Increase In Boundary Layer Thickness Research Articles

MHD effect of mixed convection boundary-layer flow of Powell-Eyring fluid past nonlinear stretching surface

Sufficient conditions are found for the existence of similar solutions of the mixed convection flow of a Powell-Eyring fluid over a nonlinear stretching permeable surface in the presence of magnetic field. To achieve this, one parameter linear group transformation is applied. The governing momentum and energy equations are transformed to nonlinear ordinary differential equations by use of a similarity transformation. These equations are solved by the homotopy analysis method (HAM) to obtain the approximate solutions. The effects of magnetic field, suction, and buoyancy on the Powell-Eyring fluid flow with heat transfer inside the boundary layer are analyzed. The effects of the non-Newtonian fluid (Powell-Eyring model) parameters ɛ and δ on the skin friction and local heat transfer coefficients for the cases of aiding and opposite flows are investigated and discussed. It is observed that the momentum boundary layer thickness increases and the thermal boundary layer thickness decreases with the increase in ɛ whereas the momentum boundary layer thickness decreases and thermal boundary layer thickness increases with the increase in δ for both the aiding and opposing mixed convection flows.

Nonlinear radiation heat transfer effects in the natural convective boundary layer flow of nanofluid past a vertical plate: a numerical study.

The problem of natural convective boundary layer flow of nanofluid past a vertical plate is discussed in the presence of nonlinear radiative heat flux. The effects of magnetic field, Joule heating and viscous dissipation are also taken into consideration. The governing partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations via similarity transformations and then solved numerically using the Runge–Kutta fourth-fifth order method with shooting technique. The results reveal an existence of point of inflection for the temperature distribution for sufficiently large wall to ambient temperature ratio. Temperature and thermal boundary layer thickness increase as Brownian motion and thermophoretic effects intensify. Moreover temperature increases and heat transfer from the plate decreases with an increase in the radiation parameter.

Melting heat transfer in the stagnation-point flow of Maxwell fluid with double-diffusive convection

Purpose – The purpose of this paper is to analyze the melting heat transfer in the stagnation-point flow with double-diffusive convection. Design/methodology/approach – Series solutions for velocity, temperature and concentration are constructed via homotopy analysis method. Findings – The authors observed that the behaviors of N, ?2 and M on the velocity and boundary layer thickness are qualitatively similar. Further, for A<1 the velocity profile and boundary layer thickness increase with the increase of A. However, when A>1 then the velocity profile increases but the boundary layer thickness decreases when A is increased. Originality/value – This analysis has not been discussed in the literature previously.

Large Eddy Simulation of turbulent vortex-cavitation interactions in transient sheet/cloud cavitating flows

The objectives of this study are to: (1) quantify the influence of sheet/cloud cavitation on the hydrodynamic coefficients and surrounding flow turbulent structures, (2) provide a better insight in the physical mechanisms that govern the dynamics and structure of a sheet/cloud cavity, (3) improve the understanding of the interaction between unsteady cavitating flow, vortex dynamics and hydrodynamic performance. Results are presented for a 3D Clark-Y hydrofoil fixed at an angle of attack of α=8 degrees at a moderate Reynolds number, Re=7×105, for both subcavitating (σ=2.00) and sheet/cloud cavitating conditions (σ=0.80). The experimental studies were conducted in a cavitation tunnel at Beijing Institute of Technology, China. The numerical simulations are performed via the commercial code CFX using a transport equation-based cavitation model, the turbulence model utilizes the Large Eddy Simulation (LES) approach with the Wall-Adapting Local Eddy-viscosity model. The results show that numerical predictions are capable of capturing the initiation of the cavity, growth toward the trailing edge, and subsequent shedding, in accordance with the quantitative features observed in the experiment. The detailed analysis of the vorticity transport equation shows strong correlation between the cavity and vorticity structure, the transient development of sheet/cloud cavitation has significantly changed the interaction between the leading edge and trailing edge vortices, and hence the magnitude as well as the frequency of the hydrodynamic load fluctuations. Compared to the subcavitating case, the sheet/cloud cavitation leads to much higher turbulent boundary layer thickness and substantial increase in velocity fluctuation.

