Mass transfer effects on the generalised vortex flow over a stationary surface with or without magnetic field

The effect of injection and suction on the generalised vortex flow of a steady laminar incompressible fluid over a stationary infinite disc with or without magnetic field under boundary-layer approximations has been studied. The coupled nonlinear ordinary differential equations governing the self-similar flow have been numerically solved using the finite-difference scheme. The results indicate that the injection produces a deeper inflow layer and de-stabilises the motion while suction or magnetic field suppresses the inflow layer and produces stability. The effect of decreasingn, the parameter characterising the nature of vortex flow, is similar to that of increasing the injection rate.

Free convection heat transfer to mercury in vertical annuli

Data on free convection heat transfer to water and mercury are collected using a test rig in vertical annuli of three radii ratios, the walls of which are maintained at uniform temperatures. A theoretical analysis of the boundary layer equations has been attempted using local similarity transformation and double boundary layer approach. Correlations derived from the present theoretical analysis are compared with the analysis and the experimental data available in literature for non-metallic fluids and also with the present experimental data on water and mercury. Generalised correlations are set up for expressing the ratio of heat transferred by convection to the heat transferred by pure conduction and Nusselt's number, in terms of Grashof, Rayleigh and Prandtl numbers, based on the theoretical analysis and the present data on mercury and water. The present generalised correlations agree with the reported and present data for non-metallic fluids and liquid metals with an average deviation of 9% and maximum deviation of ± 13.7%.

Microclimate and gas emissions in dairy buildings : Instrumentation, theory and measurements

The aim of this thesis was to develop measurement techniques and systems for measuring air quality and to provide information about air quality conditions and the amount of gaseous emissions from semi-insulated and uninsulated dairy buildings in Finland and Estonia. Specialization and intensification in livestock farming, such as in dairy production, is usually accompanied by an increase in concentrated environmental emissions. In addition to high moisture, the presence of dust and corrosive gases, and widely varying gas concentrations in dairy buildings, Finland and Estonia experience winter temperatures reaching below -40 ºC and summer temperatures above +30 ºC. The adaptation of new technologies for long-term air quality monitoring and measurement remains relatively uncommon in dairy buildings because the construction and maintenance of accurate monitoring systems for long-term use are too expensive for the average dairy farmer to afford. Though the documentation of accurate air quality measurement systems intended mainly for research purposes have been made in the past, standardised methods and the documentation of affordable systems and simple methods for performing air quality and emissions measurements in dairy buildings are unavailable. In this study, we built three measurement systems: 1) a Stationary system with integrated affordable sensors for on-site measurements, 2) a Wireless system with affordable sensors for off-site measurements, and 3) a Mobile system consisting of expensive and accurate sensors for measuring air quality. In addition to assessing existing methods, we developed simplified methods for measuring ventilation and emission rates in dairy buildings. The three measurement systems were successfully used to measure air quality in uninsulated, semi-insulated, and fully-insulated dairy buildings between the years 2005 and 2007. When carefully calibrated, the affordable sensors in the systems gave reasonably accurate readings. The spatial air quality survey showed high variation in microclimate conditions in the dairy buildings measured. The average indoor air concentration for carbon dioxide was 950 ppm, for ammonia 5 ppm, for methane 48 ppm, for relative humidity 70%, and for inside air velocity 0.2 m/s. The average winter and summer indoor temperatures during the measurement period were -7º C and +24 ºC for the uninsulated, +3 ºC and +20 ºC for the semi-insulated and +10 ºC and +25 ºC for the fully-insulated dairy buildings. The measurement results showed that the uninsulated dairy buildings had lower indoor gas concentrations and emissions compared to fully insulated buildings. Although occasionally exceeded, the ventilation rates and average indoor air quality in the dairy buildings were largely within recommended limits. We assessed the traditional heat balance, moisture balance, carbon dioxide balance and direct airflow methods for estimating ventilation rates. The direct velocity measurement for the estimation of ventilation rate proved to be impractical for naturally ventilated buildings. Two methods were developed for estimating ventilation rates. The first method is applicable in buildings in which the ventilation can be stopped or completely closed. The second method is useful in naturally ventilated buildings with large openings and high ventilation rates where spatial gas concentrations are heterogeneously distributed. The two traditional methods (carbon dioxide and methane balances), and two newly developed methods (theoretical modelling using Fick s law and boundary layer theory, and the recirculation flux-chamber technique) were used to estimate ammonia emissions from the dairy buildings. Using the traditional carbon dioxide balance method, ammonia emissions per cow from the dairy buildings ranged from 7 g day-1 to 35 g day-1, and methane emissions per cow ranged from 96 g day-1 to 348 g day-1. The developed methods proved to be as equally accurate as the traditional methods. Variation between the mean emissions estimated with the traditional and the developed methods was less than 20%. The developed modelling procedure provided sound framework for examining the impact of production systems on ammonia emissions in dairy buildings.

