Wall-normal Position Research Articles

On the streamwise velocity, temperature and passive scalar fields in compressible turbulent channel flows: a viewpoint from multiphysics couplings

It is generally believed that the velocity and passive scalar fields share many similarities and differences in wall-bounded turbulence. In the present study, we conduct a series of direct numerical simulations of compressible channel flows with passive scalars and employ the two-dimensional spectral linear stochastic estimation and the correlation function as diagnostic tools to shed light on these aspects. Particular attention is paid to the relevant multiphysics couplings in the spectral domain, i.e. the velocity–temperature ( $u-T$ ), scalar–temperature ( $g-T$ ) and velocity–scalar ( $u-g$ ) couplings. These couplings are found to be utterly different at a given wall-normal position in the logarithmic and outer regions. Specifically, in the logarithmic region, the $u-T$ and $u-g$ couplings are tight at the scales that correspond to the attached eddies and the very large-scale motions (VLSMs), whereas the $g-T$ coupling is robust in the whole spectral domain. In the outer region, $u-T$ and $u-g$ couplings are only active at the scales corresponding to the VLSMs, whereas the $g-T$ coupling is diminished but still strong at all scales. Further analysis indicates that although the temperature field in the vast majority of zones in a channel can be roughly treated as a passive scalar, its physical properties gradually deviate from those of a pure passive scalar as the wall-normal height increases due to the enhancement of the acoustic mode. Furthermore, the deep involvement of the pressure field in the self-sustaining process of energy-containing motions also drives the streamwise velocity fluctuation away from a passive scalar. The current work is an extension of our previous study (Cheng & Fu, J. Fluid Mech., vol. 964, 2023, A15), and further uncovers the details of the multiphysics couplings in compressible wall turbulence.

Turbulent dispersion of a passive scalar in a smooth-wall turbulent boundary layer

The scalar dispersion of a ground-level point-source plume in a smooth-wall turbulent boundary layer is experimentally investigated using simultaneous particle image velocimetry and planar laser-induced fluorescence techniques. In the near-source region, the viscous sublayer is observed to trap dye, while in the far field, the half-width, vertical profiles and peak decay of the mean concentration and concentration variance exhibit self-similar behaviour and collapse with empirical relations. Full two-dimensional maps of the turbulent scalar fluxes show a net transport direction of upward and towards the incoming flow, with the vertical profiles collapsing well with Weibull-type exponential functions and the decay of peaks following power laws. Using the first-order gradient transport to model the turbulent scalar fluxes, maps of the anisotropic turbulent diffusivity tensor and an effective turbulent diffusivity coefficient are calculated. The streamwise and wall-normal turbulent scalar fluxes are driven dominantly by the wall-normal concentration gradient. The turbulent Schmidt number, relating the turbulent diffusivity and the turbulent (eddy) viscosity calculated using the Boussinesq hypothesis, varies with wall-normal position with values of the order of unity in the logarithmic layer.

Rescaling the near-wall predictive model for passive scalars in turbulent channel flow

The predictive model for near-wall velocity fluctuations [I. Marusic, R. Mathis, and N. Hutchins, “Predictive model for wall-bounded turbulent flow,” Science 329, 193–196 (2010)] is also valid for passive scalars transported in wall-bounded turbulent flows. However, the model parameters show strong Prandtl number (Pr) dependence under the viscous scaling. In the present study, we introduced the Prandtl-number-dependent length unit to scale the model parameters. Under the proposed scaling, the wall-normal positions of the outer peak of the scalar spectra coincide with 4.5ReτPr, where Reτ is the friction Reynolds number. With the large-scale signals extracted at this position as the model input, the Prandtl number dependence of the model parameters is greatly weakened, and the wall-normal position of zero modulation is independent of Prandtl numbers.

