Incompressible Boundary Layer Research Articles

Biomagnetic flow with magnetic particles over a continuously moving sheet affected by a magnetic dipole

This research concentrates on the 2-D, steady, laminar, viscous, incompressible boundary layer flow of a biomagnetic fluid containing two different magnetic particles (CoFe2O4andFe3O4) over a continuously moving horizontal plate in the presence of a magnetic field generated by a magnetic dipole. For the mathematical formulation the comprehensive concept of Biomagnetic Fluid Dynamics (BFD) is adopted incorporating the principles of FerroHydroDynamics (FHD) and MagnetoHydroDynamics (MHD). The physical problem which is constituted by a coupled system of Partial Differential Equations (PDEs) along with corresponding boundary conditions, is transformed into a coupled system of nonlinear Ordinary Differential Equations (ODEs) subject to analogous boundary conditions by establishing newly simplified similarity transformations. The transformed ODEs along with the boundary conditions are then solved numerically by introducing an efficient numerical technique based on a finite difference algorithm. Verification of this work has been also done by comparing the obtained results with previously published results and found in quite good agreement. The significant effects caused by the variation of the governing parameters such as the skin friction, heat transfer rate and wall pressure are presented more intricately. It has been contemplated that including magnetic particles with pure blood enhances the impact of the magnetic field on the flow, temperature and pressure profiles which could be of interest engineering implementations, like, magnetic drug delivering in blood cells, separating RBCs (Red Blood Cells), controlling the flow of blood during surgeries, treating cancer by producing magnetic hyperthermia etc.

Embedded large eddy simulation of boundary layer transition behind a micro-ramp

Boundary layer transition induced by surface roughness elements plays an important role in aerodynamic and aero-thermodynamic design of subsonic/supersonic/hypersonic vehicles. However, the effect of three-dimensional isolated roughness element in the process of promoting/suppressing boundary layer transition is far from being fully understood, particularly in the incompressible laminar flow. In the present study, the laminar-to-turbulent transition induced by a three-dimensional isolated micro-ramp element immersed in an incompressible laminar boundary layer is investigated numerically. The embedded large eddy simulation (ELES) combining the intermittency transition model and the wall-modeled large eddy simulation (WMLES) S − Ω model is employed for the first time. Numerical results on the time-averaged/instantaneous flow field and the statistical flow fluctuations are analysed and validated thoroughly by the existing experimental measurements. It is found that the interaction of the secondary and the tertiary streamwise vortices causes a high level of wall shear and an inflectional velocity distribution in the near-wall region. An additional eddy system that develops nonlinearly from the unstable inflectional flow may trigger the boundary layer transition. The present study validates that the ELES combined with the WMLES S − Ω model is an efficient simulation tool for industrial wall-bounded flows allowing effective compromise between flexibility, cost, and accuracy.

Numerical heat and mass transfer in magnetized Williamson liquid motion over a sensor wall engulfed in a micro-cantilever system: An application to thin-film fluidic cells

Central focus of this numerical analysis is to investigate the influence of magnetic body force and thermal radiation on the time-dependent electrically conducting two-dimensional viscous incompressible boundary layer flow of non-Newtonian Williamson fluid over a microcantilever sensor surface suspended in a squeezed regime numerically. A novel heat source/sink and Soret effects are included in the respective governing equations. The constructed time-dependent nonlinear coupled partial differential equations are solved by using a bobust RK-4 technique. Increasing magnetic number increases the velocity distribution and decreases the temperature and concentration profiles in the flow regime.Enhancing Soret number increases the mass diffusion profile. Increasing magnetic number suppress the skin-friction coefficient. Heat transport rate booted with rising radiation number and Sherwood number decreased with enlarged Schmidt number in the channel regime. Finally, the numerical accuracy of the present similarity solutions and used numerical method is validated with existing results and observed a remarkable agreement.

New momentum integral equation applicable to boundary layer flows under arbitrary pressure gradients

By incorporating the traditionally overlooked advective term in the wall-normal momentum equation, a new momentum integral equation is developed for two-dimensional incompressible turbulent boundary layers under arbitrary pressure gradients. The classical Kármán's integral arises as a special instance of the new momentum integral equation when the pressure gradient is weak. The new momentum integral equation's validity is substantiated by direct numerical simulation data. Unlike the classical Kármán's integral, which is limited to predicting wall shear stress within mild pressure gradients, the new momentum integral equation accurately computes wall shear stress across a broad range of pressure gradients, even in the presence of strong adverse pressure gradients that lead to flow separation. Moreover, a new pressure parameter $\beta _\kappa$ is introduced through examining terms in the new momentum integral equation. This parameter naturally quantifies the pressure gradient's influence on turbulent boundary layers and offers guidance for applying the classical Kármán's integral. Additionally, to facilitate experimental determination of wall shear stress under strong pressure gradients, an approximate integral equation is proposed that relies solely on easily measurable variables. Validation against direct numerical simulation data demonstrates that this simplified equation provides reasonably accurate estimates of wall shear stress in turbulent boundary layers experiencing strong pressure gradients.

