Study of thermal flows from two-dimensional,upward-facing isothermal surfaces using a laser speckle photography technique

A laser specklegram or speckle photography technique allows a direct measurement of surface temperature gradients and provides a full field interrogation with an extremely high resolution from a single data taking. The specklegram technique has been successfully applied to investigate the natural convection heat transfer from an upward-facing isothermal plate. For a plate with a large aspect ratio of 15, both local and global Nusselt numbers have been determined from the direct measurement of local temperature gradients. The Rayleigh number, based on the length scale equivalent to the ratio of the surface area to the perimeter, has been varied from 9.0 × 10³ to 4.0 × 10⁴. The present result for the global heat transfer has shown that a 1/5-power law, i.e., Nu = C₁ Ra ^1/5, correlates the data more properly whilst previously published results showed a large scatter in the exponent, ranging from 1/8-power to 1/4-power. The proportional constant, C₁ has been determined to be 0.56 which shows a fairly good agreement with previously published theoretical results. The laser specklegram technique has shown a strong potential as a powerful and convenient method for an experimental assessment of natural convection heat transfer problems. The specklegram technique at the same time has eliminated the deficiencies of both the mass transfer analogy technique and the classical heat transfer measurement technique.List of symbols a characteristic length scale defined as a = A/P where A is the surface area and P is the perimeter of the plate edge [mm] - AR aspect ratio [L/H] - c defocusing distance [mm] - d image distance of Young's fringes from speckle negative - h thermal convection coefficient [W/m² · K] - average thermal convection coefficient [W/m² · °C] - H width of the test section measured perpendicular to the optic axis [mm] - k thermal conductivity [W/m · K] - L length of the test section measured parallel to the optical axis [mm] - n index of refraction - Nu local Nusselt number [ha/k] - global Nusselt number - Pr Prandtl number [v/] - q heat flux per unit area [W/m² · s] - Ra Rayleigh number - s fringe spacing [mm] - Sc Schmidt number [v/D] - T temperature [K] Greek symbols thermal diffusivity [m²/s] - volumetric coefficient of expansion (1/T) - v kinematic viscosity of air [m²/s] - wavelength of helium-neon laser [632.8 nm] - amount of speckle dislocation     

Wake layer in a thermal turbulent boundary layer with pressure gradient

The open equations of thermal turbulent boundary layer subjected to pressure gradient have been analysed by method of matched asymptotic expansions at large Reynolds number. The flow is divided into outer wake layer and inner wall layer. The asymptotic expansions are matched by Millikan-Kolmogorov hypothesis. The temperature profile in overlap region yields composite law which reduce to log. law for moderate pressure gradient and inverse half power law for strong adverse pressure gradient. In case of a shallow thermal wake, the matching result of outer wake layer reduces to composite temperature defect law, which is more general than the classical log. law. The comparison of data for thermal boundary layer with strong adverse pressure gradient is also considered. Received on 26 May 1998     

An efficient numerical method for solving Falkner–Skan boundary layer flows

In this paper a novel computational technique for the solution of nonlinear third‐order boundary value problems is presented. We demonstrate the application of the method by solving the famous Falkner–Skan equation on a semi‐infinite domain. Comparison with the results from other methods such as the homotopy analysis method and numerical methods demonstrates the accuracy, computational efficiency and robustness of this technique. Copyright © 2011 John Wiley & Sons, Ltd.     

VITA measurements of transition in transitional hypersonic boundary layer flows

The variable interval time-averaging (VITA) technique is applied to the hot-wire measurements made in three axisymmetric, transitional hypersonic boundary layers. The average duration of conditionally sampled events is used to detect the transition region. It is found that the stability Reynolds number at the peak in the average duration of conditionally sampled events correlates well with the stability Reynolds number that is intermediate to the onset of transition and peak heating. This VITA-identified location of transition moves upstream under the effects of both an adverse pressure gradient and wall cooling; this agrees with previous experimental and computational studies. The VITA technique, therefore, offers an alternative method to obtain details of the location of transition in hypersonic stability experiments, in which hot-wire measurements of the transitioning boundary layers are made.     

Synthetic method in thermal boundary layer transition

The problem of a general incompressible viscous fluid flow past a flat plate with heat transfer due to forced convection is considered in this paper. The synthetic method developed by Seth is applied to the Navier-Stokes equations and the equation of energy governing the flow to obtain the dynamic and thermal boundary layer solutions as asymptotic limits of an extended field. As a result, new formulas are derived for both the dynamic and thermal boundary layer thicknesses. Also, algorithms for estimating all the parameters involved in the analysis are provided and boundary layer functions based on the new solutions are determined.     

A proposed intermittency measurement method for transitional boundary layer flows

A new turbulent intermittency detector method, based on the Turbulent Energy Recognition Algorithm (TERA), has been proposed. Its performance was compared with two other available methods using the data obtained from hot-wire measurements in a developing boundary layer flow on a concave surface with constant radius of curvature of 2 m. Comparisons show that this new method is better than the other two as a turbulent detector under the same flow conditions, especially in the near-wall and in the outer and outside regions of the boundary layer.     

