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Understanding fluid flow, heat, and mass transfer over a stretching cylinder is essential in ascertaining the quality of wire coating and coper thinning. This study looks at the influence of the heat source, thermal radiation, chemical reaction, and natural convection of Carreau fluid flows over a vertical stretching cylinder immersed in a porous medium. Suitable similarity variables are applied to convert the partial governing equations arising in fluid flows, heat, and mass transfer into ordinary differential equations. The optimal homotopy analysis method is then utilized to solve the transformed highly nonlinear governing equations. The impacts of the relevant parameters such as the Weissenberg number, porosity, heat source parameter, radiative number, chemical reaction parameter, mixed convection parameter, and curvature parameter on the dimensionless velocity, temperature, and concentration distribution as well as for the skin friction, Nusselt number, and Sherwood number are discussed through graphs and tables. It is observed that the velocity shows an opposite behavior as compared to temperature, and concentration in shear-thinning, n 1 , and shear-thickening, n ≥ 1 , fluid for an increment of the Weissenberg number. Additionally, the thickness of the momentum, thermal, and concentration boundary layer is enhanced by the curvature of the cylinder.

The reattached boundary layer in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer at Mach number 2.25 is studied by means of Direct Numerical Simulation (DNS). The numerical results are carefully compared with available experimental and DNS data in terms of turbulence statistics, wall pressure and skin friction. The coherent vortex structures are significantly enhanced due to the shock interaction, and the reattached boundary layer is characterized by large-scale structures in the outer region. The space-time correlation of fluctuating wall shear stress and streamwise velocity fluctuation reveals that the structural inclination angle exhibits a gradual decrease during the recovery process. The scale interactions are analyzed by using a two-point amplitude modulation correlation. A possible mechanism is proposed to account for the strong amplitude modulation in the downstream region. Moreover, the mean skin-friction is decomposed to understand the physically informed contributions. Unlike the upstream Turbulent Boundary Layer (TBL), the contribution associated with the Turbulence Kinetic Energy (TKE) production is greatly amplified, while the spatial growth contribution induced by the pressure gradient largely inhibits skin-friction generation. Based on bidimensional empirical mode decomposition, the turbulence kinetic energy production contribution is further split into different terms with specific spanwise length scales.

Convection differential equations that include momentum, energy and mass balance equations are used for the simulations of boundary layer (BL) flows. In convection analysis, it is in execution to dimensionless the BL system through similarity variable. However, a wide range of convection differential equations cannot be non-dimensionalized using similarity variable therefore the intent of this manuscript is to develop non-similar model for the forced convective magnetic flow of a viscous fluid above an exponentially expanding surface saturated by nano-fluid. The non-similarity is due to the exponential stretching of the surface and viscous dissipation. Influences of chemical reaction and heat generation are also incorporated. The non-similarity transformation is applied to the nonlinear partial differential system (PDE’s) to transform them into dimensionless PDE’s. Non-similar system is analytically approximated by adapting local non-similarity (LNS) and then it is numerically simulated by finite difference based bvp4c algorithm to explore the influences of significant numbers named as Prandlt number, chemical reaction, magnetic field, Brownian motion, heat generation, Eckert number, thermophoresis on concentration, velocity and temperature distribution. Auxiliary consequences presume that the heat penetration in fluid rises with enhancements in Brownian motion and Prandtl number, while it can be perceived here that for positive estimations of heat generation causes the thicker temperature field. Increasing non-similarity variable and magnetic number become reason for the reduction of temperature profile and chemical reaction is reason of reduced concentration profile.

This study investigates the boundary stresses prescribed by the traction boundary condition on an incompressible magnetohydrodynamic Jeffery-Hamel flow of viscous fluid. The governing partial differential equations are transformed to a nonlinear ordinary differential equation (ODE) by the transformation obtained from continuity equation. We have modeled traction boundary conditions to solve the problem. We have not imposed flow symmetry condition and applied prescribed flow rate condition. We have computed analytical and numerical solutions of the problem. We have developed modified Adomian decomposition method based on Daun-Rach Approach (DRA) for general nonlinear third order ODE subject to Robin’s and integral boundary conditions. The governing equation is solved using the developed scheme. The Mathematica routine, NDSolve, is used to obtain numerical solution by first approximating the constant flow rate condition by Gauss-Lobatto integration formula of four and five points as well as by trapezoidal rule. Analytical and numerical results are compared and found in good agreement. The slip and no-slip scenarios are observed both for inertial and non-inertial flows. The back flow occurs both for convergent and divergent channel geometries. Flow bifurcations and boundary layer get strengthened due to presence of boundary stresses. The symmetric and asymmetric natures of flow are also captured due to presence of boundary stresses.

This paper presents the investigation of airfoil turbulent boundary-layer trailing-edge noise reduction using a parametric airfoil design. The airfoil design tool performs a parametric design start...

We present the laminar boundary layer flow over the standard tori rotating in an otherwise quiescent incompressible fluid. The mean flow equations are derived by using a specific form of the toroidal-poloidal coordinate system. A pseudo-spectral collocation method mixed with the first-order Euler scheme is employed to solve the related steady mean flow equations. A fixed aspect ratio R is defined as the ratio of radii of the torus and its tube that distinguishes each fixed torus within the general family of standard tori. Tori of spindle type turn into a sphere when the aspect ratio R = 0 and thus the mean flow results for the rotating sphere are consistently reproduced. The influence of aspect ratio R on the steady mean velocity components and the wall shear stresses are presented in detail. In a precise manner, the mean flow results for each rotating torus are explainable in a consistent way to the already established case of steady laminar boundary layer flow over the rotating sphere. The significance of the current work is discussed in terms of the hydrodynamic instabilities of boundary layer flows over the family of rotating tori.