On the method of determining instantaneous wall shear stress from near-wall velocity measurements in wall turbulence

The determination of the instantaneous wall shear stress (WSS) from near-wall velocity measurements has received considerable attention. However, the most appropriate procedure and the achievable accuracy remain open topics. The present work uses direct numerical simulation datasets of channel flow to investigate the influences of the wall-normal distribution of instantaneous velocity, the method for estimating the velocity gradient, and the wall-normal position of velocity vectors on the accuracy of the instantaneous WSS determined from near-wall velocity measurements. In general, the method of dividing instantaneous velocity vectors by their wall-normal positions performs better than the method of linearly fitting instantaneous velocity profiles for estimating the wall velocity gradients when the wall position is correctly determined. However, the nonlinear instantaneous velocity distribution within the viscous layer means that all methods introduce a negative mean bias error and non-negligible root mean square error for the instantaneous WSS and its statistics. The magnitudes of these errors increase with the wall-normal position of the velocity vectors. An empirical method for correcting the instantaneous WSS statistics is proposed based on the negligible Reynolds number dependence of the bias error of all statistics. The influence of the wall-normal position of the velocity vectors on the WSS statistics and the correction method are verified using experimental data from open channel flows. The verification results show that the correction method significantly improves the accuracy of the statistics of instantaneous WSS determined from near-wall velocity measurements under canonical wall turbulence.

Evolution of turbulent boundary layer over a three-dimensional bump

A bump is typically used in the inlet system of an aircraft engine to compress the incoming airflow and to reduce boundary layer thickness developed over fuselage. In this work, the turbulent flow over a three-dimensional bump is experimentally studied. The bump model is mounted in a closed return wind tunnel operated at the nominal velocity 10 m/s, corresponding to a friction Reynolds number of 2300. The flow field upstream the bump, along the bump centerline and at two different spanwise planes is measured with Particle Image Velocimetry (PIV). It is observed that a favorable pressure gradient develops until the suction peak of the bump, and that the average turbulence intensity within boundary layer is attenuated due to this favorable pressure gradient. The boundary layer thickness identified by examining profiles of streamwise velocity decreases significantly along the bump. The wall-normal position of the Turbulent/Non-Turbulent Interface (TNTI) identified with the vorticity criterion is also observed to decrease along the bump. When studying the behavior of the boundary layer thickness at different spanwise positions, we found that it tends to be larger in planes away from the centreline, which suggests that the bump diverts the flow.

Unsupervised modelling of a transitional boundary layer

A data-driven approach for the identification of local turbulent-flow states and of their dynamics is proposed. After subdividing a flow domain in smaller regions, the $K$ -medoids clustering algorithm is used to learn from the data the different flow states and to identify the dynamics of the transition process. The clustering procedure is carried out on a two-dimensional (2-D) reduced-order space constructed by the multidimensional scaling (MDS) technique. The MDS technique is able to provide meaningful and compact information while reducing the dimensionality of the problem, and therefore the computational cost, without significantly altering the data structure in the state space. The dynamics of the state transitions is then described in terms of a transition probability matrix and a transition trajectory graph. The proposed method is applied to a direct numerical simulation dataset of an incompressible boundary layer flow developing on a flat plate. Streamwise–spanwise velocity fields at a specific wall-normal position are referred to as observations. Reducing the dimensionality of the problem allows us to construct a 2-D map, representative of the local turbulence intensity and of the spanwise skewness of the turbulence intensity in the observations. The clustering process classifies the regions containing streaks, turbulent spots, turbulence amplification and developed turbulence while the transition matrix and the transition trajectories correctly identify the states of the process of bypass transition.