Experimental investigation on the influence of boundary layer thickness on the base pressure and near-wake flow features of an axisymmetric blunt-based body

The influence of the thickness of the boundary layer developing over the surface of an axisymmetric bluff body upon its base pressure and near-wake flow is analyzed experimentally. The model, whose diameter-to-length ratio is d/l = 0.175, has a forebody with an elliptical contour and a sharp-edged flat base; it is supported above a plate by means of a faired strut. The pressure distributions over the body lateral and base surfaces were obtained using numerous pressure taps, while the boundary layer profiles and the wake velocity field were measured through hot-wire anemometry. The tests were carried out at \(Re = u_\infty l/\nu = 5.5\times10^{5}\), at which the boundary layer over the lateral surface of the body becomes turbulent before reaching the base contour. Strips of emery cloth were wrapped in various positions around the body circumference in order to modify the thickness and the characteristics of the boundary layer. The results show that increasing the boundary layer thickness causes a decrease in the base suctions and a corresponding increase in the length of the mean recirculation region present behind the body. In the spectra of the velocity fluctuations measured within and aside the wake, a dominating peak becomes evident in the region downstream of the final part of the recirculation region. The relevant non-dimensional frequency decreases with increasing boundary layer thickness; however, a Strouhal number based on the wake width and the velocity defect at a suitable reference cross section downstream of the recirculation region is found to remain almost constant for the different cases.

Effect of free-stream turbulence on flow characteristics over a transversely-grooved surface

An experimental investigation has been performed to study the free-stream turbulence influence on the flow over a transversely-grooved surface. Free-stream flow at 8.1m/s with turbulence intensities of 0.5% and 4.4% have been provided over smooth and grooved surfaces. Mean velocity profiles, fluctuating velocity moments and turbulence length scales are studied using data obtained from hot-wire anemometry measurements. Introducing quasi-isotropic free-stream turbulence of 4.4% to the flow resulted in fuller velocity profiles, increased boundary layer thickness and significantly augmented streamwise turbulence intensity throughout the boundary layer in flows over both smooth and grooved surfaces. Probability density functions of the velocity fluctuation show that interaction of quasi-isotropic free-stream turbulence with wall turbulence leads to nearly-isotropic turbulence in a small portion of the boundary layer in the near-wall region; while the remaining boundary layer experiences an anisotropic turbulence. In other words, with the introduction of additional turbulence generated by the grooves, the momentum of the fluid particles is increased, resulting in better flow separation resistance. Accordingly, the flow over a grooved surface showed an increase in turbulence intensity, and hence in energy dissipation rate. This is amplified under free-stream turbulence conditions as a result of the interaction of groove-generated turbulence with free-stream turbulence in the boundary layer. The energy cascade span as indicated by the integral to Kolmogorov ratio is also widened by the grooves.

Heat and mass transfer of MHD convective boundary layer flow past a stretching porous wall embedded in a porous medium

The hydromagnetic convective boundary layer flow past a stretching porous wall embedded in a porous medium with heat and mass transfer in the presence of a heat source and under the influence of a uniform magnetic field is studied. Exact solutions of the basic equations of motion, heat and mass transfer are obtained after reducing them to nonlinear ordinary differential equations. The reduced equations of heat and mass transfer are solved using a confluent hypergeometric function. The effects of the flow parameters such as a suction parameter (N), magnetic parameter (M), permeability parameter (Kp), wall temperature parameter (r), wall concentration parameter (n), and heat source/sink parameter (Q) on the dynamics are discussed. It is observed that the suction parameter appears in the boundary condition ensuring the variable suction at the surface. Transverse component of the velocity increases only when magnetic field strength exceeds certain value, but the thermal boundary layer thickness and concentration distribution increase for all values. Results presented in this paper are in good agreement with the work of the previous author and also in conformity with the established theory.

Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet

The effects of thermal radiation on the flow of micropolar fluid and heat transfer past a porous shrinking sheet is investigated. The self-similar ODEs are obtained using similarity transformations from the governing PDEs and are then solved numerically by very efficient shooting method. The analysis reveals that for the steady flow of micropolar fluid, the wall mass suction needs to be increased. Dual solutions of velocity and temperature are obtained for several values of the each parameter involved. For increasing values of the material parameter K, the velocity decreases for first solution, whereas, for second solution it increases. Due to increase of thermal radiation, the temperature and thermal boundary layer thickness reduce in both solutions and also the heat transfer from the sheet enhances with thermal radiation.

SLIP EFFECT ON DIFFUSION OF CHEMICALLY REACTIVE SPECIES IN BOUNDARY LAYER FLOW OVER A VERTICAL STRETCHING SHEET WITH SUCTION OR BLOWING

In the present investigation, we study the effects of slip boundary condition on the diffusion of chemically reactive species in steady boundary layer flow of viscous incompressible fluid over a vertical stretching sheet with suction or blowing. The first-order chemical reaction is considered and wall concentration varies linearly along the sheet. The self-similar equations are obtained using similarity transformations and are solved numerically using shooting method. Our study reveals that due to the increase of diffusion parameter and blowing, the velocity increases, and it decreases with suction, Schmidt number, and reaction rate parameter. Importantly, for increase of slip parameter, the boundary layer thickness increases. In contrast, the concentration at a point increases only for increasing slip and blowing, while it decreases for increase of all other parameters.

