachment point to fluctuate. The flapping initiates at the downstream edge of the obstacle tip, rather than at the upstream edge where the instantaneous separation occurs.     

Direct numerical simulation of turbulent heat transfer in a wall-normal rotating channel flow

Investigations into the characteristics of turbulent heat transfer and coherent flow structures in a plane-channel subjected to wall-normal system rotation are conducted using direct numerical simulation (DNS). In order to investigate the influence of system rotation on the temperature field, a wide range of rotation numbers are tested, with the flow pattern transitioning from being fully turbulent to being quasilaminar, and eventually, fully laminar. In response to the Coriolis force, secondary flows appear as large vortical structures, which interact intensely with the wall shear layers and have a significant impact on the distribution of turbulence kinetic energy (TKE), turbulence scalar energy (TSE), temperature statistics, and turbulent heat fluxes. The characteristic length scales of turbulence structures responsible for the transport of TSE are the largest at the quasilaminar state, which demands a very large computational domain in order to capture the two-dimensional spectra of temperature fluctuations. The effects of the Coriolis force on the turbulent transport processes of the temperature variance and turbulent heat fluxes are thoroughly examined in terms of their respective budget balances.     

Low-pass filtering effects of viscous sublayer on high Schmidt number mass transfer close to a solid wall

Numerical simulation of high Schmidt number turbulent mass transfer at a solid wall is carried out. Particular attention is paid to the response of the concentration field to the wall-normal velocity fluctuation inside the viscous sublayer. Spatio-temporal correlation shows that the high Schmidt number concentration field becomes insensitive to the wall-normal velocity fluctuation. In addition, there exists a significant time lag in the response of the concentration field to the wall-normal velocity fluctuation. As a result, the instantaneous distribution of the local mass transfer rate is drastically changed. These facts explain why the analogy between the momentum and mass transfer does not hold close to the wall. Based on a one-dimensional advection–diffusion equation, we derive a transfer function connecting the wall-normal velocity and the concentration fluctuations. It is shown that the present model can reproduce the fundamental dynamical features of high Schmidt number concentration field.     

Velocity fluctuations in laminar fluid flow

Fluctuating hydrodynamics, originally developed for fluctuations in fluids in equilibrium, can be extended to deal also with thermally excited hydrodynamic fluctuations in non-equilibrium states. After first reviewing some results earlier obtained for temperature fluctuations in fluids subjected to an externally imposed temperature gradient, we use in this paper fluctuating hydrodynamics to determine the enhancement of velocity fluctuations in laminar fluid flow. Adopting the case of planar Couette flow as a representative example, we show how the fluctuations of the wall-normal component of the velocity and of the wall-normal component of the vorticity can be obtained as solutions of a stochastic Orr–Sommerfeld equation and a stochastic Squire equation, respectively. By solving these fluctuating hydrodynamic equations we obtain quantitative estimates of the flow-induced non-equilibrium enhancements of the velocity and vorticity fluctuations as a function of the Reynolds number and of the wave number of the fluctuations.     

Symmetries, Invariance and Scaling-Laws in Inhomogeneous Turbulent Shear Flows

An approach to derive turbulent scaling laws based on symmetry analysis is presented. It unifies a large set of scaling laws for the mean velocity of stationary parallel turbulent shear flows. The approach is derived from the Reynolds averaged Navier–Stokes equations, the fluctuation equations, and the velocity product equations, which are the dyad product of the velocity fluctuations with the equations for the velocity fluctuations. For the plane case the results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the centre of a Couette flow and in the centre of a rotating channel flow, and a new exponential mean velocity profile that is found in the mid-wake region of high Reynolds number flat-plate boundary layers. The algebraic scaling law is confirmed in both the centre and the near wall regions in both experimental and DNS data of turbulent channel flows. For a non-rotating and a moderately rotating pipe about its axis an algebraic law was found for the axial and the azimuthal velocity near the pipe-axis with both laws having equal scaling exponents. In case of a rapidly rotating pipe, a new logarithmic scaling law for the axial velocity is developed. The key elements of the entire analysis are two scaling symmetries and Galilean invariance. Combining the scaling symmetries leads to the variety of different scaling laws. Galilean invariance is crucial for all of them. It has been demonstrated that two-equation models such as the k– model are not consistent with most of the new turbulent scaling laws.     