Uniform momentum zone scaling arguments from direct numerical simulation of inertia-dominated channel turbulence

Abstract

Experimental measurement of coherent structures in turbulent boundary layers using moving time-resolved particle image velocimetry

A moving time-resolved particle image velocimetry (MTRPIV) system was designed to measure the turbulent boundary layer (TBL). The combination of time-resolved particle image velocimetry and a translational moving system enables the MTRPIV to track the coherent structures with a long period and high temporal resolution. Based on the MTRPIV, the time-evolving of coherent structures within the TBL was measured and analyzed. The observation of the large-scale sweep collision with ejection shows that the strong collision causes the large-scale high- and low-speed coherent structures to break down. The time-evolving process of the hairpin packets shows that the low-speed fluid mass under the hairpin vortices is important for the generation of a whole hairpin packet. The small-scale low-speed structures increase their spatial scales by merging so that the independent hairpin vortices can be organized by merged larger-scale structures. The shear layer exceeding the length of 0.7–0.8 δ (δ is thickness of TBL) or 350–400 υUτ (υ and Uτ denote the kinematic viscosity and friction velocity, respectively) is unstable, and it will roll-up to generate a hairpin vortex. In the hairpin packet growth process, the inclination angle of the hairpin packet decreases from ∼13° to 8° in a time duration of 120 υUτ2, and the underlying low-speed fluid is elongated and then split. The analysis of the uniform momentum zones (UMZs) shows that the topmost UMZ has a relatively stable wall-normal position and convection speed. The lower UMZ is quasi-periodically generated and tends to move upward to merge with the upper UMZs. The hairpin packets impact the lower UMZs by inducing large-scale low-speed fluid mass to modulate the probability density function distribution of instantaneous streamwise velocity. The evolution of UMZs with velocity less than 0.5U∞ (U∞ denotes the free-stream velocity) is the result of the interaction of large- and small-scale streamwise fluctuation velocity.

Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 1. Energy spectra

In wall-bounded turbulence, a multitude of coexisting turbulence structures form the streamwise velocity energy spectrum from the viscosity- to the inertia-dominated range of scales. Definite scaling-trends for streamwise spectra have remained empirically elusive, although a prominent school of thought stems from the works of Perry and Abell (J. Fluid Mech., vol. 79, 1977, pp. 785-799) and Perry et al. (J. Fluid Mech., vol. 165, 1986, pp. 163-199), which were greatly inspired by the attached-eddy hypothesis of Townsend (The Structure of Turbulent Shear Flow, Cambridge University Press, 1976). In this paper, we re-examine the turbulence kinetic energy of the streamwise velocity component in the context of the spectral decompositions of Perry and coworkers. Two universal spectral filters are derived via spectral coherence analysis of two-point velocity signals, spanning a Reynolds number range $Re_\tau \sim \mathcal{O}(10^3)$ to $\mathcal{O}(10^6)$ and form the basis for our decomposition of the logarithmic-region turbulence into stochastically wall-detached and wall-attached portions of energy. The latter is composed of scales larger than a streamwise/wall-normal ratio of $\lambda_x/z \approx 14$. If the decomposition is accepted, a $k_x^{-1}$ scaling region can only appear for $Re_\tau \geq 80\,000$, at a wall-normal position of $z^+ = 100$. Following Perry and co-workers, it is hypothesized that spectral contributions from turbulence structures other than attached eddies obscure a $k_x^{-1}$ scaling. When accepting the idea of different spectral contributions it is furthermore shown that a broad outer-spectral peak is present even at low $Re_\tau$.

Effects of solid particles and wall roughness on turbulent boundary layer in a two-phase horizontal channel flow

Particle image velocimetry (PIV) is used to study the horizontal channel flow over smooth and rough walls, and single-phase flow and particle-laden flow with two different particle diameters are analyzed. The phenomenon of the wall similarity hypothesis is verified in single-phase flow but affected by particles in particle-laden flows. The pyramidal rough elements cause a velocity defect and shorten the length scale of the vortex. The streamwise and wall-normal Reynolds stresses are enhanced by wall roughness. Two kinds of particles with different Stokes numbers are used in the experiment. The collision and dragging effect of particles in the inner region offset the influence of wall roughness on the mean velocity profile. The introduction of particles tends to increase the streamwise Reynolds stress, but makes the peak of the Reynolds stress move to a higher wall-normal position, which is contrary to the effect of wall roughness. Quadrant analysis indicates that the wall roughness and particles show a converse effect on quadrant events, but neither change the majority of second and forth quadrant events. The analysis of the spatial structure of turbulence shows that the small scale spatial structure is less affected by wall roughness compared with the large scale spatial structure. According to the statistics of the particle distribution, it was found that particles with a larger Stokes number show a more distinct prioritized deposition in the inner region, and the deposition of particles is reduced due to the existence of rough elements.

