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Large eddy simulation of transition of free convection flow over an inclined upward facing heated plate
Abstract
Transition of free convection flow of air over an inclined heated surface is investigated numerically by using a large eddy simulation method. In particular, we focus on how inclination angle of an upward-facing heated plate affects flow transition. Special attention is paid to the development of the thermal boundary layer and the transition from the laminar to turbulent stage. Results show that the transition occurs early when the plate is moved from its vertical position due to the rapid growth of both the velocity and thermal boundary layers. As a consequence, the critical Grashof number drops. Effects of the inclination of plate on the turbulent velocity fluctuations are also investigated, and the predicted results are in very good agreement with various experimental data available in the literature.
... Alzwayi et. al. [8] studied the effect of the plate inclination on critical Grashof number indicating the start of the transition mechanism and the turbulent velocity fluctuations using three-dimensional large eddy simulations but did not focus much on the quantification and detailed characteristics of the longitudinal vortices. Above studies has been performed either under isothermal [5,8] or uniform heat flux [6,7] wall conditions but with water as a working fluid. ...
... al. [8] studied the effect of the plate inclination on critical Grashof number indicating the start of the transition mechanism and the turbulent velocity fluctuations using three-dimensional large eddy simulations but did not focus much on the quantification and detailed characteristics of the longitudinal vortices. Above studies has been performed either under isothermal [5,8] or uniform heat flux [6,7] wall conditions but with water as a working fluid. Literature review points that numerical investigation of natural-convection transitional boundary-layer flow (where modified Rayleigh number is beyond the range of 10 for laminar flow [9]) in air inside an open-ended inclined channel heated from below with uniform has not been extensively addressed. ...
... Alzwayi et. al. [8] reported a wider distribution of both the velocity and thermal boundary layer with increasing inclination from the vertical position under the increasing effect of a wall-normal component of the buoyancy force for the exchange of momentum and heat across the boundary layer in addition to the streamwise component. ...
This report presents an investigation of the characteristics for transitional natural-convection flow in an open-ended inclined channel with bottom surface heated in the air under uniform heat flux intensity and non-Boussinesq condition. The investigated range of modified Rayleigh number and inclination is from 5.93 × 10^6 to 1.45 × 10^9 and 30° to 90° to the horizontal respectively. Fine resolution Implicit large Eddy simulation is performed to solve the compressible governing equations using the modified preconditioned all-speed Roe scheme, hybrid boundary condition and dual time-stepping technique. The Nusselt number based on the maximum wall-temperature differs significantly while based on averaged wall-temperature is closer to the previously proposed laminar correlations. Transition is found to be pronounced at a lower angle of inclination (30°) for the considered heat flux intensity. The absolute magnitude of the critical length for the start and end of the transition when converted to non-dimensional parameters is found to be higher compared to similar data for natural convection flow over a flat plate in water but the ratio of the end to start of the transition is found to be comparable. Single-roll longitudinal vortices periodically placed in spanwise direction exists in the transition region whose wavelength is found to be higher than those reported for channel flow under the isothermal condition and flow over a flat plate in water. Correlations for Nusselt number, critical aspect ratio and vortex wavelength to the modified Rayleigh number are presented.
... In addition to the controlling parameters, other parameters also play a role in the transition, such as stratification of ambient fluids (Pera & Gebhart 1971;Hattori et al. 2013a), the angle of the inclined plate (Pera & Gebhart 1973;Lewandowski 1991;Alzwayi, Paul & Navarro-Martinez 2014), lateral width (Kalendar & Oosthuizen 2011), edge extension (Goldstein & Lau 1983) and plume formation point (Morton, Taylor & Turner 1956;Kimura et al. 2002). ...
... Following the onset of primary instability from two-dimensional (2-D) laminar to three-dimensional (3-D) laminar, the flow becomes periodic and finally enters turbulence in the downstream of the thermal boundary (Shaukatullah & Gebhart 1978;Jeschke & Beer 2001). By increasing the inclination angle from the horizontal plate to the vertical plate, the thermal boundary layer is separated downstream of the leading edge (Paul, Rees & Wilson 2005;Alzwayi et al. 2014). The occurrence of vortex instability has been proven to be an absolute instability and a disturbance dissipates soon after being ejected into the thermal boundary layer (Paul et al. 2005). ...