PARAMETRIC STUDY OF SUCTION OR BLOWINGEFFECTS ON TURBULENT FLOW OVER A FLATPLATE

The two-dimensional, incompressible, and turbulent boundary layer flow over a flat plate with suction or blowing from a spanwise slot is examined numerically. The mathematical modeling involves the derivation of the governing partial differential equations of the problems. These are the continuity, the momentum, the energy and the (K-ε) turbulence model. Besides, the perfect gas law is also used. A numerical solution of the governing equations is approximated by using a finite volume method, with staggered grid and modified SIMPLE algorithm. A computer program in FORTRAN 90 is built to perform the numerical solution.The developed computational algorithm is tested for the flow over a flat plate (4m) long with uniform suction or blowing velocity ratios of (V/U∞ =± 0.0185, ± 0.0463 and ±0.0925 m/s) are imposed on the slot for Reynolds number of (1.36 x 107 ), based on the plate length. The position of the slot change in the range of (X/L=1/4, 1/2 and 3/4) from leading edge and also, change width of slot in the value equal (0.12, 0.2 and 0.28m).The plate temperature is (70 °C), with the free stream velocity and temperature are (8.6m/s) and (25 °C) respectively. In addition, the effects of pitch angles on the flow field are investigated in the range of (30о   150о).The numerical results show that, for a uniform blowing, location of slot equal (X/L=1/4) from leading edge, a significant reduction of skin friction coefficient, wall shear stress and boundary layer thickness [displacement and momentum] to occur. While, an increase in boundary layer shape factor. Reynolds stress (uv) is more decreased than [(uu) and (vv)], mean velocity profiles in wall coordinates and dimensionless distance (U+, y+) decreases. When slot location is moved downstream to locations (X/L=1/2 or 3/4) a similar behavior can be said and most effective slot is obtained as (slot at X/L= 3m) from leading edge. While width of slot equal (0.28m) is better than values equal (0.12m and 0.2m). An opposite observations for the case of suction. The numerical results are compared with available numerical results and experimental data and a satisfactory results are obtained.

Excitation and stability of nonlinear waves by a pair of steady waves in incompressible boundary layers

The research explores the generation and stability of nonlinear waves in incompressible boundary layers, spotlighting the effects of dual steady waves. Using the Benjamin-Ono equation, modified for the incorporation of steady waves, we provide insights into the solitary wave generation process. A perturbed wave oscillator system is used for analyzing the stability of these nonlinear waves, uncovering that the loss of stability in low-order oscillators primarily governs wave transition and energy. Further, the study highlights the enlightening significance of complex terrain on the generation of nonlinear waves. Since the influence of terrain on the fluid passing over it usually appears as the external excitation of stationary waves, our study has important implications for terrain-fluid interactions.

Instability analysis for MHD boundary layer flow of nanofluid over a rotating disk with anisotropic and isotropic roughness

The study focuses on the instability of local linear convective flow in an incompressible boundary layer caused by a rough rotating disk in a steady MHD flow of viscous nanofluid. Miklavčič and Wang's (Miklavčič and Wang, 2004) [9] MW roughness model are utilized in the presence of MHD of Cu-water nanofluid with enforcement of axial flows. This study will investigate the instability characteristics with the MHD boundary layer flow of nanofluid over a rotating disk and incorporate the effects of axial flow with anisotropic and isotropic surface roughness. The resulting ordinary differential equations (ODEs) are obtained by using von Kàrmàn (Kármán, 1921) [3] similarity transformation on partial differential equations (PDEs). Subsequently, numerical solutions are obtained using the shooting method, specifically the Runge-Kutta technique. Steady-flow profiles for MHD and volume fractions of nanoparticles are analyzed by the partial-slip conditions with surface roughness. Convective instability for stationary modes and neutral stability curves are also obtained and investigated by the formulation of linear stability equations with the MHD of nanofluid. Linear convective growth rates are utilized to analyze the stability of magnetic fields and nanoparticles and to confirm the outcomes of this analysis. Stationary disturbances are also considered in the energy analysis. The investigation indicates the correlation between instability modes Type I and Type II, in the presence of MHD, nanoparticles, and the growth rates of the critical Reynolds number. An integral energy equation enhances comprehension of the fundamental physical mechanisms. The factors contributing to convective instability in the system are clarified using this approach.

