Increase In Boundary Layer Thickness Research Articles

Control effect on the divergent and convergent riblets in particle-laden turbulent boundary layer

Particle image velocimetry was employed to investigate the impact of convergent–divergent riblets on turbulent boundary layers in both clear water and liquid–solid two-phase flow fields containing 155 μm polystyrene particles. The turbulence statistics such as turbulence intensity and Reynolds stress were investigated. The spatial topology of spanwise vortex head and the development and evolution process of hairpin vortices were explored from Euler and Lagrange perspectives, respectively. Additionally, the particle distribution, concentration, and dispersion within the turbulent boundary layer were statistically analyzed. The results indicated that the boundary layer thickness, friction resistance, integrated turbulence intensity, and Reynolds stress were significantly lower on divergent riblet walls compared to convergent riblet walls. Notably, divergent riblets with a yaw angle of 30° exhibited the best drag reduction effect in both single-phase and two-phase flow fields. The addition of particles resulted in an increase in boundary layer thickness but effectively reduced turbulent fluctuations in the logarithmic region, enhancing drag reduction. This extended the drag reduction range of divergent riblets to a yaw angle of 45°, increasing the maximum drag reduction rate to 26.18%. Through spatial multi-scale local average structure function and finite-time Lyapunov exponent field analysis, it was found that the 30° divergent riblet wall significantly inhibited the development of vortex structures and reduced momentum exchange within the boundary layer. Conversely, the 30° convergent riblet wall had the opposite effect, while the particle phase inhibited the development of all wall turbulent structures. Analysis of particle concentration variations within different regions of the turbulent boundary layer revealed that as the normal height of the boundary layer increased, particle concentration gradually increased, and particle dispersion decreased accordingly. The analysis further showed that particle dispersion was mainly influenced by flow structures, whereas concentration was significantly affected by turbulence intensity. These findings elucidate the effect of the flow field on the particle phase and provide insights into the interaction mechanism between the flow field and particles.

Relaminarization effects in hypersonic flow on a three-dimensional expansion–compression geometry

This experimental work explores the flow field around a three-dimensional expansion–compression geometry on a slender cone at Mach 8 using high-frequency pressure sensors, high-frame-rate schlieren, temperature-sensitive paint, shear-stress measurements and oil-flow visualizations. The $7^\circ$ cone geometry has a hyperbolic slice which acts as an expansion corner and suppresses the disturbances present in the upstream boundary layer. Downstream of the cone-slice corner, high-frequency boundary-layer disturbances attenuate in all cases. Under laminar conditions, second-mode instabilities from the cone diminish and lower-frequency second-mode waves develop on the slice at a frequency commensurate with the increased boundary layer thickness. For fully turbulent cases, the boundary layer over the slice shows evidence of a two-layered nature with a turbulent outer region and a near-wall region with strong attenuation of high-frequency disturbances and reappearance of lower-frequency instability waves. When a downstream compression ramp is added to the slice, the expanded boundary layer shows enhanced susceptibility to separation such that separation is observed at a $10^{\circ }$ deflection, which is smaller than expected for turbulent conditions. For a $30^{\circ }$ ramp, boundary-layer separation occurs further upstream where the heat flux contours show a decrease in heating that is characteristic of a transitional separation. These results demonstrate the effect of relaminarization caused by an upstream expansion on a subsequent shock-wave/boundary-layer interaction.

Influence of the boundary-layer thickness on the generation of tonal noise components by subsonic impinging jets

