Showing papers on "Boundary layer published in 2018"

Mathematical Models in Boundary Layer Theory

Abstract: The Navier-Stokes Equations and Prandtl Derivation of the Prandtl System Solution of the Boundary Layer System as the First Approximation to Asymptotic Solution of the Navier-Stokes Equations near the Boundary Separation of the Boundary Layer Setting of the Main Problems for the Equations of Boundary Layer Boundary Layer Equations for Non-Newtonian Fluids Boundary Layers in Magnetohydrodynamics Stationary Boundary Layer: von Mises Variables Continuation of Two-Dimensional Boundary Layer Asymptotic Behavior of the Velocity Component along the Boundary Layer Conditions for Boundary Layer Separation Self-Similar Solutions of the Boundary Layer Equations Solving the Continuation Problem by the Line Method On Three-Dimensional Boundary Layer Equations Comments Stationary Boundary Layer: Crocco Variables Axially Symmetric Stationary Boundary Layer Symmetric Boundary Layer The Problem of Continuation of the Boundary Layer Weak Solutions of the Boundary Layer System Nonstationary Boundary Layer Axially Symmetric Boundary Layer The Continuation Problem for a Nonstationary Axially Symmetric Boundary Layer Continuation of the Boundary Layer: Successive Approximations On t-Global Solutions of the Prandtl System for Axially Symmetric Flows Stability of Solutions of the Prandtl System Time-Periodic Solutions of the Nonstationary Boundary Layer System Solving the Nonstationary Prandtl System by the Line Method in the Time Variable Formation of the Boundary Layer Solutions and Asymptotic Expansions for the Problem of Boundary Layer formation: The Case of Gradual Acceleration Formation of the Boundary Layer about a Body that Suddenly Starts to Move Comments Finite-Difference Method Solving the Boundary Layer Continuation Problem by the Finite Difference Method Solving the Prandtl System for Axially Symmetric Flows by the Finite Difference Method Comments Diffraction Problems for the Prandtl System Boundary Layer with Unknown Border between Two media Mixing of Two Fluids with Distinct Properties at the Interface between Two Flows Comments Boundary Layer in Non-Newtonian Flows Symmetric Boundary Layer in Pseudo-Plastic Fluids Weak Solutions of the Boundary Layer Continuation Problem for Pseudo-Plastic Fluids Nonstationary Boundary Layer for Pseudo-Plastic Fluids Continuation of the Boundary Layer in Dilatable Media Symmetric Boundary Layer in Dilatable Media Comments Boundary Layer in Magnetic Hydrodynamics Continuation of the MHD Boundary Layer in Ordinary Fluids Solving the Equations of the MHD Boundary Layer in Pseudo-Plastic Fluids Self-Similar Solutions of the MHD Boundary Layer System for a Dilatable Fluid Solving the Equations of Boundary Layer for Dilatable Conducting Fluids in a Transversal Magnetic Field Comments Homogenization of Boundary Layer Equations Homogenization of the Prandtl System with Rapidly Oscillating Injection and Suction Homogenization of the Equations of the MHD Boundary Layer in a Rapidly Oscillating Magnetic Field Comments Some Open Problems References Index

Analysis of activation energy in Couette-Poiseuille flow of nanofluid in the presence of chemical reaction and convective boundary conditions

Abstract: The motivation of the current article is to explore the energy activation in MHD radiative Couette-Poiseuille flow nanofluid in horizontal channel with convective boundary conditions. The mathematical model of Buongiorno [1] effectively describes the current flow analysis. Additionally, the impact of chemical reaction is also taken in account. The governing flow equations are simplified with the help of boundary layer approximations. Non-linear coupled equations for momentum, energy and mass transfer are tackled with analytical (HAM) technique. The influence of dimensionless convergence parameter like Brownian motion parameter, radiation parameter, buoyancy ratio parameter, dimensionless activation energy, thermophoresis parameter, temperature difference parameter, dimensionless reaction rate, Schmidt number, Brinkman number, Biot number and convection diffusion parameter on velocity, temperature and concentration profiles are discussed graphically and in tabular form. From the results, it is elaborate that the nanoparticle concentration is directly proportional to the chemical reaction with activation energy and the performance of Brownian motion on nanoparticle concentration gives reverse pattern to that of thermophoresis parameter.

Numerical simulation of natural convection heat transfer inside a ┴ shaped cavity filled by a MWCNT-Fe3O4/water hybrid nanofluids using LBM

Abstract: Natural convection of multi-wall carbon nanotubes-Iron Oxide nanoparticles/water hybrid nanofluid (MWCNT-Fe 3 O 4 /water hybrid nanofluid) inside a ┴ shaped enclosure has been numerically investigated using Lattice Boltzmann Method. Numerical in-house code has been developed to study the effects of different parameters including the nanoparticles volume fraction, the Rayleigh number, the cavity obstruction ratio, the heat source position, and the heat source aspect ratio on the hydrodynamic and thermal characteristics. In order to validate the developed numerical code, the results have been compared with previous works and have shown a good concordance. The results indicate that Nusselt number degrades respect to the cavity obstruction ratio because of development of the thermal boundary layer thickness. In addition, an increment of the heat source aspect ratio results in better cooling condition due to decreasing in the boundary layer thickness.