An investigation of thermally stratified turbulent channel flow with temperature oscillation on the bottom wall by large eddy simulation

Thermally stratified shear turbulent channel flow with temperature oscillation on the bottom wall of the channel is calculated to investigate the behavior of turbulent flow and heat transfer by use of large eddy simulation (LES) approach coupled with dynamic subgrid-scale (SGS) models. The objective of this study is to deal with the effect of the temperature oscillation on turbulent behavior of thermally stratified turbulent channel flow and to examine the effectiveness of the LES technique for predicting statistically unsteady turbulent flow driven by time-varying buoyancy force. To validate the present calculation, thermally stratified shear turbulent channel flow is computed and compared with available data obtained by direct numerical simulation (DNS), which confirm that the present approach can be used to predict thermally stratified turbulent channel flow satisfactorily. Further, to illustrate the effect of the temperature oscillation with different Richardson numbers and periods of the oscillation on turbulence characteristics, the phase-averaged mean value and fluctuation of the resolved velocities and temperature, and instantaneous velocity fluctuation structures are analyzed.     

Corrections for spatial velocity derivatives in a turbulent shear flow

Possible corrections for measured spatial velocity derivatives have been inferred from a direct numerical simulation database for a fully developed turbulent channel flow. The magnitude of the correction depends much less on the distance from the wall for derivatives in the spanwise direction than for those in the wall-normal direction. Corrections based on local isotropy are better approximations for spanwise derivatives than for wall-normal derivatives.The support of the Australian Research Council is gratefully ackowledged.     

Layered structure of turbulent plane wall jet

This paper investigates the layered structure of a turbulent plane wall jet at a distance from the nozzle exit. Based on the force balances in the mean momentum equation, the turbulent plane wall jet is divided into three regions: a boundary layer-like region (BLR) adjacent to the wall, a half free jet-like region (HJR) away from the wall, and a plug flow-like region (PFR) in between. In the PFR, the mean streamwise velocity is essentially the maximum velocity, and the simplified mean continuity and mean momentum equations result in a linear variation of the mean wall-normal velocity and Reynolds shear stress. In the HJR, as in a turbulent free jet, a proper scale for the mean wall-normal flow is the mean wall-normal velocity far from the wall and a proper scale for the Reynolds shear stress is the product of the maximum mean streamwise velocity and the velocity scale for the mean wall-normal flow. The BLR region can be divided into four sub-layers, similar to those in a canonical pressure-driven turbulent channel flow or shear-driven turbulent boundary layer flow. Building on the log-law for the mean streamwise velocity in the BLR, a new skin friction law is proposed for a turbulent wall jet. The new prediction agrees well with the correlation of Bradshaw and Gee (1960) over moderate Reynolds numbers, but gives larger skin frictions at higher Reynolds numbers.     

Velocity statistics and flow structures observed in bypass transition using stereo PTV

It is known from smoke visualizations that in a transitional boundary layer subjected to free-stream turbulence, streaks appear and eventually break down to turbulence after wavy motions. In order to observe the streaky structures directly, a stereo particle-tracking velocimetry system using hydrogen bubbles in a water channel has been developed and validated against laser Doppler velocimetry. Mean flow statistics show good agreement with previous results. With the developed measurement system, the instantaneous spanwise distribution of the streamwise and wall-normal velocities can be measured fast enough to resolve the time development of the streaky structures. Measurements of instantaneous spanwise distributions of the streamwise and wall-normal velocity disturbances show strong negative correlation between the wall-normal and streamwise velocities in the streaks. Published online: 19 November 2002     

Numerical and experimental investigation of turbulent characteristics in a drag-reducing flow with surfactant additives

Cetyltrimethyl ammonium chloride (CTAC) surfactant additives, because of their long-life characteristics, can be used as promising drag-reducers in district heating and cooling systems. In the present study we performed both numerical and experimental tests for a 75 ppm CTAC surfactant drag-reducing channel flow. A two-component PIV system was used to measure the instantaneous streamwise and wall-normal velocity components. A Giesekus constitutive equation was adopted to model the extra stress due to the surfactant additives, with the constitutive parameters being determined by well-fitting apparent shear viscosities, as measured by an Advanced Rheometric Expansion System (ARES) rheometer. In the numerical study, we connected the realistic rheological properties with the drag-reduction rate. This is different from previous numerical studies in which the model parameters were set artificially. By performing consistent comparisons between numerical and experimental results, we have obtained an insight into the mechanism of the additive-induced drag-reduction phenomena.

