Velocity Skin Friction Research Articles

Numerical solutions for a compressible dusty fluid flow along a vertical wavy cone

The purpose of this paper is to establish the detailed parametric study for compressible natural convection flow of two-phase dusty fluid along a vertical wavy cone. Typical sinusoidal surface is used to elucidate the heat transport phenomena for the compressible dusty fluid. The governing equations are transformed into parabolic coordinates and the singularity of the leading edge is removed. The resulting equations are then solved straightforwardly by implicit finite difference method. The influence of compressibility, dusty fluid and the transverse curvature of the surface are discussed in detail in terms of local heat transfer rate, skin friction coefficient, velocity and temperature distributions. In order to ensure the accuracy, comparison with some special cases are also presented and the agreement is found to be very good. The key observation from the present study is that the half-cone angle, ϕ, and mass concentration parameter, Dρ, extensively promote the rate of heat transfer into the compressible boundary layer region.

Estimating Sediment Mass Fluxes on Surfaces Sheltered by Live Vegetation

We present a simple model based on already existing and widely used equations for estimating particle mass fluxes on surfaces sheltered by live vegetation. Wind-tunnel measurements of vertical profiles of mass flux in three different dense live plant canopies, and as a function of the spatially averaged skin friction velocity $${u_{\tau }}'$$ , provide the baseline set of data. For the bare-sand surface, the total mass flux Q shows the typical $$b({u_\tau }' - {u_{\tau t}}')^{3 }$$ increase with increasing skin friction velocity $${u_{\tau }}'$$ , where b is a constant and $${u_{\tau t}}'$$ is the threshold at the onset of particle erosion. Similar relations, however, with different values for b and $${u_{\tau t}}'$$ compared to the bare-sand surface were found for experiments with 5.25 and 24.5 plants $$\hbox {m}^{-2}$$ and can be explained by the spatial variations of $$u_{\tau }$$ for the canopy cases. Based on the resulting parameters b and $${u_{\tau t}}'$$ , which are found to be functions of the roughness density $$\lambda $$ , we present a final simple relation $$Q(\lambda ,\, {u_{\tau }}')$$ used for estimating the total mass flux for surfaces sheltered by live vegetation.

Unsteady viscous MHD flow over a permeable curved stretching/shrinking sheet

Purpose The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a uniform magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically. Design/methodology/approach The transformed system of ordinary differential equations was solved using a fourth-order Runge-Kutta integration scheme. Results for the reduced skin friction coefficient and velocity profiles are presented through graphs and tables for several sets of values of the governing parameters. The effects of these parameters on the flow characteristics are thoroughly examined. Findings Results show that for the both cases of stretching and shrinking surfaces, multiple solutions exist for a certain range of the curvature, mass suction, unsteadiness, stretching/shrinking parameters and magnetic field parameter. Originality/value The paper describes how multiple (dual) solutions for the flow reversals are obtained. It is shown that the solutions exist up to a critical value of the shrinking parameter, beyond which the boundary layer separates from the surface and the solution based upon the boundary layer approximations is not possible.

Compressible dusty gas along a vertical wavy surface

This analysis deals with the numerical solutions for the compressible natural convection flow of two-phase dusty gas. In particular, it gives the solutions for the flow having spherical particles suspended in the gas (air) over the surface with sharp lateral curvatures. The governing equations are converted into dimensionless equations by using a set of suitable continuous transformations and solved through the implicit finite difference method. The effect of compressibility, dusty gas and sinusoidal waveform are discussed in detail in terms of local heat transfer rate, skin friction coefficient, velocity and temperature distributions. This investigation reveals the fact that the air–particle mixture reduces the rate of heat transfer, significantly.

Non-uniform mass transfer in MHD mixed convection flow of water over a sphere with variable viscosity and Prandtl number

Purpose The purpose of this paper is to consider axisymmetric mixed convection flow of water over a sphere with variable viscosity and Prandtl number and an applied magnetic field. Design/methodology/approach The non-similar solutions have been obtained from the origin of the streamwise co-ordinate to the point of zero skin friction using quasilinearization technique with an implicit finite-difference scheme. Findings The effect of M is not notable on the temperature and heat transfer coefficient when λ is large. The skin friction coefficient and velocity profile are enhance with the increase of MHD parameter M when λ is small. Viscous dissipation has no significant on the skin friction coefficient under MHD effect. For M=1, the movement of the slot or slot suction or slot injection do not cause any effect on flow separation. The slot suction and the movement of the slot in downstream direction delay the point of zero skin friction for M=0. Originality/value The present results are original and new for water boundary-layer flow over sphere in mixed convection flow with MHD effect and non-uniform mass transfer. So this study would be useful in analysing the skin friction and heat transfer coefficient on sphere of mixed convection flow of water boundary layer with MHD effect.