In the current study, a mathematical model is developed to visualize the mixed convection boundary layer flow of a nanofluid containing gyrotactic microorganisms past a permeable vertical surface saturated in a porous medium with variable viscosity and velocity slip effects. Suction/injection impact is taken into detail through the flow with heat and mass transfer analysis. Appropriate transformations are applied to transform the governing partial differential equations into non-linear ordinary differential equations, before being solved numerically using Runge-Kutta procedure is used with shooting technique. A parametric study focusing the influence of involved parameters on various fields such as the local skin friction coefficient, local Nusselt number are graphed via plots along with the local Sherwood number and motile microorganisms density number. The present results indicate that the motile microorganism number is enhanced for increasing Peclet number estimations. Moreover, the growing in the thermophoresis parameter leads to sufficient enhancement in the skin friction coefficient, Sherwood number and the density of the motile microorganism number for injection case, while the opposite behavior occurred with suction case.

Turbulent flow over a wall-mounted cube presents an important canonical problem with applications in circuit design, urban building design, or aerodynamics. Flow over a cube placed in a fully devel...

We investigate the error scaling and computational cost of wall-modeled large-eddy simulation (WMLES) for external aerodynamic applications. The NASA Juncture Flow is used as representative of an aircraft with trailing-edge smooth-body separation. Two gridding strategies are examined: i) constant-size grid, in which the near-wall grid size has a constant value and ii) boundary-layer-conforming grid (BL-conforming grid), in which the grid size varies to accommodate the growth of the boundary-layer thickness. Our results are accompanied by a theoretical analysis of the cost and expected error scaling for the mean pressure coefficient ($C_p$) and mean velocity profiles. The prediction of $C_p$ is within less than $5\%$ error for all the grids studied, even when the boundary layers are marginally resolved. The high accuracy in the prediction of $C_p$ is attributed to the outer-layer nature of the mean pressure in attached flows. The errors in the predicted mean velocity profiles exhibit a large variability depending on the location considered, namely, fuselage, wing-body juncture, or separated trailing-edge. WMLES performs as expected in regions where the flow resembles a zero-pressure-gradient turbulent boundary layer such as the fuselage ($, arXiv admin note: text overlap with arXiv:2101.00331

Implicit large-eddy simulations of reflecting shock-wave turbulent boundary-layer interactions at a freestream Mach number of 2.05 were carried out for sweep angles of 0, 20, and 40 deg. The simula...

This article has the objective of examining to perform unstable magnetohydrodynamic flow over an inclined plate enclosed in a penetrable mechanism with Soret-aligned magnetic field and chemical reaction. Once momentum and energy and mass are equal, they can be combined using the diffusion equation to yield the dimensionless momentum/energy/mass model. Aligned Magnetic field, Jeffrey Parameter, Inclined angle, and Chemical Reaction Model outlines are used to study the effect of numerous physical parameters on boundary layer properties, including Soret temperature, chemical reaction velocity, Temperature and concentration on the resulting heat accumulation profile, are tested using parametric models. The findings derived from skin friction, Nusselt number, and Sherwood numbers are included in the tables provided for several parameters. It is observed from the results that the velocity profile increases with increase Thermal and Mass Grashof Numbers, Jeffery Parameter and Porous media but the opposite trends are seen with increase in the magnetic field parameter, inclined parameter and Aligned magnetic field parameter. One of the important findings of this analysis includes that intensification in the Newtonian heating effect causes a gradual downfall in the rate of heat transfer at the plate and the concentration of the fluid decreases under the impact of chemical reaction. Their physic- Chemical features have been dealt with in detail. This fluid flow model has several industrial applications in the field of chemical, polymer, medical sciences, etc.

The effect of the surface conductivity on the electrical and mechanical characteristics of the surface dielectric barrier discharge actuator has been numerically investigated in this study. Two typical AC-surface dielectric barrier discharge actuators, wire-to-plate and plate-to-plate have been considered to control airflow alongside a flat dielectric plate. A sinusoidal high voltage of varied frequencies and amplitudes is supplied to the active electrode, and the passive electrode, which is grounded, is encapsulated inside a dielectric plate. Two-species ion transport model, involving generic positive and negative ions, coupled to the electrostatics model is assumed. The electrostatic field is affected by both the space and the surface charges. The surface charge is accumulated due to ion deposition, but its distribution varies due to the surface ohmic conduction. The Navier-Stokes equations for the flow simulation, which include the time-averaged electrohydrodynamic body force determined from the discharge model, are solved to analyze the flow field and the boundary layer morphology. The numerical algorithm has been implemented in the COMSOL commercial package. The significance of the dielectric surface conductivity on the discharge behavior and the flow field has been shown. The dielectric surface conductivity behaves non-monotonically and affects the flow field by altering the EHD force strength, direction and distribution.

The paper focuses on a theoretically study of fluid flow and heat transfer of Eyring-Powell fluid in a boundary layer over a flat surface. For the first time, groups of symmetry transformations were obtained for the full rheological law of Eyring-Powell fluid. This enabled obtaining self-similar forms of nonlinear differential equations different from the classical Blasius forms, which describe the limiting case for the large values of the parameter A. At the same time, the self-similar Blasius forms correctly describe the transition from the velocity profiles for a Newtonian fluid to linear profiles for Eyring-Powell fluid. The velocity and temperature profiles become less full due to the increasing parameter A, so that finally these profiles exhibit a linear shape. The friction coefficients and the Nusselt numbers decrease with the increasing parameter А.

Numerical modeling of turbulent fluid flow generally valid only for fully developed turbulent flow without consideration of laminar flow region. Generally in any flow past body consist of laminar flow region eventually it turn to turbulent over a finite length. The prediction of laminar to turbulent transition boundary flow is influence the boundary separation in the turbulent zone and its effects in delay of separation. In this paper transition flow is predicted by fully turbulent flow solved by turbulent Kinetic energy and Specific turbulent dissipation models, transition is modeled by coupling of turbulent scalars and kinetic energy of laminar fluctuations. Transition model is analyzed over flow past aerofoil.