Simulating the propagation of boundary-layer disturbances by solving boundary-value and initial-value problems

Abstract The article deals with the downstream propagation of small–amplitude disturbances of viscous incompressible laminar boundary layers, using the linearized equations for disturbance amplitudes. Two different methods are proposed. The first one solves a two-dimensional boundary-value problem, using a buffer-domain technique to mimic the outflow boundary condition. The second one solves a streamwise initial-value problem, using a spectral parabolization at each integration step. Both methods show good performance in simulating the propagation of the Tollmien–Schlichting waves and the Görtler vortices and can be applied to compute the spatial optimal disturbances.

Inflow turbulence generation for compressible turbulent boundary layers

It is still challenging to generate high-quality inflow turbulence for the direct numerical and large-eddy simulations of compressible turbulent boundary layers (CTBL). Recently, Wang et al. [“Inflow turbulence generation using an equivalent boundary layer model,” Phys. Fluids 35, 075110 (2023)] proposed a new inflow turbulence generation method based on an equivalent boundary layer model for incompressible turbulent boundary layers. In the present study, the compressible equivalent boundary layer (CEBL) model is proposed and applied to the direct numerical simulation of supersonic turbulent boundary layers. The streamwise equilibrious CEBL approximates the streamwise developing CTBL by adding source terms to the governing equations to recover the mean mass, momentum, and energy balances at a given Reynolds number. Direct numerical simulation is performed to CEBL at free-stream Mach number 5.86 and friction Reynolds number 380. Comparison with the CTBL statistics at the same parameters validates the fidelity and reliability of the CEBL model. Turbulence generated by CEBL as well as the digital filtering and recycling-rescaling methods is used, respectively, to construct the inflow conditions for the direct numerical simulation of supersonic turbulent boundary layers. Results show that the CEBL method has great superiority in reducing the adjustment length compared with the other two methods. In addition, a correction method designed for the high inflow Reynolds number is also introduced.

Transient energy growth analysis of flat-plate boundary layer with an oblique and non-uniform wall suction and injection

This paper presents a non-modal bi-global linear stability analysis of an incompressible flat-plate boundary layer under the effects of oblique and non-uniform wall suction and injection. The base flow velocity profile is two-dimensional and fully non-parallel. The flow is laminar at the inflow boundary, and no reverse flow occurs in the flow domain. The Chebyshev spectral collocation method has been used for the discretization of the governing stability equations. The discretized stability equations along with appropriate boundary conditions form an initial value problem (IVP). The transient energy growth (G(t)) and associated optimal perturbations are computed for different oblique angles (θ=30°,60°,90°,120°, and 150°), suction and injection intensities (I=0.5%, 1.5%, and 2.5% of U∞), Reynolds numbers (Re=195,284, and 411), and different spanwise wavenumbers (β=0−2) for uniform and non-uniform profiles of wall suction and injection. The behaviour of the boundary layer is found to be approximately similar but opposite in nature for θ=90° to 180° and θ=0° to 90° due to lower transpiration intensity. The G(t) decreases with the increase in θ from 0° to 90° for wall suction due to the damping of T–S modes. However, an opposite trend has been observed for injection due to the amplification of T–S modes. The uniform profile is found to be more effective than the non-uniform profiles of suction and injection in terms of their impact on the stability of the boundary layer. The 2D spatial structures of the optimal perturbations are damped and flow becomes modally stable as the spanwise wavenumber (β) is increased.

NUMERICAL STUDY OF CARREAU FLUID FLOW ALONG AN EXPONENTIAL CURVED STRETCHING SURFACE

A two-dimensional incompressible boundary layer Carneau fluid flow with heat-transfer analysis over a curved stretching surface is analyzed. The energy equation with the inclusion of thermal radiation and viscous dissipation effects is considered. The governing partial differential equations which govern such flow phenomena are transformed into suitable form of ordinary differential equations for integration by using stream function formulation. The developed non-linear problem has been solved by computational approach based on shooting technique using sixth-order Runge-Kutta method and Matlab built-in function bvp4c program. The effects of non-dimensional controlling parameters on temperature and velocity profile are analyzed with the aid of tables and figures. The surface drag force and Nusselt numbers are studied for the different values of the governing parameters. It is predicted that velocity of the fluid and boundary layer thickness is decreased when radius of curvature parameter δ is increased. Furthermore, the temperature profile dwindles for the growing values of δ. Other important information is that for shear-thinning fluid the velocity profile shows its increasing nature, whereas for shear-thickening fluid the opposite trend has been observed. For increasing values of curvature parameter δ from 2 to 1000, the temperature distribution and velocity profile is decreased. The radiative heat flux is included to enhance the temperature of the system, so, for the increasing values of radiation parameter <i>R<sub>d</sub></i> from 0.2-0.5 the temperature distribution is increased. Further, as the Biot number and Eckert number are increased from 0.2-2 and 0.1-1, respectively, the temperature distribution is increased.