Influence of sinusoidal riblets on the coherent structures in turbulent boundary layer studied by time-resolved particle image velocimetry

Drag reduction by riblets has drawn the attention of many researchers because of its low production cost and easy maintenance. But due to the fact that the rather low drag reduction riblets can offered, an easy modification to the structure of riblets to improve the performance would be more than necessary. In this work, an investigation of the influences on coherent structure of straight riblets and sinusoidal riblets (s-riblets) in a turbulent boundary layer (TBL) at various Reynolds numbers is carried out experimentally by using the time-resolved particle image velocimetry (TR-PIV). It is found that the skin friction of the turbulent boundary layer is reduced close to the wall, and the logarithmic velocity profile shifts upwards over riblets and s-riblets. The turbulence intensity and Reynolds shear stress are also reduced in the near wall region compared with the scenario of the smooth case, and a better performance on drag reduction is obtained over s-riblets. Coherent structures including hairpin vortex and low speed streaks are extracted over test plates by using the correlation coefficient and <inline-formula><tex-math id="M2">\begin{document}$\lambda_{ci}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20181875_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20181875_M2.png"/></alternatives></inline-formula> vortex identification method, to study the mechanism of drag reduction caused by riblets. It is shown that the spatial scale of coherent structure in streamwise and wall-normal direction decrease over riblets and s-riblets to various degrees, the inclination angle between the mainstream and coherent structure also decreases, meaning that the wall-normal movement and upwash motion are suppressed over riblets and s-riblets. Results from the conditional sampling method demonstrate that the induction of ejection and sweep motions by hairpin vortex are inhibited over riblets and hence the exchange of energy and momentum and the self-sustaining mechanism in turbulence are influenced. Furthermore, at the same <inline-formula><tex-math id="M3">\begin{document}$Re_{\tau}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20181875_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20181875_M3.png"/></alternatives></inline-formula>, the spanwise spacing of low speed streaks turns wider with wall-normal position increasing. At the same <inline-formula><tex-math id="M4">\begin{document}$ y^{+} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20181875_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20181875_M4.png"/></alternatives></inline-formula>, a larger spacing is seen over riblets and s-riblets, implying that spanwise movement of the streaks is restrained and hence becomes more stable.

Passive locomotion of freely movable flexible fins near the ground

We numerically examine the hydrodynamic interaction between a flexible fin and surrounding fluid near the ground when four relevant parameters of initial position, bending rigidity, mass ratio and Reynolds number are varied. The leading edge of the fin is fixed in the streamwise direction, whereas the lateral motion is freely movable by the fluid–flexible body interaction near the ground. When the fin is initially positioned far from the ground, the fin passively migrates toward another wall-normal position near the ground for an equilibrium state due to larger positive deflection angle for the fin than the negative angle by the effects of vorticity generated by the lateral velocity gradient near the ground. In addition, as the flapping amplitude of the fin is small for large bending rigidity and small mass ratio, the great asymmetry between the positive and negative deflection angles reduces the transient time of the fin to reach the equilibrium position near the ground, and thus the fins can quickly take the hydrodynamic benefits with low drag at an equilibrium state without any energy consumption for lift force due to local balance between the flapping motion and the ground. The most important observation is that the equilibrium position of the fin is invariant to the initial position, bending rigidity and mass ratio of the fin. However, the equilibrium position of the fin is dramatically affected by the Reynolds number. The present results provide new insights into the functional role of the relevant parameters in passively flapping-based locomotion near the ground.