The influence of the distributed leading-edge roughness on the stall characteristics of NACA0012 airfoil is analyzed in full turbulence flow or transition flow. The Menter shear-stress transport model and the $\gamma - \overline{Re_{\theta t}}$($\overline{Re_{\theta t}}$ is transition momentum-thickness Reynolds number, γ is intermittency)transition model are used to simulate the flow around the airfoil by coupling the roughness model and the roughness amplification factor transport equation respectively. The airfoil stall characteristics and the pre-stall boundary layer development are analyzed. The results show that the trailing-edge stall occurs for the NACA0012 airfoil in full turbulence flow, and the stall characteristic is not changed by the leading-edge roughness. The maximum lift coefficients are significantly decreased with the leading-edge roughness at a lower angle of attack. In transition flow, the leading-edge roughness inhibits the formation of leading edge laminar separation bubbles, and the stall characteristic of airfoil is changed from leading-edge stall to trailing-edge stall. The maximum lift coefficient is significantly increased with the leading-edge roughness at a higher angle of attack.

The ferrofluid transport phenomena have a considerable interest in the boundary layer flow due to its versatility in advancing emerging industrial applications, such as printing. In this concern, the current theoretical model examines the particulate suspension's transport phenomena in the magnetite ferrofluid past a permeable non-isothermal moving surface with the viscous dissipation effect. Self-similarity quantities are applied to ease the solving process in the built-in collocation method, bvp4c function in the MATLAB software. The kerosene-based ferrofluid showed a better convective heat transfer rate than the water-based ferrofluid as the governing parameters vary. The dust particles’ increment in the ferrofluid increases the frictional drag force exerted on the shrinking sheet significantly. Dual solutions are obtainable only when the sheet shrinks to some extent. However, stability analysis confirmed that one of the numerical solutions is not stable.

In order to investigate the two-dimensional flow of a non-Newtonian fluid, such as an elastomer liquid over a cylinder, a simplified model is applied. The analysis is carried out to study the thermophysical properties of the melt elastomer flow with Prandtl variable in the presence of internal heat generation. The temperature-dependent physical properties such as velocity, contour temperature, surface temperature as a function of contour velocity, and pressure are considered and discussed. Moreover, the exchange of energy from the surface to the fluids is examined through the variation in the Rayleigh number.

The aerodynamic shape of the hypersonic forebody/inlet integrated vehicle is usually designed according to the inviscid flow. However, due to the effect of air viscosity, there is a boundary layer flow near the wall surface. In order to get the actual flow characteristics and performance parameters of the inviscid design vehicle close to the inviscid design values, the inviscid design surface must be corrected by considering the viscous boundary layer. In this paper, the theory and method of the boundary-layer viscous correction (BLVC) for the forebody/inlet integrated configuration are studied. Firstly, two modification schemes of the BLVC for the forebody/inlet integrated configuration are proposed. The calculation method of boundary-layer displacement thickness (BLDT) based on the momentum integral equation of steady two-dimensional (2D) axisymmetric compressible flow is described in detail, and two calculation methods of the BLDT are compared and analyzed. Secondly, the numerical simulation method used in this paper and its validation are introduced. Thirdly, an axisymmetric configuration of the forebody/inlet integration is selected as the first case, and two modification schemes of BLVC are studied and analyzed by numerical simulation. The effects of the two modification schemes of BLVC on the internal and external flow characteristics and aerodynamic performance of the axisymmetric configuration of the forebody/inlet integration are compared and analyzed. Finally, a full-waverider configuration of the forebody/inlet integration is selected as the second case, and the second modification scheme of the BLVC is used to modify the full-waverider configuration. The shock wave characteristics and inlet performance parameters of the modified full-waverider configuration are studied by both the numerical simulation and the wind tunnel experiment. The obtained results prove that the calculation method of the BLDT by a numerical integration method to solve the momentum integral equation of the steady 2D axisymmetric compressible flow is correct and the BLVC method and scheme for the forebody/inlet integrated configuration are effective. The modification scheme 1 of the BLVC can only improve the characteristics of forebody shock wave incident on the inlet lip under viscous conditions, that is, to improve the performance of inlet to capture precompressed air flow, while the modification scheme 2 of the BLVC can simultaneously improve the characteristics of forebody shock wave incident on the inlet lip and the characteristics of the lip shock wave cancelled on the shoulder of the inlet under viscous conditions, and make the air flow capture performance of the inlet and the pressure rise ratio at the inlet exit close to those of the inviscid design state.

This work is devoted to the analysis of the linear temporal stability of a laminar dynamic boundary layer on a horizontal porous plane plate. The basic flow is assumed to be laminar and two-dimensional. The basic flow velocity profiles are obtained by numerically solving the Blasius equation using the Runge-Kutta method. The perturbations of these basic solutions are expressed in the form of three-dimensional Tollmien-Schlichting waves. The formulation of the stability problem leads to the Orr-Sommerfeld equation modified by the permeability parameter (Darcy number) and the small Reynolds number. This equation is given in a general form which can be applied to the Chebyshev domain and the boundary layer domain and solved numerically using the Chebyshev spectral collocation method. The marginal stability diagrams, the critical Reynolds numbers and the eigenvalue spectra are obtained for different values of the parameters which have modified the stability equation. Numerical solutions indicate the importance of the effect of these parameters on the flow stability characteristics.

