Mixed convection along a vertical flat plate in a non-absorbing medium

Here mixed convection boundary layer flow of a viscous fluid along a heated vertical semi-infinite plate is investigated in a non-absorbing medium. The relationship between convection and thermal radiation is established via boundary condition of second kind on the thermally radiating vertical surface. The governing boundary layer equations are transformed into dimensionless parabolic partial differential equations with the help of appropriate transformations and the resultant system is solved numerically by applying straightforward finite difference method along with Gaussian elimination technique. It is worthy to note that Prandlt number, Pr, is taken to be small (<< 1) which is appropriate for liquid metals. Moreover, the numerical results are demonstrated graphically by showing the effects of important physical parameters, namely, the modified Richardson number (or mixed convection parameter), Ri*, and surface radiation parameter, R, in terms of local skin friction and local Nusselt number coefficients.

Numerical study of lid-driven square cavity with heat generation using LBM

In this study, the mixed convection heat transfer and fluid flow behaviors in a lid-driven square cavity filled with high Prandtl number fluid (Pr = 5400, ν = 1.2×10-4 m2/s) at low Reynolds number is studied using thermal Lattice Boltzmann method (TLBM) where ν is the viscosity of the fluid. The LBM has built up on the D2Q9 model and the single relaxation time method called the Lattice-BGK (Bhatnagar-Gross-Krook) model. The effects of the variations of non dimensional mixed convection parameter called Richardson number(Ri) with and without heat generating source on the thermal and flow behavior of the fluid inside the cavity are investigated. The results are presented as velocity and temperature profiles as well as stream function and temperature contours for Ri ranging from 0.1 to 5.0 with other controlling parameters that present in this study. It is found that LBM has good potential to simulate mixed convection heat transfer and fluid flow problem. Finally the simulation results have been compared with the previous numerical and experimental results and it is found to be in good agreement.

Experiments on a plume with off-source heating: Implications for cloud fluid dynamics

We report here on a series of laboratory experiments on plumes, undertaken with the object of simulating the effect of the heat release that occurs in clouds on condensation of water vapor. The experimental technique used for this purpose relies on ohmic heating generated in an electrically conducting plume fluid subjected to a suitable alternating voltage across specified axial stations in the plume flow [Bhat et al., 1989]. The present series of experiments achieves a value of the Richardson number that is toward the lower end of the range that characteristics cumulus clouds. It is found that the buoyancy enhancement due to heating disrupts the eddy structures in the flow and reduces the dilution owing to entrainment of ambient fluid that would otherwise have occurred in the central region of the plume. Heating also reduces the spread rate of the plume, but as it accelerates the flow as well, the overall specific mass flux in the plume does not show a very significant change at the heat input employed in the experiment. However, there is some indication that the entrainment rate (proportional to the streamwise derivative of the mass flux) is slightly higher immediately after heat injection and slightly lower farther downstream. The measurements support a previous proposal for a cloud scenario [Bhat and Narasimha, 1996] and demonstrate how fresh insights into certain aspects of the fluid dynamics of clouds may be derived from the experimental techniques employed here.

The possible influence of curvature and rotation on ocean currents

Recent laboratory investigations have shown that rotation and (streamwise) curvature can have spectacular effects on momentum transport in turbulent shear flows. A simple model that takes account of these effects (based on an analogy with buoyant flows) utilises counterparts of the Richardson number Rg and the Monin-Oboukhov length. Estimates of Rg for meanders in ocean currents like the Gulf Stream show it to be of order 1 or more, while laboratory investigations reveal strong effects even at |Rg|∼0·1. These considerations lead to the conclusion that at a cyclonic bend in the Gulf Stream, a highly unstable flow in the outer half of the jet rides over a highly stable flow in the inner half. It is conjectured that the discrepancies noticed between observation and the various theories of Gulf Stream meanders, and such phenomena as the observed detachment of eddies from the Gulf Stream, may be due to the effects of curvature and rotation on turbulent transport.

