Mixed Convection Boundary Layer Flow Past a Horizontal Circular Cylinder Embedded in a Bidisperse Porous Medium

Adopting a two-temperature and two-velocity model, appropriate to a bidisperse porous medium (BDPM) proposed by Nield and Kuznetsov (2008), the classical steady, mixed convection boundary layer flow about a horizontal, isothermal circular cylinder embedded in a porous medium has been theoretically studied in this article. It is shown that the boundary layer analysis leads to expressions for the flow and heat transfer characteristics in terms of an inter-phase momentum parameter, a thermal diffusivity ratio, a thermal conductivity ratio, a permeability ratio, a modified thermal capacity ratio, and a buoyancy or mixed convection parameter. The transformed partial differential equations governing the flow and heat transfer in the f-phase (the macro-pores) and the p-phase (the remainder of the structure) are solved numerically using a very efficient implicit finite-difference technique known as Keller-box method. A good agreement is observed between the present results and those known from the open literature in the special case of a traditional Darcy formulation (monodisperse system).

Forced convection along a longitudinal cylinder embedded in a saturated porous medium

The thermal boundary layer along an isothermal cylinder in a porous 3edium is studied numerically by a finite difference scheme and also using the method of extended perturbation series. The series in terms of the transverse curvature parameter ξ extended to seven terms and is subsequently improved by applying the Shanks transformation twice and thrice, respectively. Results for heat transfer characteristics are found in very good agreement.

CFD Analysis of conjugate natural convection in a vertical annulus

Conjugate natural convection in a vertical annulus with a centrally located vertical heat generating rod is studied numerically. The governing equations are discretized on a staggered mesh and are solved using a pressure-correction algorithm. A parametric study is performed by varying the Grashof number, aspect ratio, and the solid-to-fluid thermal conductivity ratio over wide ranges with the Prandtl number fixed at 0.7. Results are presented for the variation of several quantities of interest such as the local Nusselt numbers on the inner and outer boundaries, the axial variation of the centerline and interface temperatures, maximum solid, average solid and average interface temperature variations with Grashof number, and the average Nusselt number variation for the inner and outer boundaries with Grashof number. The average Nusselt number from the conjugate analysis is found to be between the Nusselt numbers of the isothermal and the isoflux cases. The average Nusselt numbers on the inner and outer boundaries show an increasing trend with the Grashof number. Correlations are presented for the Nusselt number and the dimensionless temperatures of interest in terms of the parameters of the problem.

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%.

A computer code for enclosed natural convection in the boundary layer regime

A computer code is developed for the numerical prediction of natural convection in rectangular two-dimensional cavities at high Rayleigh numbers. The governing equations are retained in the primitive variable form. The numerical method is based on finite differences and an ADI scheme. Convective terms may be approximated with either central or hybrid differencing for greater stability. A non-uniform grid distribution is possible for greater efficiency. The pressure is dealt with via a SIMPLE type algorithm and the use of a fast elliptic solver for the solenoidal velocity correction field significantly reduces computing times. Preliminary results indicate that the code is reasonably accurate, robust and fast compared with existing benchmarks and finite difference based codes, particularly at high Rayleigh numbers. Extension to three-dimensional problems and turbulence studies in similar geometries is readily possible and indicated.

The influence of the Coriolis force on flux tubes rising through the solar convection zone

In order to study the effect of the Coriolis force due to solar rotation on rising magnetic flux, the authors consider a flux ring, azimuthally symmetric around the rotation axis, starting from rest at the bottom of the convection zone, and then follow the trajectory of the flux ring as it rises. If it is assumed that the flux ring remains azimuthally symmetric during its ascent, then the problem can be described essentially in terms of two parameters: the value of the initial magnetic field in the ring when it starts, and the effective drag experienced by it. For field strengths at the bottom of the convection zone of order 10,000 G or less, it is found that the Coriolis force plays a dominant role and flux rings starting from low latitudes at the bottom are deflected and emerge at latitudes significantly poleward of sunspot zones.

On the ignition and extinction problems in forced convection systems

In this paper the problem of ignition and extinction has been formulated for the flow of a compressible fluid with Prandtl and Schmidt numbers taken as unity. In particular, the problems of (i) a jet impinging on a wall of combustible material and (ii) the opposed jet diffusion flame have been studied. In the wall jet case, three approximations in the momentum equation namely, (i) potential flow, (ii) viscous flow, (ii) viscous incompressible with k = 1 and (iii) Lees' approximation (taking pressure gradient terms zero) are studied. It is shown that the predictions of the mass flow rates at extinction are not very sensitive to the approximations made in the momentum equation. The effects of varying the wall temperature in the case (i) and the jet temperature in the case (ii) on the extinction speeds have been studied. The effects of varying the activation energy and the free stream oxidant concentration in case (ii), have also been investigated.