The current work aims at studying a constructed mathematical model with an examination of heat transfer in water-based nanofluids containing ferromagnetic nanoparticles flowing between parallel stretchable spinning discs with variable viscosity influence and variable conductivity. The nonlinear coupling of the ordinary differential equations of the momentum and energy equation with the partial differential equations based on the Navier-Stokes equation employing some influential similarity transformations. The transformed system of ordinary differential equations has been solved through the Chebyshev spectral collocation procedure (CSCP). The numerical results for the velocity and temperature distributions are shown in terms of graphical presentations. The existing available literature was utilized to test for validation of the numerical findings. The outcomes demonstrate that the stretching of the lower and upper disks and spinning parameters strengthens the impetus boundary layer and diminished the temperature boundary layer, whilst the variable thermal conductivity improved the convective and conductive strength of the ferromagnetic nanoparticles considered, and the Fe3O4 nanofluid displays a higher thermal conductivity strength than the Mn-ZnFe2O4 nanofluid.

A numerical study was performed on the three-dimensional interaction between a laminar boundary layer and the shock wave induced by a sharp, unswept fin mounted perpendicularly on a flat plate at f...

Here, continuous two-dimensional boundary layer flow of a Fe2O3 CuO/water hybrid nanofluid over a porous stretching/shrinking wedge with radiation and MHD effects has been investigated semi–analytically. The dual solutions of the problem and also its stability analysis are taken into account. Moreover, the mass-based procedure for hybrid nanofluid modeling has been used. According to this procedure, the volume fraction of first and second nanoparticles is written in terms of both nanoparticles as well as base fluid masses. The Tiwari-Das model joined with mass-based hybrid nanofluid procedure is applied to find the governing partial differential equations which are then transferred to a set of dimensionless ordinary differential equations with help of the similarity transform method. The numerical method of solution has been chosen based on a famous finite difference scheme (bvp4c) from MATLAB software. The results demonstrate that dual solutions exist for a certain domain of the wedge stretching/shrinking parameter. Also it is observed that always the first solutions have thinner boundary layer thickness than the second ones. Moreover, the critical value in which the solution is in existence increase with the enhancement of magnetic parameter and suction parameter. The magnetic parameter and the mass suction at the wedge's surface also leads to the increase in the local Nusselt number. Further, it is inferred that the second nanoparticle's mass enhancement results in the amplification of the skin friction coefficient and the local Nusselt number for the first solutions. In addition, the rise in radiation parameter tends to enhance the thermal boundary layer thickness.

In this paper, we discuss the solution of the magneto hydrodynamics (MHD) thermal boundary layer flow of Casson liquid over a penetrable extending wedge with ohmic heating and convective boundary condition (BC). Important applications of such flows and condition include the MHD pump, radiation therapy, MHD generator, soil mechanics, melt spinning process, thermal insulation and many others. Practical applications of convective BC are often encountered in laser damage or laser processing. The problem is non dimensionalized and computational solutions are achieved for the governing nonlinear coupled ordinary differential equations (PDEs) by using homotopy analysis method (HAM) and influence of various emerging parameters on momentum and temperature field are examined. A table containing computational data for the wall shear stress f ′ ′ ( 0 ) and local Nusselt - θ ′ ( 0 ) number is also provided. Major findings/objectives of the present study are: an increasing in Casson fluid parameter δ decreases velocity when wedge stretches faster than free stream velocity for R = 2 . However, velocity increases for R = 0.1 case. Temperature velocity decreases for R = 2 or R = 0.1 cases for δ escalations. Enhancing B i for convective heat transfer increases the momentum and thermal boundary layer thickness in the presence of suction C. Computational outcomes for velocity, drag force, temperature velocity and heat transfer rate are discussed through tables numerically. Results are verified with varied choices of suction parameter C. It is noted that the convective parameter magnified the heat transfer rate.

In the present contribution, a numerical treatment is provided to describe unsteady nanofluid flow near a vertical heated wavy surface. A memorable feature of the present work is the investigation of nanofluid flow associated with thermal radiation that acts as a catalyst for heat transfer rates. Likewise, the effectiveness of variable viscosity is examined as it controls fluid flow as well as heat transfer. It is necessary to study heat and mass transfer for complex geometries because predicting heat and mass transfer for irregular surfaces is a topic of fundamental importance, and irregular surfaces frequently appear in many applications, such as flat-plate solar collectors and flat-plate condensers in refrigerators. A simple coordinate transformation from the wavy surface into a flat one is employed. The non-dimensional boundary layer equations that governing both heat transfer and nanofluid flow phenomena along the wavy surface are solved via a powerful numerical approach called the implicit Chebyshev pseudospectral (ICPS) method with Mathematica code. A comparison graph of the current numerical computation and the published data shows a perfect match. Figures depict the effect of various physical parameters on nanofluid velocities, temperature, salt concentration, nanoparticle concentration, skin friction, Sherwood, nanoparticle Sherwood, and Nusselt numbers. According to the numerical results, increasing the variable viscosity parameter value causes a drop in the local skin friction coefficient value and an increase in the steady-state axial nanofluid velocity profile near the wavy surface. Furthermore, as heat radiation is increased, the local Nusselt number decreases but the nanoparticle Sherwood number increases.

Strong laminar/transitional shock boundary layer interactions (SBLIs) have been investigated in a Mach 4 vacuum-driven wind tunnel with supporting computational fluid dynamics analysis. Such flows ...