Direct numerical simulation of the incompressible temporally developing turbulent boundary layer

We perform a direct numerical simulation (DNS) investigation of the incompressible temporally developing turbulent boundary layer. The approach is inspired by temporal simulations of flows which are generally thought of as developing in space, such as wakes and mixing layers. Compressible boundary layers have previously been studied in this manner yet the temporal approach appears to be under-exploited in the literature concerning incompressible boundary layers. The flow is the turbulent counterpart to the laminar Rayleigh problem or Stokes’ first problem, in which a fluid at rest is set into motion by a wall moving at constant velocity. An initial profile that models the effect of a wall-mounted trip wire is implemented and allows the characterisation of initial conditions by a trip Reynolds number. For the current set-up, a trip Reynolds number of 500 based on the trip-wire diameter successfully triggers transition yet only mildly perturbs the flow so it assumes a natural development at the lowest possible Reynolds number based on momentum thickness. A systematic trip study reveals that as the ratio of momentum thickness to trip-wire diameter approaches unity, our flow approaches a state free from the effects of its starting trip Reynolds number. The transport of a passive scalar by this flow is also simulated. The role played by domain size is investigated with two boxes, sized to accommodate two chosen final Reynolds numbers. Comparisons of the skin friction coefficient, velocity and scalar statistics demonstrate that the temporally developing boundary layer is a good model for the spatially developing boundary layer once initial conditions can be neglected. Analysis of similarity solutions suggests such a rapprochement of the spatial and temporal boundary layers may be expected at high Reynolds numbers given that the only terms that asymptotically persist are those common to both cases. If one seeks statistics for the turbulent boundary layer, the temporal boundary layer is therefore a viable method if modest convergence is sufficient. We suggest that such a temporal set-up could prove useful in the study of turbulence dynamics.

Influence of the gap ratio on variations in the surface shear stress and on sand accumulation in the lee of two side-by-side obstacles

Changes in the surface shear stress in the lee of two side-by-side obstacles result in sand deposition and the development of aeolian sand drifts. Through direct wind tunnel measurements using Irwin-type sensors, surface shear stress behind two side-by-side obstacles separated by gaps with different gap ratios (the ratio of the gap spacing between the obstacles to the center-to-center distance for the obstacles) was measured. Particular attention to the effects of the spacing between the two obstacles on the initiation of sand drifts has been paid. The results showed that the gap ratio was the key factor that determined the shear stress patterns. Wind speed increased through the gap, but decreased a short distance downwind, causing higher peak skin-friction velocities and higher shear stress immediately behind the obstacles, producing a range of sand deposition patterns in the sheltered lee side of the obstacles. Comparison of plots of surface shear stress and isoline plots of ψ (for the fraction of the total time in which a given threshold skin-friction velocity was exceeded) with the sand deposition patterns confirmed that sand drift may form in the lee of a gap between two adjacent obstacles when the gap ratio g* ≤ 0.44, and it may disappeared when the gap ratio larger than this value.

An analytical solution of MHD flow of two visco-elastic fluids over a sheet shrinking with quadratic velocity

The steady laminar boundary layer flow of two classes of incompressible visco-elastic and electrically conducting fluids over a nonlinearly shrinking sheet with appropriate wall transpiration under the influence of a magnetic field is analyzed. It is shown that the problem permits an analytical solution of two classes of visco-elastic fluids, namely the second grade fluid and fluid obeying Walters’ liquid B model. The effects of visco-elasticity, suction/blowing parameter and magnetic parameter on both the skin friction parameter and velocity profiles are studied. It is shown that dual solution exists for certain range of physical parameters.

Review of backward-facing step flow and separation reduction

This article reviews the development of research work on backward-facing step flow and separation reduction techniques. Firstly, the effects of inflow conditions and geometry parameters on the bubble length, pressure coefficient, skin friction coefficient, velocity profiles and profiles of Reynolds stresses of the backward-facing step flow are identified. Secondly, we find that the unsteadiness of backward-facing step flow is dominated by shear layer mode and shedding mode, the former including Kelvin-Helmholtz instability, vortex pairing and step mode. Furthermore, the lower-frequency characteristics are consist of shear layer flapping and reattachment oscillating, resulting from the interaction between the coherent structures in the shear layer and the wall. Finally, the flow control practice on the backward-facing step flow has also been discussed. It is found that the recirculating bubble length can be significantly reduced with appropriate excitation frequency in the harmonic excitation practice. The optimum excitation frequency, Sth, is of about 0.2, and a physical explanation is given by the authors.