Investigation of biomagnetic nanofluid flow configured by a stretchable surface in the presence of magnetic dipole

AbstractThe field of fluid dynamics has expanded to study of biological fluids in a magnetic field, a new area known as biomagnetic fluid dynamics. The most notable biomagnetic fluid is blood. The growing interest in problems related to biomagnetic fluid dynamics among researchers is due to its vast applications in biotechnology and biomedical sciences. These applications include magnetic devices for cell separation, blood reduction during surgeries, targeted drug delivery using magnetic nanoparticles to trigger drug release, magnetically induced hyperthermia therapy for most malignant tumors, and magnetic resonance imaging of specific regions of the human body. This study examines the effect of nonlinear radiation on a biomagnetic fluid, specifically blood, flowing through a two‐dimensional, incompressible boundary layer via a stretchable sheet. The flow under consideration is electrically conductive, adhering to the laws of magnetohydrodynamics and ferrohydrodynamics. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation and solved using the built‐in bvp4c function of MATLAB software. The effects of various physical parameters on velocity and thermal fields are investigated. The influences of the Nusselt number and skin friction are also evaluated against the main parameters. Furthermore, the average Nusselt number is 27.73% at M = 1.1, and when M = 2.5, the value of the average number decreases by 17.73%.

Singularity Formation in an Incompressible Boundary Layer on an Upstream Moving Wall under Given External Pressure

The two-dimensional laminar flow of a viscous incompressible fluid over a flat surface is considered at high Reynolds numbers. The influence exerted on the Blasius boundary layer by a body moving downstream with a low velocity relative to the plate is studied within the framework of asymptotic theory. The case in which a small external body modeled by a potential dipole moves downstream at a constant velocity is investigated. Formally, this classical problem is nonstationary, but, after passing to a coordinate system comoving with the dipole, it is described by stationary solutions of boundary layer equations on the wall moving upstream. The numerically found solutions of this problem involve closed and open separation zones in the flow field. Nonlinear regimes of the influence exerted by the dipole on the boundary layer with counterflows are calculated. It is found that, as the dipole intensity grows, the dipole-induced pressure acting on the boundary layer grows as well, which, after reaching a certain critical dipole intensity, gives rise to a singularity in the flow field. The asymptotics of the solution near the isolated singular point of the flow field is studied. It is found that, at this point, the vertical velocity grows to infinity, viscous stress vanishes, and no solution of the problem exists at higher dipole intensities.

Singularity Formation in an Incompressible Boundary Layer on an Upstream Moving Wall under Given External Pressure

Singularity Formation in an Incompressible Boundary Layer on an Upstream Moving Wall under Given External Pressure

Global stability analysis of axisymmetric boundary layer on a rotating circular cylinder

In this manuscript, we comprehensively investigated the global stability of the incompressible axisymmetric boundary layer (ABL) developed on a rotating circular cylinder. A finite length of a rotating cylinder was considered in an axial stream of incompressible fluid. The rotation of a cylinder produces centrifugal force in the radial direction, which produces a pressure gradient (PG) in the radial direction. The axial flow (U∞) develops shear in the BL which has a stabilization effect on the BL. Thus, the Reynolds number (Re) and rotation rate (S) are two important control parameters of the BL and they are calculated based on a cylinder radius. The spectral collocation method has been used to discretize the linearized Navier–Stokes equations (LNS) and Arnold’s iterative algorithm for the numerical solution of the 2D eigenvalues problem. The computations were performed for Reynolds numbers Re=2600, 5200, and 20,800, rotation rates S=0.5, 1.0, and 2.0 for azimuthal wave-numbers N=0, 1, 2, and 3. Thus, the effects of S, Re, and N were studied on the stability of the rotating ABL. The temporal and spatial properties of the small disturbances were studied to understand the effect of shear and centrifugal force by varying S and Re. The increased rotation of a cylinder makes the BL unstable while increased axial flow stabilizes the ABL. The small disturbances are found globally unstable for N=1 at a small Re with an even small S.

