Study of fluid layer gravity motion over vertical surface

Chapter 1 - INTRODUCTION

The calculation of the external boundary layer and associated heat transfer to turbine blading is described. Three separate Two-Dimensional Boundary Layer programs were utilised in this study. The programs incorporated the k-epsilon turbulence model with several different formulations. The test case chosen for this study was the von Karman Institute blade VKI Tech. Note-174, Sept-1990. It is shown that in most cases all programs tend to predict the correct behaviour of the onset of transition. However, the transition length between the laminar and turbulent values is predicted too abruptly on the blade suction side. It was found that the magnitude of the predicted heat transfer coefficient was most consistent with experimental values for exit Mach numbers between 0.7–0.9, and for all inlet turbulence levels and Reynolds numbers. For higher blade exit Mach numbers in the transonic region (M > 0.95) it was difficult to correctly predict the heat transfer in comparison with experimental data. The predicted values were all higher than the measurement. For this blade, the pressure side is quite well predicted for most of the operating conditions.

Transitional two-dimensional boundary-layer flows are considered. The algebraic eddy-viscosity model for a simulation of nonturbulent (laminar) boundary layers is proposed. It takes into account, in a simple form, an intensity and a length scale of the free stream turbulence (FST) and a value of the favorable pressure gradient. Transition is modeled by employing the intermittency factor. The Baldwin-Lomax model is used to calculate turbulent portions of the boundary layers. The boundary layer (BL) and heat transfer measurements for flows over a flat plate were employed to verify the proposed nonturbulence model and for an evaluation of the numerical code abilities to predict heat transfer for transitional flows. The code was applied for the calculation of heat transfer coefficients of two different gas turbine vanes, and the results were compared with available experimental data at different free-stream turbulence and Reynolds number conditions

Transient free convection flow of a viscoelastic fluid over vertical surface

The flow characteristics and the heat transfer rate on a surface by interaction of a pair of vortices were studied experimentally. The test facility consisted of a boundary-layer wind tunnel with a vortex introduced into the flow by half-delta wings protruding from the surface. In order to control the strength of the longitudinal vortices, the angles of attack of the vortex generators were varied from - 20 degree to - 45 degree, but spacings between the vortex generators were fixed to 4 cm. The 3-dimensional mean velocity measurements were made using a five-hole pressure probe. Heat transfer measurements were made using the thermochromatic liquid to provide the local distribution of the heat transfer coefficient. Unlike common flow down, common flow up vortices moved toward the centerline as they developed and interacted strongly with each other but not with the boundary layer. Spanwise profiles of Stanton number were similar for , but not similar for . The case of showed the two peak Stanton number, but the case of showed the only one peak Stanton number.

An asymptotic model of the flow in the laminar boundary layer of a gas-evaporating droplet mixture is constructed within the framework of the two-continuum approximation. The case of evaporation of the droplets into an atmosphere of their own vapor is examined in detail with reference to the example of longitudinal flow over a hot flat plate. Numerical and asymptotic solutions of the boundary layer equations constructed are found for a number of limiting situations (low droplet concentration, no droplet deposition, significant droplet deposition). The development of the flow with respect to the longitudinal coordinate is studied and it is shown that in the absence of droplet deposition a region of pure vapor may be formed near the surface. Similarity criteria are established and the mechanism of surface heat transfer enhancement is studied for a low evaporating droplet concentration in the boundary layer. In the inertial deposition regime the results of calculating the integral heat transfer coefficient are found to correspond with the experimental data [1].

A boundary layer transition model is developed that accounts for the effects of periodic unsteady wake flow on the boundary layer transition. To establish the model, comprehensive unsteady boundary layer and heat transfer experimental investigations are conducted. The experiments are performed on a curved plate at zero-streamwise pressure gradient under periodic unsteady wake flow, where the frequency of the periodic unsteady flow is varied. The analysis of the time-dependent velocities, turbulence intensities, and turbulence intermittencies has identified three distinct quantities as primarily responsible for the transition of an unsteady boundary layer. These quantities, which exhibit the basis of the transition model presented in this paper, are: (1) relative intermittency, (2) maximum intermittency, and (3) minimum intermittency. To validate the developed transition model, it is implemented in an existing boundary layer code, and the resulting velocity profiles and the heat transfer coefficients are compared with the experimental data.