The development of thermal boundary layers and plume near a section-triangular roof under different isothermal heating conditions has been the focus of numerous numerical studies. However, flow transition in this type of flow has never been observed experimentally. Here, phase-shifting interferometry and thermistor measurements are employed to experimentally observe and quantify the flow transitions in a buoyancy-driven flow over an isothermal section-triangular roof. Visualisation of temperature contours is conducted across a wide range of Rayleigh numbers from laminar at 10 ³ to chaotic state at 4 × 10 ⁶ . Power spectral density of the temperature measurements reveals the type of bifurcations developing as the Rayleigh number is increased. This flow transition is characterised as a complex bifurcation route with the presence of two fundamental frequencies, a low and a high frequency. We found that the thermal stratification in the environment plays a significant role in the flow transition. The spatial development of flow is also quantitatively and qualitatively described. In addition to clarifying flow transition in experiments, the work demonstrates the implementation of phase-shifting interferometry and punctual temperature measurements for characterisation of near-field flow over a heated surface.
... It is demonstrated that the critical distance where the slope flow starts to destabilize is dependent on the Prandtl number. The experiment shows that the separation occurs in the transitional slope flow and is also dependent on the inclination angle [19,20], which is consistent with the results of large eddy simulation [21]. The study [22] indicates that the slope flow may be turbulent if the Rayleigh number is sufficiently large (e.g., Ra = 10 6 -10 9 ) based on direct numerical simulation. ...
... In the steady stage, letting the ratio of convection to conduction terms O(δ p 2 / κt) be unity, we can obtain the two time scales t Pνκ and t Pgκ based on Eqs. (21) and (23), ...
Natural convection and heat transfer on a section-triangular roof are common around buildings. In this study, the slope flow and the plume on the suddenly heated section-triangular roof are investigated using scaling analysis and numerical simulation. The dynamics and heat transfer are discussed. It has been demonstrated that there exist different regimes of transient natural convection on the roof, which depends on the Rayleigh number, the aspect ratio of the roof and the Prandtl number. The scaling laws in different scenarios including inertial and viscous regimes are obtained and verified by numerical results. There is agreement between the scaling laws and numerical results. Further, the formulae of heat transfer and natural convection on the roof are presented.
... Following the onset of primary instability from 2D laminar to 3D laminar, the flow becomes periodic and finally enters turbulence in the downstream of the thermal boundary 39,40 . By increasing the inclination angle from the horizontal plate to the vertical plate, the thermal boundary layer is separated downstream of the leading edge 41,42 . The occurrence of vortex instability has been proven to be an absolute instability and a disturbance dissipates soon after being ejected into the thermal boundary layer 41 . ...
The development of thermal boundary layers and plume near a section-triangular roof under different isothermal heating conditions is experimentally investigated using phase-shifting interferometry and thermocouple measurements. The spatially averaged temperature contours are visualized for the Rayleigh number varying from 10^3 to 4 × 10^6. The measurements reveal a flow transition in the steady-state regime from conduction dominance to convection dominance, finally transitioning to a periodic flow regime with an increase in the Rayleigh number. The temperature series of the monitoring points reveal that the flow has a complex bifurcation route containing an inverse period bifurcation and an inverse quasi-periodic bifurcation. The oscillation of the flow depending on the Rayleigh number is also quantitatively and qualitatively described.
... Specific surface on the transition process was also concluded to have a crucial effect on transition [32]. Further, research [33][34][35] showed that the separation point and stability of the slope flow are also influenced by the inclination angle and Pr. Puigjaner et al. [36] used the Galerkin spectral method to simulate the bifurcation in a cubical enclosure heated from below. ...
Natural convection over a roof-shaped triangular surface is investigated using direct numerical simulations. The Rayleigh number (Ra) was varied from 1 to 5×106 with air as working fluid (Prandtl number of 0.71) at a fixed geometrical aspect ratio of 0.1, defined as the ratio of roof height to half-width. The transition route from a steady flow to a chaotic flow on the surface is characterized by the topological method with the increase of Ra. A weak flow, dominated by conduction, occurs when Ra was relatively small. As Ra increases, the convective flow becomes stronger and a sequence of bifurcations is found. Between Ra=102 and 103, a primary pitchfork bifurcation occurs. Secondary and tertiary pitchfork bifurcations are observed in the range Ra=[103,104] and [104,105], respectively. After another pitchfork bifurcation at Ra=[1.4,1.5]×106, which makes the plume tilt to either side of the roof top edge, a Hopf bifurcation is observed in Ra=[1.9,2]×106, after which both the slope flow and plume become periodic. This is followed by further bifurcations including a period doubling bifurcation at Ra≈3×106 and a quasiperiodic bifurcation firstly arising at Ra≈3.4×106. Finally, the flow becomes chaotic for Ra>3.7×106. The state space, the maximum Lyapunov exponent, the fractal dimension, and the power spectral density are presented to analyze the flows in the transition to chaos. This work is a comprehensive description of the flow transition from steady state to chaos on surface of a section-triangular roof that is pertinent to various settings where fluid flow develops.