The influence of the boundary layer (BL) thickness on the tonal noise generated by subsonic impinging jets is investigated. For that, initially laminar jets at Mach numbers $0.6$ and $0.9$ with BL thicknesses $0.05r_0$ , $0.1r_0$ and $0.2r_0$ , where $r_0$ is the pipe-nozzle radius, impinging on a plate at $6r_0$ from the nozzle, are simulated. For Mach number $0.9$ , acoustic tones due to feedback loops of axisymmetric nature between the nozzle and the plate are generated at frequencies that do not vary with the BL thickness. The two dominant tones are, however, $17$ and $26\ \mathrm {dB}$ stronger for the thickest BL compared with the thinnest one. For Mach number $0.6$ , for the thinnest BL no acoustic peaks appear, as observed in the experiments of the literature, but narrow peaks resulting from axisymmetric feedback loops emerge for thicker BLs. Therefore, low subsonic impinging jets can be resonant for specific nozzle-exit conditions. The increase in tone amplitude for Mach number $0.9$ , and the establishment of feedback loops for Mach number $0.6$ with increasing BL thickness, are found to result from two changes in the jet flow. The first change is that the shear-layer laminar–turbulent transition occurs farther downstream for a thicker BL, leading to a greater predominance of the axisymmetric aerodynamic fluctuations near the plate. The second change is that the amplification of the flow fluctuations between the nozzle and the plate at the tone frequencies is stronger for thicker BLs.

NUMERICAL AND EXPERIMENTAL INVESTIGATIONOF STEAM FILM CONDENSATION ON A VERTICAL TUBE

NUMERICAL AND EXPERIMENTAL INVESTIGATIONOF STEAM FILM CONDENSATION ON A VERTICAL TUBE

Bi-directional Forced Convective Stagnation Points Flow of Oldroyd-B Liquid with Joule Heating Effects: A Finite Difference Simulations

The impact of Joule heating for the three-dimensional stagnation point flow of non-Newtonian liquid (namely Oldroyd-B) nanomaterial has been inspected. The influence of mixed convection and the magnetic force is also considered. The flow is induced by the bidirectional stretched surface which moves linearly. The partial differential equations for the developed model are altered into dimensionless statements first. The numerical simulations with the implementation of a finite difference scheme are used for the numerical description. The physical description of parameters is presented against the flow parameters. The results reveal that there is a reverse change in velocity observed for both the relaxation time constant and the retardation constant. Furthermore, the heat transfer rate decreases as the ratio parameter increases. The thickness of the boundary layer increases due to the retardation time and can also be regulated by the application of a magnetic field. An increase in the magnetic parameter leads to an enhancement in temperature and an increase in thermal boundary layer thickness.

Study on the steady-oscillatory transition of three-dimensional (3D) natural convection via Hopf bifurcation

The transition from steady-state flow to periodic oscillatory flow for the natural convection by Hopf bifurcation is investigated in a three-dimensional (3D) cavity. The spectral collocation method (SCM) in combination with the artificial compressibility method (ACM), which is developed by ourselves as a numerical method SCM-ACM with high accuracy, is employed to solve the governing equations directly instead of linear stability analysis method that is commonly used for the research on flow instability. The results show that the amplitude decays exponentially with time and the decay rate is linear with the Grashof number (Gr). The critical Grashof number for steady-oscillatory transition is obtained as Grcr = 3.423 × 106. The dimensionless angular frequency ωcr = 0.24 is also determined by Fourier analysis. In this work, we also examine the heat-momentum interactions within the boundary layers, visualize the periodic oscillations of temperature and velocity amplitudes, and analyze the origin of instability from multiple angles. The results show that large oscillations of velocity and temperature are observed near the isothermal walls. The oscillation is enhanced by the increase of thermal boundary layer thickness and flow velocity at both ends of isothermal walls. The maximum velocity and temperature amplitudes appear at the lower left and upper right corners of the mid-plane (Z = 0.5), where are the origin of instability, and the spanwise walls are almost independent of oscillations. The oscillatory flow of natural convection in three-dimensional cavity originates from the continuously increasing buoyancy force, and its transition occurs by Hopf bifurcation. Moreover, the temperature amplitude exhibits a wavy distribution on the mid-plane (X = 0.5) and strongly depends on the depth Z. These results provide benchmark data for future numerical studies and engineering application.