Motivated by recent trends in spin coating operations in chemical engineering which are\ud exploiting nanomaterials, the present article investigates theoretically and numerically the steady\ud mass and heat transfer in Von Karman swirling slip flow of a nanofluid from a rotating disk\ud touching to a homogenous non-Darcy porous medium. The porous medium is simulated with a\ud Darcy-Forchheimer-Brinkman model. To track the thermophoresis and Brownian movement of\ud the nanoparticles the Buongiorno nanoscale model is used. Von Karman similarity variables are\ud deployed to transform the partial differential conservation equations into a system of highly\ud coupled, nonlinear, dimensionless ordinary differential equations (ODE's). These similarity\ud boundary layer equations i. e. continuity, momentum, energy and nanoparticle concentration\ud (volume fraction) are solved with bvp4c shooting quadrature in MATLAB. Validation with\ud earlier studies is included. Further verification with an Adams-Moulton predictor-corrector\ud method is conducted. The influence of velocity (momentum) slip coefficient, thermal slip,\ud Darcian bulk drag parameter (inverse permeability), Forchheimer inertial parameter,\ud Browninan motion parameterm Schmidt number, thermophoresis parameter and Prandtl number\ud on radial, tangential (azimuthal) and axial velocity components, temperature and nanoparticle\ud concentration are visualized graphically. The distributions for skin friction component and\ud Nusselt number are also computed. Radial, axial and tangential velocities are reduced with\ud increasing Forchheimer inertial drag and hydrodynamic wall slip whereas they are elevated with\ud increasing permeability (decreasing inverse Darcy parameter). Thermal and nanoparticle\ud concentration boundary layers are also markedly modified with an increment in Forchheimer inertial parameter, Schmidt number, Prandtl number, thermophoresis and Brownian motion\ud parameters.

Free convective of nanofluid inside dispersive porous medium adjacent to a vertical plate under the effects of the zero mass nanoparticles flux condition and the thermal and solutal dispersions is studied. Buongiorno's model revised is used considering Darcy and non Darcy laminar flows, and isothermal or convective flux outer the wall. Dimensionless governing equations formulated using velocity, temperature, concentration and nanoparticle volume fraction have been solved by finite difference method that implements the 3-stage Lobatto collocation formula. The numerical data obtained with semi or full dispersions cases are compared to predictions made using the non dispersive porous medium. Taking into account the dispersions, the influence of the zero mass nanoparticles flux condition is examined to test the validity of the control active nanoparticle assumption. It is found mainly that the thermal transfers can reach more than 100% in connection with the case where of a semi-dispersion of the porous medium is applied. Realistic condition, i.e. zero mass flux should be addressed for the heat transfer rate rather than the mass transfer rate, discovered markedly different to the active condition. This signifies the importance of considering the zero nanoparticles mass flux and dispersions in the performance characterization of nanofluid flow in porous media.

This paper reports the experimental investigations of the wake of a rotating and translating sphere in the close proximity of a plane wall at moderate Reynolds numbers (Re = 450–2020, defined based on velocity of translation and diameter of the sphere) and for a non-dimensional rotation rate, Ω* (ratio of surface velocity to the translation velocity of the sphere), of 1. For the current gap (h)-to-diameter (d) ratio of the sphere (h/d = 1/16), at Re = 1000, hairpin vortices shed in the wake where looping of small-scale vortices increases with the increase in Re. At Re > 1000, the transition from hairpin type to shear layer vortex shedding occurs. At a relatively high Reynolds number (Re = 1130), the separated vortex sheets from both sides of the sphere exhibit Kelvin–Helmholtz instability, and the wake shows multiple vortical structures. At Re = 2020, a strong interaction of vortex rings in the wake of the sphere and boundary layer at plane wall results in the breakdown of larger vortical structures into smaller scales. The separation angle changes from the equatorial region to the pole of the sphere because of differential rotational speeds at other planes. At midplane, the separation angle increases with Re, and it decreases again when hairpin–shear layer vortex shedding transition occurs. The Strouhal number as a function of Re indicates the presence of dual frequency beyond this transition.

The supersonic mode in hypersonic flows is studied numerically. The radiation characteristics of this mode in a Ma=6 flat-plate boundary layer with cooled walls are focused on. The linear stability...

Experimental studies were conducted in a super-large wave flume, aiming at uncovering the hydrodynamic characteristics involved in the turbulent wave boundary layer of full scale environment. An explicit formula of boundary layer thickness on rough turbulent flow was presented based on the measured velocity data of the present study and collected experimental data on wave boundary layer. It was found that the bottom wave-associated nominal stresses under the conditions of prototype scale tests suppress the vertical turbulence scattering upward over the boundary layer, which accounts for thickening of the boundary layer under wave condition. Such effect has yet not been reported in the literatures using oscillatory U-tube or small-sized wave flume. The phase inconsistency in the turbulent boundary layer to the free stream velocity (velocity immediately outside the boundary layer) is within 15°, which is remarkably smaller than the results from oscillatory U-tubes, as well as the larger wave flume experiment presented by Xie et al. (2021), showing that the coarser bed would further reduce the phase lead. The intensity of the vertical turbulent component is approximately 1/2 of the horizontal component, which has larger ratio compared with the value of 1/5 reported by previous studies. Especially, it was also found that the vertical turbulent energy was approximately 3/4 of the turbulent energy in spanwise directions (y-direction). This means that the turbulent fluctuation has similar order in all three-directions (x, y, z) in a full scale environment and highlights that the turbulent components in all the three directions should not be neglected when calculating the total turbulent energy.

The flow physics associated with shock-wave/boundary-layer interactions (SBLIs) on an axisymmetric body, simulating a projectile near an aircraft, is of significant interest to the aerodynamic comm...

Boundary layer development in a supersonic inlet is studied, focusing on the flow over the compression ramp and the ramp–isolator junction. Two designs of the junction, a backward-facing step (BFS)...

Carreau fluid flows past a stretching cylinder is elucidated in the present study. The transformed self-similarity and dimensionless boundary layer equations are solved by using the Homotopy analysis method. A convergence study of the method is illustrated explicitly. Series solutions of the highly nonlinear differential equations are computed and it is very efficient in demonstrating the characteristic of the Carreau fluid. Validation of the series solutions is achieved via comparing with earlier published results. Those results are obtained by using the Keller-Box method. The effects of the Weissenberg number and curvature parameter on the velocity profiles are discussed by graphs and tabular. The velocity curves have shown different behavior in and for an increase of the Weissenberg number. Further, the curvature parameter K does increase the velocity profiles.