Turbulent free convection above a heated plate inclined at a small angle to the horizontal Journal

An investigation has been made of the structure of the motion above a heated plate inclined at a small angle (about 10°) to the horizontal. The turbulence is considered in terms of the similarities to and differences from the motion above an exactly horizontal surface. One effect of inclination is, of course, that there is also a mean motion. Accurate data on the mean temperature field and the intensity of the temperature fluctuations have been obtained with platinum resistance thermometers, the signals being processed electronically. More approximate information on the velocity field has been obtained with quartz fibre anemometers. These results have been supplemented qualitatively by simultaneous observations of the temperature and velocity fluctuations and also by smoke experiments. The principal features of the flow inferred from these observations are as follows. The heat transfer and the mean temperature field are not much altered by the inclination, though small, not very systematic, variations may result from the complexities of the velocity field. This supports the view that the mean temperature field is largely governed by the large-scale motions. The temperature fluctuations show a systematic variation with distance from the lower edge and resemble those above a horizontal plate when this distance is large. The largescale motions of the turbulence start close to the lower edge, but the smaller eddies do not attain full intensity until the air has moved some distance up the plate. The mean velocity receives a sizable contribution from a ‘through-flow’ between the side-walls. Superimposed on this are developments that show that the momentum transfer processes are complex and certainly not capable of representation by any simple theory such as an eddy viscosity. On the lower part of the plate there is surprisingly large acceleration, but further up the mixing action of the small eddies has a decelerating effect.

Natural convection in a series of thermally interacting cavities with wall mounted heaters

Laminar natural convection in a series of thermally interacting cavities is numerically studied. Each cavity consists of a conducting bottom wall with a surface mounted heater. The side walls of the cavities are isothermally cooled. Each cavity thermally interacts with its adjacent cavities through the conducting walls. Flow and heat transfer characteristics are studied in detail for various Rayleigh numbers. The convection characteristics in multiple cavities are compared with those in single independent cavity. The thermal interaction between the cavities results in lower temperatures compared with those in independent cavities. While heat is rejected into the adjacent upper cavity through some portion of the conducting wall, heat is received from the adjacent cavity through the remaining portion of the wall. The influence of substrate conductivity on heat exchange between adjacent cavities are examined. Substrate conductivity shows strong effect on temperature distribution. When cooling at both vertical sides is changed to one side cooling, the heat transfer characteristics are changed drastically and many interesting flow features are observed. Effects of cavity aspect ratio is studied and higher heat transfer rates are observed at higher aspect ratios. Correlations for dimensionless temperature maximum and average Nusselt number are presented in terms of Rayleigh number.

Experimental studies on evaporation of fuel droplets under forced convection using spray in crossflow methodology

Experimental data on evaporation of droplets of decane, Jet-A1, and Jet-A1 surrogate are generated using a spray in crossflow configuration. The advantage of a crossflow configuration is that it enables us to study droplet evaporation under forced convective conditions involving droplet diameters of size relevant in practical combustors. Specifically, spray from an airblast atomizer is injected into a preheated crossflow of air and the resulting spray is characterized in terms of spray structure along with droplet size and velocity. An existing correlation for the spray trajectory is modified to incorporate the effect of elevated temperature, and is found to be in good agreement with the experimental data. Droplet sizes and velocities are measured at different locations along the crossflow direction to assess droplet evaporation. Specifically, droplets having size less than 25-mu m are selected for further analysis since these droplets are observed to exhibit velocities which are aligned with the crossflow. By comparing the droplet diameter profiles at upstream and downstream locations, the evaporation constant k for the d(2)-law is obtained iteratively. To assess the efficacy of the values of k obtained, the calculated droplet size distribution using the proposed k values at the downstream location is compared with the measured droplet size distribution at that location. A reasonably good match is found for all the three liquids confirming the validity of the analysis. (C) 2015 Elsevier Ltd. All rights reserved.

Complex Transition of Double-Diffusive Convection in a Rectangular Enclosure with Height-to-Length Ratio Equal to 4: Part I

This is the first part of direct numerical simulation (DNS) of double-diffusive convection in a slim rectangular enclosure with horizontal temperature and concentration gradients. We consider the case with the thermal Rayleigh number of 10^5, the Pradtle number of 1, the Lewis number of 2, the buoyancy ratio of composition to temperature being in the range of [0,1], and height-to-width aspect ration of 4. A new 7th order upwind compact scheme was developed for approximation of convective terms, and a three-stage third-order Runge-Kutta method was employed for time advancement. Our DNS suggests that with the buoyancy ratio increasing form 0 to 1, the flow of transition is a complex series changing fromthe steady to periodic, chaotic, periodic, quasi-periodic, and finally back to periodic. There are two types of periodic flow, one is simple periodic flow with single fundamental frequency (FF), and another is complex periodic flow with multiple FFs. This process is illustrated by using time-velocity histories, Fourier frequency spectrum analysis and the phase-space rajectories.