Long waves in inviscid compressible atmosphere II

Solitary waves have been found in an adiabatic compressible atmosphere which, in ambient state, has winds and temperature gradient, generalizing our earlier results for the isothermal atmosphere. Explicit results are obtained for the special case of linear temperature and linear wind distributions in the undisturbed conditions. An important result of the study is that the number of possible critical speeds of the flow depends crucially on whether the maximum Richardson number (which is variable in the present example) is greater or less than 1/4.

Long waves in inviscid compressible atmospheres: Isothermal atmosphere

Solitary waves and cnoidal waves have been found in an adiabatic compressible atmosphere which, under ambient conditions, has winds, and is isothermal. The theory is illustrated with an example for which the background wind is linearly increasing. It is found that the number of possible critical speeds of the flow depends crucially on whether the Richardson number is greater or less than one‐fourth.

Long waves in inviscid compressible atmospheres: Isothermal atmosphere

Solitary waves and cnoidal waves have been found in an adiabatic compressible atmosphere which, under ambient conditions, has winds, and is isothermal. The theory is illustrated with an example for which the background wind is linearly increasing. It is found that the number of possible critical speeds of the flow depends crucially on whether the Richardson number is greater or less than one‐fourth.

Transition to turbulence in the free convection boundary layers on an inclined heated plate

An experimental study has been made of transition to turbulence in the free convective flows on a heated plate. Observations have been made with the plate vertical and inclined at angles up to about 50° to the vertical, both above and below the plate. A fibre anemometer was used to survey the region of intermittent turbulence. Information has thus been obtained about the range of Grashof numbers over which transition takes place. Even when the plate is vertical the region of intermittent turbulence is long. When it is inclined, this region becomes still longer in the flow below the plate as a result of the stabilizing stratification, a Richardson number effect. It is possible to have a whole flow such that it should be described as transitional, not laminar or turbulent. It was noticed that in this flow and the vertical plate one, the velocity during the laminar periods could be either of two characteristic values, one of them close to zero. The behaviour above an inclined plate could be interpreted largely as a trend towards the behaviour described in a preceding paper.

Effect of angle of incidence on mixed convective wake dynamics and heat transfer past a square cylinder in cross flow at Re=100

In this paper, a numerical investigation is performed to study the mixed convective flow and heat transfer characteristics past a square cylinder in cross flow at incidence. Utilizing air (Pr = 0.71) as an operating fluid, computations are carried out at a representative Reynolds number (Re) of 100. Angles of incidences are varied as, 0 degrees <= alpha <= 45 degrees. Effect of superimposed positive and negative cross-flow buoyancy is brought about by varying the Richardson number (RI) in the range -1.0 <= Ri <= 1.0. The detail features of flow topology and heat transport are analyzed critically for different angles of incidences. The thermo fluidic forces acting on the cylinder during mixed convection are captured in terms of the drag (C-D), lift (C-L), and moment (C-M) coefficients. The results show that the lateral width of the cylinder wake reduces with increasing alpha and the isotherms spread out far wide. In the range 0 degrees < alpha < 45 degrees, C-D reduces with increasing Ri. The functional dependence of C-M with Ri reveals a linear relationship. Thermal boundary layer thickness reduces with increasing angle of incidences. The global rate of heat transfer from the cylinder increases with increasing alpha. (C) 2014 Elsevier Ltd. All rights reserved.