Measurement of an axisymmetric temperature field by speckle photography methods

Two alternative procedures to measure the temperature distribution in an axisymmetric hot water jet using the principle of speckle photography are reported. The two methods differ in the position of the speckle generator with respect to the jet and light source. They produce comparable results, but the uncertainties associated with them are different owing to dissimilar fringe visibilities.Financial support from Conicyt, Chile, research grants 1930620 and 1950914, is gratefully acknowledged. A preliminary version of this paper was presented at a Conference (Lira and Keller, 1994).     

Approximate method for calculating turbulent boundary layer with positive pressure gradient

A single-parameter integral method is proposed for calculating the turbulent boundary layer with positive pressure gradient which makes it possible to calculate the friction, thermal flux, and layer thickness both ahead of the separation point and in some region behind the separation point.Notation u velocity - density - ^* displacement thickness - ^** momentum thickness - energy thickness - M Mach number - r radius - dynamic viscosity - c_p specific heat at constant pressure - Reynolds number based on initial boundary layer thickness - P Prandtl number - p₁ static pressure at point of initial interaction - p₂ static pressure at pressureplateau - p₀ stagnation pressure - T₀ stagnation temperature - I enthalpy - T_e recovery temperature - T_w ⁰ temperature factor - H form parameter - r₁ recovery coefficient Indices 0 denotes initial section of boundary layer - 1 parameters taken at edge of boundary layer - w parameters taken at the wall temperature - * parameters referred to flow on a flat plate with =0     

Simultaneous measurements of velocity and temperature fluctuations in thermal boundary layer in a drag-reducing surfactant solution flow

The mechanism of turbulent heat transfer in the thermal boundary layer developing in the channel flow of a drag-reducing surfactant solution was studied experimentally. A two-component laser Doppler velocimetry and a fine-wire thermocouple probe were used to measure the velocity and temperature fluctuations simultaneously. Two layers of thermal field were found: a high heat resistance layer with a high temperature gradient, and a layer with a small or even zero temperature gradient. The peak value of was larger for the flow with the drag-reducing additives than for the Newtonian flow, and the peak location was away from the wall. The profile of was depressed in a similar manner to the depression of the profile of in the flow of the surfactant solution, i.e., decorrelation between v and compared with decorrelation between u and v. The depression of the Reynolds shear stress resulted in drag reduction; similarly, it was conjectured that the heat transfer reduction is due to the decrease in the turbulent heat flux in the wall-normal direction for a flow with drag-reducing surfactant additives.List of symbols ensemble averaged value - (·)⁺ normalized by the inner wall variables - (·) root-mean-square value - C concentration of cetyltrimethyl ammonium chloride (CTAC) solution - c _p heat capacity - D hydraulic diameter - f friction factor - H channel height - h heat transfer coefficient - j _H Colburn factor - l length - Nu Nusselt number, h - Pr Prandtl number, c _p/ - q _w wall heated flux - Re Reynolds number, U _b/ - T temperature - T _b bulk temperature - T _i inlet temperature - T _w wall temperature - T friction temperature, q _w /c _p u - U local time-mean streamwise velocity - U ₁ velocity signals from BSA1 - U ₂ velocity signals from BSA2 - U _b bulk velocity - u streamwise velocity fluctuation - u1 velocity in abscissa direction in transformed coordinates - u friction velocity, - v wall-normal velocity fluctuation - v1 velocity in ordinate direction in transformed coordinates - var(·) variance - x streamwise direction - y wall-normal direction - z spanwise direction - _j junction diameter of fine-wire TC - _w wire diameter of fine-wire TC - angle of principal axis of joint probability function p(u,v) - _f heat conduction of fluid - _w heat conduction of wire of fine-wire TC - kinematic viscosity - local time-mean temperature difference, T _w –T - temperature fluctuation - standard deviation - density - _w wall shear stress     

Evaluation of a laser velocity gradient probe and measurements in a boundary layer

Mean and rms profiles of the wall-normal gradient of the streamwise velocity were obtained in a boundary layer using a recently proposed laser velocity gradient technique (LVG). An analysis was also carried out to estimate data rates and to determine potential sources of measurement error. The results of this study demonstrate the viability of this novel measurement technique in shear flows.     

二维边界层方程的迭代求解

针对二维边界层方程,提出了分析积分迭代法.首先将该方法应用于Blasius方程和Falkner-Skan方程的求解,数值计算结果稳定,计算精度高;然后对外部有势流不能达到自相似要求、必须二维求解的二维层流边界层问题,在分析积分迭代法中加上计算力学的松弛迭代法,形成了一套有效的算法.数值结果表明该方法用于层流边界层的计算是很有效的.     