Natural convection flow of a non-Newtonian nanofluid between two vertical flat plates

In this research, natural convection of a non-Newtonian copper-water nanofluid between two infinite parallel vertical flat plates is investigated. The basic partial differential equations are reduced to ordinary differential equations which are solved analytically using the differential transformation method. The results obtained using the differential transformation method and those from a numerical method are in good agreement which demonstrates the ability of the differential transformation method to solve such problems. It is shown that as the nanoparticle volume fraction increases, the momentum boundary layer thickness increases, whereas the thermal boundary layer thickness decreases.

Study of choked flows through a convergent nozzle

When sonic nozzles of significantly smaller diameter are used as standard flow meters, the critical back pressure ratio is affected by the boundary layer at the nozzle throat. However, the effect of the boundary layer on choking criteria is still controversial. Then, the choking phenomenon of a convergent nozzle flow has been experimentally investigated using four convergent nozzles with the same diameter followed by a straight pipe of a variable length. As a result, it is shown that the critical back pressure ratio is smaller than that for the steady one-dimensional isentropic flow and decreases as the boundary layer thickness increases. Moreover, the main flow Mach number at the nozzle exit is supersonic when the back pressure ratio is equivalent to the choking condition, and the Mach number increases as the boundary layer thickness increases.

New visions in experimental investigations of a supersonic under-expanded jet into a high subsonic crossflow

A series of experiments was performed to investigate the interaction of an under-expanded axisymmetric supersonic jet exhausted from a flat plate with a high subsonic crossflow. The goal was to study the effect of boundary layer thickness (δ) and jet to freestream dynamic pressure ratio ( J) on flow field pressure distributions. The resulting measurements upstream of the jet showed that with increasing boundary layer thickness, the magnitude of the pressure coefficient decreases, whereas downstream of the jet, the recovery of the back-pressure moved closer to the nozzle exit. Flow field measurements indicated that with increasing boundary layer thickness, the jet plume dissipation rate increased, whereas the strength of the counter-rotating vortex pair (CRVP) did not vary significantly. In addition, it was clearly observed that with increasing J, the CRVP penetrated into the crossflow and the magnitude of the pressure coefficient on the surface upstream and downstream of the jet increased.

Stretching a Curved Surface in a Viscous Fluid

This work is concerned with the viscous flow due to a curved stretching sheet. The similarity solution of the problem is obtained numerically by a shooting method using the Runge–Kutta algorithm. The physical quantities of interest like the fluid velocity and skin friction coefficient are obtained and discussed under the influence of dimensionless curvature. It is evident from the results that dimensionless curvature causes an increase in boundary layer thickness and a decrease in the skin friction coefficient.

Ground Viscous Effect on 2d Flow of Wing in Ground Proximity

:Viscous effect of wing in ground effect in wind tunnel test was investigated numerically. Ground settings in wind tunnel test were simulated by specifying different ground boundary conditions in CFD. It was revealed for fixed-ground based wind tunnel test that: boundary layer developed from the ground deforms effective ground surface and introduces a decreased effective ground clearance; a sharp increase in boundary layer thickness and adverse pressure gradient are captured, which is attributed to deceleration of flow under the leading edge; a separation bubble on ground forms in very small ground clearance and large angle of attack, which helps air flow around the leading edge and delays the stall; measured aerodynamics in fixed-ground based wind tunnel test are not accurate due to ground viscous boundary layer flow; ground viscous flow simulation is of great importance in indepth studies on ground effect. The results obtained will be useful in developing and evaluating wind tunnel tests and studies for wing in ground effect craft.

Numerical analysis of the effect of boundary layer thickness on vortex structures and heat transfer in the wake behind a hill

AbstractThis study presents a three‐dimensional numerical analysis of the effect of boundary layer thickness on vortex structures and heat transfer behind a hill mounted in a laminar boundary layer. When the thickness of the velocity boundary layer is comparable to the hill height, a hairpin vortex is formed symmetrically to the center of the spanwise direction in the wake. A secondary vortex is formed between the legs, and horn‐shaped secondary vortices appear under the concave parts of the hairpin vortex. When the boundary layer thickness increases, the legs and horn‐shaped secondary vortices move toward the center of the spanwise direction, and thus heat transport and heat transfer increase there. At this time, high‐turbulence areas generated locally move toward the center of the spanwise direction with an increase in the boundary layer thickness. With a further increase in the boundary layer thickness, steady streamwise vortices are formed downstream of the hill, but the heat transfer decreases. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20261