Evolution of disturbances in three-dimensional boundary layers

The unsteady shock-induced laminar boundary layer on a flat plate is theoretically studied for shock speeds ranging from 1.12 to 9 km/sec. Boundary layer flows for real air, assumed to be in thermochemical equilibrium, are analyzed by extending Lam's work on shock-induced laminar boundary layers to equilibrium dissociated and ionized flows. A complete description of the unsteady nature of the boundary layer is presented in terms of heat transfer and several boundary layer thickness quantities as functions of a single time-position variable. Boundary layer development is considered for two points of view. Time-dependent boundary layer development and approach to steady state for any fixed position on the plate is described, as is the configuration of the boundary layer with position on the plate at any point in time. Quantities presented in graphical form permit accurate values for descriptive boundary layer quantities to be easily obtained for post shock pressures at or near 1 atm. Results indicate that in shock-tube experiments where observations of the flow are made through a boundary layer that influences experimental measurements, it is desirable to employ a flat plate to generate a boundary layer that minimizes the boundary layer thickness and diminishes or eliminates boundary layer unsteadiness.

We derive an integral formula for the skin-friction coefficient of compressible boundary layers by extending the formula of Elnahhas and Johnson [“On the enhancement of boundary layer skin friction by turbulence: An angular momentum approach,” J. Fluid Mech. 940, A36 (2022)] for incompressible boundary layers. The skin-friction coefficient is decomposed into the sum of the contributions of the laminar coefficient, the change of the dynamic viscosity with the temperature, the Favre–Reynolds stresses, and the mean flow. This decomposition is applied to numerical data for laminar and turbulent boundary layers, and the role of each term on the wall-shear stress is quantified. We also show that the threefold integration identity of Gomez et al. [“Contribution of Reynolds stress distribution to the skin friction in compressible turbulent channel flows,” Phys. Rev. E 79(3), 035301 (2009)] and the twofold integration identities of Wenzel et al. [“About the influences of compressibility, heat transfer and pressure gradients in compressible turbulent boundary layers,” J. Fluid Mech. 930, A1 (2022)] and Xu et al. [“Skin-friction and heat-transfer decompositions in hypersonic transitional and turbulent boundary layers,” J. Fluid Mech. 941, A4 (2022)] for turbulent boundary layers all simplify to the compressible von Kármán momentum integral equation when the upper limit of integration is asymptotically large. The dependence of these identities on the upper integration bound is studied. By using asymptotic methods, we prove that the multiple-integration identity of Wenzel et al. [“About the influences of compressibility, heat transfer and pressure gradients in compressible turbulent boundary layers,” J. Fluid Mech. 930, A1 (2022)] degenerates to the definition of the skin-friction coefficient when the number of integrations is asymptotically large.

Instability of three-dimensional boundary layers was studied intensively both theoretically and experimentally last decade [1, 2]. Such boundary layers take place, in particularly, on swept wings of airplanes in the regions of negative and positive pressure gradients. Practically, all investigations were conducted for subsonic speeds. This problem is not solved till now in spite of a large number of the investigations. There is a qualitative difference in calculations and experimental data and in experimental results of different research groups. The complication of the problem lies in the fact that additional instability waves connected with cross-flows are developing in three-dimensional case side by side with well-known Tollmien-Schlichting waves, development of which leads to the laminar-turbulent transition in two-dimensional boundary layers. They are steady vortexes with axis directed approximately in the directions of outer flow streamlines and some traveling (not Tollmien-Schlichting waves). The development of all of these waves and their relative role in the transition process depends strongly on outer conditions.KeywordsSupersonic Boundary LayerFlat Plate Boundary LayerTransition Reynolds NumberPositive Pressure GradientSteady VortexThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A general series method is reviewed for the solution of laminar, two-dimensional boundary layers on moving surfaces. Various methods for the determination of the radius of convergence of such series are discussed. Three illustrative examples are given, namely the vapour boundary layer induced by film condensation on a vertical plate and the outer layer boundary layers produced by natural convection at high Prandtl number on horizontal and vertical plates.

