Incompressible Boundary Layer Research Articles

Combined Blowing/Suction Flow Control on Low-Speed Airfoils

The paper focuses on the application of the blowing/suction technique to control incompressible turbulent boundary layer on 2-D low-speed airfoils. Analysis of the experimental and numerical results obtained with the combined flow control technique through the high-technological perforated sections is carried out. This control method turns out to be a more effective way to improve aerodynamic performance of airfoil compared to isolated forcing. Such technology allows us in the studied conditions to provide an effect, characterized by an increase in the airfoil lift and, ultimately, an increment in lift-to-drag ratio ΔK/Kmax by about 0.06. For all combinations of the control forcing, the simplified mechanism responsible for changes in the airfoil aerodynamic performances is almost identical: the pressure increases due to blowing on one side of the airfoil and decreases due to suction on the opposite side, thus, leading to enhancement of the lift force and, as a consequence, to a gain in the lift-to-drag ratio. Also evaluation of the efficiency of the considered control technique with allowance for energy expenses is given.

Analytical study of joint heat transfer between a gasdynamic boundary layer and an anisotropic strip

When solving the problems of coupled heat transfer between viscous flows and streamlined bodies under the conditions of aerodynamic heating of aircraft, it is necessary to overcome significant difficulties. They associated primarily with determining the boundary conditions. The paper investigates the joint (coupled) heat transfer between a heat and gas dynamic boundary layer and an anisotropic strip under conditions of aerodynamic heating based on the obtained analytical solution of the second initial boundary value problem of thermal conductivity in an anisotropic strip with arbitrary boundary conditions. Since the system of equations of the gasdynamic boundary layer is essentially nonlinear, mainly numerical methods are used to solve it. For an incompressible boundary layer near the critical point of a blunt wedge, an analytical solution is obtained to determine the components of the velocity vector, density, temperature, and heat fluxes. The closed-form solution to the conjugate problem was received in the form of a Fredholm integral equation of second kind. The results of numerical experiments are obtained and analyzed.

Inviscid Instability of an Incompressible Boundary Layer on a Compliant Surface

The instability of an incompressible boundary layer on a compliant plate with respect to inviscid perturbations is analyzed on the basis of triple-deck theory. It is shown that unstable inviscid perturbations persist only if the inertia of the plate is taken into account. It is found that an important role is played by the bending stiffness of the plate. Specifically, as it approaches a certain value, the instability can become arbitrarily high, but, with a further increase in the bending stiffness, it vanishes completely as soon as the bending stiffness reaches a threshold value.

Analysis of the factors contributing to the skin friction coefficient in adverse pressure gradient turbulent boundary layers and their variation with the pressure gradient

This paper reports on a study of the various factors contributing to the skin friction in incompressible adverse pressure gradient turbulent boundary layer (APG-TBL) flows. Specifically, it deals with the contributions to the skin friction coefficient from the Reynolds stresses and the viscous effects and the role of the pressure gradient. The skin friction coefficient is calculated based on the theoretical decomposition for mean skin friction generation introduced by Renard and Deck (2016). This decomposition is compatible with spatially developing flows as it is applicable to every local streamwise position. The turbulent flows are generated through the direct numerical simulation of a TBL on a smooth flat plate with the desired farfield pressure gradient. It is observed that the Reynolds shear stress provides the dominant positive contribution to the skin friction coefficient for all the pressure gradient cases. However, with increasing adverse pressure gradient, the skin friction coefficient continues to decrease and approaches zero as the positive contribution from the Reynolds shear stress is diminished by the negative contribution of the pressure gradient. When the flow reaches the verge of separation, the predominant Reynolds shear stress contribution to the skin friction coefficient is from a spatially localized outer peak at an approximate height of the displacement thickness (y=δ1) which coincides with the inflection point of the mean streamwise velocity. Even though, the decompositions in Renard and Deck (2016) and Fukagata et al. (2002) give a different distribution for the skin friction coefficient in the zero pressure gradient (ZPG) and the mild APG cases, both of the identities capture the dominant outer peak of the Reynolds shear stress contribution when the flow reaches the verge of separation. This emphasizes the growing importance of the outer layer dynamics with increasing pressure gradient as it pertains to skin friction generation.

