Near-wall Velocity Research Articles

Characteristics of the shedding vortex around the Coanda surface and its impact on circulation control airfoil performance

This study investigates the characteristics of a shedding vortex around the Coanda surface and its impact on circulation control (CC) performance. Delay detach-eddy simulation based on the two-equation k−ω shear stress transport (SST) turbulence model is performed to solve the flow field. The simulation results show that near the Coanda trailing edge, large vortices periodically shed from the lip above the jet slot, and the shedding vortex is surrounded by a series of strip vortices during its downstream movement. The shedding vortex transfers the disturbance to the jet boundary layer and affects the near-wall velocity. Dynamic mode decomposition shows that the shedding vortex and its high-order harmonic flow structures attenuate very slowly and dominate the flow field. The mode with sub-harmonic frequency of the shedding vortex displays the strip vortices dragged out by the shedding vortex. A larger shedding vortex can intensify the mixing of the jet shear and boundary layers, making the jet velocity decay faster. The size of the shedding vortex can be reduced by decreasing the lip height, thus slowing down the attenuation of the jet velocity and improving the CC performance.

Sex-Specific and Dose-Dependent Effects of Drag-Reducing Polymers on Microcirculation and Tissue Oxygenation in Rats After Traumatic Brain Injury.

Traumatic brain injury (TBI) ultimately leads to a reduction in the cerebral metabolic rate for oxygen due to ischemia. Previously, we showed that 2ppm i.v. of drag-reducing polymers (DRP) improve hemodynamic and oxygen delivery to tissue in a rat model of mild-to-moderate TBI. Here we evaluated sex-specific and dose-dependent effects of DRP on microvascular CBF (mvCBF) and tissue oxygenation in rats after moderate TBI. In vivo two-photon laser scanning microscopy over the rat parietal cortex was used to monitor the effects of DRP on microvascular perfusion, tissue oxygenation, and blood-brain barrier (BBB) permeability. Lateral fluid-percussion TBI (1.5 ATA, 100ms) was induced after baseline imaging and followed by 4h of monitoring. DRP was injected at 1, 2, or 4ppm within 30 min after TBI. Differences between groups were determined using a two-way ANOVA analysis for multiple comparisons and post hoc testing using the Mann-Whitney U test. Moderate TBI progressively decreased mvCBF, leading to tissue hypoxia and BBB degradation in the pericontusion zone (p<0.05). The i.v. injection of DRP increased near-wall flow velocity and flow rate in arterioles, leading to an increase in the number of erythrocytes entering capillaries, enhancing capillary perfusion and tissue oxygenation while protecting BBB in a dose-dependent manner without significant difference between males and females (p<0.01). TBI resulted in an increase in intracranial pressure (20.1±3.2mmHg, p<0.05), microcirculatory redistribution to non-nutritive microvascular shunt flow, and stagnation of capillary flow, all of which were dose-dependently mitigated by DRP. DRP at 4ppm was most effective, with a non-significant trend to better outcomes in female rats.

An improved pressure drop correlation for modeling localized effects in a pebble bed reactor

Advances in the development of pebble bed reactors (PBRs) has created a desire for accurate and cost-effective simulation tools for design scoping studies and safety analysis. The current state-of-the-art for these simulations is the use of porous media models, although these models rely on correlations to capture the effects of flow features that are not explicitly modeled. One of the areas where correlation accuracy is currently lacking is in the near-wall region of the bed. In this region, the presence of the wall causes the pebbles to pack more orderly, drastically changing the geometry and flow behavior in this region.This work presents a new generalized pressure drop correlation for PBRs based on the KTA equation. A high-to-low methodology is applied, where large eddy simulation (LES) is performed on two beds of 1568 and 1700 pebbles to generate a high-fidelity dataset. The flow fields are then averaged in time and separated into concentric rings of 0.05 Dpeb width. Average porosity, velocity, and pressure drop are extracted for each ring and the friction and form losses are calculated. The Reynolds number range for this study is 625–10,000, and thus the form losses are dominant over the friction losses. The form losses across the rings are investigated, and a correction term for the form loss calculation is determined and applied to the KTA equation to drastically improve the capability of modeling localized porosity effects in a porous media code. The improved correlation reduces near-wall velocity prediction error from over 50% with the KTA correlation to around 5%. Agreement in pressure drop prediction between LES and porous media simulations is also improved.