핀틀 형상이 추력 크기에 미치는 영향에 대한 수치해석적 연구

본 논문에서는 Fluent의 Spalart-Allmaras 난류모델을 적용하여 연소실 내부에 설치된 핀틀 형상이 핀틀 추진기관 추력 크기에 미치는 영향을 수치해석으로 분석하였다. 핀틀이 존재하면 노즐목을 지나는 질량 유량율은 이론적으로 예측된 값 보다 항상 작았으며, 핀틀 직경이 커질수록 노즐목에서 경계층 두께가 차지하는 비율이 증가되어 노즐목의 질량 유량율이 더욱 감소하였다. 핀틀 직경이 커질수록 핀틀 팁에 나타나는 재순환 영역의 압력에 의한 추력은 증가하지만 노즐 및 연소실 압력에 의한 추력은 감소하여 총 추력은 핀틀 직경이 작은 것 보다 감소하였다. 핀틀 추진기관의 비추력은 큰 차이가 없었다. The effect of pintle shape on the thrust level of pintle-nozzle Solid Rocket Motor(PNSRM) was studied numerically using the Spalart-Allmaras turbulent model of Fluent. Mass flow rate of PNSRM was always less than theoretical value and the extent of decrease in mass flow rate grew in the large pintle because of increase in the relative boundary layer thickness between pintle body and nozzle wall. The bigger pintle size was, the more thrust of pintle tip pressure was obtained. Meanwhile the more thrust of nozzle and chamber pressure decreased. Hence, total thrust of big pintle was less than a small pintle under same throat area condition. Specific impulse was relatively flat for all pintle shape.

UNSTEADY HYDRODYNAMIC AND THERMAL BOUNDARY LAYERS OVER A FLAT PLATE WITH UNIFORM INJECTION OR SUCTION

A computational algorithm for calculating the unsteady compressible and turbulent hydrodynamic and thermal boundary layers over a porous flat plate with uniform suction or injection is developed in the present work. The mathematical modeling involves the derivation of the governing partial differential equations of the problem. These are the continuity, the momentum, the ( κ −ε ) turbulence model and the energy equations. Besides, the perfect gas law and the Sutherland' s law of molecular viscosity are also used. A proper initial and boundary conditions are specified to be used in the solution of the governing equations. A numerical solution of the governing equations is made by using the control volume approach, with non-staggered grid technique and modified SIMPLE algorithm. The numerical solution is capable of calculating the velocity and temperature distributions of the calculation domain, the kinetic energy and dissipation of turbulence, the local and average skin-friction and heat transfer coefficients and Nusselt number, and the hydrodynamic and thermal boundary layers thicknesses. All these parameters are calculated at the transient and steady states. The numerical results show that the developed algorithm is capable of calculating the flow field, properly and accurately. The results show that injection causess light decrease in the temperature inside the thermal boundary layer, a decrease in skin – friction coefficient, a slight increase in the Nusselt number, a decrease in hydrodynamic boundary layer thickness, an increase in thermal boundary layer thickness and an increase in the time required to reach the steady state. Suction almost causes reverse effects.

A simple method for deducing properties of laminar wall jets in uniform pressure fields, with undetermined far-field conditions

A simple method is proposed in order to draw various information concerning boundary layers that develop axisymmetrically on a flat plate, when the outer pressure field is uniform, and when the far-field conditions, perpendicularly to the plate, are unknown. It is shown that if, at an arbitrary radial coordinate r0, one measures both the value of the maximum radial velocity (i.e., Um) and the height (i.e., δ) where the radial velocity reaches its maximum value, one can build a nondimensional number, which we shall call A. This number is an invariant in this study. It also allows us to calculate several parameters, such as, for instance, the local shear rate on the plate or the power laws for the radial velocity decrease and the boundary layer thickness increase, according to the downstream distance, corresponding here to the radial coordinate r.

Stagnation flow towards a shrinking sheet

The stagnation flow towards a shrinking sheet is studied. A similarity transform reduces the Navier–Stokes equations to a set of non-linear ordinary differential equations which are then integrated numerically. Both two-dimensional and axisymmetric stagnation flows are considered. It is found that solutions do not exist for larger shrinking rates and may be non-unique in the two-dimensional case. The non-alignment of the stagnation flow and the shrinking sheet complicates the flow structure. Convective heat transfer decreases with the shrinking rate due to an increase in boundary layer thickness.

Few exact solution of the stokes’ problem with slip at the wall in case of suction/blowing

We provide an analytic solution for the problem of the unsteady, incompressible viscous fluid flow in the case of variable suction/blowing by applying similarity transform; the ‘slip’ condition at the boundary is considered. Several special cases with their solutions are given and are discussed graphically. It is observed that with an increase in suction the velocity increases and hence the boundary layer thickness decreases and with increase in blowing the velocity decreases and boundary layer thickness increases. It is also found that with an increase in slip parameter the velocity decreases.