Similarity solution of MHD slip with energy mass transport through chemically reacting stretching permeable surface in porous media with variable properties

In this paper, a mathematical model is presented for magnetohydrodynamic viscous incompressible boundary layer flow of an electrically conducting chemically reacting fluid over a moving permeable flat vertical surface in a porous medium with variable fluid properties. A linear momentum slip boundary condition is included. Temperature and concentration difference between the wall and the environment are assumed to vary with the axial distance according to power law forms. Furthermore, a concentration-dependent mass diffusivity is featured to provide for a more realistic simulation of relevance to materials processing systems. The governing equations with associated boundary conditions are transformed into similarity equations using appropriate variables furnished with Lie group algebraic methods. The resulting nonlinear differential ordinary boundary value problem is then solved numerically with a Runge–Kutta–Fehlberg fourth–fifth order numerical method. The effects of the governing parameters on the boundary layer flow characteristics (velocity, temperature, concentration, wall shear stress, heat and mass transfer rates) have been investigated, displayed graphically and discussed. The computations indicate that variable mass diffusivity plays a significant role on transport characteristics. It is also shown that concentration magnitudes increase whereas the rate of mass transfer at the wall decreases with increasing mass diffusivity. Comparison of numerical and analytical results with results from the open literature show excellent agreement. Further verification of the general model is conducted with the Spectral Relaxation Method (SRM). The study is relevant to electroconductive polymeric sheet processing in manufacturing operations and smart coating systems.

Spatial organisation of velocity structures for large passive scalar gradients

Velocity structures associated with large streamwise density gradients in an incompressible turbulent boundary layer (with air as the working fluid, Pr = 0.71) are analysed experimentally using planar image velocimetry and aero-optic measurements. The resulting flow topologies for the velocity fluctuations associated with large negative and positive density gradients are in excellent agreement with results for coolings and heatings in time, respectively (Antonia & Fulachier, J. Fluid Mech., vol. 198, 1989, pp. 429–451). The current results are complimentary to those from Saxton-Fox et al. (AIAA J., vol. 57 (7), 2019, pp. 2828–2839), on the signature of the vertical velocity structures associated with large density gradients. In the present work, these structures are shown to exhibit a sign change, consistent with the scalar gradient, and are localised in the wall-normal direction with an average height of approximately 0.1δ, almost constant for increasing distance from the wall. The corresponding small-scale streamwise fluctuations also exhibit a consistent sign change, which is found to originate, on average, from upstream leaning structures. The emerging picture for the velocity field is then that of a multiscale phenomenon, where small-scale structures, responsible for large optical aberrations, are superimposed on the back of large-scale bulge-like structures that are known to populate the outer layers. The proposed conceptual model is consistent with early ideas of ‘typical’ eddies (Falco, Phys. Fluids, vol. 20 (10), 1977, pp. S124–S132), the hairpin vortex model and associated shear layers (Adrian et al., J. Fluid Mech., vol. 422, 2000, pp.1–54), as well as with notions of multiscale velocity organisation in shear layers (Klewicki & Hirschi, Phys. Fluids, vol. 16 (11), 2004, pp. 4163–4176; Saxton-Fox et al. 2019), and it provides new insight into the geometry of the small-scale velocity structures.

Analytical and numerical solutions of heat and mass transfer of boundary layer flow in the presence of a transverse magnetic field

AbstractThe present investigation aims to study the effect of a transverse magnetic field with the presence of an adverse pressure gradient on the two‐dimensional laminar incompressible boundary layer flow over a flat plate. Using appropriated similarity transformations, the partial differential equations governing the studied problems are transformed into the ordinary nonlinear differential equations. Thereafter, these equations are solved numerically and analytically using the fourth‐order Runge‐Kutta method featuring shooting technique and the Adomian decomposition method, respectively. Obtained results reveal an excellent agreement between analytical and numerical data for temperature and concentration profiles.