Properties of the mean momentum balance in polymer drag-reduced channel flow

Mean momentum equation based analysis of polymer drag-reduced channel flow is performed to evaluate the redistribution of mean momentum and the mechanisms underlying the redistribution processes. Similar to channel flow of Newtonian fluids, polymer drag-reduced channel flow is shown to exhibit a four layer structure in the mean balance of forces that also connects, via the mean momentum equation, to an underlying scaling layer hierarchy. The self-similar properties of the flow related to the layer hierarchy appear to persist, but in an altered form (different from the Newtonian fluid flow), and dependent on the level of drag reduction. With increasing drag reduction, polymer stress usurps the role of the inertial mechanism, and because of this the wall-normal position where inertially dominated mean dynamics occurs moves outward, and viscous effects become increasingly important farther from the wall. For the high drag reduction flows of the present study, viscous effects become non-negligible across the entire hierarchy and an inertially dominated logarithmic scaling region ceases to exist. It follows that the state of maximum drag reduction is attained only after the inertial sublayer is eradicated. According to the present mean equation theory, this coincides with the loss of a region of logarithmic dependence in the mean profile.

Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation

The statistical properties are presented for the direct numerical simulation of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) at the verge of separation. The APG TBL has a momentum thickness-based Reynolds number range from $Re_{\unicode[STIX]{x1D6FF}_{2}}=570$ to 13 800, with a self-similar region from $Re_{\unicode[STIX]{x1D6FF}_{2}}=10\,000$ to 12 300. Within this domain the average non-dimensional pressure gradient parameter $\unicode[STIX]{x1D6FD}=39$, where for a unit density $\unicode[STIX]{x1D6FD}=\unicode[STIX]{x1D6FF}_{1}P_{\!e}^{\prime }/\unicode[STIX]{x1D70F}_{w}$, with $\unicode[STIX]{x1D6FF}_{1}$ the displacement thickness, $\unicode[STIX]{x1D70F}_{w}$ the mean shear stress at the wall and $P_{\!e}^{\prime }$ the far-field pressure gradient. This flow is compared with previous zero pressure gradient and mild APG TBL ($\unicode[STIX]{x1D6FD}=1$) results of similar Reynolds number. All flows are generated via the direct numerical simulation of a TBL on a flat surface with far-field boundary conditions tailored to apply the desired pressure gradient. The conditions for self-similarity, and the appropriate length and velocity scales, are derived. The mean and Reynolds stress profiles are shown to collapse when non-dimensionalised on the basis of these length and velocity scales. As the pressure gradient increases, the extent of the wake region in the mean streamwise velocity profiles increases, whilst the extent of the log-layer and viscous sublayer decreases. The Reynolds stress, production and dissipation profiles of the APG TBL cases exhibit a second outer peak, which becomes more pronounced and more spatially localised with increasing pressure gradient. This outer peak is located at the point of inflection of the mean velocity profiles, and is suggestive of the presence of a shear flow instability. The maximum streamwise velocity variance is located at a wall normal position of $\unicode[STIX]{x1D6FF}_{1}$ of spanwise wavelength of $2\unicode[STIX]{x1D6FF}_{1}$. In summary as the pressure gradient increases the flow has properties less like a zero pressure gradient TBL and more akin to a free shear layer.

Sensitivity of the Orr–Sommerfeld equation to base flow perturbations with application to airfoils

The sensitivity of the Orr–Sommerfeld equation due to base flow deviations is investigated by means of a Monte Carlo-type perturbation strategy and a Chebyshev collocation method. In particular, the sensitivities of the peak growth rate and frequency, both of which are of importance in airfoil applications, are investigated in the low Reynolds number regime. A separated boundary layer with a nominal shape factor of H=5.9 was perturbed for both velocity and wall-normal position deviations. Wide bands of eigenvalue spectra are obtained due to both types of perturbations. The standard deviation of the peak growth rate and frequency due to both perturbations does not exhibit a pronounced Reynolds number dependence. To broaden the results, six boundary layers were investigated with shape factors ranging from H=5.9−22. Perturbations resulting in a standard deviation of 1% of the nominal shape factor were applied. It is found that sensitivities of both the peak growth rate and frequency are more pronounced at lower shape factors, with a decrease in sensitivity with increasing shape factor. This result suggests that, at low Reynolds numbers, boundary layers with larger separated regions are less sensitive to base flow perturbations.