The streamwise turbulence intensity in the intermediate layer of turbulent pipe flow

The spectral model of Perryet al. (J. Fluid Mech., vol. 165, 1986, pp. 163–199) predicts that the integral length scale varies very slowly with distance to the wall in the intermediate layer. The only way for the integral length scale’s variation to be more realistic while keeping with the Townsend–Perry attached eddy spectrum is to add a new wavenumber range to the model at wavenumbers smaller than that spectrum. This necessary addition can also account for the high-Reynolds-number outer peak of the turbulent kinetic energy in the intermediate layer. An analytic expression is obtained for this outer peak in agreement with extremely high-Reynolds-number data by Hultmarket al. (Phys. Rev. Lett., vol. 108, 2012, 094501;J. Fluid Mech., vol. 728, 2013, pp. 376–395). Townsend’s (The Structure of Turbulent Shear Flows, 1976, Cambridge University Press) production–dissipation balance and the finding of Dallaset al. (Phys. Rev. E, vol. 80, 2009, 046306) that, in the intermediate layer, the eddy turnover time scales with skin friction velocity and distance to the wall implies that the logarithmic derivative of the mean flow has an outer peak at the same location as the turbulent kinetic energy. This is seen in the data of Hultmarket al. (Phys. Rev. Lett., vol. 108, 2012, 094501;J. Fluid Mech., vol. 728, 2013, pp. 376–395). The same approach also predicts that the logarithmic derivative of the mean flow has a logarithmic decay at distances to the wall larger than the position of the outer peak. This qualitative prediction is also supported by the aforementioned data.

Numerical simulation of aerodynamic characteristics of a BWB UCAV configuration with transition models

A numerical simulation for a nonslender BWB UCAV configuration with a rounded leading edge and span of 1.0 m was performed to analyze its aerodynamic characteristics. Numerical results were compared with experimental data obtained at a free stream velocity of 50 m/s and at angles of attack from -4 to <TEX>$26^{\circ}$</TEX>. The Reynolds number, based on the mean chord length, is <TEX>$1.25{\times}106$</TEX>. 3D multi-block hexahedral grids are used to guarantee good grid quality and to efficiently resolve the boundary layer. Menter's shear stress transport model and two transition models (<TEX>${\gamma}-Re_{\theta}$</TEX> model and <TEX>${\gamma}$</TEX> model) were used to assess the effect of the laminar/turbulent transition on the flow characteristics. Aerodynamic coefficients, such as drag, lift, and the pitching moment, were compared with experimental data. Drag and lift coefficients of the UCAV were predicted well while the pitching moment coefficient was underpredicted at high angles of attack and influenced strongly by the selected turbulent models. After assessing the pressure distribution, skin friction lines and velocity field around UCAV configuration, it was found that the transition effect should be considered in the prediction of aerodynamic characteristics of vortical flow fields.

DNS of a Single Low-Speed Streak Subject to Spanwise Wall Oscillations

Direct numerical simulation (DNS) is performed to study the effect of steady streamwise oscillations of the spanwise wall velocity on a single low-speed streak in a laminar boundary layer. The low-speed streak is numerically generated by simulating a screen which creates a momentum loss. The wall oscillations are shown to reduce the skin friction which drops below the laminar Blasius flow value (without the presence of streaks) for certain cases of wall oscillations. In addition, the peak streamwise velocity fluctuation of the streaks are reduced drastically by up to 90 %, the trend in reduction being monotonic with respect to higher amplitude oscillations. The effect of oscillation is also studied during transition (breakdown of the streak) and it is found that the optimum wavenumber of the oscillation changes by nearly an order of magnitude during transition. The reduction of peak streamwise velocity fluctuations shows a phase dependent behaviour which is explained based on the regeneration of turbulence in the absence of a streamwise gradient of the spanwise velocity. The general trend of reduction in streamwise fluctuations across different wavenumbers does not correlate well with the decrease in skin friction. A much better qualitative correlation is found when comparing the relative trends for skin friction and wall-normal velocity fluctuations for different oscillation wavenumbers.