Our simulation showed that the addition of surfactant additives introduces several changes in turbulent flow characteristics: (1) In the viscous sublayer, the mean velocity gradient becomes gentler due to the viscoelastic forces introduced by the additives. The buffer layer becomes expanded and the slope of the velocity profile in the logarithmic layer increases. (2) The locations where the streamwise velocity fluctuation and Reynolds shear stress attain their maximum value shifted from the wall region to the bulk flow region. (3) The root-mean-square velocity fluctuations in the wall-normal direction decrease for the drag-reducing flow. (4) The Reynolds shear stress decreases dramatically and the deficit of the Reynolds shear stress is mainly compensated by the viscoelastic shear stress. (5) The turbulent production becomes much smaller and its peak-value position moves toward the bulk flow region. All of these findings agree qualitatively with experimental measurements.

Regarding flow visualization, the violent streamwise vortices in the near wall region become dramatically suppressed, indicating that the additives weaken the ejection and sweeping motion, and thereby inhibit the generation of turbulence. The reduction in turbulence is accomplished by additive-introduced viscoelastic stress. Surfactant additives have dual effects on frictional drag: (1) introduce viscoelastic shear stress, which increases frictional drag; and (2) dampen the turbulent vortical structures, decrease the turbulent shear stress, and then decrease the frictional drag. Since the second effect is greater than the first one, drag-reduction occurs.     

Temporal Evolution of Vortical Structures in the Wall Region of Turbulent Channel Flow

Hairpin-like vortical structures that form in the wall region of turbulent channel flow are investigated. The analysis is performed by following a procedure in which the Navier-Stokes equations are first integrated by means of a computational code based on a mixed spectral-finite difference technique in the case of the flow in a plane channel. A DNS turbulent-flow database, representing the turbulent statistically steady state of the velocity field through 10 viscous time units, is computed and the vortex-detection method of the imaginary part of the complex eigenvalue pair of the velocity-gradient tensor is applied to the velocity field. As a result, hairpin-like vortical structures are educed. Flow visualizations are provided of the processes of evolution that characterize hairpin vortices in the wall region of turbulent channel flow. The relationship is investigated between vortex dynamics and 2nd- and 4th- quadrant events, showing that ejections and sweeps play a fundamental role in the way the morphological evolution of a hairpin vortex develops with time.     

Turbulence and transport of passive scalar in magnetohydrodynamic channel flows with different orientations of magnetic field

DNS of turbulent flow and passive scalar transport in a channel are conducted for the situation when the fluid is electrically conducting (for example, a liquid metal) and the flow is affected by an imposed magnetic field. The cases of wall-normal, spanwise, and streamwise orientation of the magnetic field are considered. As main results, we find that the magnetic fields, especially those in the wall-normal and spanwise directions, significantly reduce the turbulent scalar transport and modify the properties of the scalar distribution.     

Turbulent heat transfer characteristics of water flow in a rotating pipe

Large-Eddy-Simulation of turbulent heat transfer for water flow in rotating pipe is performed, for various rotation ratios (0 ≤ N ≤ 14). The value of the Reynolds number, based on the bulk velocity and pipe diameter, is Re = 5,500. The aim of this study is to examine the effect of the rotating pipe on the turbulent heat transfer for water flow, as well as the reliability of the LES approach for predicting turbulent heat transfer in water flow. Some predictions for the case of non-rotating pipe are compared to the available results of literature for validation. To depict the influence of the rotation ratio on turbulent heat transfer, many statistical quantities are analyzed (distributions of mean temperature, rms of fluctuating temperature, turbulent heat fluxes, higher-order statistics). Some contours of instantaneous temperature fluctuations are examined.     

A study on coherent structures and drag-reduction in the wall turbulence with polymer additives by TRPIV

An experimental measurement was performed using time-resolved particle image velocimetry (TRPIV) to investigate the spatial topological character of coherent structures in wall-bounded turbulence of polymer additive solution. The fully developed near-wall turbulent flow fields with and without polymer additives at the same Reynolds number were measured by TRPIV in a water channel. The comparisons of turbulent statistics confirm that due to viscoelastic structure of long-chain polymers, the wall-normal velocity fluctuation and Reynolds shear stress in the near-wall region are suppressed significantly. Furthermore, it is noted that such a behavior of polymers is closely related to the decease of the motion of the second and forth quadrants, i.e., the ejection and sweep events, in the near-wall region. The spatial topological mode of coherent structures during bursts has been extracted by the new mu-level criteria based on locally averaged velocity structure function. Although the general shapes of coherent structures are unchanged by polymer additives, the fluctuating velocity, velocity gradient, velocity strain rate and vorticity of coherent structures during burst events are suppressed in the polymer additive solution compared with that in water. The results show that due to the polymer additives the occurrence and intensity of coherent structures are suppressed, leading to drag reduction.