Wall Skin Friction Research Articles

Nanofluid bioconvection with variable thermophysical properties

Abstract The prime purpose of this analysis is to investigate the effect of variable thermophysical properties of nanofluid on bioconvection boundary layer flow along a uniformly heated vertical cone. The governing equations with associated boundary conditions for this phenomenon are converted into a non-dimensional form via continuous transformations, which are then solved by using the implicit finite difference method. How does the phenomena of heat transfer is effected due to the temperature-dependent thermophysical properties of the fluid is the question investigated in this manuscript. Comprehensive numerical computations are carried out for a wide range of the parameters that are describing the flow characteristics. The influence of the physical parameters on the distribution of velocity and temperature profiles, wall skin friction and local rate of heat transfer is explored. Comparison with some special cases is also done and good agreement is found. It is recorded that the variable thermophysical properties of the fluid are more likely to promote the rate of heat transfer, Qw as compared to fluid having constant properties.

MHD boundary layer slip flow of a casson fluid over an exponentially stretching surface in the presence of thermal radiation and chemical reaction

An analysis is carried out to investigate the steady two-dimensional magnetohydrodynamic boundary layer flow of a Casson fluid over an exponentially stretching surface in the presence of thermal radiation and chemical reaction. Velocity, thermal and solutal slips are considered instead of no-slip conditions at the boundary. Stretching velocity, wall temperature and wall concentration are considered in the exponential forms. The non-linear partial differential equations are converted into a system of non-linear ordinary differential equations by similarity transformations. The resultant non-linear ordinary differential equations are solved numerically by fourth order Runge-Kutta method along with shooting technique. The influence of various parameters on the fluid velocity, temperature, concentration, wall skin friction coefficient, the heat transfer coefficient and the Sherwood number have been computed and the results are presented graphically and discussed quantitatively. Comparisons with previously published works are performed on various special cases and are found to be in excellent agreement.

DNS Analysis of Wall Heat Transfer and Combustion Regimes in a Turbulent Non-premixed Wall-jet Flame

Understanding the heat-release effects on the wall heat transfer in turbulent reacting flows, i.e. heat transfer with or without significant density variation, is essential for a wide variety of industrial flows, especially combustion problems. The present study focuses on the wall heat transfer and the near-wall reaction characteristics. The heat-release effects on the wall heat transfer and skin-friction coefficients are investigated using three-dimensional direct numerical simulations of a turbulent reacting wall-jet flow with and without heat release. Reductions in the skin-friction coefficient are observed in the exothermic case, compared to the isothermal one, and the underlying mechanism is explained. The absolute wall heat flux also increases, while the corresponding Nusselt number decreases with increasing heat release. Furthermore, the wall effects on the near-wall average burning rate are assessed. It is found that the isothermal cold wall results in an appreciable decrease of the burning rate in the exothermic cases. We observed indications that the wall increases the chances for the development of the premixed mode and its occurrence is very fast in the wall-normal direction.

Stagnation Point Flow of a Williamson Fluid over a Nonlinearly Stretching Sheet with Thermal Radiation

The present analysis deals with the study of stagnation point flow of a Williamson fluid over a nonlinearly stretching sheet with thermal radiation. The partial differential equations governing this phenomenon were transformed into coupled nonlinear ordinary differential equations with suitable similarity transformations. These equations were then solved by numerical technique known as Keller Box method. The various parameters such as Prandtl number (Pr), velocity ratio parameter( �), Williamson parameter ( λ) and Radiation parameter (R) and non linear stretching parameter (n) determining the velocity and temperature distributions, the local Skin friction coefficient and the local Nusselt number governing such a flow were also analyzed. On analysis it was found that the Williamson fluid parameter ( λ) decreased both the fluid velocity whereas an increase in ( λ) increased wall skin-friction coefficient. The wall temperature gradient increased with an increase in Pr but decreased with radiation parameter R.