This paper reports an experimental study on the supersonic jet surface flow structure visualization and shear stress field measurement issuing from a rectangular nozzle with extended shelf. The evolution of the near-field surface flow structures with an increased Nozzle Pressure Ratio (NPR) is successfully captured by the surface oil flow, infrared detection technology, and the Shear-Sensitive Liquid Crystal Coating (SSLCC) technique. Results reveal that under smaller NPR, the wall flow structure is similar to that of a jet without the extended shelf i.e., clean jets, and this is caused by insufficient effect on the boundary layer. However, at higher amplitudes of NPR, there exists a significant effect of the boundary layer, as a near triangular separation forms on the trailing edge of the Mach stem due to the adverse pressure gradient, which is visualized for the very first time in this paper. Furthermore, the vector field of shear stress is measured quantitatively by SSLCC technique. Results shows that the magnitude of shear stress heightened with NPR increasing, and the directions of shear stress changes across the shock wave and expansion fans. In addition, surface streamlines measured by SSLCC is significantly consistent with the streamlines visualized using the oil flow technique.

With increasing resolution of numerical weather prediction (NWP) models, classical subgrid‐scale processes become increasingly resolved on the model grid. In particular, turbulence in the planetary boundary layer (PBL) is vertically already partially resolved in contemporary models. For classical local PBL schemes, resulting up‐gradient heat transports cannot be treated correctly. Thus, nonlocal turbulence schemes have been developed in the past. As the horizontal grid sizes of NWP models become smaller than a few kilometers, the large turbulence eddies in the PBL will also start to become partially resolved in the horizontal direction. A very flexible way to formulate nonlocal turbulent exchange is the transilient matrix method, which is used here to develop a new turbulence parameterization. The resulting NLT3D scheme applies transilient mixing matrices to subgrid‐scale transports in all three dimensions. We compare results of WRF real‐case simulations including our scheme, a classical local turbulence scheme (MYNN), and an existing nonlocal one‐dimensional scheme (ACM2) with observations from field campaigns over homogeneous terrain (CASES‐99) and complex terrain (CAPTEX). Over homogeneous terrain, all three schemes similarly well capture the observed surface fluxes and radiosonde profiles, whereas over complex terrain more differences become obvious. During a tracer release experiment (CAPTEX) over the Appalachian mountain region, the mixing and vertical extent of the PBL turn out to be decisive to reproduce the observed advection speed of the tracer‐marked air mass. Deeper mixing not only accelerates surface winds but also enables tracer to travel faster at higher altitudes and then mix back to the ground. As results from a version of NLT3D with only standard horizontal Smagorinsky diffusion (NLT1D) demonstrate, simulating three‐dimensional turbulence can be beneficial already at horizontal grid sizes of a few kilometers., Decreasing grid sizes in numerical weather prediction models demand the inclusion of nonlocal effects and horizontal turbulence in turbulence parameterizations. This is the motivation for the development of the nonlocal three‐dimensional turbulence (NLT3D) scheme. Vertical nonlocal mixing accelerates the horizontal transport of near‐surface tracers by fast advection at higher altitudes (see figure), and horizontal turbulence enhances tracer dispersion. As validated by observations, both effects are beneficial to the forecast quality already at grid sizes of a few kilometers., Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659

Experimental and numerical study of active and passive flow control are notable and highly practical subjects in aircraft and missiles. Fluid jets are invaluable tools for this purpose. Accordingly, the present study delves into the effects of a pair of air microjets on turbulent flow over a plate. For this purpose, numerical model results were verified by experimental data of flow over a plate in the presence of a pair of air jets. Next, vortex formation, merging, and dissipation into the flow were studied at velocity ratio, VR = 4.0, by changing the spacing between the pair of jets and their orientations. The vortex position relative to the floor and other vortices, vortex intensity, flow velocity, Reynolds stresses in different directions, and pressure are discussed. The best vortex-merging results were found in a pair of co-directional jets (d/D = 10) condition. A pair of co-directional jets (d/D = 10) produced better results than opposite ones (d/D = 10—ccr). In the configuration with d/D = 10, the vortex intensity was nearly 80% higher than that of the single jet case. Further, the pair of jets pushed the post-jet pressure rise around 30 cm away.

We shall prove the validity of the Prandtl boundary layer expansion for the two-dimensional Navier-Stokes flows around the Rayleigh boundary layer, which is the first result verifying the stability of the formation of the boundary layer in the inviscid limit with respect to the perturbations in the Gevrey $$\frac{3}{2}$$ class.

In order to perform flow velocity measurements without interfering in the flow field itself, a flow velocity measurement method based on the characteristics (the rule by which the power spectrum varies with the flow velocity) of turbulent pressure fluctuations is proposed. This method is based on the characteristics of turbulent pressure fluctuations in the turbulent boundary layer (TBL) and uses a polyvinylidene fluoride (PVDF) sensor to convert pressure fluctuations into voltage outputs. First, TBL pressure fluctuation characteristics are studied. Second, the piezoelectric characteristics of PVDF piezoelectric sensors are studied and a sensor array signal processing method that can improve the signal-to-noise ratio is provided. Then, numerical simulations are performed to verify the characteristics of turbulent pressure fluctuations in the TBL. Finally, a PVDF sensor is made and flow velocity measurement experiments are performed. The results show that the power spectrum of the PVDF sensor response to excitation by turbulent pressure fluctuations is proportional to the fourth power of the flow velocity. It is feasible to use this characteristic to measure the flow velocity.