... (2.2c) 2.1. Flow solver The governing system of (2.1) and (2.2) is solved using a variant of the Imperial College in-house DNS flow solver with the acronym BOFFIN (boundary fitted flow integrator) (Jones & Wille 1996;Mare & Jones 2003;Paul & Molla 2012;Alzwayi, Paul & Navarro-Martinez 2014). The flow solver is a low Mach number formulation and therefore neglects the terms ∂p/∂t + u i (∂p/∂x i ) and τ ij (∂u i /∂x j ) in (2.1c). ...
State prediction of an entropy wave advecting through a turbulent channel flow - Volume 882 - Loizos Christodoulou, Nader Karimi, Andrea Cammarano, Manosh Paul, Salvador Navarro-Martinez
... The behaviors of local and integral heat transfer on the cavity walls were investigated for different types of heated and cooled wall temperatures. The other group of numerical approaches is to compute the turbulent flow directly, such as the large-eddy simulation (LES) [25,26] and direct numerical simulation (DNS) [27]. The LES and DNS methods can capture the detailed flow behaviors and unsteady turbulent structures, but they require high computational resource and thus are less used than the RANSbased approaches. ...
The natural convection flow is commonly encountered in many engineering applications, and extensive studies were conducted to analyze the natural convection flow in the vertical and inclined rectangular cavities. However, most published studies assumed the cavity with infinite width and neglected the impact of cavity width. The present work mainly focuses on the natural convective heat transfer in the inclined rectangular cavities with low width-to-height ratios, through both experimental and computational fluid dynamics (CFD) analyses. A three-dimensional (3-D) model is firstly built up using the CFD code Fluent to simulate the airflow movement and convective heat transfer in the inclined rectangular cavity. The 3-D CFD model is then validated by the experiments performed on both the inclined and vertical rectangular cavities. Good agreements are observed between the theoretically simulated and experimentally measured airflow velocities and temperatures, as well as the temperatures of cavity walls. After validation, the 3-D CFD model is employed to analyze the impacts of width on the airflow velocity and convective heat transfer in the cavities with the width-to-height ratios of 1, 2, 4 and 8 respectively. It is concluded that increasing the width-to-height ratio and cavity inclination contributes to accelerate the natural convection flow and enhance the convective heat transfer in the cavity. In addition, the impact of the cavity width-to-height ratio becomes minimal on the natural convection flow, when it increases beyond 4.
Flame spread along discrete fuel element is of great interest for both fundamental science and fire prevention, whose combustion properties may be different from those of homogenous materials. It has been a long time for researchers in fire science to find a simple and effective method to construct a discrete flame spread model. This work was motivated by the research of 2‐D horizontal discrete flame spread behaviors with different spacings and rows, establishing the prediction model of ignition time and global mass loss rate (MLR). In this work, burning characteristics of the 2‐D discrete flame spread were experimentally studied with six different row numbers (1–11 with an interval of 2) of cylindrical dowels (birch wood, 3 mm diameter × 50 mm height) under three selected spacings (6, 7, and 8 mm). Based on the heat transfer model developed, the theoretical models of ignition time and MLR were obtained and validated. Moreover, combined with previous studies, the numerical correlation between dimensionless flame height and dimensionless heat release rate for the 2‐D horizontal discrete flame spread scenario was established. This study provided an insight into the horizontal discrete flame spread mechanism in the aspect of heat and mass transfer, which may be applied in the prediction and assessment of discrete fuel fires in reality.
In an inclined parallel plate channel, the influence of the angle of inclination on the transition of the free convection flow has been explored. Three dimensional large eddy simulations have been carried out employing the wall adaptive local eddy viscosity sub-grid scale model. The inclination angles of 15°, 30°, and 60° with respect to the horizontal are considered. The upper wall of the parallel plates is kept at constant heat flux, while the bottom one is adiabatic. The Grashof number, GrL considered in the present study is 8.22 × 10¹². The variation of the transition zone of the flow with variation in inclination angle is shown using thermal boundary layer formation, variation of velocity fluctuations, Nusselt number variation, and Q criterion. Investigation of the thermal boundary layer shows the formation of flume structure at the early stage of the flow in the case of lower inclination of the channel. As the degree of inclination increases, the transition is delayed, and the transition region shifts downstream.
Unsteady flows commonly exist on the roof owing to sun radiation or weather change and are also of fundamental significance for ventilation and energy conservation of buildings. In this paper, a study of the dynamics and heat transfer on the roof imposed by a periodic heat flux is reported. Unsteady flows on the roof are discussed using 2D simulation and scaling analysis. Analytical results show that unsteady flows are dominated under different regimes and scenarios, which are dependent on the time of the heating period, the aspect ratio of the roof, the Prandtl number and the Rayleigh number. Further, heat transfer is also quantified. The scaling relations are obtained under different regimes. Additionally, numerical simulation has been performed for the Rayleigh number of 10⁶ to 10⁹ and the aspect ratio of 0.5–1. Numerical results are used to describe flow structures and to verify the scaling relations. The scaling prediction is consistent with the corresponding numerical result.