Boundary layer effects in He and Ar driven disk MHD generators

In recent years, there has been considerable interest in the study of bump-based methods to modulate the stability of boundary layers (Breuer & Haritonidis, 1990; Breuer & Landahl, 1990; Fischer & Choudhari, 2004; Gaster et al., 1994; Joslin & Grosch, 1995; Rizzetta & Visbal, 2006; Tumin & Reshotko, 2005; White et al., 2005; Worner et al., 2003). These studies are mostly focused on the incompressible regime and have revealed several interesting aspects of bump modulated flows. Surface roughness can influence the location of laminar-turbulent transition by two potential mechanisms. First, they can convert external large-scale disturbances into small-scale boundary layer perturbations, and become possible sources of receptivity. Second, they may generate new disturbances to stabilize or destabilize the boundary layer. Breuer and Haritonidis (Breuer & Haritonidis, 1990) and Breuer and Landahl (Breuer & Landahl, 1990) performed numerical and experimental simulations to study the transient growth of localized weak and strong disturbances in a laminar boundary layer. They demonstrated that the three-dimensionality in the evolution of localized disturbances may be seen at any stage of the transition process and is not necessarily confined to the nonlinear regime of the flow development. For weak disturbances, the initial evolution of the disturbances resulted in the rapid formation of an inclined shear layer, which was in good agreement with inviscid calculations. For strong disturbances, however, transient growth gives rise to distinct nonlinear effects, and it was found that resulting perturbation depends primarily on the initial distribution of vertical velocity. Gaster et al.(Gaster et al., 1994) reported measurements on the velocity field created by a shallow oscillating bump in a boundary layer. They found that the disturbance was entirely confined to the boundary layer, and the spanwise profile of the disturbance field near the bump differed dramatically from that far downstream. Joslin and Grosch (Joslin & Grosch, 1995) performed a Direct Numerical Simulation (DNS) to duplicate the experimental results by Gaster et al. (Gaster et al., 1994). Far downstream, the bump generated a pair of counter-rotating streamwise vortices just above the wall and on either side of the bump location, which significantly affected the near-wall flow structures. Worner et al. (Worner et al., 2003) numerically studied the effect of a localized hump on Tollmien-Schlichting waves traveling across it in a two-dimensional laminar boundary layer. They observed that the destabilization by a localized humpwasmuch strongerwhen its height was increased as opposed to its width. Further, a rounded shape was less destabilizing than a rectangular shape.

Purpose – The purpose of this paper is to report a numerical solution for the problem of steady, two dimensional boundary layer buoyant flow on a vertical magnetized surface, when both the viscosity and thermal conductivity are assumed to be temperature-dependent. In this case, the motion is governed by a coupled set of three nonlinear partial differential equations, which are solved numerically by using the finite difference method (FDM) by introducing the primitive variable formulation. Calculations of the coupled equations are performed to investigate the effects of the different governing parameters on the profiles of velocity, temperature and the transverse component of magnetic field. The effects of the thermal conductivity variation parameter, viscosity variation parameter, magnetic Prandtl number Pmr, magnetic force parameter S, mixed convection parameter Ri and the Prandtl number Pr on the flow structure and heat transfer characteristics are also examined. Design/methodology/approach – FDM. Findings – It is noted that when the Prandtl number Pr is sufficiently large, i.e. Pr=100, the buoyancy force that driven the fluid motion is decreased that decrease the momentum boundary layer and there is no change in thermal boundary layer is noticed. It is also noted that due to slow motion of the fluid the magnetic current generates which increase the magnetic boundary layer thickness at the surface. It is observed that the momentum boundary layer thickness is increased, thermal and magnetic field boundary layers are decreased with the increase of thermal conductivity variation parameter =100. The maximum boundary layer thickness is increased for =100 and there is no change seen in the case of thermal boundary layer thickness but magnetic field boundary layer is deceased. The momentum boundary layer thickness shoot quickly for =40 but is very smooth for =50.There is no change is seen for the case of thermal boundary layer and very clear decay for =40 is noted. Originality/value – This work is original research work.