Les oscillations torsionnelles dans la zone de convection solaire

Nous analysons les oscillations torsionnelles se développant dans une simulation magnétohydrodynamique de la zone de convection solaire produisant des champs magnétiques de type solaire (champs axisymétriques subissant des inversions de polarités régulières sur des échelles temporelles décadaires). Puisque ces oscillations sont également similaires à celles observées dans le Soleil, nous analysons les dynamiques zonales aux grandes échelles. Nous séparons donc les termes aux grandes échelles (force de Coriolis exercée sur la circulation méridienne et les champs magnétiques aux grandes échelles) de ceux aux petites échelles (les stress de Reynolds et de Maxwell). En comparant les flux de moments cinétiques entre chacune des composantes, nous nous apercevons que les oscillations torsionnelles sont maintenues par l’écoulement méridien aux grandes échelles, lui même modulé par les champs magnétiques. Une analyse d’échange d’énergie confirme ce résultat, puisqu’elle montre que seul le terme comprenant la force de Coriolis injecte de l’énergie dans l’écoulement. Une analyse de la dynamique rotationnelle ayant lieu à la limite de la zone stable et de la zone de convection démontre que celle-ci est fortement modifiée lors du passage de la base des couches convectives à la base de la fine tachocline s’y formant juste en-dessous. Nous concluons par une discussion au niveau du mécanisme de saturation en amplitude dans la dynamo s’opérant dans la simulation ainsi que de la possibilité d’utiliser les oscillations torsionnelles comme précurseurs aux cycles solaires à venir.

Precipitating convection in cold air: virtual potential temperature structure

Simulations of precipitating convection are used to illustrate the importance of the turbulent kinetic energy (TKE) budget in determining the virtual potential-temperature structure of the convecting atmosphere. Two sets of simulations are presented: in one the surface temperature was increased to simulate cold air flowing over a warmer surface and in the second a cooling profile, representing cold-air advection, was imposed. It is shown that the terms in the TKE budgets for both sets of simulations scale in the same way, but that the non-dimensional profiles are different. It is suggested that this is associated with the effects of sublimation of ice. It is shown that the magnitudes of the transport and precipitation terms in the virtual potential temperature budget are determined by the scaling of the TKE budget. Some implications of these results for parametrizations of moist convection are discussed. Copyright © 2007 Royal Meteorological Society

Ensemble prediction for nowcasting with a convection-permitting model - II: forecast error statistics

A 24-member ensemble of 1-h high-resolution forecasts over the Southern United Kingdom is used to study short-range forecast error statistics. The initial conditions are found from perturbations from an ensemble transform Kalman filter. Forecasts from this system are assumed to lie within the bounds of forecast error of an operational forecast system. Although noisy, this system is capable of producing physically reasonable statistics which are analysed and compared to statistics implied from a variational assimilation system. The variances for temperature errors for instance show structures that reflect convective activity. Some variables, notably potential temperature and specific humidity perturbations, have autocorrelation functions that deviate from 3-D isotropy at the convective-scale (horizontal scales less than 10 km). Other variables, notably the velocity potential for horizontal divergence perturbations, maintain 3-D isotropy at all scales. Geostrophic and hydrostatic balances are studied by examining correlations between terms in the divergence and vertical momentum equations respectively. Both balances are found to decay as the horizontal scale decreases. It is estimated that geostrophic balance becomes less important at scales smaller than 75 km, and hydrostatic balance becomes less important at scales smaller than 35 km, although more work is required to validate these findings. The implications of these results for high-resolution data assimilation are discussed.

Plasma structure within poleward-moving cusp/cleft auroral transients: EISCAT Svalbard radar observations and an explanation in terms of large local time extent of events

We report high-resolution observations of the southward-IMF cusp/cleft ionosphere made on December 16th 1998 by the EISCAT (European incoherent scatter) Svalbard radar (ESR), and compare them with observations of dayside auroral luminosity, as seen at a wavelength of 630 nm by a meridian scanning photometer at Ny Alesund, and of plasma flows, as seen by the CUTLASS (co-operative UK twin location auroral sounding system) Finland HF radar. The optical data reveal a series of poleward-moving transient red-line (630 nm) enhancements, events that have been associated with bursts in the rate of magnetopause reconnection generating new open flux. The combined observations at this time have strong similarities to predictions of the effects of soft electron precipitation modulated by pulsed reconnection, as made by Davis and Lockwood (1996); however, the effects of rapid zonal flow in the ionosphere, caused by the magnetic curvature force on the newly opened field lines, are found to be a significant additional factor. In particular, it is shown how enhanced plasma loss rates induced by the rapid convection can explain two outstanding anomalies of the 630 nm transients, namely how minima in luminosity form between the poleward-moving events and how events can re-brighten as they move poleward. The observations show how cusp/cleft aurora and transient poleward-moving auroral forms appear in the ESR data and the conditions which cause enhanced 630 nm emission in the transients: they are an important first step in enabling the ESR to identify these features away from the winter solstice when supporting auroral observations are not available.