In view of the characteristic of Photovoltaic (PV) conversion, an experimental study has been conducted to investigate the natural convection heat transfer from a flat plate. In order to simulate the real PV cells, three electrical heating circuits were employed to achieve a linear nonuniform heat flux boundary condition. The major parameters, such as the gradient parameter of heat flux k, tilt angle θ and heat flux qw were introduced to analyze their influence on heat transfer ability. Both the local temperature distribution and the overall trend of Nusselt number have been presented. Comparing with the uniform thermal boundary condition, the results show that the local convection heat transfer coefficient is fluctuated at the positions where heat flux has changed. When gradient parameter of heat flux increases, the difference of local convection heat transfer coefficient at the top of the plate between tilt angle θ = 0° and 90° becomes smaller. Moreover, it is observed that the gradient parameter of heat flux has a promotion effect on average convection Nusselt number at larger tilt angle, but the effect becomes complex as tilt angle is smaller. Finally, a correlation combining all significant factors has been put forward to estimate the natural convection heat transfer.
Transition of free convection flow in an inclined parallel walled channel has been investigated numerically by employing k-epsilon turbulent model. Particular attention is paid on how the inclination angle and width of the channel affect the transition process of the flow developing in the channel. The upper plate of the channel is heated isothermally and facing downward, while the lower one is kept under the adiabatic condition. The inclination angle of the channel is varied from 00 to 85 with respect to its vertical position while the distance separating the two plates is systematically reduced from 0.45 to 0.06 m. Distributions of velocity, turbulent kinetic energy and local heat flux are presented to examine the critical distance and the results obtained show good agreement with experimental data available in the literature.
In the present study a Large Eddy Simulation and Filtered Density Function model is applied to three premixed piloted turbulent methane flames at different Reynolds Numbers using the Eulerian stochastic fields approach. The model is able to reproduce the flame structure and flow characteristics with a low number of fields (between 4 and 16 fields). The results show a good agreement with experimental data with the same closures employed in non-premixed combustion without any adjustment for combustion regime. The effect of heat release on the flow field is captured correctly. A wide range of sensitivity studies is carried out, including the number of fields, the chemical mechanism, differential diffusion effects and micro-mixing closures. The present work shows that premixed combustion (at least in the conditions under study) can be modelled using LES-PDF methods.. Finally, the ability of the model to predict flame quenching is studied. The model can accurate capture the conditions at which combustion is not sustainable and large pockets of extinction appear.
Physiological pulsatile flow in a 3D model of arterial stenosis is investigated by using large eddy simulation (LES) technique. The computational domain chosen is a simple channel with a biological type stenosis formed eccentrically on the top wall. The physiological pulsation is generated at the inlet using the first harmonic of the Fourier series of pressure pulse. In LES, the large scale flows are resolved fully while the unresolved subgrid scale (SGS) motions are modelled using a localized dynamic model. Due to the narrowing of artery the pulsatile flow becomes transition-to-turbulent in the downstream region of the stenosis, where a high level of turbulent fluctuations is achieved, and some detailed information about the nature of these fluctuations are revealed through the investigation of the turbulent energy spectra. Transition-to-turbulent of the pulsatile flow in the post stenosis is examined through the various numerical results such as velocity, streamlines, velocity vectors, vortices, wall pressure and shear stresses, turbulent kinetic energy, and pressure gradient. A comparison of the LES results with the coarse DNS are given for the Reynolds number of 2000 in terms of the mean pressure, wall shear stress as well as the turbulent characteristics. The results show that the shear stress at the upper wall is low just prior to the centre of the stenosis, while it is maximum in the throat of the stenosis. But, at the immediate post stenotic region, the wall shear stress takes the oscillating form which is quite harmful to the blood cells and vessels. In addition, the pressure drops at the throat of the stenosis where the re-circulated flow region is created due to the adverse pressure gradient. The maximum turbulent kinetic energy is located at the post stenosis with the presence of the inertial sub-range region of slope −5/3.
Most applications of the dynamic subgrid-scale stress model use volume- or planar-averaging to avoid ill-conditioning of the model coefficient, which may result in numerical instabilities. Furthermore, a spatially-varying coefficient is mathematically inconsistent with the original derivation of the model. A localization procedure is proposed here that removes the mathematical inconsistency to any desired order of accuracy in time. This model is applied to the simulation of rotating channel flow, and results in improved prediction of the turbulence statistics. The model coefficient vanishes in regions of quiescent flow, reproducing accurately the intermittent character of the flow on the stable side of the channel. Large-scale longitudinal vortices can be identified, consistent with the observation from experiments and direct simulations. The effect of the unresolved scales on higher-order statistics is also discussed.