Surface capillary currents: Rediscovery of fluid-structure interaction by forced evolving boundary theory

Any boundary surface evolving in viscous fluid is driven with surface capillary currents. By step function defined for the fluid-structure interface, surface currents are found near a flat wall in a logarithmic form. The general flat-plate boundary layer is demonstrated through the interface kinematics. The dynamics analysis elucidates the relationship of the surface currents with the adhering region as well as the no-slip boundary condition. The wall skin friction coefficient, displacement thickness, and the logarithmic velocity-defect law of the smooth flat-plate boundary-layer flow are derived with the advent of the forced evolving boundary method. This fundamental theory has wide applications in applied science and engineering.

MHD Stagnation Point Flow of a Casson Fluid over a Nonlinearly Stretching Sheet with Viscous Dissipation

Study to analyze the MHD stagnation point flow of a Casson fluid over a nonlinearly stretching sheet with viscous dissipation was carried out. The partial differential equations governing this phenomenon were transformed into coupled nonlinear ordinary differential equations with suitable similarity transformations. These equations were then solved by finite difference technique known as Keller Box method. The various parameters such as Prandtl number (Pr), Eckert number (Ec), Magnetic parameter (M), Casson parameter (β) and non linear stretching parameter (n) determining the velocity and temperature distributions, the local Skin friction coefficient and the local Nusselt number governing such a flow were also analyzed. On analysis it was found that the Casson fluid parameter (β) decreased both the fluid velocity and temperature whereas an increase in (β) increased both the heat transfer rate and wall skin-friction coefficient.

Improved k–ω–γ model for hypersonic boundary layer transition prediction

Two improvements of the k–ω–γ transition model have been developed in this paper. One is reformulating the γ transport equation to retain the physical information contained in the empirical correlations of Dhawan and Narasimha; the other is modifying the timescale of the second-mode to improve the prediction accuracy of nose bluntness effects. Test cases including a supersonic flat plate, a straight cone at different Reynolds numbers, and straight cones with different nose bluntness are employed to assess the performance of the improved k–ω–γ transition model. It is demonstrated that both the original and improved k–ω–γ transition models can predict the correct trends of transition onsets with respect to Reynolds number and nose bluntness effects for hypersonic flow. The reasons for this have also been investigated. Compared with the original k–ω–γ transition model, the improved k–ω–γ transition model with reformulated γ transport equation can provide more accurate transition onsets at different Reynolds numbers, but not quite accurate transition onsets for different nose bluntness; while the improved k–ω–γ transition model with modified second-mode timescale can provide more accurate transition onsets for different nose bluntness. However, both the original and improved k–ω–γ transition models fail to predict the overshoot in wall skin friction and heat transfer observed in DNS and experimental results.

二次元オフセット噴流の流動特性と熱伝達

The flow field of an offset jet is complex and is frequently found in many engineering devices. In this paper, the fluid flow and heat transfer characteristics of two-dimensional offset jet are investigated experimentally. The offset jet is produced by the flow of air which issue from the end of a long parallel channel. The exit Reynolds number Re is changed in 1.5×103 to 7.0×103, and the offset ratio H/h (H : step height, h : channel height) is changed in 0.5, 1.0 and 1.5. The wall shear stress is measured using a micro flow sensor. Flow visualization is carried out using a CCD camera and laser light. The velocity profiles are measured by a PIV system. When the flow at the channel exit is laminar, fluid in the outer region has a counter-clockwise vorticity and fluid in the inner region has a clockwise vorticity, and a lifting-off of the wall jet flow into the ambient fluid is occurred. The Strouhal number of the vortex frequency is almost constant against the offset ratio. The formation of those vortices is not seen at the turbulent flow. Two peaks exist in the wall static pressure, Nusselt number and skin friction coefficient distributions of the laminar flow with H/h = 0.5 and 1.0. The 1st peak appears near the reattachment point, and the 2nd peak appears in the neighborhood of the lifting-off of the wall jet flow. The two peaks coalesce into one at H/h = 1.5. As the offset ratio increases, the reattachment point moves to downstream direction and Nu becomes large both the laminar and turbulent flows. The reattachment point of the turbulent flow moves to upstream direction compared with the laminar flow because Coanda-effect is strengthen.