Importance of the nozzle-exit boundary-layer state in subsonic turbulent jets

Abstract: To investigate the effects of the nozzle-exit conditions on jet flow and sound fields, large-eddy simulations of an isothermal Mach 0.9 jet issued from a convergent-straight nozzle are performed at a diameter-based Reynolds number of 1 x 10^6. The simulations feature near-wall adaptive mesh refinement, synthetic turbulence and wall modelling inside the nozzle. This leads to fully turbulent nozzle-exit boundary layers and results in significant improvements for the flow field and sound predictions compared with those obtained from the typical approach based on laminar flow in the nozzle. The far-field pressure spectra for the turbulent jet match companion experimental measurements, which use a boundary-layer trip to ensure a turbulent nozzle-exit boundary layer to within 0.5 dB for all relevant angles and frequencies. By contrast, the initially laminar jet results in greater high-frequency noise. For both initially laminar and turbulent jets, decomposition of the radiated noise into azimuthal Fourier modes is performed, and the results show similar azimuthal characteristics for the two jets. The axisymmetric mode is the dominant source of sound at the peak radiation angles and frequencies. The first three azimuthal modes recover more than 97 % of the total acoustic energy at these angles and more than 65 % (i.e. error less than 2 dB) for all angles. For the main azimuthal modes, linear stability analysis of the near-nozzle mean-velocity profiles is conducted in both jets. The analysis suggests that the differences in radiated noise between the initially laminar and turbulent jets are related to the differences in growth rate of the Kelvin–Helmholtz mode in the near-nozzle region.

Turbulent superstructures in Rayleigh-Bénard convection.

Abstract: Turbulent Rayleigh-Benard convection displays a large-scale order in the form of rolls and cells on lengths larger than the layer height once the fluctuations of temperature and velocity are removed. These turbulent superstructures are reminiscent of the patterns close to the onset of convection. Here we report numerical simulations of turbulent convection in fluids at different Prandtl number ranging from 0.005 to 70 and for Rayleigh numbers up to 107. We identify characteristic scales and times that separate the fast, small-scale turbulent fluctuations from the gradually changing large-scale superstructures. The characteristic scales of the large-scale patterns, which change with Prandtl and Rayleigh number, are also correlated with the boundary layer dynamics, and in particular the clustering of thermal plumes at the top and bottom plates. Our analysis suggests a scale separation and thus the existence of a simplified description of the turbulent superstructures in geo- and astrophysical settings.

Exchange Processes in the Atmospheric Boundary Layer Over Mountainous Terrain

Abstract: The exchange of heat, momentum, and mass in the atmosphere over mountainous terrain is controlled by synoptic-scale dynamics, thermally driven mesoscale circulations, and turbulence. This article reviews the key challenges relevant to the understanding of exchange processes in the mountain boundary layer and outlines possible research priorities for the future. The review describes the limitations of the experimental study of turbulent exchange over complex terrain, the impact of slope and valley breezes on the structure of the convective boundary layer, and the role of intermittent mixing and wave–turbulence interaction in the stable boundary layer. The interplay between exchange processes at different spatial scales is discussed in depth, emphasizing the role of elevated and ground-based stable layers in controlling multi-scale interactions in the atmosphere over and near mountains. Implications of the current understanding of exchange processes over mountains towards the improvement of numerical weather prediction and climate models are discussed, considering in particular the representation of surface boundary conditions, the parameterization of sub-grid-scale exchange, and the development of stochastic perturbation schemes.

Investigation on ethylene glycol Nano fluid flow over a vertical permeable circular cylinder under effect of magnetic field

Abstract: In this research, the mixed convection stationary point flow of an incompressible viscous Nano fluid into a vertical permeable circular cylinder along with electric conductivity is analyzed. Ethylene glycol is used as an ordinary liquid, while nanoparticles include copper and silver. The problem has been calculated without the presence of an inductive and electrical magnetic field while taking into account homogeneous and heterogeneous reactions. The strong nonlinear systems calculations are presented using the Numerical Method after non-dimensionalization. Graphical analysis of the effective parameters such as Prandtl number ( Pr ) , permeability parameter ( V w ) , Schmidt number ( Sc ) , magnetic parameter ( M ) , mixed convection parameter ( λ ) and curvature parameter ( γ ) is precisely investigated on the profiles of velocity, concentration and temperature for different nanoparticles. Conclusions indicate that: The thickness of the thermal boundary layer changes more than the thickness of the hydro-dynamic boundary layer for injection and suction. Also, due to the higher thermal conductivity of silver nanoparticles, the temperature increase in these nanoparticles is more than that of copper. In fact, this paper shows that the heat transfer rate increases with the addition of nanoparticles. In addition, the role of the curvature parameter ( γ ) on the concentration profile shows that the concentration profile decreases with the gradual increase of γ .