Mean Velocity Scaling of High-Speed Turbulent Flows Under Nonadiabatic Wall Conditions

The problem of scaling the near-wall mean velocity profiles of turbulent flows and collapsing them with the law of the wall has been traditionally studied using the conservation of momentum, by employing various levels of assumptions. In the van Driest transformation (“Turbulent Boundary Layer in Compressible Fluids,” Journal of the Aeronautical Sciences, Vol. 18, No. 3, 1951, pp. 145–216), the viscous stress was neglected, whereas in the Trettel and Larsson transformation (“Mean Velocity Scaling for Compressible Wall Turbulence with Heat Transfer,” Physics of Fluids, Vol. 28, No. 2, 2016, Paper 026102), the Reynolds stress was assumed to cancel out. Recent work by Griffin, Fu, and Moin (“Velocity Transformation for Compressible Wall-Bounded Turbulent Flows with and Without Heat Transfer,” Proceedings of the National Academy of Sciences of the United States of America, Vol. 118, No. 34, 2021, Paper e2111144118) used a quasi-equilibrium assumption between turbulence production and dissipation in the log layer and demonstrated success for a wide variety of canonical flows. However, the extent of quasi-equilibrium is not verified, particularly for noncanonical flows. In this work, an alternate transformation is developed using the semilocal gradient of the van Driest transformed velocity, which is principally tied to the dynamics of vorticity transport in the boundary layer. In addition, a modified stress balance is utilized to directly account for and scale the buffer region. The transformation was benchmarked using a similar dataset as in Griffin et al., and comparable performance was obtained. Moreover, at supercritical pressures, the present transformation is found to produce significantly better collapse than existing works.

Experimental investigation of boundary layer flow near the cylinder wall in a direct-injection spark-ignition engine using particle image velocimetry

In a direct-injection spark-ignition (DISI) optical engine with a constant motored speed of 800 rpm, particle image velocimetry measurements on the in-cylinder bulk flow and the boundary layer flow near the cylinder wall were performed during the intake and compression strokes. Two different tumble flow levels were explored using a flap inserted in the intake port. The near-wall flow pattern under the effect of the bulk flow is more stable when the flap is fully closed with a higher intensity tumble. The serious optical distortion in the near-cylinder wall region under high magnification was addressed, and a high resolution of 76 μm × 76 μm within a field of view of 5 mm × 5 mm was achieved in six different measurement regions. Using inner scaling parameters (friction velocity uτ and viscous length-scale δυ), the dimensionless ensemble-averaged wall-tangential velocity profiles exhibit good consistency with the law-of-the-wall in the viscous sublayer but considerably departure in the logarithmic region. According to the low friction Reynolds number, the absence of the logarithmic layer was mainly attributed to the complete overlap between the viscosity-affected inner region and the outer region of the boundary layer. The near-wall velocity profiles were also normalized by three different outer scaling parameters. The collapse is significantly improved for y/ δ &gt;0.07 when the velocity profiles are normalized by δ/ δ*(1− u/ u∞). The fluctuation RMS velocity in the wall-normal direction is greater, particularly for the high tumble flow level condition.

Experimental study on mechanism of stable drag reduction with hydrogel interface

The hydrogel is a novel material with drag-reducing ability, which has great potential to be applied in marine applications. In this paper, a series of superhydrophilic hydrogels were prepared by photoinitiated radical polymerization. The Couette flow and particle image velocimeter (PIV) observation in the water tunnel were conducted to investigate the drag-reducing characteristics of the prepared hydrogels. The results show that the hydrogel thickness of 1500 µm is the critical value corresponding to the maximum drag reduction rate of about 68%. The drag reduction is induced by the boundary slip phenomenon on the hydrophilic surface, and the further mechanism can be explained in two aspects. On one hand, the generated vorticities in the grooves between the macroscopic convex structures of the hydrogel induce the fluid sliding state converted into the rolling state. This state transformation reduces the near-wall velocity gradient, and thus promotes the generation of boundary slip. On the other hand, fluorescence particle experiments reveal that there exists water exchange between the inside and outside of the hydrogel. This exchange would promote the relative velocity, and thus strengthens the boundary slip. The present work is expected to make a certain contribution to reveal the drag reduction mechanism of hydrogel.