A steady incompressible boundary layer flow and heat transfer past on a moving thin needle saturated with hybrid nanofluid are investigated with the effects of solar radiation and viscous dissipation. The simulation is also influenced by the effects of thermophoresis and Brownian motion. We consider (Al2O3-Cu-water) as a hybrid nanofluid, where water is the base fluid and alumina and copper are the hybrid nanoparticles. By utilizing the technique of similarity transformations, we transformed the dimensional partial differential equations into dimensionless ordinary differential equations. Using the MAPLE software scheme, the transformed equations have been solved numerically. The graphical representation of different parameters including Mixed convection, Power-law exponent, Buoyancy ratio parameter, Eckert number are illustrated on velocity, temperature, the concentration of nanoparticles profiles and explained in detail. Skin friction coefficient, heat transfer rate, and mass transfer rate are also obtained numerically. With the presence of hybrid nanoparticles, the heat transfer rate is higher in all cases. In the temperature profile, we observed a reduction with the increasing values of the mixed convection parameter. It also revealed that greater values of volume fraction of nanoparticle (Cu) reduce the mass transfer rate but accelerates the heat transfer rate.

We study a forced convective three-dimensional flow and heat transfer in the porous medium. Temperatures of the fluid and solid phases are not identical leading to local thermal non-equilibrium (LTNE) conditions, and hence we require two heat transport equations: one for each phase. This model arises when a hot (cold) fluid flows through a relatively cold (hot) porous medium. This situation usually appears in geothermal and chemical engineering applications. The flows outside the boundary layers are approximated by a linear variation along with the streamwise directions. The governing equations that model the problem are solved numerically using the Chebyshev collocation method. The chief focus is on the application of the Chebyshev collocation method for the system of ordinary differential equations that essentially governing the fluid flow and heat transfer in the boundary layers. The numerical results show that the thickness of the boundary layer is thinner in the streamwise direction, and also predicts the reverse flow in the other direction for a negative three-dimensionality parameter. The thinning of the boundary layer thickness is found for higher permeability values. In the case of forced convection regime, both interphase rate of heat transfer and porosity scaled conductivity are decreased towards zero, the temperature of the fluid phase gradually deviates from solid porous medium temperature thereby showing LTNE effects. The various results corresponding to the LTNE are shown to be a continuation of the classical heat transfer already present in the local thermal equilibrium. The temperature difference which arises out of the LTNE is suitable in most industrial applications. Further, to assess the nature of these flows for a large time, a linear stability analysis is performed to see whether or not the obtained solutions are practically realizable. It is found that all the obtained solutions are always stable, and hence are indicative of practically significant. The fluid dynamics of these mechanisms are discussed in detail.

The computational approaches of CFD are more powerful than the analytical solutions for high-speed compressible flows over a flat plate. A small number of expensive experimental data can be generated to aid high-speed vehicle design. However, CFD can be used to simulate a large variety of flows with different freestream and wall conditions in a cost-effective manner. The current work aims to numerically calculate the turbulent boundary layer flows over a flat plate at different Mach numbers in the range of 2–8 at different wall conditions and unit Reynolds numbers. The Reynolds-averaged Navier–Stokes method with k − ω turbulence model is applied to resolve the flow over the flat plate at zero angle of attack. The computed skin friction coefficient and Stanton number are compared with the available experimental data in the literature. The calculated results indicate some agreement with the experimental data. An increase in the Mach number and wall temperature decreases the skin friction and the Stanton number. A polynomial curve fit data estimation is proposed for skin friction under adiabatic wall conditions for Mach numbers in the range of 2–8. Numerical simulations over compression corner flows are also presented in the present work. The freestream Mach number influences the thickness of the subsonic layer in the undisturbed boundary layer on the flat plate in compression corner flows. The higher freestream Mach number results in a lower subsonic thickness near the wall, leading to a small separation bubble and lower peak heat transfer in shock/boundary-layer interaction flows.

Cone-straight nozzle has been widely used in well bore cleaning, assisting drilling in petroleum industries due to its good clustering properties. The structure including cone angle and throat length has also been studied by scholars and been optimized. However, the internal flow properties have not been investigated clearly especially the boundary layer flow. In this paper LES model is used to capture the small-scale flow state near the nozzle wall. The RNG k-epsilon model is used to validate the accuracy of the LES simulation, the simulation data shows a good agreement. Three different inlet velocities are considered in simulations. The velocity distribution, shear stress, boundary layer thickness, skin friction coefficient and Reynolds stress are analyzed, the boundary layer separation and transition are discussed. The state of flow inside nozzle is laminar with inlet velocity of 1 m/s and gradually transferred into turbulent with the increasing inlet velocity. The most severe turbulence is at the entrance of the throat section, the vortex structure appears at the entrance of converging section and dose not survive, the vortex structure appears in sequence along the throat section wall when the inlet velocity is set to 5 m/s and 10 m/s the flow properties along the conical nozzle are revealed clearly, the main flow resistance is mainly produced in throat section. All these works aim to provide theoretical support for the further processing optimization of the nozzle structure and reduce the flow resistance of nozzle.

A free axisymmetric nonswirling submerged jet of viscous incompressible fluid is considered. For large Reynolds numbers, the unknown constant in the asymptotic Landau–Rumer–Gol’dshtik–Yavorsky solution to the Navier–Stokes equations that describes the far jet field is determined. A similar constant in Loitsyanskii’s solution in the boundary layer approximation is found. These constants are expressed in terms of the distribution of velocity in the jet source using a nonlocal conservation law.