천이효과를 고려한 BWB UCAV 형상의 공력 특성 전산해석

A computational simulation for a nonslender BWB UCAV configuration with rounded leading edge and span of 1.0m was performed to analyze its aerodynamic characteristics. The freestream is 50m/s over –4 to 26 degree A.o.A.s. Reynolds number based on the mean chord length is × . 3D multi block hexahedral grids are used which allow good grid quality and ease to capture boundary layer.  model as well as  SST model is employed to assess the effect of transition for flow behavior. Drag and lift of the UCAV were well predicted while  is under predicted at high angle of attacks and influenced by the turbulence models strongly. After assessing pressure distribution, skin friction lines and velocity field around the UCAV configuration, it was found that transition effect should be considered to enhance the prediction of aerodynamic behavior by a vortical flowfield.

Scaling of the turbulent/non-turbulent interface in boundary layers

AbstractScaling of the interface that demarcates a turbulent boundary layer from the non-turbulent free stream is sought using theoretical reasoning and experimental evidence in a zero-pressure-gradient boundary layer. The data-analysis, utilising particle image velocimetry (PIV) measurements at four different Reynolds numbers ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\delta u_{\tau }/\nu =1200\mbox{--}14\, 500$), indicates the presence of a viscosity dominated interface at all Reynolds numbers. It is found that the mean normal velocity across the interface and the tangential velocity jump scale with the skin-friction velocity$u_{\tau }$and are approximately$u_{\tau }/10$and$u_{\tau }$, respectively. The width of the superlayer is characterised by the local vorticity thickness$\delta _{\omega }$and scales with the viscous length scale$\nu /u_{\tau }$. An order of magnitude analysis of the tangential momentum balance within the superlayer suggests that the turbulent motions also scale with inner velocity and length scales$u_{\tau }$and$\nu /u_{\tau }$, respectively. The influence of the wall on the dynamics in the superlayer is considered via Townsend’s similarity hypothesis, which can be extended to account for the viscous influence at the turbulent/non-turbulent interface. Similar to a turbulent far-wake the turbulent motions in the superlayer are of the same order as the mean velocity deficit, which lends to a physical explanation for the emergence of the wake profile in the outer part of the boundary layer.

Unsteady MHD flow and heat transfer near stagnation point over a stretching/shrinking sheet in porous medium filled with a nanofluid

In this article, the unsteady magnetohydrodynamic (MHD) stagnation point flow and heat transfer of a nanofluid over a stretching/shrinking sheet is investigated numerically. The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using the fourth-order Runge–Kutta method with shooting technique. The ambient fluid velocity, stretching/shrinking velocity of sheet, and the wall temperature are assumed to vary linearly with the distance from the stagnation point. To investigate the influence of various pertinent parameters, graphical results for the local Nusselt number, the skin friction coefficient, velocity profile, and temperature profile are presented for different values of the governing parameters for three types of nanoparticles, namely copper, alumina, and titania in the water-based fluid. It is found that the dual solution exists for the decelerating flow. Numerical results show that the extent of the dual solution domain increases with the increases of velocity ratio, magnetic parameter, and permeability parameter whereas it remains constant as the value of solid volume fraction of nanoparticles changes. Also, it is found that permeability parameter has a greater effect on the flow and heat transfer of a nanofluid than the magnetic parameter.

Stagnation-point Flow and Heat Transfer of a Nanofluid Adjacent to Linearly Stretching/Shrinking Sheet: A Numerical Study

In this study, the steady stagnation point flow and heat transfer of three different types of nanofluid over a linearly shrinking/stretching sheet is investigated numerically. A similarity transformation is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using the fourth-order Runge-Kutta method with shooting technique. The effects of the governing parameters on the nanofluid flow and heat transfer characteristics are analyzed and discussed. Numerical results for the local Nusselt number, skin friction coefficient, velocity profiles and temperature profiles are presented for different values of the solid volume fraction (&phi) and for three different types of nanoparticles (Cu, Al₂O₃ and TiO₂) in stretching or shrinking cases. It is found that the skin friction coefficient and the heat transfer rate at the surface are highest for Cu-water nanofluid compared to the Al₂O₃-water and TiO₂-water nanofluids. Furthermore, it was seen that the effect of the solid volume fraction of nanoparticles on the heat transfer and fluid flow characteristics is more important compared to the type of the nanoparticles.