Divergence of the normalized wall shear stress as an effective computational template of low-density lipoprotein polarization at the arterial blood-vessel wall interface

Background and ObjectiveNear-wall transport of low-density lipoproteins (LDL) in arteries plays a relevant role in the initiation of atherosclerosis. Although it can be modelled in silico by coupling the Navier–Stokes equations with the 3D advection-diffusion (AD) equation, the associated computational cost is high. As wall shear stress (WSS) represents a first-order approximation of the near-wall velocity in arteries, we aimed at identifying computationally convenient WSS-based quantities to infer LDL near-wall transport based on the underlying near-wall hemodynamics in five models of three human arterial districts (aorta, carotid bifurcations, coronary arteries). The simulated LDL transport and its WSS-based surrogates were qualitatively compared with in vivo longitudinal measurements of wall thickness growth on the coronary artery models. MethodsNumerical simulations of blood flow coupled with AD equations for LDL transport and blood-wall transfer were performed. The co-localization of the simulated LDL concentration polarization patterns with luminal surface areas characterized by low cycle-average WSS, near-wall flow stagnation and WSS attracting patterns was quantitatively assessed by the similarity index (SI). In detail, the latter two represent features of the WSS topological skeleton, obtained respectively through the Lagrangian tracking of surface-born particles, and the Eulerian analysis of the divergence of the normalized cycle-average WSS vector field. ResultsConvergence of the solution of the AD problem required the simulation of 3 (coronary artery) to 10 (aorta) additional cardiac cycles with respect to the Navier-Stokes problem. Co-localization results underlined that WSS topological skeleton features indicating near-wall flow stagnation and WSS attracting patterns identified LDL concentration polarization profiles more effectively than low WSS, as indicated by higher SI values (SI range: 0.17–0.50 for low WSS; 0.24–0.57 for WSS topological skeleton features). Moreover, the correspondence between the simulated LDL uptake and WSS-based quantities profiles with the in vivo measured wall thickness growth in coronary arteries appears promising. ConclusionsThe recently introduced Eulerian approach for identifying WSS attracting patterns from the divergence of normalized WSS provides a computationally affordable template of the LDL polarization at the arterial blood-wall interface without simulating the AD problem. It thus candidates as an effective biomechanical tool for elucidating the mechanistic link amongst LDL transfer at the arterial blood-wall interface, WSS and atherogenesis.

Experimental Investigation Into the Effect of a Ceramic Matrix Composite Surface on Film Cooling

Abstract Ceramic matrix composite (CMC) components enable high turbine entry temperatures, which can lead to improved efficiencies in gas turbines. Implementing film cooling over CMC components, similar to how it is employed for conventional metal components, can extend part life and push operating temperatures beyond the temperature capabilities of CMCs alone. However, CMCs have a unique surface topology that can influence film cooling performance. Often this topology takes the form of an irregular wavy pattern due to the weave of the fibers that make up the strengthening component of the composite. In this study, shaped 7–7–7 film cooling holes are embedded in a five-harness-satin weave pattern representative of a CMC, at two orientations of the pattern. Detailed adiabatic film effectiveness measurements are obtained in a wind tunnel using an infrared camera while near-wall flowfield measurements are obtained with a high-speed particle image velocimetry system. A range of blowing ratios between one and three are investigated at a density ratio of 1.5 and freestream turbulence intensities of 0.5% and 13%. Across the majority of the tested conditions, the CMC surfaces result in lower film cooling performance than a smooth surface. At a freestream turbulence intensity of 0.5%, the adiabatic film effectiveness is moderately insensitive to the blowing ratio for both weave orientations. The boundary layer over the CMC surfaces increases the mixing between the coolant and the mainstream through a combination of increased turbulence, reduced near-wall velocities, and a thicker boundary layer.

Visualizing the velocity fields and fluid behavior of a solution using artificial intelligence during EndoActivator activation

Background: Electrical devices driven sonically have been found in several studies to be effective to clean root canals but the effect of the EndoActivator irrigant activation flow behavior on cleaning efficacy is not completely understood. Purpose: The study aimed to provide an initial understanding of flow behavior and velocity field generation during the irrigant activation process by EndoActivator using artificial intelligence (AI). Methods: A straight glass model was filled with a solution containing 17% EDTA. Meanwhile, a medium activator tip with 22-mm polymer noncutting #25, 0.04 file driven by an electrical sonic hand-piece at 190 Hz (highest level) was used to induce velocity field to produce micro-bubbles. The physical mechanisms involved were recorded using a Miro 320S highspeed imaging system, the hydrodynamic responses were recorded, and analyzed using a motion estimation program supported by LiteFlowNet (AI). Results: The rapid fluid flow was visualized clearly in the model when it was activated by an EndoActivator tip. It was also observed that the distal end of the EndoActivator tip generated a near-wall high gradient velocity apically in all directions of the oscillation. Conclusion: The analysis showed that the proposed motion estimation program, supported by LiteFlowNet (AI), was able to capture velocity magnitude estimation of a non-PIV experiment and visualize the bubbles generated in the solution.