Computational study of supersonic flow past non-stationary obstructions part-I - moving ramp

For an upward moving ramp, compression waves of progressively increasing strengths emanate from the ramp surface and eventually coalesce into an oblique shock. A lag in wall pressure build up relative to fixed ramp values is observed which depends on ramp angle and angular velocity in a direct fashion. For an oscillating ramp, wall pressure response to varying ramp angles displays a hysteretic behaviour. Compressive/expansive effects generated during the ramp's upward/downward motions persist after the ramp changes its direction. Lags are observed during both wall pressure build up and relaxation which exhibit a similar dependence to ramp angle and angular velocity as in case I. The effect of ramp motion on boundary layer (thinning/thickening during upward/downward motions) is explained on the basis of fluid inertia and is reflected in increasing/decreasing velocity gradients inside the boundary layer. This in turn affects wall skin friction and temperature distributions inside the boundary layer.

Investigation of low-dissipation monotonicity-preserving scheme for direct numerical simulation of compressible turbulent flows

The influence of numerical dissipation on direct numerical simulation (DNS) of decaying isotropic turbulence and turbulent channel flow is investigated respectively by using the seventh-order low-dissipation monotonicity-preserving (MP7-LD) scheme with different levels of bandwidth dissipation. It is found that for both benchmark test cases, small-scale turbulence fluctuations can be largely suppressed by high level of scheme dissipation, while the appearance of numerical errors in terms of high-frequency oscillations could destabilize the computation if the dissipation is reduced to a very low level. Numerical studies show that reducing the bandwidth dissipation to 70% of the conventional seventh-order upwind scheme can maximize the efficiency of the MP7-LD scheme in resolving small-scale turbulence fluctuations and, in the meantime preventing the accumulation of non-physical numerical errors. By using the optimized MP7-LD scheme, DNS of an impinging oblique shock-wave interacting with a spatially-developing turbulent boundary layer is conducted at an incoming free-stream Mach number of 2.25 and the shock angle of 33.2°. Simulation results of mean velocity profiles, wall surface pressure, skin friction and Reynolds stresses are validated against available experimental data and other DNS predictions in both the undisturbed equilibrium boundary layer region and the interaction zone, and good agreements are achieved. The turbulence kinetic energy transport equation is also analyzed and the balance of the equation is well preserved in the interaction region. This study demonstrates the capability of the optimized MP7-LD scheme for DNS of complex flow problems of wall-bounded turbulent flow interacting with shock-waves.

Accurate measurement of wall skin friction by single-pixel ensemble correlation

The present work deals with accurately estimating wall-skin friction from near-wall mean velocity by means of PIV measurement. The estimation accuracy relies on the spatial resolution and the precision of the resolved velocity profile inside the viscous sublayer, which is a big challenge for conventional window-based correlation method (Kahler C J, et al. Exp Fluids, 2012, 52: 1641–1656). With the help of single-pixel ensemble correlation, the ensemble-averaged velocity vector can be resolved at significant spatial resolution, thus improving the measurement accuracy. To demonstrate the feasibility of this single-pixel ensemble correlation method, we first study the velocity estimation precision in a case of steady near-wall flow. Synthetic particle images are used to investigate the effect of different image parameters. It is found that the velocity RMS-uncertainty level of the single-pixel ensemble correlation method can be equivalent to the conventional window correlation method once the effective particle number used for the ensemble correlation is large enough. Furthermore, a canonical turbulent boundary layer is synthetically simulated based on velocity statistics resolved by previous Direct Numerical Simulation (DNS) work (Schlatter P, et al. J Fluid Mech, 2010, 659: 116–126). The relative error of wall skin friction coefficient is shown to be one-order smaller than that of the window correlation method. And the optimization strategy to further minimize the measurement uncertainty is discussed in the last part.