A mathematical model of MHD nanofluid flow having gyrotactic microorganisms with thermal radiation and chemical reaction effects

Abstract: In this article, we have examined three-dimensional unsteady MHD boundary layer flow of viscous nanofluid having gyrotactic microorganisms through a stretching porous cylinder. Simultaneous effects of nonlinear thermal radiation and chemical reaction are taken into account. Moreover, the effects of velocity slip and thermal slip are also considered. The governing flow problem is modelled by means of similarity transformation variables with their relevant boundary conditions. The obtained reduced highly nonlinear coupled ordinary differential equations are solved numerically by means of nonlinear shooting technique. The effects of all the governing parameters are discussed for velocity profile, temperature profile, nanoparticle concentration profile and motile microorganisms' density function presented with the help of tables and graphs. The numerical comparison is also presented with the existing published results as a special case of our study. It is found that velocity of the fluid diminishes for large values of magnetic parameter and porosity parameter. Radiation effects show an increment in the temperature profile, whereas thermal slip parameter shows converse effect. Furthermore, it is also observed that chemical reaction parameter significantly enhances the nanoparticle concentration profile. The present study is also applicable in bio-nano-polymer process and in different industrial process.

Trailing-edge flow and noise control using porous treatments

Abstract: This paper is concerned with the application of porous treatments as a means of flow and aerodynamic noise reduction. An extensive experimental investigation is undertaken to study the effects of flow interaction with porous media, in particular in the context of the manipulation of flow over blunt trailing edges and attenuation of vortex shedding. Comprehensive boundary layer and wake measurements have been carried out for a long flat plate with solid and porous blunt trailing edges. Unsteady velocity and surface pressure measurements have also been performed to gain an in-depth understanding of the changes to the energy–frequency content and coherence of the boundary layer and wake structures as a result of the flow interaction with a porous treatment. Results have shown that permeable treatments can effectively delay the vortex shedding and stabilize the flow over the blunt edge via mechanisms involving flow penetration into the porous medium and discharge into the near-wake region. It has also been shown that the porous treatment can effectively destroy the spanwise coherence of the boundary layer structures and suppress the velocity and pressure coherence, particularly at the vortex shedding frequency. The flow–porous scrubbing and its effects on the near-wall and large coherent structures have also been studied. The emergence of a quasi-periodic recirculating flow field inside highly permeable surface treatments has also been investigated. Finally, the paper has identified several important mechanisms concerning the application of porous treatments for aerodynamic and aeroacoustic purposes, which can help more effective and tailored designs for specific applications.

Comparative investigation of five nanoparticles in flow of viscous fluid with Joule heating and slip due to rotating disk

Abstract: Present article addresses the comparative study for flow of five water based nanofluids. Flow in presence of Joule heating is generated by rotating disk with variable thickness. Nanofluids are suspension of Silver ( A g ), Copper ( C u ), Copper oxide ( C u O ), Aluminum oxide or Alumina ( A l 2 O 3 ), Titanium oxide or titania ( T i O 2 ) and water. Boundary layer approximation is applied to partial differential equations. Using Von Karman transformations the partial differential equations are converted to ordinary differential equations. Convergent series solutions are obtained. Graphical results are presented to examine the behaviors of axial, radial and tangential velocities, temperature, skin friction and Nusselt number. It is observed that radial, axial and tangential velocities decay for slip parameters. Axial velocity decays for larger nanoparticle volume fraction. Effect of nanofluids on velocities dominant than base material. Temperature rises for larger Eckert number and temperature of silver water nanofluid is more because of its higher thermal conductivity. Surface drag force reduces for higher slip parameters. Transfer of heat is more for larger disk thickness index.

Moving beyond Moody

Abstract: Thakkar et al. (J. Fluid Mech., vol. 837, 2018, R1) represents a significant advancement in the ability to computationally model rough wall flows. Direct numerical solution (DNS) of turbulent boundary layer flow over an industrial grit blasted surface at relevant roughness Reynolds numbers, from hydraulically smooth to fully rough regimes, is a path forward to parametrically study a wide range of surface roughness. The methodology described in this paper, coupled with validation experiments, ultimately should lead to improved frictional drag predictions.