Direct numerical simulation of shock-wave/boundary layer interaction controlled with convergent–divergent riblets

In this paper, a section of convergent–divergent (C–D) riblets is applied upstream of a compression ramp in a supersonic turbulent boundary layer in a Mach 2.9 flow with a Reynolds number of Reθ=2240. Direct numerical simulations are undertaken to examine the impact of C–D riblets on the shock wave/boundary layer interaction and the feasibility of using them to mitigate flow separation. Over the riblet section, a large-scale secondary roll mode is produced by C–D riblets with the downwelling motion occurring around the diverging region and upwelling motion near the converging region. This consequently leads to a spanwise heterogeneity in mean quantities and turbulent structures over the riblet section and also in the interaction zone. Compared with the baseline case, the area of the separation zone for the riblet case experiences a dramatic local reduction of 92% in the diverging region, owing to the downwelling motion that injects the high-momentum fluid toward the wall and the near-wall spanwise velocity that transports the low-momentum fluid away. The enhanced upwelling motion around the converging region induced by C–D riblets, on the one hand, contributes to the decrease of the near-wall momentum and subsequently the increase of the local separation area. On the other hand, the upwelling motion effectively reduces the incoming Mach number upstream of the compression corner. This appears to reduce the strength of the separation shock, leading to a more gradual compression of the incoming flow that helps ease the enlargement of the separation area nearby. Overall, the area of the mean flow separation is reduced by 56%, indicating an effective flow separation control by the C–D riblets.

A procedure for computing the spot production rate in transitional boundary layers

The present work describes a method for the computation of the nucleation rate of turbulent spots in transitional boundary layers from particle image velocimetry (PIV) measurements. Different detection functions for turbulent events recognition were first tested and validated using data from direct numerical simulation, and this latter describes a flat-plate boundary layer under zero pressure gradient. The comparison with a previously defined function adopted in the literature, which is based on the local spanwise wall-shear stress, clearly highlights the possibility of accurately predicting the statistical evolution of transition even when the near-wall velocity field is not directly available from the measurements. The present procedure was systematically applied to PIV data collected in a wall-parallel measuring plane located inside a flat plate boundary layer evolving under variable Reynolds number, adverse pressure gradient (APG) and free-stream turbulence. The results presented in this work show that the present method allows capturing the statistical response of the transition process to the modification of the inlet flow conditions. The location of the maximum spot nucleation is shown to move upstream when increasing all the main flow parameters. Additionally, the transition region becomes shorter for higher Re and APG, whereas the turbulence level variation gives the opposite trend. The effects of the main flow parameters on the coefficients defining the analytic distribution of the nucleation rate and their link to the momentum thickness Reynolds number at the point of transition are discussed in the paper.Graphical abstract

An investigation of the near-wall multi-modal turbulent velocity behavior in the boundary layer

In this research study, the dynamical behaviors in the near-wall region within the turbulent boundary layer were investigated using planar Particle Image Velocimetry (PIV) performed over multiple orthogonal planes with respect to the mean flow direction. Flow measurements were performed over a range of Reynolds numbers between Reθ=280 and 1700. The probability density function (PDF) of the stream-wise turbulent velocity field manifested a multi-modal behavior within the buffer layer. This behavior was extensively investigated in the horizontal plane (i.e., the plane parallel to the wall), a perspective of turbulent boundary layer behavior infrequently reported in the literature. The origin of the observed multi-modality was investigated using Proper Orthogonal Decomposition (POD) technique to characterize the dynamical aspects associated with the manifestation of this phenomena. Results indicate that the higher-order POD modes with about 15% of the total energy content and length scales smaller than the Taylor scale, have significantly higher magnitudes of energy dissipation rates, and play a vital role in the manifestation of the multi-modal behavior in the buffer layer. It is hypothesized that the energy exchange processes between large- and small-scale turbulent motions, previously reported only at moderate to high Reθ (Reθ>3000), is responsible for the observed multi-modal behavior at low Reθ (Reθ<2000). The present findings establish a clear link between the manifestation of multi-modality in the turbulent stream-wise velocity field and the energy exchange processes in the near-wall region of the turbulent boundary layer.