Computational investigations of the effects of wall surface temperature on a hypersonic inlet isolator

Flow and shock train development in a hypersonic inlet isolator at various wall surface temperatures, Tw, and freestream static temperatures, T?, were studied through numerical simulations. A non-dimensional parameter, Tw /T?, is used to characterize flow behaviors in hypersonic isolator. With the increase of Tw /T?, boundary-layer thickness increases and boundary-layer momentum thickness decreases at the entrance of isolator. Inside the isolator without the presence of backpressure, skin friction decreases with the increase of Tw /T?. The main cause is a lower velocity gradient near the wall at high temperature. A lower skin friction on high wall temperature results in a stronger separation with shock impingement. Under backpressure conditions, with the increase of Tw /T?, an upstream movement of the starting position of the shock train inside the isolator, an increase in the length of the shock train, and an increase in pressure coefficient on the wall surface are observed.

Unsteady Hiemenz Flow of Cu-SiO2 Hybrid Nanofluid with Heat Generation/Absorption

The use of hybrid nanofluid as an alternate heat transfer fluid has shown great potential, and ongoing research to improve its thermal conductivity is important. This study focuses on the impact of heat generation/ absorption on the unsteady Hiemenz flow of aqueous hybrid nanofluid containing copper and silica nanoparticles. Mathematical equations for the hybrid nanofluid model are derived using suitable similarity transformations and solved numerically using bvp4c codes in Matlab software. The results indicate that increased heat generation/absorption leads to an increase in both momentum and thermal boundary layer thickness. The effects of suction and nanoparticle concentration are also analysed and presented graphically. Additionally, a stability analysis is also performed, which discloses that the first solution produced is stable, however, the second solution is not. The findings of this study provide valuable insights into the behaviour of hybrid nanofluid in unsteady flow and can aid in the development of more efficient heat transfer fluids for various engineering applications.

Stagnation point on MHD boundary layer flow of heat and mass transfer over a non-linear stretching sheet with effect of Casson nanofluid

ABSTRACT The present study analyzes the effects of the magnetohydrodynamic stagnation point and Casson fluid flow considered over the stretching surface. Due to the growing need for non-Newtonian nanofluid flows in industry and engineering areas, the present work focuses on the Casson nanofluid flow over a non-linear stretching surface with effects. The Casson nanofluid is more helpful for cooling and friction-reducing agents compared to Newtonian-based nanofluid flow. The mathematical explanation of the problem is elaborated with the help of partial differential equations. The coupled nonlinear form of ordinary differential equations (ODEs) is solved numerically by the Keller-Box method using a suitable MATLAB program. On the effect of the Casson parameter on the velocity parameter, it is observed that for large values of the Casson parameter, the velocity profile decreases. The reason behind this behavior is that increasing the values of the Casson parameter increases the fluid viscosity, i.e. reduces the yield stress. Therefore, the momentum boundary layer thickness reduces and the thermal boundary layer thickness increases.

Critical analysis of generalized Newtonian fluid flow past a non‐linearly stretched curved surface: A numerical solution for Carreau model

AbstractThe underlying intention of the present work is to elaborate the boundary layer flow of Carreau fluid over a non‐linear stretching curved surface. Firstly, we derived the equation of motion for a two‐dimensional curved surface using the Carreau constitutive relation. Employing the well‐known approximations of the boundary layer theory (order of magnitude analysis), the terms of higher and next order have been neglected. We developed an appropriate similarity transformation that reduced the considered partial differential equation into an ordinary differential equation (self‐similar formulation). The MATLAB built‐in function usually known as bvp5c is utilized to get the numerical solution of the considered problem. The impact of the power‐law index (n), Weissenberg number and curvature parameter (k) on velocity profile and skin friction are analyzed through several graphs and tables. The obtained results are also verified by employing the shooting method through Maple software. The results reveal that both boundary layer thickness and velocity profile increase by enlarging the dimensionless curvature parameter of the curved surface.