nvestigations on the Stability and Extinction of a Laminar Diffusion Flame Over a Porous Flat Plate

The limits of stability and extinction of a laminar diffusion flame have been experimentally studied in a two-dimensional laminar boundary layer over a porous flat plate through which n-pentane vapour was uniformly injected. The stability and extinction boundaries are mapped on a plot of free stream oxidant velocity versus fuel injection velocity. Effects of free stream temperature and of dilution of fuel and oxidant on these boundaries have been examined. The results show that there exists a limiting oxidant flux beyond which the diffusion flame cannot be sustained. This limiting oxidant flux has been found to depend_on the free stream oxygen concentration, fuel concentration and injection'velocity of the fuel.

Effect of inclination on laminar film condensation

The effect of inclination on laminar film condensation over and under isothermal flat plates is investigated analytically. The complete set of Navier Stokes equations in two dimensions is considered. Analysed as a perturbation problem, the zero-order perturbation represents the boundary layer equations. First and second order perturbations are solved to bring about the leading edge effects. Corresponding velocity and temperature profiles are presented. The results show decrease in heat transfer with larger ∥inclinations∥ from the vertical. Comparison with experimental data of Gerstmann and Griffith indicates a closer agreement of the present results than the analytical results of the same authors.

Mass transfer with surface reaction in arrays of cylinders at low reynolds and high peclet numbers

Creeping flow hydrodynamics combined with diffusion boundary layer equation are solved in conjunction with free-surface cell model to obtain a solution of the problem of convective transfer with surface reaction for flow parallel to an array of cylindrical pellets at high Peclet numbers and under fast and intermediate kinetics regimes. Expressions are derived for surface concentration, boundary layer thickness, mass flux and Sherwood number in terms of Damkoehler number, Peclet number and void fraction of the array. The theoretical results are evaluated numerically.

Zero-crossings in turbulent signals

A primary motivation for this work arises from the contradictory results obtained in some recent measurements of the zero-crossing frequency of turbulent fluctuations in shear flows. A systematic study of the various factors involved in zero-crossing measurements shows that the dynamic range of the signal, the discriminator characteristics, filter frequency and noise contamination have a strong bearing on the results obtained. These effects are analysed, and explicit corrections for noise contamination have been worked out. New measurements of the zero-crossing frequency N0 have been made for the longitudinal velocity fluctuation in boundary layers and a wake, for wall shear stress in a channel, and for temperature derivatives in a heated boundary layer. All these measurements show that a zero-crossing microscale, defined as Λ = (2πN0)−1, is always nearly equal to the well-known Taylor microscale λ (in time). These measurements, as well as a brief analysis, show that even strong departures from Gaussianity do not necessarily yield values appreciably different from unity for the ratio Λ/λ. Further, the variation of N0/N0 max across the boundary layer is found to correlate with the familiar wall and outer coordinates; the outer scaling for N0 max is totally inappropriate, and the inner scaling shows only a weak Reynolds-number dependence. It is also found that the distribution of the interval between successive zero-crossings can be approximated by a combination of a lognormal and an exponential, or (if the shortest intervals are ignored) even of two exponentials, one of which characterizes crossings whose duration is of the order of the wall-variable timescale ν/U2*, while the other characterizes crossings whose duration is of the order of the large-eddy timescale δ/U[infty infinity]. The significance of these results is discussed, and it is particularly argued that the pulse frequency of Rao, Narasimha & Badri Narayanan (1971) is appreciably less than the zero-crossing rate.