On the aerodynamic loads and flow statistics of airfoil with deformable vortex generators

The aerodynamic performances and flow statistics for a Delft University-91-W2-250 airfoil with deformable vortex generators (DVG) were experimentally studied in a wind tunnel across various angle of attacks and wind speeds. A high-resolution force sensor was used to measure the time-averaged lift force, while a planar particle image velocimetry system was applied to characterize the mean velocity and vortex shedding over airfoil surface. The results highlighted that, similar to conventional rigid vortex generators (RVG), DVG can effectively enhance lift coefficient after the stall angle of airfoil with clean surface under low incoming winds. However, the deformation of DVGs increased with the growth of wind speed; this suppressed the effectiveness of wake mixing where the aerodynamic performance of DVGs gradually converged to clean surface configurations. The flow measurements demonstrated that the deformation of DVG can lead to significant decrease in near-wall flow velocities close to the airfoil trailing edge and generate more dispersed vorticity distributions. To further investigate the linkage between DVG deformation and its wake mixing effectiveness, complementary tomographic particle image velocimetry measurements were conducted. The results indicated that the vorticity strength presented monotonic decay with the bending angle of DVG within both near and intermediate wake regions. The capability of DVGs passively adjusts their bending angle, and therefore, the airfoil lift coefficients provide a novel approach to reduce aerodynamic load fluctuations for aircraft within unsteady flows.

On the links between unsteady separation and Nusselt number deterioration during vortex-wall interaction

A CFD study of an axisymmetric vortex ring interacting with a flat, constant-temperature, heated wall is conducted to study the physical nature of the mechanisms leading to deterioration in wall heat transfer due to the unsteady boundary layer separation resulting from vortex-wall interaction. The study utilizes a supplemental computation of a hypothetical flow configuration in which slip is allowed at the heated wall to eliminate separation of the boundary layer during the interaction. Comparison between the physical and hypothetical cases enables “isolation”, and hence understanding of the role of separation in the deterioration of Nusselt number (Nu). It is found that the nature of the near-wall upwash velocity leading to Nu deterioration is fundamentally altered by the presence of spearation. Without separation, the upwash is driven directly by the primary vortex ring. In contrast, with separation, the near-wall upwash is modified significantly by blockage from boundary layer separation and interaction with the secondary vortex ring. The modification is associated with the development of a near-wall “sublayer” that is responsible for the deterioration of Nu independent of the behavior of the overall thermal boundary layer thickness.

Near‐wall velocities of particles suspended in shear flow and a streamwise electric field

Particles with a diameter of ∼0.5µm in a dilute (volume fractions φ∞ <4×10-3 ) suspension assemble into highly elongated structures called "bands" under certain conditions in combined Poiseuille and electroosmotic flows in opposite directions through microchannels at particle-based Reynolds numbers Rep <<1. The particles are first concentrated near, then form "bands" within ∼6µm of, the channel wall. The experiments described here examine the near-wall dynamics of individual "tracer" particles during the initial concentration, or accumulation, of particles, and the steady-state stage when the particles have formed relatively stable bands at different near-wall shear rates and electric field magnitudes. Surprisingly, the near-wall upstream particle velocities are found to be consistently greater in magnitude than the expected values based on the particles being convected by the superposition of both flows and subject to electrophoresis, which is in the same direction as the Poiseuille flow. However, the particle velocities scale linearly with the change in electric field magnitude, suggesting that the particle dynamics are dominated by linear electrokinetic phenomena. If this discrepancy with theory is only due to changes in particle electrophoresis, electrophoresis is significantly reduced to values as small as 20%-50% of the Smoluchowski relation, or well below previous model predictions, even for high particle potentials.