Three measuring techniques for assessing the mean wall skin friction in wall-bounded flows

The present paper aims at evaluating the mean wall skin friction data in laminar and turbulent boundary layer flows obtained from two optical and one thermal measuring techniques, namely, laser-Doppler anemometry (LDA), oil-film interferometry (OFI), and surface hot-film anemometry (SHFA), respectively. A comparison among the three techniques is presented, indicating close agreement in the mean wall skin friction data obtained, directly, from both the OFI and the LDA near-wall mean velocity profiles. On the other hand, the SHFA, markedly, over estimates the mean wall skin friction by 3.5–11.7% when compared with both the LDA and the OFI data, depending on the thermal conductivity of the substrate and glue material, probe calibration, probe contamination, temperature drift and Reynolds number. Satisfactory agreement, however, is observed among all three measuring techniques at higher Reynolds numbers, Rex>106, and within ±5% with empirical relations extracted from the literature. In addition, accurate velocity data within the inertial sublayer obtained using the LDA supports the applicability of the Clauser method to evaluate the wall skin friction when appropriate values for the constants of the logarithmic line are utilized.

Computational study of a turbulent wall jet flow on an oblique surface

Purpose – The purpose of the present study is to investigate the flow and turbulence characteristics of a turbulent wall jet flowing over a surface inclined with the horizontal and to investigate the effect of variation of the angle of inclination of the wall on the flow structure of the wall jet. Design/methodology/approach – The high Reynolds number two-equation κ− model with standard wall function is used as the turbulence model. The Reynolds number considered for the present study is 10,000. The Reynolds averaged Navier-Stokes (RANS) equations are used for predicting the turbulent flow. A staggered differencing technique employing both contravariant and Cartesian components of velocity has been applied. Results for distribution of wall static pressure and skin friction, decay of maximum streamwise velocity, streamwise variation of integral momentum and energy flux have been compared for the cases of α=0°, 5°, and 10°. Findings – Flow field has been represented in terms of streamwise and lateral velocity contours, static pressure contour, vorticity contour and streamwise velocity and static pressure profiles at different locations along the oblique offset plate. Distribution of Reynolds stresses in terms of spanwise, lateral and turbulent shear stresses, and turbulent kinetic energy and its dissipation rate have been presented to describe the turbulent characteristics. Similarity of streamwise velocity and the velocity parallel to the oblique wall has been observed in the developed region of the wall jet flow. A decaying trend is observed in the variation of total integral momentum flux in the developed region of the wall jet which becomes more evident with increase in oblique angle. Developed flow region has indicated trend of similarity in profiles of streamwise velocity as well as velocity component parallel to the oblique wall. A depression in wall static pressure has been observed near the nozzle exit when the wall is inclined and the depression increases with increase in inclination. Effect of variation of oblique angles on skin friction coefficient has indicated that it decreases with increase in oblique angle. Growth of the outer and inner shear layers and spread of the jet shows linear variation with distance along the oblique wall. Decay of maximum streamwise velocity is found to be unaffected by variation in oblique angle except in the far downstream region. The streamwise variation of spanwise integral energy shows increase in oblique angle and decreases the magnitude of energy flux through the domain. In the developed flow region, streamwise variation of centreline turbulent intensities shows increased values with increase in oblique angle, while turbulence intensities along the jet centreline in the region X<12 remain unaffected by change in oblique angles. Normalized turbulent kinetic energy distribution highlights the difference in turbulence characteristics between the wall jet and reattached offset jet flow. Near wall velocity distribution shows that the inner region of boundary layer of the developed oblique wall jet follows a logarithmic profile, but it shows some difference from the standard logarithmic curve of turbulent boundary layers which can be attributed to an increase in skin friction coefficient and a decrease in thickness of the wall attached layer. Originality/value – The study presents an in-depth investigation of the interaction between the jet and the inclined wall. It is shown that due to the Coanda effect, the jet follows the nearby wall. The findings will be useful in the study of combined flow of wall jet and offset jet and dual offset jet on oblique surfaces leading to a better design of some mechanical jet flow devices.

A study on turbulence transportation and modification of Spalart–Allmaras model for shock-wave/turbulent boundary layer interaction flow

It is of great significance to improve the accuracy of turbulence models in shock-wave/boundary layer interaction flow. The relationship between the pressure gradient, as well as the shear layer, and the development of turbulent kinetic energy in impinging shock-wave/turbulent boundary layer interaction flow at Mach 2.25 is analyzed based on the data of direct numerical simulation (DNS). It is found that the turbulent kinetic energy is amplified by strong shear in the separation zone and the adverse pressure gradient near the separation point. The pressure gradient was non-dimensionalised with local density, velocity, and viscosity. Spalart–Allmaras (S–A) model is modified by introducing the non-dimensional pressure gradient into the production term of the eddy viscosity transportation equation. Simulation results show that the production and dissipation of eddy viscosity are strongly enhanced by the modification of S–A model. Compared with DNS and experimental data, the wall pressure and the wall skin friction coefficient as well as the velocity profile of the modified S–A model are obviously improved. Thus it can be concluded that the modification of S–A model with the pressure gradient can improve the predictive accuracy for simulating the shock-wave/turbulent boundary layer interaction.