Mean force structure and its scaling in rough-wall turbulent boundary layers

AbstractThe combined roughness/Reynolds number problem is explored. Existing and newly acquired data from zero pressure gradient rough-wall turbulent boundary layers are used to clarify the leading order balances of terms in the mean dynamical equation. For the variety of roughnesses examined, it is revealed that the mean viscous force retains dominant order above (and often well above) the roughness crests. Mean force balance data are shown to be usefully organized relative to the characteristic length scale, which is equal or proportional to the width of the region from the wall to where the leading order mean dynamics become described by a balance between the mean and turbulent inertia. This is equivalently the width of the region from the wall to where the mean viscous force loses leading order. For both smooth-wall and rough-wall flows, the wall-normal extent of this region consistently ends just beyond the zero-crossing of the turbulent inertia term. In smooth-wall flow this characteristic length is a known function of Reynolds number. The present analyses indicate that for rough-wall flows the wall-normal position where the mean dynamics become inertial is an irreducible function of roughness and Reynolds number, as it is an inherent function of the relative scale separations between the inner, roughness, and outer lengths. These findings indicate that, for any given roughness, new dynamical regimes will typically emerge as the Reynolds number increases. For the present range of parameters, there appear to be three identifiable regimes. These correspond to the ratio of the equivalent sand grain roughness to the characteristic length being less than, equal to, or greater than$O(1)$. The relative influences of the inner, outer, and roughness length scales on the characteristic length are explored empirically. A prediction for the decay rate of the mean vorticity is developed via extension of the smooth-wall theory. Existing data are shown to exhibit good agreement with this extension. Overall, the present results appear to expose unifying connections between the structure of smooth- and rough-wall flows. Among other findings, the present analyses show promise toward providing a self-consistent and dynamically meaningful way of identifying the domain where the wall similarity hypothesis, if operative, should hold.

A reformulated synthetic turbulence generation method for a zonal RANS–LES method and its application to zero-pressure gradient boundary layers

A synthetic turbulence generation (STG) method for subsonic and supersonic flows at low and moderate Reynolds numbers to provide inflow distributions of zonal Reynolds-averaged Navier–Stokes (RANS) – large-eddy simulation (LES) methods is presented. The STG method splits the LES inflow region into three planes where a local velocity signal is decomposed from the turbulent flow properties of the upstream RANS solution. Based on the wall-normal position and the local flow Reynolds number, specific length and velocity scales with different vorticity content are imposed at the inlet plane of the boundary layer. The quality of the STG method for incompressible and compressible zero-pressure gradient boundary layers is shown by comparing the zonal RANS–LES data with pure LES, pure RANS, and direct numerical simulation (DNS) solutions. The distributions of the time and spanwise wall-shear stress, Reynolds stress distributions, and two point correlations of the zonal RANS–LES simulations are smooth in the transition region and in good agreement with the pure LES and reference DNS findings. The STG approach reduces the RANS-to-LES transition length to less than four boundary-layer thicknesses.