过渡Reynolds数下Stokes层的间歇湍流特性

The characteristics of intermittent turbulence induced by wall surface roughness in a finite Stokes layer were investigated numerically, including the velocity gradient at the wall, the velocity profile and the Reynolds stress, etc.， with a transitional Reynolds number Re=495.The results show that, the velocity profile does not follow the logarithmic law in most phases, but does only in some rare phases during the decelerating stage. The comparison between the Reynolds stress and the result in the case of the incompressible boundary layer indicates that, the Reynolds stress distribution in the turbulence stage is similar to that in the case of the incompressible boundary layer, including the peak amplitude and the peak position, but there is significant discrepancy in the turbulence core region between the 2 cases. Above characteristics reveal the strong nonequilibrium behaviors of intermittent turbulence in the Stokes layer.

Homogeneous–heterogeneous reactions in flow past a horizontal circular cylinder with an induced magnetic field and nonlinear thermal radiation

AbstractIn this study, we investigate the steady, two‐dimensional, incompressible viscous boundary layer flow of an electrically conducting Casson fluid over a horizontal circular cylinder. The cylinder is impermeable and the flow is assumed to be subject to homogeneous–heterogeneous reactions. The homogeneous–heterogeneous reactions are also assumed to have unequal diffusion coefficients. The novelty in this study is in the consideration of a nonlinear radiative flux together with Joule heating and an induced magnetic field. The magnetodynamic pressure gradient in induced magnetic flows is important as it gives insights into the boundary layer characteristics. The flow velocity and the magnetic field in the free stream are assumed to be uniform and directed vertically over the cylinder. The partial differential equations are solved using the bivariate spectral quasi‐linearization method. An analysis and comparison of results with existing literature are provided. Among the findings, we show, inter alia, that the reactants dominate while the autocatalysts have a negligible impact on the flow progression. The skin friction coefficient decreases with an increase in the Casson parameter and increases when the Joule heating parameter is increased. The rate of heat transfer increases with increasing the Casson parameter and decreases when the Joule heating parameter is increased.

A novel hybridity model for TiO2-CuO/water hybrid nanofluid flow over a static/moving wedge or corner

In this study, we are going to investigate semi-analytically the steady laminar incompressible two-dimensional boundary layer flow of a TiO2-CuO/water hybrid nanofluid over a static/moving wedge or corner that is called Falkner-Skan problem. A novel mass-based approach to one-phase hybrid nanofluid model that suggests both first and second nanoparticles as well as base fluid masses as the vital inputs to obtain the effective thermophysical properties of our hybrid nanofluid, has been presented. Other governing parameters are moving wedge/corner parameter (λ), Falkner-Skan power law parameter (m), shape factor parameter (n) and Prandtl number (Pr). The governing partial differential equations become dimensionless with help of similarity transformation method, so that we can solve them numerically using bvp4c built-in function by MATLAB. It is worthwhile to notice that, validation results exhibit an excellent agreement with already existing reports. Besides, it is shown that both hydrodynamic and thermal boundary layer thicknesses decrease with the second nanoparticle mass as well as Falkner-Skan power law parameter. Further, we understand our hybrid nanofluid has better thermal performance relative to its mono-nanofluid and base fluid, respectively. Moreover, a comparison between various values of nanoparticle shape factor and their effect on local heat transfer rate is presented. It is proven that the platelet shape of both particles (n1 = n2 = 5.7) leads to higher local Nusselt number in comparison with other shapes including sphere, brick and cylinder. Consequently, this algorithm can be applied to analyze the thermal performance of hybrid nanofluids in other different researches.

Flow structures in transitional and turbulent boundary layers

The basic problems of transition in both incompressible and compressible boundary layers are reviewed. Flow structures in low-speed transitional and developed turbulent boundary layers are presented, together with almost all of the physical mechanisms that have been proposed for their formation. Comparisons of different descriptions of the same flow structures are discussed as objectively as possible. The importance of basic structure such as solitonlike coherent structure is addressed. For compressible flows, the receptivity and instability of boundary layer are reviewed, including the effect of different parameters on the transition. Finally, the principle of aerodynamic heating of hypersonic boundary layer is presented.