On the asymptotic state of high Reynolds number, smooth-wall turbulent flows

It is argued that the extrapolation of the log-wake law for the mean turbulent velocity profile to arbitrarily large Reynolds numbers, and also the similarity scaling for the intensity of stream-wise turbulent velocity fluctuations indicated by recent experimental measurements, are consistent with the hypothesis that smooth-wall turbulence is asymptotically transitory in the sense that these fluctuations almost everywhere decay with respect to the outer velocity scale when 1/log (Reτ) ≪ 1, where Reτ is the Reynolds number based on the skin-friction velocity uτ. The existence of one or more near-wall maxima in these turbulent velocity fluctuations whose value may grow with Reτ, does not invalidate the main scaling arguments. At gigantic Reτ, this paradigm suggests that nonlinear motions and “turbulent” energy production are still present immediately adjacent to the wall, but that their amplitude becomes vanishingly small compared to the outer velocity scale.

Approximation approach to multiple singularities of flow through a porous pipe with decelerating wall

The multiple singularity behaviour of flow through a porous pipe with decelerating wall is numerically studied in the present paper. The behaviour of the Riccati equation is introduced as a model problem. Then the steady axisymmetric flow of a viscous incompressible fluid driven along a pipe by the combined effect of the wall deceleration and suction is investigated. Our approach uses the power series in order to observe the instability of the problems. The series is then summed by using various generalizations of the Pade´-Hermite approximants. Analysis based on approximate method suggests that the convergence of the series of stream-function, skin friction and centerline axial velocity in powers of Reynolds number is limited by a number of singularities. The location and nature of the singularities in the real plane are presented. The bifurcations of skin friction and centerline axial velocity are also depicted graphically. DOI: http://dx.doi.org/10.3329/jname.v9i1.9283 Journal of Naval Architecture and Marine Engineering 9(2012) 35-42

Spatially resolved skin friction velocity measurements using Irwin sensors: A calibration and accuracy analysis

This study investigates the accuracy of spatially resolved skin friction velocity uτ measurements using a large number of Irwin sensors (Irwin, 1981). A fast and simple procedure to calibrate the sensors against a two-component hot-film anemometer is introduced which leads to a universal calibration function that can then be used for all sensors. Insignificantly lower accuracies are obtained using the universal calibration function instead of individual calibration functions for each sensor. The overall accuracy of the skin friction velocity measurements averages about ±5% for uτ>0.13ms−1 and decreases strongly to ±20% at lower uτ. The main sources of errors are as follows: (i) deviations from flush mounting of the sensors with the wall surface, (ii) inhomogeneous boundary layers produced in wind tunnels, (iii) pressure transducer inaccuracies, (iv) Irwin sensor geometry variations and (v) Irwin sensor calibration errors. An excellent linear relationship between uτ measured with the Irwin sensors and the free stream velocity as well as the good agreement of Irwin sensor with independent hot-film measurements validate the reliability of the measurement setup. An exemplary measurement of the skin friction velocity distribution around a single wall-mounted rectangular block is presented, discussed and compared to literature and can serve as a test case for simulations.

Spatio-Temporal Surface Shear-Stress Variability in Live Plant Canopies and Cube Arrays

This study presents spatiotemporally-resolved measurements of surface shear-stress τs in live plant canopies and rigid wooden cube arrays to identify the sheltering capability against sediment erosion of these different roughness elements. Live plants have highly irregular structures that can be extremely flexible and porous resulting in considerable changes to the drag and flow regimes relative to rigid imitations mainly used in other wind-tunnel studies. Mean velocity and kinematic Reynolds stress profiles show that well-developed natural boundary layers were generated above the 8 m long wind-tunnel test section covered with the roughness elements at four different roughness densities (λ = 0, 0.017, 0.08, 0.18). Speed-up around the cubes caused higher peak surface shear stress than in experiments with plants at all roughness densities, demonstrating the more effective sheltering ability of the plants. The sheltered areas in the lee of the plants are significantly narrower with higher surface shear stress than those found in the lee of the cubes, and are dependent on the wind speed due to the plants ability to streamline with the flow. This streamlining behaviour results in a decreasing sheltering effect at increasing wind speeds and in lower net turbulence production than in experiments with cubes. Turbulence intensity distributions suggest a suppression of horseshoe vortices in the plant case. Comparison of the surface shear-stress measurements with sediment erosion patterns shows that the fraction of time a threshold skin friction velocity is exceeded can be used to assess erosion of, and deposition on, that surface.