Unsteady tip leakage characteristics and heat transfer on turbine blade tip and casing

An unsteady numerical investigation was performed to examine time dependent behaviors of the tip leakage flow structures and heat transfer on the rotor blade tip and casing in a single stage gas turbine engine. A transonic, high-pressure
turbine stage was modeled and simulated using a stage pressure ratio of 3.2. The rotor’s tip clearance was 1.2 mm in height (3% of the rotor span) and its speed was set at 9500 rpm. Periodic flow is observed for each vane passing period. Tip leakage flow as well as heat transfer data showed highly time dependent behaviors. A stator trailing edge shock appears as the turbine stage is operating at transonic conditions. The shock alters the flow condition in the rotor section, namely, the tip leakage flow structures and heat transfer rate distributions. The instantaneous Nusselt number distributions are compared to the time averaged and steady-state results. The same patterns in tip leakage flow
structures and heat transfer rate distributions were observed in both unsteady and steady simulations. However, the unsteady simulation captured the locally time-dependent high heat transfer phenomena caused by the unsteady interaction with the upstream vane trailing-edge shock and the passing wake.

Heat transfer coefficients from Newtonian and non-Newtonian fluids flowing in laminar regime in a helical coil

This study aimed to carry out experimental work to obtain, for Newtonian and non-Newtonian fluids, heat transfer coefficients, at constant wall temperature as boundary condition, in fully developed laminar flow inside a helical coil. The Newtonian fluids studied were aqueous solutions of glycerol, 25%, 36%, 43%, 59% and 78% (w/w) and the non-Newtonian fluids aqueous solutions of carboxymethylcellulose (CMC), a polymer, with concentrations 0.1%, 0.2%, 0.3%, 0.4% and 0.6% (w/w) and aqueous solutions of xanthan gum (XG), another polymer, with concentrations 0.1% and 0.2% (w/w). According to the rheological study performed, the polymer solutions had shear thinning behavior and different values of elasticity. The helical coil used has internal diameter, curvature ratio, length and pitch, respectively: 0.004575 m, 0.0263, 5.0 m and 11.34 mm. The Nusselt numbers for the CMC solutions are, on average, slightly higher than those for Newtonian fluids, for identical Prandtl and generalized Dean numbers. As outcome, the viscous component of the shear thinning polymer tends to potentiate the mixing effect of the Dean cells. The Nusselt numbers of the XG solutions are significant lower than those of the Newtonian solutions, for identical Prandtl and generalized Dean numbers. Therefore, the elastic component of the polymer tends to diminish the mixing effect of the Dean cells. A global correlation, for Nusselt number as a function of Péclet, generalized Dean and Weissenberg numbers for all Newtonian and non-Newtonian solutions studied, is presented.

FORCED CONVECTION TO LAMINAR FLOW OF LIQUID EGG YOLK IN CIRCULAR AND ANNULAR DUCTS

The steady-state heat transfer in laminar flow of liquid egg yolk - an important pseudoplastic fluid food - in circular and concentric annular ducts was experimentally investigated. The average convection heat transfer coefficients, determined by measuring temperatures before and after heating sections with constant temperatures at the tube wall, were used to obtain simple new empirical expressions to estimate the Nusselt numbers for fully established flows at the thermal entrance of the considered geometries. The comparisons with existing correlations for Newtonian and non-Newtonian fluids resulted in excellent agreement. The main contribution of this work is to supply practical and easily applicable correlations, which are, especially for the case of annulus, rather scarce and extensively required in the design of heat transfer operations dealing with similar shear-thinning products. In addition, the experimental results may support existing theoretical analyses.

Convection in fluid overlying porous layer : an application to Hall-Heroult cell

Finite-element method is used to predict the buoyancy-driven convection in a horizontal layer of fluid (aluminum melt) overlying a porous layer (cathode) saturated with the same fluid. This work aims to compare the Hall–Héroult process in electrolytic cell, where a layer of molten aluminum is reduced over the porous cathode surface. In this study, the physical system of the aluminum melt (fluid) and cathode (porous) together is considered as a composite system of fluid overlying porous layer. The main objective of this study to analyse the velocity components in thin fluid layer and its impact on a porous cathode surface if there is any. In addition, an externally imposed time-independent uniform magnetic field is used to analyse its influence on natural convective forces. The physical system of fluid overlying porous layer is analysed at different Hartmann, Darcy, and fluid-Rayleigh numbers for a fixed Prandtl number (Pr = 0.014). The predicted data show that the convective forces, caused by buoyancy-driven flow, are significant. It is shown that the velocity peaks moves toward the solid wall because of the presence of a magnetic field creating a stronger boundary-layer growth over the permeable cathode surface. The predicted results are plotted in terms of average Nusselt number and Darcy number to indicate the influence of pores and permeability on overall convective heat-transfer characteristics.

Natural convection in domed porous enclosures : non-darcian flow

The natural-convection flow and associated heat transfer in a fluid-saturated porous medium have been investigated using the generalized porous medium approach for a dome-shaped enclosure. Many new features have been predicted with the connective heat transfer and the shape of the top dome cover. The solutions are obtained for a wide range of Darcy and Rayleigh numbers for different offsets and eccentricities of the top dome covers. The detailed parametric study reveals that there is a significant change in heat transfer rate when the offset is between 0.2 and 0.4. Different shapes of conic section, such as circular, elliptical, parabolic, and hyperbolic are used for the top dome cover, and their effects on natural convection and heat transfer rates are studied.