Global Stability Analysis of Spatially Developing Boundary Layer: Effect of Streamwise Pressure Gradients

The paper presents a global stability analysis of the two-dimensional incompressible boundary layer with the effect of streamwise pressure gradient. A symmetric wedge flow is considered at different values of the dimensionless pressure gradient parameter βH. The pressure gradient dp/dx in the flow direction is zero, when βH = 0, favorable (negative) for βH > 0, and adverse (positive) for βH < 0. The base flow is computed by numerical solution of Falkner—Skan equation. The Reynolds number is based on the displacement thickness δ* at the inflow boundary. The stability equations governing the flow are derived in body-fitted coordinates. The stability equations are discretized using the Chebyshev spectral collocation method. The discretized equations, together with boundary conditions, form a general eigenvalue problem and are solved using Arnoldi’s algorithm. The temporal global modes are computed for βH = 0.022, 0.044, and 0.066, for favorable and adverse pressure gradients. The temporal growth rate ωi is found to be negative for all the global modes. The ωi value is smaller for the favorable pressure gradient (FPG) than for the adverse pressure gradient (APG) at the same Reynolds number (Re = 340). Thus, the FPG has a stabilizing effect on the boundary layer. The comparison of the spatial eigenmodes and spatial amplification rates for FPG and APG show that FPG has a stabilizing effect, whereas APG has a destabilizing effect on the disturbances.

Boundary-Layer Flow and Heat Transfer over a Rotating Porous Disk in a Non-Newtonian Williamson Nanofluid

Objectives: The present study analyses the effects of nanoparticles over steady, incompressible boundary-layer flow of non-Newtonian Williamson fluid flowing over a rotating porous disk. Methods/statistical analysis: The analysis used nonlinear partial differential equations associated with the non-Newtonian Williamson fluid flow and used an abridged, simplified version of ordinary differential equations under the Boussines q and boundary-layer approximations. The resulting system of nonlinear ordinary differential equations is then solved analytically using the homotopy analysis. Findings: The behavior of three non-dimensional velocity profiles and the non-dimensional temperature profile for important physical parameters like Williamson number, Prandtl number and surface suction/ injection parameters is tabulated and the results are graphed. Application/improvements: Nanoparticles like Copper, Alumina and titania are commonly used with liquid coolants to increase the heat-dissipating capability. Keywords: Boundary-Layer Flow; Heat Transfer; Porous Disk; non-Newtonian; Williamson Nanofluid

The instability of non-Newtonian boundary-layer flows over rough rotating disks

We are concerned with the local linear convective instability of the incompressible boundary-layer flows over rough rotating disks for non-Newtonian fluids. Using the Carreau model for a range of shear-thinning and shear-thickening fluids, we determine, for the first time, steady-flow profiles under the partial-slip model for surface roughness. The subsequent linear stability analyses of these flows (to disturbances stationary relative to the disk) indicate that isotropic and azimuthally-anisotropic (radial grooves) surface roughness leads to the stabilisation of both shear-thinning and -thickening fluids. This is evident in the behaviour of the critical Reynolds number and growth rates of both Type I (inviscid cross flow) and Type II (viscous streamline curvature) modes of instability. The underlying physical mechanisms are clarified using an integral energy equation.