Analysis of Entropy Generation During Mixed Convective Heat Transfer of Nanofluids Past a Rotating Circular Cylinder

The entropy generation due to mixed convective heat transfer of nanofluids past a rotating circular cylinder placed in a uniform cross stream is investigated via streamline upwind Petrov-Galerkin based finite element method. Nanosized copper (Cu) particles suspended in water are used with Prandtl number (Pr)=6.9. The computations are carried out at a representative Reynolds number (Re) of 100. The dimensionless cylinder rotation rate, a, is varied between 0 and 2. The range of nanoparticle volume fractions (phi) considered is 0 <= phi <= 5%. Effect of aiding buoyancy is brought about by considering two fixed values of the Richardson number (Ri) as 0.5 and 1.0. A new model for predicting the effective viscosity and thermal conductivity of dilute suspensions of nanoscale colloidal particles is presented. The model addresses the details of the agglomeration-deagglomeration in tune with the pertinent variations in the effective particulate dimensions, volume fractions, as well as the aggregate structure of the particulate system. The total entropy generation is found to decrease sharply with cylinder rotation rates and nanoparticle volume fractions. Increase in nanoparticle agglomeration shows decrease in heat transfer irreversibility. The Bejan number falls sharply with increase in alpha and phi.

Effect of Channel Confinement on Mixed Convective Flow Past an Equilateral Triangular Cylinder

The present work investigates the mixed convective flow and heat transfer characteristics past a triangular cylinder placed symmetrically in a vertical channel. At a representative Reynolds number, Re = 100, simulations are carried out for the blockage ratios beta = 1/3; 1/4; and 1/6. Effect of aiding and opposing buoyancy is brought about by varying the Richardson number in the range -1.0 <= Ri <= 1.0. At a blockage ratio of 1/3, suppression of vortex shedding is found at Ri = 1, whereas von Karman vortex street is seen both at beta = 1/4 and 1/6, respectively. This is the first time that such behavior of blockage ratio past a triangular cylinder in the present flow configuration is reported. Drag coefficient increases progressively with increasing Ri and a slightly higher value is noticed at beta = 1/3. For all b, heat transfer increases with increasing Ri. Flattening of Nu(avg)-Ri curve beyond Ri > 0: 75 is observed at beta = 1/3.

Potential energy model for turbulent entrainment across density interface in a linearly stratified fluid

A potential energy model is developed for turbulent entrainment in the absence of mean shear in a linearly stratified fluid. The relation between the entrainment distance D and the time t and the relation between dimensionless entrainment rate E and the local Richardson number are obtained. An experiment is made for examination. The experimental results are in good agreement with the model, in which the dimensionless entrainment distance D is given by DBAR = A(i)(SBAR)-1/4(fBAR)1/2(tBAR)1/8, where A(i) is the proportional coefficient, S is the dimensionless stroke, fBAR is the dimensionless frequency of the grid oscillation, tBAR the dimensionless time.

Growth of zero-mean-shear turbulent-mixed layer with suspended particles in a 2-layer fluid system

The growth behaviour of zero-mean-shear turbulent-mixed layer containing suspended solid particles has been studied experimentally and analysed theoretically in a two-layer fluid system. The potential model for estimating the turbulent entrainment rate of the mixed layer has also been suggested, including the results of the turbulent entrainment for pure two-layer fluid. The experimental results show that the entrainment behaviour of a mixed layer with the suspended particles is well described by the model. The relationship between the entrainment distance and the time, and the variation of the dimensionless entrainment rate E with the local Richardson number Ri1 for the suspended particles differ from that for the pure two-layer fluid by the factors-eta-1/5 and eta-1, respectively, where eta = 1 + sigma-0-DELTA-rho/DELTA-rho-0.

Towards understanding the mixing characteristics of turbulent buoyant flows

This work proposes a new simulation methodology in which variable density turbulent flows can be studied in the context of a mixing layer with or without the presence of gravity. Specifically, this methodology is developed to probe the nature of non-buoyantly-driven (i.e. isotropically-driven) or buoyantly-driven mixing deep inside a mixing layer. Numerical forcing methods are incorporated into both the velocity and scalar fields, which extends the length of time over which mixing physics can be studied. The simulation framework is designed to allow for independent variation of four non-dimensional parameters, including the Reynolds, Richardson, Atwood, and Schmidt numbers. Additionally, the governing equations are integrated in such a way to allow for the relative magnitude of buoyant energy production and non-buoyant energy production to be varied.