The influences of boundary layer thickness on the characteristics of saltation sand flow – A large eddy simulation study

In this paper, Large Eddy Simulation (LES) of turbulence and Lagrangian model of sand particle motion are adopted to study the characteristics of wind-blown sand flow for different boundary layer thickness. The simulations are conducted within computational domain height (boundary layer thickness) of δ = 0.5 m, 1 m, 5 m and 12 m, respectively. It is found by comparing the computational results that the mass flux and sand transport rate increase with the increase of boundary layer thickness for the same frictional wind velocity, and the fluctuation of particle velocity and sand transport rate increase significantly too. The spatial scales of particle structure, defined by the correlation of sand particle concentration, significantly increase with δ, so does the time scale of statistical stability of sand transport rate. For two computational domains of δ = 1 m and 12 m, the statistical relative error of sand transport rate reduce to less than 5 % only when the average time goes higher than 45 δ/Ub, where Ub is the bulk fluid velocity. In the context of turbulence, it might take about 10 mins to obtain reliable sand statistics in the neutral atmospheric boundary layer whose boundary layer thickness is about 100–200 m.

Study on the heat transfer enhancement of self-excited oscillating pulsating flow by the boundary vortex group

In this work, the self-excited oscillating pulsating circular pipe is the object of study. Based on the flow evolution characteristics of the boundary layer and vortex, the mechanism of enhanced heat transfer by self-excited oscillating pulsating flow is investigated. Moreover, a vital flow structure, the boundary vortex ring (BVR for short), is proposed. The study results show that the vortex evolution within the shear layer inside the self-excited oscillating pulsating chamber has an important influence on the formation of the downstream boundary vortex ring. Both have the same period but different phases. The boundary vortex group formed by the BVR is distributed at intervals in the pipe, and its role in promoting fluid flow increases first and then decreases. At the same time, the strength of the central mainstream area is gradually strengthened. The boundary vortex group's flow state determines the downstream pipe's heat transfer characteristics. The low-velocity zone on both sides determines the position of the heat transfer coefficient enhancement, and the central vorticity determines the amplitude of the enhancement. The boundary vortex group with a complete structure can effectively promote heat transfer, while the boundary vortex group with an incomplete structure can suppress heat transfer. The time-averaged boundary layer thickness increase ratio δ′ and the time-averaged equal diameter circular tube performance evaluation index ηT provide the fundamental indexes for designing and optimizing variable cross section heat transfer circular tubes. Furthermore, the heat transfer coefficient of the tube wall varies synchronously with the thickness of the boundary layer.

Experimental study of wall temperature effect on shock wave/turbulent boundary layer interaction in hypersonic aircraft

The wall temperature effects on turbulent boundary layer and shock wave/turbulent boundary layer interaction are studied experimentally at Ma 2.7 with wall-to-recovery temperature ratio Tw/Tr from 0.67 to 1.2. The high-resolution turbulent flow structures are captured and analyzed by applying the nano-tracer planar laser scattering and particle image velocimetry techniques. The influence mechanisms of wall temperature on the vortices and interaction flow field are explained. The results indicate that under the heating wall condition, the increase of gas viscosity and volume causes the turbulent boundary layer to develop thicker and faster. The thickness increases 0.79 mm as Tw/Tr increases 0.2. The boundary layer shape presents intermittence with large-scale vortices increasing in size and number. The shock wave interaction point moves 1.43 mm upstream as Tw/Tr increases 0.2 due to the increasing boundary layer thickness. More intensive separation of the boundary layer leads to the height and length extension of the separation region and the increase of the separation shock angle. Under the wall cooling effect, the boundary layer thickness decreases, and the global vorticity reduces. The velocity field becomes more uniform. The present study can provide an important experimental reference for the design of hypersonic aircraft.