Numerical study of turbulent wall jet over multiple-inclined flat surface

In the present work flow field of a turbulent oblique wall jet with multiple flat inclined wall has been numerically investigated. The Reynolds averaged Navier–Stokes (RANS) equations for incompressible flow are solved in transformed geometry using boundary-fitted coordinate system. The aim of the work is to investigate the influence of three inlet conditions: uniform, parabolic and trapezoidal inlet velocity profiles, on the mean flow and turbulent characteristics of the jet flowing tangentially along a multiple inclined solid wall. The results show that the inlet conditions affect the flow in the vicinity of the nozzle exit area and also the far field region. Mean flow has been presented in terms of evolution of mean velocity profiles, jet spread, decay of streamwise maximum velocity, distribution of wall pressure and skin friction coefficients, and streamwise variations of integrated momentum and energy fluxes. Discontinuities in the boundary slope of the segmented wall produces oscillations in distribution of skin friction and pressure coefficients. Reduced pressure in the region of wall discontinuity appeared to be causing the deflected jet to remain attached to the wall. The growth of the inner layer of the jet is relatively high with uniform inlet velocity profiles in the near-field region, but in the far-field region the inner layer grows with higher rate for the trapezoidal and the parabolic profiles. The rate of decay of maximum streamwise velocity for oblique wall jet on segmented wall is higher than that of plane wall jet. The jet with parabolic and trapezoidal inlet profiles show higher rate of decay than that with a uniform inlet profile. Similarity of streamwise velocity and velocity component parallel to the oblique wall has been observed in the developed region of flow. The volume flow rate of the jet varies linearly along the flow direction due to entrainment of the fluid from the surrounding. Sudden change in slope of the wall causes a sharp rise in entrained volume of fluid. The distribution of near wall velocity in the inner coordinates of the boundary layer is grossly altered and the profiles do not conform to the universal velocity profiles in the form of the law of the wall. Relatively higher position of defect law data signifies comparatively lower turbulence in the outer mixing layer. Cross-stream distribution of Reynolds stresses shows that the effect of inlet velocity profiles is more pronounced in the near field region of flow. Self-similarity is observed in the normalized turbulent shear stress profiles whereas considerable scatter can be noticed in the profiles of turbulent normal stresses for all the inlet velocity conditions. Two distinct peaks in the normalized turbulent kinetic energy profiles characterize the two shear layers of the jet and shifting of the outer peak toward the wall suggests a strong interaction of the outer layer with the inner layer as the jet develops.

Shock wave boundary layer interactions in hypersonic flows

Shock-wave boundary layer interaction (SWBLI) and associated changes in wall properties for ramp induced flow breakdown have been considered in the present studies. A two dimensional finite volume based CFD solver has been developed and implemented successfully to study the SWBLI. Pressure measurements are invariantly considered in the literature for qualitative prediction of various SWBLI parameters. Hence efforts are made herewith to understand the laminar boundary layer separation in the presence of ramp induced shock wave through surface heat transfer rates, wall skin friction coefficient and wall pressure distributions. Effect of variation of freestream and wall properties along with geometric changes is considered in present studies. It has been observed from present limited investigations that ratio of wall temperature to freestream stagnation temperature is the governing parameter for SWBLI instead of the individual temperatures. Increase in Mach number is found to suppress the upstream influence which results in decrease in extent of separation. Efforts are also made to study the effect of leading edge bluntness on the SWBLI. These studies are found useful to confirm the earlier reported experimental observations regarding turbulent re-attachment.