Simultaneous measurement of the structures of the velocity and thermal boundary layers in the rod bundle channel

The complex geometry of the rod bundle fuel assemblies makes the measurement of velocity and temperature difficult, which hinders the design and optimization of the thermohydraulic performance of the advanced fuel assemblies. In the present study, Particle Image Velocimetry (PIV) and Laser-Induced Fluorescence (LIF) techniques are used to simultaneously measure and reconstruct the structures of the velocity and thermal boundary layers. The velocity and temperature distributions near the rod surface under different flow and heat transfer conditions are quantitatively analyzed and compared. The experimental results indicate that increasing the heat flux would increase the near-wall velocity gradient and decrease the temperature gradient. The buoyancy increases with the increase of the heat flux, reducing the turbulent fluctuation in the channel, thereby weakening the generation and diffusion of the turbulent vortex. The dimensionless velocity distribution is obtained by fitting the experimental data to the Spalding formula. Based on the structure of the boundary layer, the increase of buoyancy significantly reduces the proportion of the logarithmic law layer in comparison to the inner layer of the boundary layer. This weakens the convective heat transfer in the channel. The increase of the Reynolds number increases the turbulent fluctuation in the channel and weakens the influence of the buoyancy. Thus, under constant heat flux, the increase of the Reynolds number increases the proportion of the logarithmic law layer in comparison to the inner layer, which enhances the convective heat transfer in the channel.

Predictive models for near-wall velocity and temperature fluctuations in supersonic wall-bounded turbulence

Predictive models for near-wall velocity and temperature fluctuations in compressible wall-bounded turbulence are developed in the present study based on the model proposed by Marusic et al. (Science, vol. 329 (5988), 2010, pp. 193–196), which incorporates the superposition and amplitude modulation effects of the large-scale motions in the outer region on near-wall turbulence. The density variation is involved in the predictive model for velocity fluctuations to achieve Mach number independence. The predictive model for temperature fluctuations is derived to keep its consistency with the strong Reynolds analogy, in which the modulation effect is supposed to be cast as the quadratic function of the large-scale velocity fluctuations. An algebraic method is proposed to directly determine the modulation coefficients and extract the universal signals. A direct numerical simulation (DNS) of turbulent channel flow at the friction Reynolds number of $1170$ and bulk Mach number of $2.88$ is carried out for parameter calibration and validations. The variances and joint probability density functions of the predicted velocity and temperature fluctuations agree well with the DNS results.

Accurate PIV measurement on slip boundary using single-pixel algorithm

To accurately measure the near-wall flow by particle image velocimetry (PIV) is a big challenge, especially for the slip boundary condition. Apart from high-precision measurements, an appropriate PIV algorithm is important to resolve the near-wall velocity profile. In our study, the single-pixel algorithm is employed to calculate the near-wall flow, which is demonstrated to be capable of accurately resolving the flow velocity near the slip boundary condition. Based on synthetic particle images, the advantages of the single-pixel algorithm are manifested in comparison with the conventional window-correlation algorithm. In particular, the single-pixel algorithm has higher spatial resolution and accuracy, and lower systematic error and random error for the case of the slip boundary condition. Furthermore, for experimental verification, micro-PIV measurements are conducted over a liquid–gas interface, and the single-pixel algorithm is successfully applied to the calculation of near-wall velocity under the slip boundary condition, especially negative slip velocity. The current work demonstrates the advantages of the single-pixel algorithm in analyzing complex flows under the slip boundary condition, such as in drag reduction, wall skin-friction evaluation, and near-wall vortex structure measurement.

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.

Near-wall Taylor-series expansion solution for compressible Navier–Stokes–Fourier system

This paper presents the Taylor-series expansion solution of near-wall velocity and temperature for a compressible Navier–Stokes–Fourier system with a no-slip curved boundary surface. When the shear viscosity is a single-valued function of local fluid temperature, the near-wall velocity and temperature are explicitly expressed using the surface quantities including skin friction, surface pressure, surface dilatation, surface heat flux, surface temperature, surface curvature, and their relevant derivatives at the wall. In addition, the wall-normal pressure gradient at the wall is found to be contributed by three physical mechanisms including the skin friction divergence and surface dilatation effect as well as the coupled skin friction and surface heat flux with varying shear viscosity. Furthermore, without losing generality, we derive the near-wall Taylor-series expansion solution for the Lamb vector under the assumption of constant viscosities. Different physical mechanisms that are responsible for initial formation of the Lamb vector in the viscous sublayer are elucidated. The significance of the skin friction divergence and surface dilatation to the near-wall Lamb vector is highlighted.