A turbulent air‐flow corrugating photovoltaic model to enhance power output

AbstractThis paper investigated the influence of the cooling of turbulent blowing air on the photovoltaic (PV) modules using the corrugation technique. The well‐known five‐parameter diode equation side by side with conservation principles were used to study the effect of corrugating lower PV sides to cool PV's and enhance efficiency. As the main restriction of PV systems is low efficiency that is powerfully counting on its operational temperature, therefore, reducing the operating temperature of PV cells is critical for the PV panel to work. To achieve this aim, a mathematical model describing PV temperatures and efficiency using continuity, momentum, and energy side by side with the Shockley diode equation was built. It was found that the corrugating of lower sides of PV's up to 1 mm in a distance of 20 mm considering turbulent flow conditions considerably reduced temperature and consequently enhanced thermal efficiency from 13% to 15%; the eddy viscosity and Reynolds shear stress increased boundary layer thickness and velocities, so increased the coefficient of heat transfer and consequently electrical power output and thermal efficiency.

Investigation of onset of velocity transition in free convection over an inclined flat plate by PIV

In this work, the experimental investigation of onset of velocity transition in free convection boundary layer over a 45° inclined plate has been carried out. Experiments were performed on a 150 mm long flat plate with uniform heat flux ranging from 100 W/m2 to 5000 W/m2. Particle image velocimetry (PIV) technique was used to determine the flow characteristics over an inclined plate. The impact of various hydrodynamic parameters such as shear stress and velocity boundary layer thickness for defining or identifying the onset of velocity transition has been discussed. Also, the influence of various values of the heat fluxes on the onset of transition has been examined. It has been observed that the initiation of transition is first manifested as an increase in the overall velocity boundary layer thickness. Therefore, the thickness of the velocity boundary layer has been used as a hydrodynamic measure to determine the streamwise distance from the leading edge where the transition begins. This distance decreases with an increase of heat flux. The critical Rayleigh number for the onset of the transition under various heating conditions has been reported. For example, the critical Rayleigh numbers for the beginning of transition at heat fluxes of 100 W/m2 and 5000 W/m2 are 6.07 × 108 and 2.73 × 109 respectively.

Effects of Surface Roughness on Shock-Wave/Turbulent Boundary-Layer Interaction at Mach 4 over a Hollow Cylinder Flare Model

Although it is understood that surface roughness can impact boundary layer physics in high-speed flows, there has been little research aimed at understanding the potential impact of surface roughness on high-speed shock-wave/boundary-layer interactions. Here, a hollow cylinder flare model was used to study the potential impact of distributed surface roughness on shock-wave/boundary-layer interaction unsteadiness. Two surface conditions were tested—a smooth steel finish with an average roughness of 0.85 μm and a rough surface (3K carbon fiber) with an average roughness value of 9.22 μm. The separation shock foot from the shock-wave/boundary-layer interaction on the hollow cylinder flare was tracked by analyzing schlieren images with a shock tracking algorithm. The rough surface increased boundary layer thickness by approximately a factor of 10 compared to the smooth case, significantly altering the interaction scaling. Despite normalizing results, based on this boundary layer scaling, the rough surface case still exhibited mean shock foot positions further upstream more than the smooth surface case. Power spectra of the unsteady shock foot location data demonstrated that the rough surface case exhibited unsteady motion with attenuated energy relative to the smooth-wall case.

A Conservation-Based Transitional Boundary Layer Model

Abstract A simple, flow-physics-based model of flat-plate, transitional boundary layer skin friction and heat transfer is presented. The model is based on the assumption of negligible time-, spanwise-, and streamwise-average wall-normal velocity at the top of the boundary layer. This results in a threefold increase in boundary layer thickness over the transition region. This simple velocity assumption and its boundary-layer growth implications seem to be reasonably consistent with more sophisticated (direct numerical simulation (DNS)) modeling simulations. Only two modeling parameters need to be assumed, the Reynolds numbers at the onset and at the completion of transition, for which there is guidance based on freestream turbulence intensity for smooth plates. Several experimental datasets for air are modeled. New criteria are proposed to help define the onset and completion of transition: zero net vertical (wall-normal) velocity or mass flux (integrated in time and space, spanwise and streamwise) at the top of the boundary layer, and tripling of boundary layer thickness. Also presented is a minor improvement to a previously published unheated starting length factor for flat-plate laminar boundary layers with uniform wall heat flux.