Direct numerical simulation of a zero-pressure-gradient turbulent boundary layer with passive scalars up to Prandtl number Pr = 6

The objective of the present study is to provide a numerical database of thermal boundary layers and to contribute to the understanding of the dynamics of passive scalars at different Prandtl numbers. In this regard, a direct numerical simulation (DNS) of an incompressible zero-pressure-gradient turbulent boundary layer is performed with the Reynolds number based on momentum thickness ${\textit {Re}}_{\theta }$ ranging up to $1080$ . Four passive scalars, characterized by the Prandtl numbers ${\textit {Pr}} = 1,2,4,6$ are simulated using the pseudo-spectral code SIMSON (Chevalier et al., SIMSON : a pseudo-spectral solver for incompressible boundary layer flows. Tech. Rep. TRITA-MEK 2007:07. KTH Mechanics, Stockholm, Sweden, 2007). To the best of our knowledge, the present DNS provides the thermal boundary layer with the highest Prandtl number available in the literature. It corresponds to that of water at ${\sim }24\,^{\circ }{\rm C}$ , when the fluid temperature is considered as a passive scalar. Turbulence statistics for the flow and thermal fields are computed and compared with available numerical simulations at similar Reynolds numbers. The mean flow and scalar profiles, root-mean-squared velocity and scalar fluctuations, turbulent heat flux, turbulent Prandtl number and higher-order statistics agree well with the numerical data reported in the literature. Furthermore, the pre-multiplied two-dimensional spectra of the velocity and of the passive scalars are computed, providing a quantitative description of the energy distribution at the different length scales for various wall-normal locations. The energy distribution of the heat-flux fields at the wall is concentrated on longer temporal structures with increasing Prandtl number. This is due to the thinner thermal boundary layer as thermal diffusivity decreases and, thereby, the longer temporal structures exhibit a different footprint at the wall.

A provably stable and high-order accurate finite difference approximation for the incompressible boundary layer equations

In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner. We first derive continuous energy estimates, and then proceed to the discrete setting. We formulate the discrete approximation using high-order finite difference methods on summation-by-parts form and implement the boundary conditions weakly using the simultaneous approximation term method. By applying the discrete energy method and imitating the continuous analysis, the discrete estimate that resembles the continuous counterpart is obtained proving stability. We also show that these newly derived boundary conditions removes the singularities associated with the null-space of the nonlinear discrete spatial operator. Numerical experiments that verifies the high-order accuracy of the scheme and coincides with the theoretical results are presented. The numerical results are compared with the well-known Blasius similarity solution as well as that resulting from the solution of the incompressible Navier–Stokes equations.

Influence of Damping of a Compliant Surface on Inviscid Instability of Overlying Incompressible Boundary Layer

The instability of an incompressible boundary layer on a compliant plate with respect to inviscid perturbations in the limit of high Reynolds numbers is analyzed using triple-deck theory. It is shown that unstable inviscid perturbations can exist only if the inertia and/or damping of the plate are taken into account. A twofold role of damping is revealed: it suppresses instability under certain conditions, while leading to its generation under other conditions.

Influence of Damping of a Compliant Surface on Inviscid Instability of Overlying Incompressible Boundary Layer

Influence of Damping of a Compliant Surface on Inviscid Instability of Overlying Incompressible Boundary Layer

Coexistence of stationary Görtler and crossflow instabilities in boundary layers

The coexistence of stationary Görtler and crossflow instabilities in boundary layers covering incompressible to hypersonic regimes is investigated by varying the local sweep angle, pressure gradient, wall curvature, and wall temperature using linear stability analysis. The results show that increasing the local sweep angle under a fixed concave curvature in incompressible boundary layers leads to the appearance of two unstable modes at certain sweep angles, which is conventionally known as the “changeover” regime between the crossflow and Görtler modes. This study identifies a synchronization between the two modes under this condition, which is similar to multiple Görtler modes and thus referred to as Görtler–crossflow modes. Three scenarios are presented to describe the possible development of these modal instabilities. In addition, increasing the concave curvature destabilizes the instability, while introducing a pressure gradient stabilizes the instability and results in a shrinkage of the unstable band of the spanwise wavenumber, as reported in the literature. In supersonic and hypersonic boundary layers, synchronization can occur near specific sweep angles and under cold wall conditions in supersonic boundary layers. As Mach number increases, the synchronization regime shifts toward lower sweep angles and wall temperature, in which the former reflects a decline in crossflow strength relative to Görtler instability, while the latter indicates the influence of thermal effects on synchronization. In hypersonic boundary layers, the crossflow instability is insignificant compared with the Görtler instability. No synchronization is identified under various parameter changes, and the first Görtler–crossflow mode dominates across the entire spanwise wavenumber ranges.