Numerical simulation of all the scales of a turbulent flow, even at modest Reynolds numbers, is generally not practical; however, most information of interest can be obtained by simulating the motion of the large-scale, energy containing eddies. This chapter describes the derivation of smoothed or filtered momentum, and the continuity equations for large-scale energy containing eddies. The large-scale fluctuations satisfy the filtered or averaged momentum and continuity equations. Averaging the nonlinear advection term yields two terms; one is the Reynolds stress contribution from the subgrid-scale turbulence, and the other is the filtered advection term for the large scales. In some models, the energy cascade is viewed solely as an energy loss of the large-scales because of an artificial viscosity arising from subgrid-scale motions. However, in most cases of interest, motions on the order of the dissipation length scale cannot be treated explicitly, and modifications of the Navier-Stokes equations must be introduced to simulate properly the energy cascade. Noting that the large-scale motions vary in a nonnegligible way over an averaging volume, the chapter investigates a more accurate, modified advective term in the momentum equations for these motions.
The differential equations for heat transfer from vertical plates in free convection were rederived in dimensionless form and extended to include inclined plates. The analysis indicated that the only change in the plate was the component of the gravitational force in the plate surface direction. The limitation of the equation is that the flow be laminar and two-dimensional. Heat transfer from a flat plate in free convection was studied at angles of inclination ranging from 0 to 40 deg measured from the vertical, for a range of Grashof numbers from 106 to 109 and temperature differences from the surface to the surroundings of 200 to 260 F. The investigation shows the inclined-plate nondimensional unit thermal conductance, Nu, can be predicted from vertical plate conductances. The Grashof number in the Nusselt relation for the vertical plate, when modified by the cosine of the angle of inclination, can predict the inclined-plate conductances to within 10 per cent of those determined experimentally.
Numerical simulations are performed to study the transition of the development of the thermal boundary layer of air along an isothermal heated plate in a large channel which is bounded by an adiabatic plate. In particular, the aim is to investigate the effects of the channel width (b) on the transition of the flow under various plate temperatures. Three different RANS based turbulent k–ε models namely standard, RNG and Realizable with an enhanced wall function are employed in the simulations. The channel width was varied from 0.04 m to 0.45 m and the numerical results of the maximum values of the flow velocity, turbulent kinetic energy were recorded along the vertical axis to examine the critical distance of the developing flow. The results show that the transition delays when the width is increased from 0.04 m to 0.08 m and particularly, the critical distance at b = 0.08 m reaches its maximum with the Grashof number of 2.8 × 1010. However, the critical distance drops when b is increased further from 0.08 m to 0.45 m, indicating an early transition of the flow. The transition remains unaffected by the adiabatic plate when b is greater than 0.45 m. Comparisons of selected numerical results are made with available experimental data of turbulent flow and a satisfied agreement is received.
An LDV and a fine thermocouple were used to measure the turbulence characteristics of the free convection boundary layer along a vertical plate with uniform heat generation in air. An equation was derived for the local Nusselt number in the turbulent region. The results showed good agreement with those found in previous experiments for the free convection turbulent boundary layer. With respect to the turbulence quantities directly associated with velocity fluctuations, however, appreciable differences between the present results and earlier work using hot wire sensors were found.
Natural convective flows over upward-facing, inclined plates were investigated experimentally, with an emphasis on the role of opposing flows that appear over the plates inclined slightly from the horizontal line. The flow fields over the plates and the surface temperatures of the heated plates were visualized with both dye and a liquid-crystal thermometry. The results showed that both the descending and ascending flows appeared over the plates when the inclination angles of the plates were less than 15°. The two flows collided with each other at a certain distance from the plate edge, and then detached from the plate to become a thermal plume. It was found that the above distance was determined solely by the inclination angles and was independent of sizes and heat fluxes of the plates. The local heat transfer coefficients of the plates were also measured. The results showed that the heat transfer from the plate was enhanced by the occurrence of the descending flows. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(5): 362–375, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10036
Experiments are performed to demonstrate the occurrence and explore the characteristics of a secondary flow superposed upon the natural convection main flow on an inclined plate. A flow visualization technique is employed whereby the flow pattern is made visible by local changes of colour of the fluid itself, the colour change being brought about by a change in pH. The secondary flow consists of longitudinal vortices or rolls distributed more or less periodically across the width of the plate. The number of such vortices increases with the temperature difference between the surface and the ambient fluid, but appears to be relatively insensitive to the inclination angle of the plate. The secondary flow results from the destabilizing effect of the buoyancy force component, which acts normal to the plate surface. The longitudinal vortices are the first stage of the laminarturbulent transition process. This is in contrast to the case of natural convection on a vertical plate, where the first stage of transition is Tollmien-Schlichting waves.
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.