Mathematical analysis about influence of Lorentz force and interfacial nano layers on nanofluids flow through orthogonal porous surfaces with injection of SWCNTs

The effort is presented to numerical examine the flow behavior of non-Newtonian fluid through orthogonal porous surfaces. A two-phase model of nanofluids simulations is considered which represents speculative features of materials that are obliged in biomechanics,lubricantsformation,polymer solution, suspension, etc. The mechanism of interfacial nano layer at surfaces is deliberated through thermal conductivity. Numerical sculpting of non-Newtonian CNT fluid including the impact of chemical reaction, heat flux and mass transfer source is manifested in the form of partial differential equations. Similarity variables are capitalized to transmute governing modeled conservation laws into ordinary non-dimensional expressions. Assessment of flow attributing profiles is disclosed by implementing the Runge-Kutta procedure in collaboration with the shooting method. The numerical stability with convergence rate is also discussed here. Graphical visualization and numerical data about surface drag coefficients and heat and mass transfer rates are also presented. The effect of expansion and contraction (−2 <α < 2) on boundary layer thickness is discussed in detail. The rate of heat transfer increases with the increase of boundary layer thickness in the presence of single-wall carbon nanotubes (SWCNT) is observed. An increase in heat transfer profile due to the presence of SWCNTs with the variation of thickness and radius of sustainable particles is perceived. The nano layer thickness is a significant effect related to the heat transfer rate.

Full-scale ship stern wave with the modelled and resolved turbulence including the hull roughness effect

Stern wave flow phenomena are investigated in a full-scale Kriso container ship. The hull roughness effects are studied with and without propulsion. Reynolds-averaged Navier–Stokes (RANS) and detached eddy simulations (DES) are utilized with the ghost-fluid method (GFM). The DES is carried out with a submodel where a stationary RANS solution is used as a boundary condition. The surface roughness effect on the stern is significant due to the increased boundary layer thickness. The differences in the stern wave shape between RANS and DES become more pronounced with propulsion as DES resolves the turbulence and wave breaking. With the smooth hull, DES indicates transom wetting which RANS does not. For the heavy fouling condition RANS and DES predict a wetted transom. For the smooth hull, the DES results indicate 6.8% higher pressure (2.8% in total) resistance at the transom compared to the corresponding RANS. The resistance of the wetted transom correlates with the velocity change at the transom location. Heavy fouling does not cause pressure resistance although RANS and DES predict a wetted transom. We propose that the increased boundary layer should be taken into account in the after body design.

Effect of incoming boundary layer thickness on the flow dynamics of a square finite wall-mounted cylinder

This paper investigates the flow dynamics around a square finite wall-mounted square cylinder of two different aspect ratios (AR=H/D=6 and 10, H and D are the height and width, respectively) under six boundary layer thickness (δ/D=0.5–4.0, δ is the boundary layer thickness) using the improved delayed detached eddy simulation turbulence model. The Reynolds number based on the square cylinder width and incoming velocity is Re=1.4×104. The aerodynamic force, surface mean and fluctuating pressure, wake closure length, Reynolds stresses, turbulence production, and the anisotropy of turbulence are analyzed in detail to investigate the effect of AR and δ/D combinations. The Q-criterion vortex identification method is adopted to identify and classify the vortex structures of different AR and δ/D combinations. The parametric diagram based on AR and δ/D to predict the dipole/quadrupole wake structure proposed in Yauwenas et al. [“The effect of aspect ratio on the wake structure of finite wall-mounted square cylinders,” J. Fluid Mech. 875, 929–960 (2019)] is refined based on results of the present study (quadrupole wake for AR=6 with δ/D≥1.5 and AR=10 with δ/D≥1.0). The instantaneous space–time pressure distribution along the whole span proves the existence of cellular shedding (AR=10 for δ/D=0.5–2.0), and the spectral proper orthogonal decomposition technique is adopted to investigate the cellular shedding phenomenon and its distribution. With the increase in δ/D from 2.0 to 4.0, the cellular shedding process is absent, implying the inhibitory effect of increasing boundary layer thickness on the cellular shedding.