One promising design solution for increasing the efficiency of modern horizontal axis wind turbines is the installation of curved tip extensions. However, introducing such complex geometries may move traditional aerodynamic models based on Blade Element Momentum (BEM) theory out of their range of applicability. This motivated the present work, where a swept tip shape is investigated by means of both experimental and numerical tests. The latter group accounted for a wide variety of aerodynamic models, allowing to highlight the capabilities and limitations of each of them in a relative manner. The considered swept tip shape is the result of a design optimization, focusing on locally maximizing power performance within load constraints. For the experimental tests, the tip model is instrumented with spanwise bands of pressure sensors and is tested in the Poul la Cour wind tunnel at the Technical University of Denmark (DTU). The methods used for the numerical tests consisted of a blade element model, a near-wake model, lifting-line free-wake models, and a fully resolved Navier- Stokes solver. The comparison of the numerical and the experimental tests results is performed for a given range of angles of attack and wind speeds, which is representative of the expected conditions in operation. Results show that the blade element model cannot predict the measured normal force coefficients, but the other methods are generally in good agreement with the measurements in attached flow. Flow visualization and pressure distribution compare well with Computational Fluid Dynamics (CFD) simulations. The agreement in the clean case is better than in the tripped case, indicating an aggressive tripping of the flow in the measurements. Some uncertainties regarding the effect of the boundary layer at the inboard tunnel wall and the post stall behavior remain.

The current experimental investigation explores the viscous/inviscid interaction of a supersonic turbulent boundary layer and a sharp fin-generated shock wave. The study examines the effect of Reyn...

The aim of present study is to investigate the convective heat and mass transfer in steady MHD boundary layer flow of an electrically conducting micropolar fluid over an inclined surface. Partial differential equations resulting from the mathematical modeling of the phenomenon are reduce to nonlinear ODEs, and a finite difference based scheme has been adopted to iteratively find the numerical solution by employing the successive over-relaxation (SOR) method. A self-developed computer code has been used in the MATLAB environment. Influence of chemical reaction, Brownian motion, thermophoresis, and viscous dissipation on the relevant features of the flow are discussed and analyzed through graphs and tables. Temperature dependent thermal conductivity and viscosity enhances the flow velocity. Wall suction slows down the flow in the boundary layer and brings the optimum value of the velocity very nearer to the inclined plane. The magnetic field affects the shear stress and viscous dissipation that is parallel due to suction. A decrease in the fluid temperature is noticed throughout the boundary layer for Prandtl number, Schmidt number, and suction parameter whereas an opposite trend is seen for temperature-dependent thermal conductivity, injection parameter, magnetic field, Brownian motion, and thermophoresis.

Based on the ideas of the mechanism of turbulent flows as forming a source of turbulent vortices at the turbulent flow boundaries developed and described previously for turbulent jets [2] and turbulent flows in channels [3], we have calculated the flow parameters for a turbulent boundary layer (TBL) combining the features of flows in jets and channels. The mechanism of the influence of external turbulence on the TBL flow parameters is described. A generalization of the theory for flows with an external flow pressure gradient is proposed.

This study evaluated the effects of the adding of flow momentum using artificial external source on the controlling of oblique shock wave of a supersonic flow in a three dimensional duct with low-aspect-ratio (based on experimental data) through a numerical investigation by employing an OpenFoam extended solver. The oblique shock occurred due to a 20° compression ramp which placed on the top of the low-aspect-ratio duct. The flow characteristics were consistent with the published data, suggesting that the numerical methodology successfully resolved the interaction between the shock-waves and flow boundary-layer. To investigate the effect of momentum adding, based on literature, three different cases with various forces exerted on the upper and lower walls of the duct were considered. The results showed that momentum adding led to a decrement in the separation region and shock strength. Moreover, adding the momentum sources on the lower wall of the duct suppressed the lambda shock that happened by the collision of separated and incident shocks and Mach stem. However, by applying the momentum source on the upper wall (upstream of the compression ramp) had more effects on the interaction between shock wave and boundary layer, as compared to the lower wall. Therefore, based on the obtained results, to achieve the best performance of momentum source, it must apply at the critical point with the greatest effect on discontinuities in the flow structure.

This comparative research investigates the influence of a flexible magnetic flux and a chemical change on the freely fluid motion of a (MHD) magneto hydrodynamic boundary layer incompressible nanofluid across an exponentially expanding sheet. Water and ethanol are used for this analysis. The temperature transmission improvement of fluids is described using the Buongiorno model, which includes Brownian movement and thermophoretic distribution. The nonlinear partial differential equalities governing the boundary layer were changed to a set of standard nonlinear differential equalities utilizing certain appropriate similarity transformations. The bvp4c algorithm is then used to tackle the transformed equations numerically. Fluid motion is slowed by the magnetic field, but it is sped up by thermal and mass buoyancy forces and thermophoretic distribution increases non-dimensional fluid temperature resulting in higher temperature and thicker boundary layers. Temperature and concentration, on the other hand, have the same trend in terms of the concentration exponent, Brownian motion constraint, and chemical reaction constraint. Furthermore, The occurrence of a magnetic field, which is aided by thermal and mass buoyancies, assists in the enhancement of heat transmission and wall shear stress, whereas a smaller concentration boundary layer is produced by a first-order chemical reaction and a lower Schmidt number.

The computational study of transient immiscible and incompressible two-phase flows is one of the most common and desirable way for investigation of engineering phenomena and physics science. In the previous studies, generally bubbles current have been used as an active method for increasing heat transfer, however, due to existence of hydraulic boundary layers, the bubbles were not able to cross over this layer to thinning the thermal boundary layer and consequently the efficiency of this method was not very considerable. In this study, by considering potential of magnetic field, the effect of co-applying of external non uniform magnetic field and magnetic bubbles in enhancing the heat transfer efficiency in a 3-D tube has been investigated. The computational model consisted of the Navier–Stokes equation for liquid phase and VOF model for interface tracking are carried out by OpenFOAM. The external magnetic field has been considered non-uniform and time dependent. The results predicted that magnetic bubbles and external magnetic field due to their effect on thermal boundary layer increased significantly heat transfer and Nusselt number. Furthermore, results indicated magnetic bubbles can act as an active torbulators in the flow field and can be applied for increasing recirculation and secondary flow in the flow field. The average temperature and magnetic field over times for different cases have been discussed in the results.