Characterization of superhydrophobic surfaces for drag reduction in turbulent flow

Abstract: A significant amount of the fuel consumed by marine vehicles is expended to overcome skin-friction drag resulting from turbulent boundary layer flows. Hence, a substantial reduction in this frictional drag would notably reduce cost and environmental impact. Superhydrophobic surfaces (SHSs), which entrap a layer of air underwater, have shown promise in reducing drag in small-scale applications and/or in laminar flow conditions. Recently, the efficacy of these surfaces in reducing drag resulting from turbulent flows has been shown. In this work we examine four different, mechanically durable, large-scale SHSs. When evaluated in fully developed turbulent flow, in the height-based Reynolds number range of 10 000 to 30 000, significant drag reduction was observed on some of the surfaces, dependent on their exact morphology. We then discuss how neither the roughness of the SHSs, nor the conventional contact angle goniometry method of evaluating the non-wettability of SHSs at ambient pressure, can predict their drag reduction under turbulent flow conditions. Instead, we propose a new characterization parameter, based on the contact angle hysteresis at higher pressure, which aids in the rational design of randomly rough, friction-reducing SHSs. Overall, we find that both the contact angle hysteresis at higher pressure, and the non-dimensionalized surface roughness, must be minimized to achieve meaningful turbulent drag reduction. Further, we show that even SHSs that are considered hydrodynamically smooth can cause significant drag increase if these two parameters are not sufficiently minimized.

Magnetic source impact on nanofluid heat transfer using CVFEM

Abstract: Influence of variable magnetic field on Fe3O4–H2O heat transfer in a cavity with circular hot cylinder is investigated. Innovative numerical method is chosen, namely CVFEM. The effects of radiation parameter, Rayleigh and Hartmann numbers on hydrothermal characteristics are presented. Results indicated that Lorentz forces cause the nanofluid motion to decrease and augment the thermal boundary layer thickness. Temperature gradient augments with augmentation of radiation parameter, Rayleigh number, but it reduces with augmentation of Lorentz forces.

Active and Passive Turbulent Boundary-Layer Drag Reduction

Abstract: A 50 year journey through flow control strategies that seek to achieve viscous drag reduction in turbulent boundary layers is presented. These are shown to focus on different mechanisms underlying ...

Determination of epsilon for Omega vortex identification method

Abstract: In the present paper, epsilon (e) in the Omega vortex identification criterion (Ω method) is defined as an explicit function in order to apply the Ω method to different cases and even different time steps for the unsteady cases. In our method, e is defined as a function relating with the flow without any subjective adjustment on its coefficient. The newly proposed criteria for the determination of e is tested in several typical flow cases and is proved to be effective in the current work. The test cases given in the present paper include boundary layer transition, shock wave and boundary layer interaction, and channel flow with different Reynolds numbers.

Fully resolved measurements of turbulent boundary layer flows up to

Abstract: Fully resolved measurements of turbulent boundary layers are reported for the Reynolds number range . Despite several decades of research in wall-bounded turbulence there is still controversy over the behaviour of streamwise turbulence intensities near the wall, especially at high Reynolds numbers. Much of it stems from the uncertainty in measurement due to finite spatial resolution. Conventional hot-wire anemometry is limited for high Reynolds number measurements due to limited spatial resolution issues that cause attenuation in the streamwise turbulence intensity profile near the wall. To address this issue we use the nano-scale thermal anemometry probe (NSTAP), developed at Princeton University to conduct velocity measurements in the high Reynolds number boundary layer facility at the University of Melbourne. The NSTAP has a sensing length almost one order of magnitude smaller than conventional hot-wires. This enables us to acquire fully resolved velocity measurements of turbulent boundary layers up to . Results show that in the near-wall region, the viscous-scaled streamwise turbulence intensity grows with in the Reynolds number range of the experiments. A second outer peak in the streamwise turbulence intensity is also shown to emerge at the highest Reynolds numbers. Moreover, the energy spectra in the near-wall region show excellent inner scaling over the small to moderate wavelength range, followed by a large-scale influence that increases with Reynolds number. Outer scaling in the outer region is found to collapse the energy spectra over high wavelengths across various Reynolds numbers.

Wall-attached structures of velocity fluctuations in a turbulent boundary layer

Abstract: Wall turbulence is a ubiquitous phenomenon in nature and engineering applications, yet predicting such turbulence is difficult due to its complexity. High-Reynolds-number turbulence arises in most practical flows, and is particularly complicated because of its wide range of scales. Although the attached-eddy hypothesis postulated by Townsend can be used to predict turbulence intensities and serves as a unified theory for the asymptotic behaviours of turbulence, the presence of coherent structures that contribute to the logarithmic behaviours has not been observed in instantaneous flow fields. Here, we demonstrate the logarithmic region of the turbulence intensity by identifying wall-attached structures of the velocity fluctuations ( structures. These findings suggest that the identified structures are prime candidates for Townsend’s attached-eddy hypothesis and that they can serve as cornerstones for understanding the multiscale phenomena of high-Reynolds-number boundary layers.