An immersed boundary method for fluid flows around rigid objects

In this paper, we present an immersed boundary method for solving fluid flow problems in the presence of static and moving rigid objects. A FEM is used starting from a base mesh that does not represent exactly rigid objects (non?body?conforming mesh). At each time step, the base mesh is locally modified to provide a new mesh fitting the boundary of the rigid objects. The mesh is also locally improved using edge swapping to enhance the quality of the elements. The Navier–Stokes equations are then solved on this new mesh. The velocity of moving objects is imposed through standard Dirichlet boundary conditions. We consider a number of test problems and compare the numerical solutions with those obtained on classical body?fitted meshes whenever possible. Copyright © 2014 John Wiley & Sons, Ltd.     

An immersed boundary method for simulation of inviscid compressible flows

In this paper, an immersed boundary method for simulating inviscid compressible flows governed by Euler equations is presented. All the mesh points are classified as interior computed points, immersed boundary points (interior points closest to the solid boundary), and exterior points that are blanked out of computation. The flow variables at an immersed boundary point are determined via the approximate form of solution in the direction normal to the wall boundary. The normal velocity is evaluated by applying the no‐penetration boundary condition, and therefore, the influence of solid wall in the inviscid flow is taken into account. The pressure is computed with the local simplified momentum equation, and the density and the tangential velocity are evaluated by using the constant‐entropy relation and the constant‐total‐enthalpy relation, respectively. With a local coordinate system, the present method has been extended easily to the three‐dimensional case. The present work is the first endeavor to extend the idea of hybrid Cartesian/immersed boundary approach to compressible inviscid flows. The tedious task of handling multi‐valued points can be eliminated, and the overshoot resulting from the extrapolation for the evaluation of flow variables at exterior points can also be avoided. In order to validate the present method, inviscid compressible flows over fixed and moving bodies have been simulated. All the obtained numerical results show good agreement with available data in the literature. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of the secondary stability of compressible boundary layer flows over a two-dimensional plate

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Velocity measurements in the field of an internal gravity wave by means of speckle photography

Speckle velocimetry with forward scattering has been applied to measure and visualize the two-dimensional velocity field in an internal gravity wave. The wave was produced by towing a cylinder in vertical direction, normal to its axis, through stratified salt water. Neutrally buoyant tracer particles whose density was matched with the density distribution of the stratification were uniformly distributed in the test fluid. The experimental results verify the results of a linear theory in the far field of the wave.Most part of this work was performed when the three authors were with Institut für Thermo- und Fluiddynamik, Ruhr-Universität Bochum.     

Condensation by heterogeneous nucleation in a thermal boundary layer

Condensation can occur by the nucleation and growth of water droplets on particles in the air. This mode of mass transport can readily occur in a thermal boundary layer. The primary condition required for droplet nucleation is the existence of supersaturation in the boundary layer. Equations are developed to described droplet nucleation an d transport for the boundary layer on a horizontal, upward facing surface. These equations allow diffusion and nucleation mass fluxes and droplet concentration at a point in the boundary layer to be calculated. Experimental data were collected and compared to the theoretical calculations. Accurately predicting droplet concentration is difficult, but the presence of nucleation condensation can be readily predicted.     

An unsteady-state thermal boundary layer on a flat isothermal plate

The Kármán-Polhausen integral method is used to investigate the problem of an unsteady-state thermal boundary layer on an isothermal plate with a stepwise change in the conditions of flow around the plate; analytical expressions are obtained for the thickness of the thermal boundary layer. A dependence is found for the rate of movement of the boundary between the steady-state and unsteady-state regions of the solution on the Prandtl number. A similar problem was solved in [1, 2] for a dynamic layer, Goodman [3] discusses the more partial problem of an unsteady-state thermal boundary layer under steady-state flow conditions. Rozenshtok [4] considers the problem in an adequate statement but, unfortunately, he permitted errors of principle to enter into the writing of the system of characteristic equations; this led to absolutely invalid results. In an evaluation of the advantages and shortcomings of the integral method under consideration, given in [4], it must only be added that the method is applicable to problems in which the initial conditions differ from zero since, in this case, approximation of the velocity and temperature profiles by polynomials is not admissible.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 64–69, July–August, 1970.     

An iterative method for solution of a boundary value problem in non-newtonian fluid flow

The boundary value problem

arises in boundary layer equations for the steady flow of a power-law fluid over an impermeable, semi-infinite flat plane. The parameter μ is equal to $\text{1}\text{n}$ where n is the exponent of the strain rate in the expression for the shear stress. We develop and prove the convergence of an iterative method for the solution of the given boundary value broblem for dilatant fluids (0 < μ <1). The iterative method can be easily implemented computationally. An added feature of our technique is that it accurately yields y(0), an important parameter which is related to the drag at the plate. The iterative method works well computationally not only for 0 < μ < 1 but for the range 1 < μ < 4 (pseudoplastic fluids with 1 > n > $\text{1}\text{4}$), as well.