Turbulence and internal waves in stably-stratified channel flow with temperature-dependent fluid properties

AbstractDirect numerical simulation (DNS) is used to study the behaviour of stably-stratified turbulent channel flow with temperature-dependent fluid properties: specifically, viscosity ($\ensuremath{\mu} $) and thermal expansion coefficient ($\ensuremath{\beta} $). The governing equations are solved using a pseudo-spectral method for the case of turbulent water flow in a channel. A systematic campaign of simulations is performed in the shear Richardson number parameter space (${\mathit{Ri}}_{\tau } = \mathit{Gr}/ {\mathit{Re}}_{\tau } $, where $\mathit{Gr}$ is the Grashof number and ${\mathit{Re}}_{\tau } $ the shear Reynolds number), imposing constant-temperature boundary conditions. Variations of ${\mathit{Ri}}_{\tau } $ are obtained by changing ${\mathit{Re}}_{\tau } $ and keeping $\mathit{Gr}$ constant. Independently of the value of ${\mathit{Ri}}_{\tau } $, all cases exhibit an initial transition from turbulent to laminar flow. A return transition to turbulence is observed only if ${\mathit{Ri}}_{\tau } $ is below a threshold value (which depends also on the flow Reynolds number). After the transient evolution of the flow, a statistically-stationary condition occurs, in which active turbulence and internal gravity waves (IGW) coexist. In this condition, the transport efficiency of momentum and heat is reduced considerably compared to the condition of non-stratified turbulence. The crucial role of temperature-dependent viscosity and thermal expansion coefficient is directly demonstrated. The most striking feature produced by the temperature dependence of viscosity is flow relaminarization in the cold side of the channel (where viscosity is higher). The opposite behaviour, with flow relaminarization occurring in the hot side of the channel, is observed when a temperature-dependent thermal expansion coefficient is considered. We observe qualitative and quantitative modifications of structure and wall-normal position of internal waves compared to previous results obtained for uniform or quasi-uniform fluid properties. From the trend we observe in the investigated low-Reynolds-number range, we can hypothesize that, whereas the effects of temperature-dependent viscosity may be masked at higher Reynolds number, the effects of temperature-dependent thermal expansion coefficient will persist.

Radial basis function neural network model for mean velocity and vorticity of capillary flow

The radial basis function neural network (RBFNN) simulation has been designed to simulate and predict the mean velocity of capillary flow in transition from laminar to turbulent flow and the root-mean-square vorticity as a function of wall-normal position at different values of Reynolds number. The system was trained on the available data of the two cases. Therefore, we designed the system to work in automatic way for finding the best network that has the ability to have the best test and prediction. The proposed system shows an excellent agreement with that of an experimental data in these cases. The technique has been also designed to simulate the other distributions not presented in the training set and predicted them with effective matching. Copyright © 2010 John Wiley & Sons, Ltd.

Interfacial PIV to resolve flows in the vicinity of curved surfaces

PIV measurements near a wall are generally difficult due to low seeding density, low velocity, high velocity gradient, and strong reflections. Such problems are often compounded by curved boundaries, which are commonly found in many industrial and medical applications. To systematically solve these problems, this paper presents two novel techniques for near-wall measurement, together named Interfacial PIV, which extracts both wall-shear gradient and near-wall tangential velocity profiles at one-pixel resolution. To deal with curved walls, image strips at a curved wall are stretched into rectangles by means of conformal transformation. To extract the maximal spatial information on the near-wall tangential velocity field, a novel 1D correlation function is performed on each horizontal pixel line of the transformed image template to form a “correlation stack”. This 1D correlation function requires that the wall-normal displacement component of the particles be smaller than the particle image diameter in order to produce a correlation signal. Within the image regions satisfying this condition, the correlation function yields peaks that form a tangential velocity profile. To determine this profile robustly, we propose to integrate gradients of tangential velocity outward from the wall, wherein the gradient at each wall-normal position is measured by fitting a straight line to the correlation peaks. The capability of Interfacial PIV was validated against Particle Image Distortion using synthetic image pairs generated from a DNS velocity field over a sinusoidal bed. Different velocity measurement schemes performed on the same correlation stacks were also demonstrated. The results suggest that Interfacial PIV using line fitting and gradient integration provides the best accuracy of all cases in the measurements of velocity gradient and velocity profile near wall surfaces.