The computational requirements needed to implement the proposed configuration are presented. They are justified in terms of grid resolution, order of accuracy, and transport scheme. Canonical features of turbulent buoyant flows are reproduced as validation of the proposed methodology. These features include the recovery of isotropic Kolmogorov scales under buoyant and non-buoyant conditions, the recovery of anisotropic one-dimensional energy spectra under buoyant conditions, and the preservation of known statistical distributions in the scalar field, as found in other DNS studies.

This simulation methodology is used to perform a parametric study of turbulent buoyant flows to discern the effects of varying the Reynolds, Richardson, and Atwood numbers on the resulting state of mixing. The effects of the Reynolds and Atwood numbers are isolated by looking at two energy dissipation rate conditions under non-buoyant (variable density) and constant density conditions. The effects of Richardson number are isolated by varying the ratio of buoyant energy production to total energy production from zero (non-buoyant) to one (entirely buoyant) under constant Atwood number, Schmidt number, and energy dissipation rate conditions. It is found that the major differences between non-buoyant and buoyant turbulent flows are contained in the transfer spectrum and longitudinal structure functions, while all other metrics are largely similar (e.g. energy spectra, alignment characteristics of the strain-rate tensor). Also, despite the differences noted between fully buoyant and non-buoyant turbulent fields, the scalar field, in all cases, is unchanged by these. The mixing dynamics in the scalar field are found to be insensitive to the source of turbulent kinetic energy production (non-buoyant vs. buoyant).

Uma Metodologia de Estudo de Simulação Tridimensional de Escoamento Turbulento Estratificado no Reservatório de Plantas Hidrelétricas.

Uma simulação numérica que leva em conta os efeitos de estratificação e mistura escalar (como a temperatura, salinidade ou substância solúvel em água) é necessária para estudar e prever os impactos ambientais que um reservatório de usina hidrelétrica pode produzir. Este trabalho sugere uma metodologia para o estudo de escoamentos ambientais, principalmente aqueles em que o conhecimento da interação entre a estratificação e mistura pode dar noções importantes dos fenômenos que ocorrem. Por esta razão, ferramentas de simulação numérica 3D de escoamento ambiental são desenvolvidas. Um gerador de malha de tetraedros do reservatório e o modelo de turbulência algébrico baseado no número de Richardson são as principais ferramentas desenvolvidas. A principal dificuldade na geração de uma malha de tetraedros de um reservatório é a distribuição não uniforme dos pontos relacionada com a relação desproporcional entre as escalas horizontais e verticais do reservatório. Neste tipo de distribuição de pontos, o algoritmo convencional de geração de malha de tetraedros pode tornar-se instável. Por esta razão, um gerador de malha não estruturada de tetraedros é desenvolvido e a metodologia utilizada para obter elementos conformes é descrita. A geração de malha superficial de triângulos utilizando a triangulação Delaunay e a construção do tetraedros a partir da malha triangular são os principais passos para o gerador de malha. A simulação hidrodinâmica com o modelo de turbulência fornece uma ferramenta útil e computacionalmente viável para fins de engenharia. Além disso, o modelo de turbulência baseado no número de Richardson leva em conta os efeitos da interação entre turbulência e estratificação. O modelo algébrico é o mais simples entre os diversos modelos de turbulência. Mas, fornece resultados realistas com o ajuste de uma pequena quantidade de parâmetros. São incorporados os modelos de viscosidade/difusividade turbulenta para escoamento estratificado. Na aproximação das equações médias de Reynolds e transporte de escalar é utilizando o Método dos Elementos Finitos. Os termos convectivos são aproximados utilizando o método semi-Lagrangeano, e a aproximação espacial é baseada no método de Galerkin. Os resultados computacionais são comparados com os resultados disponíveis na literatura. E, finalmente, a simulação de escoamento em um braço de reservatório é apresentada.