Computation of turbulent flow in an IFRF quarl burner

A computational model for isothermal axisymmetric turbulent flow in a quarl burner is set up using the CFD package FLUENT, and numerical solutions obtained from the model are compared with available experimental data. A standard k-e model and and two versions of the RNG k-e model are used to model the turbulence. One of the aims of the computational study is to investigate whether the RNG based k-e turbulence models are capable of yielding improved flow predictions compared with the standard k-e turbulence model. A difficulty is that the flow considered here features a confined vortex breakdown which can be highly sensitive to flow behaviour both upstream and downstream of the breakdown zone. Nevertheless, the relatively simple confining geometry allows us to undertake a systematic study so that both grid-independent and domain-independent results can be reported. The systematic study includes a detailed investigation of the effects of upstream and downstream conditions on the predictions, in addition to grid refinement and other tests to ensure that numerical error is not significant. Another important aim is to determine to what extent the turbulence model predictions can provide us with new insights into the physics of confined vortex breakdown flows. To this end, the computations are discussed in detail with reference to known vortex breakdown phenomena and existing theories. A major conclusion is that one of the RNG k-e models investigated here is able to correctly capture the complex forward flow region inside the recirculating breakdown zone. This apparently pathological result is in stark contrast to the findings of previous studies, most of which have concluded that either algebraic or differential Reynolds stress modelling is needed to correctly predict the observed flow features. Arguments are given as to why an isotropic eddy-viscosity turbulence model may well be able to capture the complex flow structure within the recirculating zone for this flow setup. With regard to the flow physics, a major finding is that the results obtained here are more consistent with the view that confined vortex breakdown is a type of axisymmetric boundary layer separation, rather than a manifestation of a subcritical flow state.

Experiments on the fine structure of turbulence

Investigations have been carried out of some aspects of the fine-scale structure of turbulence in grid flows, in boundary layers in a zero pressure gradient and in a boundary layer in a strong favourable pressure gradient leading to relaminarization. Using a narrow-band filter with suitable mid-band frequencies, the properties of the fine-scale structure (appearing as high frequency pulses in the filtered signal) were analysed using the variable discriminator level technique employed earlier by Rao, Narasimha & Badri Narayanan (1971). It was found that, irrespective of the type of flow, the characteristic pulse frequency (say Np) defined by Rao et al. was about 0·6 times the frequency of the zero crossings. It was also found that, over the small range of Reynolds numbers tested, the ratio of the width of the fine-scale regions to the Kolmogorov scale increased linearly with Reynolds number in grid turbulence as well as in flat-plate boundarylayer flow. Nearly lognormal distributions were exhibited by this ratio as well as by the interval between successive zero crossings. The values of Np and of the zero-crossing rate were found to be nearly constant across the boundary layer, except towards its outer edge and very near the wall. In the zero-pressure-gradient boundary-layer flow, very near the wall the high frequency pulses were found to occur mostly when the longitudinal velocity fluctuation u was positive (i.e. above the mean), whereas in the outer part of the boundary layer the pulses more often occurred when u was negative. During acceleration this correlation between the fine-scale motion and the sign of u was less marked.

Steady mixed convection stagnation-point flow of upper convected Maxwell fluids with magnetic field

The steady MHD mixed convection flow of a viscoelastic fluid in the vicinity of two-dimensional stagnation point with magnetic field has been investigated under the assumption that the fluid obeys the upper-convected Maxwell (UCM) model. Boundary layer theory is used to simplify the equations of motion. induced magnetic field and energy which results in three coupled non-linear ordinary differential equations which are well-posed. These equations have been solved by using finite difference method. The results indicate the reduction in the surface velocity gradient, surface heat transfer and displacement thickness with the increase in the elasticity number. These trends are opposite to those reported in the literature for a second-grade fluid. The surface velocity gradient and heat transfer are enhanced by the magnetic and buoyancy parameters. The surface heat transfer increases with the Prandtl number, but the surface velocity gradient decreases.

A numerical study of crack tip constraint in ductile single crystals

In this work, the effect of crack tip constraint on near-tip stress and deformation fields in a ductile FCC single crystal is studied under mode I, plane strain conditions. To this end, modified boundary layer simulations within crystal plasticity framework are performed, neglecting elastic anisotropy. The first and second terms of the isotropic elastic crack tip field, which are governed by the stress intensity factor K and T-stress, are prescribed as remote boundary conditions and solutions pertaining to different levels of T-stress are generated. It is found that the near-tip deformation field, especially, the development of kink or slip shear bands, is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the crack tip are also strongly influenced by the level of T-stress, with progressive loss of crack tip constraint occurring as T-stress becomes more negative. A family of near-tip fields is obtained which are characterized by two terms (such as K and T or J and a constraint parameter Q) as in isotropic plastic solids.