Experiments are carried out to establish the relationship between the nature of the flow instability and the inclination angle of the plate. The angular dependence of the Rayleigh number characterizing the onset of instability is also determined. An electrochemical flow visualization technique is utilized to expose the patterns of fluid motion. It is found that for inclination angles of less than 14° (relative to the vertical), waves are the mode of instability. On the other hand, for inclination angles in excess of 17°, the instability is characterized by longitudinal vortices. The range between 14° and 17° is a zone of continuous transition, with the two modes of instability co-existing.
The present study deals with fluid flow and heat transfer in the transition process of natural convection over an inclined plate. In order to examine the mechanism of the transition process, experiments on the flow and heat transfer were performed for various plate inclination angles in the range of 20 to 75°. The wall temperature and fluid flow fields were visualized using a liquid crystal sheet and fluorescent paint, respectively. The visualization confirmed that separation of a boundary layer flow took place, and the onset point of streaks appeared over the plate wall when the modified Rayleigh number exceeded a characteristic value for each inclination angle. The local Nusselt number in the transition range was proportional to the one-third power of the local modified Rayleigh number. By introducing a nondimensional parameter, a new correlation between visualizations of the flow and temperature fields and heat transfer was proposed. © 2001 Scripta Technica, Heat Trans Asian Res, 30(8): 648–659, 2001
Large eddy simulations of natural convection along a vertical isothermal surface have been carried out using a parallel CFD code SMAFS (Smoke Movement And Flame Spread) developed by the first author to study the dynamics of the natural convection flow and the associated convective heat transfer, with sub-grid scale turbulence modeled using the Smagorinsky model. In the computation, the filtered governing equations are discretized using finite volume method, with the variables at the cell faces in the finite volume discrete equations approximated by a second order bounded QUICK scheme and the diffusion term computed based on central difference scheme. The computation was time marched explicitly, with momentum equations solved based on a second order fractional-step Adams–Bashford scheme and enthalpy computed using a second order Runge–Kutta scheme. The Poisson equation for pressure from the continuity equation was solved using a multi-grid solver. The results including the temperature and velocity profiles of the boundary layer and the local heat transfer rate are analyzed. Comparison is made with experimental data and good agreement is found.
Turbulence in the convective boundary layer (CBL) uniformly heated from below and topped by a layer of uniformly stratified fluid is investigated for zero mean horizontal flow using large-eddy simulations (LES). The Rayleigh number is effectively infinite, the Froude number of the stable layer is 0.09 and the surface roughness height relative to the height of the convective layer is varied between 10-6 and 10-2. The LES uses a finite-difference method to integrate the three-dimensional grid-volume-averaged Navier-Stokes equations for a Boussinesq fluid. Subgrid-scale (SGS) fluxes are determined from algebraically approximated second-order closure (SOC) transport equations for which all essential coefficients are determined from the inertial-range theory. The surface boundary condition uses the Monin-Obukhov relationships. A radiation boundary conditions at the top of the computational domain prevents spurious reflections of gravity waves. The simulation uses 160 × 160 × 48 grid cells.
A differential interferometer is used to provide flow visualization and measurement of the local heat-transfer coefficient for free convection from an inclined isothermal plate. The flow structure within the turbulent thermal boundary layer can be separated into a relatively constant thickness "thermal sublayer" and a core region that contains randomly fluctuating fluid typical of turbulent flow. The thermal sublayer is shown to contain "thermal waves" that traverse the surface of the heated plate and cause significant variations in the local heat-transfer coefficient. The frequency of occurance of the thermal waves increases in the transitional regime and is practically constant in the turbulent regime. The frequency of the thermal waves is decreased as the plate is inclined toward a horizontal position. Data for the time-average local Nusselt number for laminar, transitional and turbulent regimes are presented in addition to critical Rayleigh number values for the onset of transitional and turbulent flow.
The paper presents a perturbation analysis for two-dimensional laminar free convection about an inclined isothermal plate, using the classical boundary-layer solution as the zeroth-order approximation. First-order perturbation solution has been found for the velocity and temperature fields. The distributions of both components of the velocity field and temperature field, calculated in detail for Prandtl number 0·7 and inclination angles ϑ = 0, ± 15, ± 30, ± 45 are compared with experimental data. Good agreement is found between the theoretical solution and experimental results.RésuméOn présente ici une analyse théorique par la méthode des perturbations pour la convection naturelle laminaire tridimensionnelle le long d'une plaque isotherme inclinée, en employant la solution du type de la couche limite classique comme approximation d'ordre zéro. La solution de perturbation du premier ordre a été trouvée pour les champs de vitesse et de température. Les distributions à la fois des composantes du champ de vitesse et du champ de température calculées en détail pour un nombre de Prandtl de 0,7 et des inclinaisons de 0°, ± 15°, ± 30°, et ± 45° sont comparées avec les données expérimentales. On a trouvé un bon accord entre la solution théorique et les résultats expérimentaux.ZusammenfassungDie Arbeit behandelt eine Störanalyse für zweidimensionale laminare freie Konveklion entlang einer geneigten isothermen Platte auf Grund der klassischen Grenzschichtlösung als Näherung militer Ordnung. Eine Störlösung erster Ordnung liess sich für Geschwindigkeits- und Temperaturfelder finden. Die für die Prandll-Zahl 0,7 und für Neigungswinkel = 0° ± 15° ± 30° ± 45° berechneten Verteilungen beider Komponenten des Geschwindigkeits- und Temperaturfeldes wurden mit Versuchswerten verglichen. Gute Übereinstimmung ergab sich zwischen der theoretischen Lösung und den Versuchsergebnissen.