MHD Stagnation-Point Flow of Casson Fluid and Heat Transfer over a Stretching Sheet with Thermal Radiation

The two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of electrically conducting non-Newtonian Casson fluid and heat transfer towards a stretching sheet have been considered. The effect of thermal radiation is also investigated. Implementing similarity transformations, the governing momentum, and energy equations are transformed to self-similar nonlinear ODEs and numerical computations are performed to solve those. The investigation reveals many important aspects of flow and heat transfer. If velocity ratio parameter (B) and magnetic parameter (M) increase, then the velocity boundary layer thickness becomes thinner. On the other hand, for Casson fluid it is found that the velocity boundary layer thickness is larger compared to that of Newtonian fluid. The magnitude of wall skin-friction coefficient reduces with Casson parameter (β). The velocity ratio parameter, Casson parameter, and magnetic parameter also have major effects on temperature distribution. The heat transfer rate is enhanced with increasing values of velocity ratio parameter. The rate of heat transfer is enhanced with increasing magnetic parameter M for B > 1 and it decreases with M for B < 1. Moreover, the presence of thermal radiation reduces temperature and thermal boundary layer thickness.

Divergence-free turbulence inflow conditions for large-eddy simulations with incompressible flow solvers

Synthetic turbulence for inflow conditions formulated on a 2-D plane generally produces unphysically large pressure fluctuations in direct numerical and large-eddy simulations. To reduce such artificial fluctuations a divergence-free method is developed with incompressible flow solvers. The procedure of the velocity–pressure solvers is slightly modified on a vertical plane near (rather than at) the inlet by inserting the synthetic turbulence on that plane during the procedure. Simple analytic and numerical error estimations are used to show that the impact of the modified solvers on solution accuracy is small. The final synthetic turbulence satisfies the divergence-free condition. No additional CPU time is required to achieve this condition. The method was tested via simulations of a plane channel flow with Reτ=395. Reynolds stresses, wall skin friction and power spectra of velocity fluctuations are compared with those obtained from using periodic inlet–outlet boundary conditions. In particular, the variances and power spectra of pressure fluctuations are shown to be accurately predicted only when the divergence-free inlet condition is used.

Predicting Rough Wall Heat Transfer and Skin Friction in Transitional Boundary Layers—A New Correlation for Bypass Transition Onset

This paper summarizes the experimental results of a comprehensive study on the heat transfer and aerodynamic losses of a highly loaded turbine blade with surface roughness. A few hundred test cases conducted at several Reynolds numbers, freestream turbulence levels, and different deterministic roughness geometry have been examined. Some of these results have been published in two previous papers, showing a strong effect of roughness on laminar-turbulent bypass transition on the airfoil suction side. Beside roughness height, roughness anisotropy has turned out to be one of the major influencing factors. The airfoil heat transfer distribution of these measurements is used for detecting the transition onset. Additionally, further transition onset data from the literature is reevaluated. Thus, important roughness (geometry) parameters are identified and a new correlation for the transition onset is deduced, including roughness parameters along with freestream turbulence. Moreover, a method to extract the relevant roughness parameters from realistic surface roughness is presented. Additional heat transfer and aerodynamic measurements are conducted for two different real surface roughness types. Calculations with a 2D-boundary layer code on these surfaces are presented in order to validate the new model.

Comparison of Different Wall Boundary Treatments for Preconditioning Method Coupled with Building-cube Method

Preconditioning method developed by the authors was coupled with Building-Cube Method (BCM). Wall boundary treatment is a critical issue for Building-Cube Method as a Cartesian mesh method. In the paper, the classical case, flow past a cycle cylinder at low Reynolds number is used, with three different boundary treatments tested: direct data transfer, staircase treatment and immersed boundary method (IBM). Also, two sets of numerical simulations with different number of grid points are conducted to assess the sensitivity of the three schemes to grid density. The numerical results of separation vortex length, pressure coefficient distribution and wall skin friction coefficient distribution are derived and compared with those existing experimental and numerical data sets. Comparison shows that immersed boundary method is a best choice of the three schemes, in both boundary orientation and pressure/velocity estimation. Moreover, immersed boundary method is also proved to be less sensitive to grid density than the other two, since the accuracy loss of immersed boundary method case with less grid points is much less.