Direct numerical simulation of incompressible turbulent boundary layers and planar jets at high Reynolds numbers initialized with implicit large eddy simulation

A direct numerical simulation (DNS) initialized with an implicit large eddy simulation (ILES) is performed for temporally evolving planar jets and turbulent boundary layers. In the ILES, an initial laminar flow develops into a fully developed state of the planar jet or the boundary layer. Subsequently, the DNS is started from the flow field obtained by the ILES. This hybrid ILES/DNS methodology is tested for the planar jet and boundary layer by comparing the results with full DNS started from the initial laminar flow. The ILES results used as the initial conditions of the DNS do not possess small-scale fluctuations. However, the small-scale fluctuations in the DNS grow with time and develop well within an interval of the integral time scale, where the influences of initial conditions taken from the ILES disappear for an energy spectrum of velocity fluctuations. The DNS initialized with the ILES well reproduces small-scale characteristics of turbulence, such as Reynolds number dependence of skewness and flatness of velocity derivative and energy spectrum of velocity fluctuations in the inertial subrange and viscous range. The DNS initialized with the ILES predicts well statistics dominated by large scales, such as 1st- and 2nd-order statistics and longitudinal auto-correlation function, in agreement with previous experimental and numerical studies. Reynolds number dependence of the mean velocity, root-mean-squared velocity fluctuations, Reynolds stress, shape factor, and skin friction in the turbulent boundary layers in the present DNS are consistent with previous experimental studies. These investigations confirm advantages of applying the ILES at the transitional flow region in the DNS of turbulent shear flows at high Reynolds numbers.

Computational unsteady flow analysis for third‐grade fluid from an isothermal vertical cylinder through a Darcian porous medium

AbstractThe present study describes a mathematical model for free‐convective laminar incompressible boundary layer flow of a third‐grade fluid of the Reiner‐Rivlin differential type, external to an evenly heated semi‐infinite vertical cylinder through a two‐dimensional porous medium. Assuming a homogenous‐isotropic porous medium, simulation of bulk drag effects at low Reynolds number is conducted with the Darcy model. The resulting partial differential equation boundary value problem is normalized using suitable transformation variables. The highly nonlinear time‐dependent coupled conservation equations along with boundary conditions are resolved computationally with an optimized Crank‐Nicolson finite difference code. Validation with previous studies is included. The heat transport and skin‐friction coefficients are computed for different values of emerging nondimensional parameters. Furthermore, steady‐state and transient fluid flow variables are shown graphically. An enhanced fluid velocity is observed for increased Darcy number and the reverse trend is computed for higher values of third‐grade viscoelastic parameter. Also, the rate of heat transfer is observed to increase with greater Darcy number and a reduction in third‐grade viscoelastic parameter. A key observation which is drawn from the present study is that for third‐grade fluid the flow variables deviate significantly from a hot cylindrical wall as compared with a Newtonian fluid. The study is relevant to thermal polymer coating applications in aerospace materials processing.

Model of Distributed Receptivity to Kinetic Fluctuations in High-Speed Boundary Layers

The receptivity of high-speed compressible boundary layers to kinetic fluctuations is considered within the framework of fluctuating hydrodynamics. The formulation is based on the idea that KF-induced dissipative fluxes may lead to the generation of unstable modes in the boundary layer. Fedorov and Tumin (“Receptivity of High-Speed Boundary Layers to Kinetic Fluctuations,” AIAA Journal, Vol. 55, No. 7, 2017, pp. 2335–2348) solved the receptivity problem using an asymptotic matching approach, which used a resonant inner solution in the vicinity of the neutral point. This study adopts a method of multiple scales approach, which requires fewer assumptions about the locus of primary excitation. The approach is modeled after the one taken by Luchini (“Receptivity to Thermal Noise of the Boundary Layer over a Swept Wing,” AIAA Journal, Vol. 55, No. 1, 2017, pp. 121–130) to study low-speed incompressible boundary layers over a swept wing. The new framework is used to study examples of high-speed flat plate boundary layers whose spectra exhibit nuanced behavior near the generation point, such as first-mode instabilities and near-neutral evolution over moderate length scales.

Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis

AbstractSteady incompressible magnetohydrodynamic mixed convection boundary layer flow of a Casson fluid on an exponentially vertical shrinking sheet using the non‐Newtonian heating equation is investigated in this paper. There are three main objectives of this study, namely, to develop a new mathematical model, to obtain multiple solutions, and to perform stability analysis. The governing partial differential equations have been changed into nonlinear ordinary differential equations. The resultant equations of boundary value problems are then converted into the equivalent initial value problems using the shooting method before they can be solved using Runge‐Kutta of order four. The numerical results are obtained and found to be in good agreement with the published literature. The results also indicate that the velocity boundary layer becomes thinner as the magnetic, slip, and Casson parameters increase. Dual solutions for temperature and velocity distributions are obtained. Furthermore, the results suggest that the presence of the force of buoyancy (opposing flow case) would cause the occurrence of dual solutions. However, based on the stability analysis, only the first solution is stable.

Non-similar solutions of the boundary layers equations with favorable and adverse pressure gradients, isothermal wall and slip boundary conditions: Application to Falkner–Skan gaseous flow

Abstract This article presents the non-similar solutions of the steady incompressible two-dimensional boundary layers equations of momentum and energy for Falkner–Skan gaseous flow with favorable and adverse pressure gradient under slip boundary conditions at a relatively low Mach number. By considering the slip boundary conditions at the fluid–wallinterface for the velocity and temperature, the non-dimensional boundary layer equations are solved numerically by using the centered implicit finite difference Keller Box methods. The results of the effects of different dimensionless parameters involved in the problem, namely the modified boundary layer Knudsen number, i.e., the slip parameter K and the shape parameter β on the local hydrodynamic and heat transfer characteristics of the flow are investigated and discussed. The results of these characteristics obtained from non-similar solutions are compared to those obtained from local similarity approach often used by several authors in the last decades. We show that for small shape parameter β and moderate or large values of the slip parameter, the self-similarity of the Falkner–Skan flows is generally lost because of slip boundary conditions. Therefore, the use of the local similarity approach may produce substantial errors for hydrodynamic and thermal characteristics of the flow as compared to non-similar solution. But in contrast, when β becomes larger than 2/3 up to 1, the flow regains its self-similarity character, in this case, the local similarity approach remains valid and may be used. While for β > 1 up to 2, the solutions of the boundary layer equations again become non-similar. Furthermore, a special attention was made to evaluate the separation point under rarefaction, the results show that the effect of slip parameter leads to decrease the separation point β s and it is concluded that separation of the boundary layer should be delayed in the slip flow regime.

Transient analysis of Casson fluid thermo-convection from a vertical cylinder embedded in a porous medium: Entropy generation and thermal energy transfer visualization

Thermal transport in porous media has stimulated substantial interest in engineering sciences due to increasing applications in filtration systems, porous bearings, porous layer insulation, biomechanics, geomechanics etc. Motivated by such applications, in this article a numerical investigation of entropy generation effects on the heat and momentum transfer in unsteady laminar incompressible boundary layer flow of a Casson viscoplastic fluid over a uniformly heated vertical cylinder embedded in a porous medium is presented. Darcy’s law is employed to simulate bulk drag effects at low Reynolds number for an isotropic, homogenous porous medium. Heat line visualization is also included. The mathematical model is derived and normalized using appropriate transformation variables. The resulting time-dependent non-linear coupled partial differential conservation equations with associated boundary conditions are solved with an efficient unconditionally stable implicit finite difference Crank Nicolson scheme. The time histories of average values of momentum and heat transport coefficients, entropy generation and Bejan number, as well as the steady-state flow variables are computed for several values of non-dimensional parameters arising in the flow equations. The results indicate that entropy generation parameter and Bejan number are both elevated with increasing values of Casson fluid parameter, Darcy number, group parameter and Grashof number. To analyze the heat transfer process in a two-dimensional domain, plotting heat lines provides an excellent approach in addition to streamlines and isotherms. The dimensionless heat function values are shown to correlate closely with the overall rate of heat transfer. Bejan’s heat flow visualization implies that the heat function contours are compact in the neighbourhood of the leading edge of the boundary layer on the hot cylindrical wall. It is observed that as the Darcy number increases, the deviations of heat lines from the hot wall are reduced. Furthermore the deviations of flow variables from the hot wall for a Casson fluid are significant compared with those computed for a Newtonian fluid and this has important implications in industrial thermal materials processing operations.