Experimental local and average heat transfer data are obtained for natural convection heat transfer from isothermal vertical and inclined plates facing upwards to air. The employed apparatus enabled the isolation of the effect of side edges, thus ensuring the condition of infinite plate width. The experiments covered both the laminar and the turbulent regions. Equations representing the results are suggested.RésuméDes données expérimentales locales et globales sur le transfert thermique sont présentées pour la convection thermique naturelle sur des plaques isothermes verticales et inclinées tournées vers le haut dans l'air. Le montage employé permet l'isolement de l'effet de bord, assurant ainsi la condition d'une étendue infinie de plaque. Les expériences couvrent les régions de mouvement laminaire et turbulent. On propose des équations représentant les résultats.ZusammenfassungEs wurden die örtlichen und mittleren Wärmeübergangskoeffizienten bei natürlicher Konvektion an senkrechten und geneigten (Oberseite), isothermen Platten untersucht. Die verwendete Apparatur ermöglicht es, seitliche Randeffekte auszugrenzen, so daβ die Situation einer unendlich breiten Platte gegeben ist. Die Experimente umfassen den laminaren und turbulenten Strömungsbereich. Es werden Ausgleichsfunktionen der Meβergebnisse vorgeschlagen.РефератПoлyчeны зкcпepимeитaльиыe дaииыe для мecтиыч н cpeднич кoзффициeнтoB тeплooтдaчи ecтecтBeииoй кoиBeкциeй oт изoтepмичecкич нлacтии, pacнoлoзeииыч B Boздyчe Bepтикaльиo и c нaклoнoм иapyзиoй пoBepчнocти. B иcпoльзyeмoй ycтaнoBкe иcключaлocь Bлияинe бoкoBыч кpoмoк, чтo дaBaлo Boзмoзиocть cчитaть щиpинy плacтии бecкoнeчнoй. B зкcпepимeитaч иccлeдoBaлиcь кaк лaмииapныe, тaк и тypбyлeнтныe peзимы. Пpeдлoзeиы ypaBнeиия, oпиcыBaющиe пoлyчeииыe peзyльтaты.
Local heat-transfer coefficients along a flat plate in natural convection in air were measured using Boelter-Schmidt type heat flux meters. Experiments were carried out for different temperature differences in heating and cooling, and with inclinations varying from the horizontal "facing upwards" position, through the vertical position, to the horizontal "facing downwards" position. The results are presented in terms of local Nusselt number as a function of the local Grashof number "tangential component". All runs were in the range accepted as that of laminar boundary layer flow. However, under certain conditions when the normal velocity component of the air is directed away from the surface, separated flow is indicated along the trailing part of the surface, well before turbulence sets in in the boundary layer. Separation starts at a certain point along the surface. This point is nearer to the leading edge the higher the temperature difference, and the larger the inclination of the surface to the vertical. In a separation region, the flux density is uniform. In all other regions the results agreed closely with established theories of laminar boundary layer flow. A leading adiabatic section, used in some of the experiments, did not affect the results. An appendix gives relations recommended for engineering calculations.
A turbulent natural convection boundary layer, the structure of which still remains a matter of conjecture for want of reliable measurement, is investigated with the V-shaped hot-wire technique. The reliability of Reynolds stress and turbulent heat flux measurements is verified by the excellent agreement with the indirect measurements estimated by integrating momentum and thermal energy equations with measured mean velocity and mean temperature. Turbulent quantities clarified quantitatively in the present study indicate that the natural convection boundary layer has a unique turbulent structure rarely seen in other turbulent boundary layers.
A three-dimensional numerical study is conducted to investigate the radiative heat transfer in a model gas turbine combustor. The Discrete Ordinates Method (DOM/Sn) has been implemented to solve the filtered Radiative Transfer Equation (RTE) for the radiation modelling and this has been combined with a Large Eddy Simulation (LES) of the flow, temperature and composition fields within the combustion chamber. The radiation considered in the present work is due only to the hot combustion gases notably carbon dioxide (CO2) and water vapour (H2O), which is also known as the ‘non-luminous’ radiation. A benchmark problem of the ideal furnace is considered first to examine the accuracy and computational efficiency of the DOM in the three-dimensional general body fitted co-ordinate systems.