A non-darcian numerical modeling in domed enclosures filled with heat-generating porous media

Numerical study of the natural-convection flow and heat transfer in a dome-shaped, heat-generating, porous enclosure is considered. The general conic equation for the top dome is used to consider various conical top sections such as circular, elliptical, parabolic, and hyperbolic. The individual effect of fluid Rayleigh, Darcy, and heat-generating parameters on flow patterns and heat transfer rates are analyzed and presented. The predicted results show that the heat-generating parameter has the most significant contribution toward the growth of bicellular core flow. Moreover, there is significant change in temperature distribution in comparison to rectangular enclosures, due to the existence of the domed-shape top adiabatic cover. The results also show that, regardless of Darcy and Rayleigh values, a flat adiabatic top cover tends to yield the highest value of Nusselt number, followed by circular, elliptical, parabolic, and hyperbolic top covers, respectively.

Transferência de calor combinando radiação e convecção no interior de dutos de geradores de vapor fumotubulares

Esta dissertação de mestrado considera a transferência de calor combinando convecção e radiação térmica no escoamento de gases participantes em dutos de seção circular. Partindo de uma metodologia geral, o trabalho enfoca principalmente os casos típicos de aplicação em geradores de vapor fumotubulares de pequeno e médio porte, em que gases em alta temperatura escoam através de um tubo mantido em temperatura uniforme. O escoamento é turbulento e o perfil de velocidade é plenamente desenvolvido desde a entrada do duto. A temperatura do gás, contudo, é uniforme na entrada, considerando-se a região de desenvolvimento térmico. Duas misturas de gases são tratadas, ambas constituídas por dióxido de carbono, vapor d’água e nitrogênio, correspondendo a produtos típicos da combustão estequiométrica de óleo combustível e metano. As propriedades físicas dos gases são admitidas uniformes em todo o duto e calculadas na temperatura de mistura média, enquanto que as propriedades radiantes são modeladas pela soma-ponderada-de-gases-cinzas. O campo de temperatura do gás é obtido a partir da solução da equação bidimensional da conservação da energia, sendo os termos advectivos discretizados através do método de volumes de controle com a função de interpolação Flux-Spline; as trocas de energia radiantes são avaliadas por meio do método das zonas, onde cada zona de radiação corresponde a um volume de controle. Em um primeiro passo, a metodologia é verificada pela comparação com resultados apresentados na literatura para a transferência de calor envolvendo apenas convecção e combinando convecção com radiação. Em seguida, discutem-se alguns efeitos da inclusão da radiação térmica, por exemplo, no número de Nusselt convectivo e na temperatura de mistura do gás. Finalmente, são propostas correlações para o número de Nusselt total, que leva em conta tanto a radiação quanto a convecção. Essa etapa exige inicialmente uma análise dos grupos adimensionais que governam o processo radiante para redução do número elevado de parâmetros independentes. As correlações, aplicáveis a situações encontradas em geradores de vapor fumotubulares de pequeno e médio porte, são validadas estatisticamente pela comparação com os resultados obtidos pela solução numérica.

Heat transfer in laminar flow of non-Newtonian fluids in ducts of elliptical section

Laminar forced convection inside tubes of various cross-section shapes is of interest in the design of a low Reynolds number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of simple geometries such as a circular tube, parallel plate, or annular duct has been well studied in the literature and documented in various books, but for elliptical duct there are not much work done. The main assumption used in this work is a laminar flow of a power flow inside elliptical tube, under a boundary condition of first kind with constant physical properties and negligible axial heat diffusion (high Peclet number). To solve the thermally developing problem, we use the generalized integral transform technique (GITT), also known as Sturm-Liouville transform. Actually, such an integral transform is a generalization of the finite Fourier transform where the sine and cosine functions are replaced by more general sets of orthogonal functions. The axes are algebraically transformed from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the elliptical duct wall. The GITT is then applied to transform and solve the problem and to obtain the once unknown temperature field. Afterward, it is possible to compute and present the quantities of practical interest, such as the bulk fluid temperature, the local Nusselt number and the average Nusselt number for various cross-section aspect ratios. (C) 2006 Elsevier. SAS. All rights reserved.

Friction factors, convective heat transfer coefficients and the Colburn analogy for industrial sugarcane juices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Forced convection to laminar flow of liquid egg yolk in circular and annular ducts

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A finite element free convection model for the side wall heated cavity

This paper presents a finite element numerical solution of free convection in a cavity with side walls maintained at constant but different temperatures. The predictions from the model and the method of solution were validated by comparison with the 'bench mark' solution and Vahl Davis' results and good agreement was found. The present model was used to obtain additional results over a wide range of Rayleigh number (10(3)-10(6)) and L/H ratios varying from 0.1 to 1.0. The predicted stream function patterns, temperature and velocity profiles as well as the mean Nusselt number were presented and discussed. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

Numerical and experimental analysis of natural convection in a cavity heated from below

In this work, an analysis of the natural convection flow caused by heat sources dissipating energy at a constant rate simulating electronic components mounted at the bottom surface of a cavity symmetrically cooled from the sides and insulated at the top is performed. This problem was studied numerically and experimentally for several aspect ratios (height/width), for different levels of dissipation in the sources, and for different side wall temperatures. Temperature and velocity fields were determined as well as the temperature variation along the surface where the sources are mounted and the average Nusselt number in the source surfaces. Numerical and experimental results were found to agree.