Eddy diffusivity: A single dispersion analysis of high resolution drifters in a tidal shallow estuary

In an estuary, mixing and dispersion resulting from turbulence and small scale fluctuation has strong spatio-temporal variability which cannot be resolved in conventional hydrodynamic models while some models employs parameterizations large water bodies. This paper presents small scale diffusivity estimates from high resolution drifters sampled at 10 Hz for periods of about 4 hours to resolve turbulence and shear diffusivity within a tidal shallow estuary (depth < 3 m). Taylor's diffusion theorem forms the basis of a first order estimate for the diffusivity scale. Diffusivity varied between 0.001 – 0.02 m2/s during the flood tide experiment. The diffusivity showed strong dependence (R2 > 0.9) on the horizontal mean velocity within the channel. Enhanced diffusivity caused by shear dispersion resulting from the interaction of large scale flow with the boundary geometries was observed. Turbulence within the shallow channel showed some similarities with the boundary layer flow which include consistency with slope of 5/3 predicted by Kolmogorov's similarity hypothesis within the inertial subrange. The diffusivities scale locally by 4/3 power law following Okubo's scaling and the length scale scales as 3/2 power law of the time scale. The diffusivity scaling herein suggests that the modelling of small scale mixing within tidal shallow estuaries can be approached from classical turbulence scaling upon identifying pertinent parameters.

Unsteady MHD mixed convection flow over an impulsively stretched permeable vertical surface in a quiescent fluid

The unsteady mixed convection flow of an incompressible laminar electrically conducting fluid over an impulsively stretched permeable vertical surface in an unbounded quiescent fluid in the presence of a transverse magnetic field has been investigated. At the same time, the surface temperature is suddenly increased from the surrounding fluid temperature or a constant heat flux is suddenly imposed on the surface. The problem is formulated in such a way that for small time it is governed by Rayleigh type of equation and for large time by Crane type of equation. The non-linear coupled parabolic partial differential equations governing the unsteady mixed convection flow under boundary layer approximations have been solved analytically by using the homotopy analysis method as well as numerically by an implicit finite difference scheme. The local skin friction coefficient and the local Nusselt number are found to decrease rapidly with time in a small time interval and they tend to steady-state values for t* >= 5. They also increase with the buoyancy force and suction, but decrease with injection rate. The local skin friction coefficient increases with the magnetic field, but the local Nusselt number decreases. There is a smooth transition from the unsteady state to the steady state. (C) 2010 Elsevier Ltd. All rights reserved.

Free convection heat transfer in vertical annuli

Free convection heat transfer in vertical concentric, cylindrical annuli is investigated analytically and experimentally. The approximate double boundary layer model used by Emery and Chu for the case of vertical parallel plates is extended to the present case in obtaining heat transfer correlations in laminar free convection. Different correlations for the inner cylinder depending on the radius to the length ratio of the inner cylinder and the Rayleigh number, were used in the derivation of correlations for the annuli. The results for the case of short cylinders inside tubes are in agreement (within about 10 per cent) with the existing correlations. For other cases, namely long cylinders in annuli and wires in annuli, experiments conducted show the agreement of the analysis with experiments.

Free convection heat transfer between vertical parallel plates

A new mathematical model for the solution of the problem of free convection heat transfer between vertical parallel flat isothermal plates under isothermal boundary conditions, has been presented. The set of boundary layer equations used in the model are transformed to nonlinear coupled differential equations by similarity type variables as obtained by Ostrach for vertical flat plates in an infinite fluid medium. By utilising a parameter ηw* to represent the outer boundary, the governing differential equations are solved numerically for parametric values of Pr = 0.733. 2 and 3, and ηw* = 0.1, 0.5, 1, 2, 3, 4, ... and 8.0. The velocity and temperature profiles are presented. Results indicate that ηw* can effectively classify the system into (1) thin layers where conduction predominates, (2) intermediate layers and (3) thick layers whose results can be predicted by the solutions for vertical flat plates in infinite fluid medium. Heat transfer correlations are presented for the 3 categories. Several experimental and analytical results available in the literature agree with the present correlations.