Large Eddy Simulation (LES) is applied to investigate the turbulent non-premixed combustion flow, including species concentrations and temperature, in a cylindrical combustor. Gaseous propane (C3H8) is injected through a circular nozzle which is attached at the centre of the combustor inlet. Preheated air with a temperature of 773 K is supplied through the annulus surrounding of this fuel nozzle. In LES a spatial filtering is applied to the governing equations to separate the flow field into large-scale and small-scale eddies. The large-scale eddies which carry most of the turbulent energy are resolved explicitly, while the unresolved small-scale eddies are modelled using the Smagorinsky model with Cs = 0.1 as well as dynamically calibrated Cs. The filtered values of the species mass fraction, temperature and density, which are the functions of the mixture fraction (conserved scalar), are determined by integration over a beta probability density function (β-PDF). The computational results are compared with those of the experimental investigation conducted by Nishida and Mukohara [1]. According to this experiment, the overall equivalence ratio of 0.6, which is calculated from the ratio of the air flow rate supplied to the combustion chamber to that of the stoichiometric reaction, is kept constant so that the turbulent combustion at the fuel nozzle exit starts under the fuel-rich conditions.
This paper applies the Eulerian stochastic field method to the solution of the subgrid joint probability density function (PDF) of the reacting scalars in a large eddy simulation (LES) of a jet of hydrogen issuing into a co-flow of vitiated air. The hot co-flow induces autoignition of the mixture and a lifted flame results downstream of the nozzle exit. The simulations were performed using a detailed H2–air mechanism. The results were found to be sensitive to the co-flow temperature even with temperatures varied within the experimental uncertainty. The results obtained were in excellent agreement with the experimental data, both quantitatively and qualitatively. The method was able to capture partially premixed and partially extinguish zones with a relatively small number of stochastic fields. The radical HO2 was found to be the trigger for autoignition. The fact that no large-scale premixed flame propagation was observed suggests that the stabilization mechanism is associated mainly with the chemistry.
The technique of obtaining high resolution, second order, oscillation free, explicit scalar difference schemes, by the addition of a limited antidiffusive flux to a first order scheme is explored and bounds derived for such limiters. A class of limiters is presented which includes a very compressive limiter due to P. L. Roe, and various limiters are compared both theoretically and numerically.
A new iterative method for the solution of systems of linear equations has been recently proposed by Meijerink and van der Vorst [1]. This method has been applied to real laser fusion problems taken from typical runs of the laser fusion simulation code LASNEX [2]. These same problems were also solved by various standard iteration methods. On a typical hard problem, the new method is about 8000 times faster than the point Gauss-Seidel method, 200 times faster than the alternating direction implicit method, and 30 times faster than the block successive overrelaxation method with optimum relaxation factor. The new method has two additional virtues. (1) Most of the algorithm is trivially vectorizable with a vector length equal to the full dimension of the system of linear equations. Thus, great savings are possible on vector machines. (2) The new method has a universal scope of application for solution of implicitly differenced partial differential equations. The only restrictions are that the matrix be symmetric and positive definite. The algorithm of Meijerink and van der Vorst which applied only to positive definite symmetric M-matrices is generalized to apply to positive definite symmetric matrices and further generalized to apply to nonsingular matrices arising from partial differential equations. A general description of the method is given. Numerical results are discussed and presented, and an explanation is given for the success of the method.
We reconsider the onset of streamwise vortices in the thermal boundary layer flow induced by an inclined upward-facing heated semi-infinite surface placed within a Newtonian fluid. Particular emphasis is laid upon how the induced flow in the isothermal region outside the boundary layer affects the boundary layer itself at higher order, and how this, in turn, affects the stability criterion for the onset of vortices. We find that the stability criterion for thermal boundary layers in air is less susceptible to changes in external geometry than for boundary layers in water. In general, we conclude that the variation of the stability criterion with wedge angle (between the heated and the outer boundary surface) is too great for the theory to predict reliably where disturbances first begin to grow.
Temperature iso-surface contour plots at θ = 0° (a)
- Fig
Fig. 6. Temperature iso-surface contour plots at θ = 0° (a), θ = 20° (b), θ = 45° (c) and θ = 70° (d).
Characteristics of Turbulence in Free Convection Flow Past a Vertical Plate
- R R Smith
R.R. Smith, Characteristics of Turbulence in Free Convection Flow Past a Vertical
Plate, (Ph.D. Thesis) Univ. of London, 1972..
Critical Grashof number compared at various angular orientations of the heated plate
- Fig
Fig. 10. Critical Grashof number compared at various angular orientations of the heated
plate.