Analysis of Turbulent Thermal Convection Between Horizontal Plates

1983 ◽  
Vol 105 (4) ◽  
pp. 789-794 ◽  
Author(s):  
M. Kaviany ◽  
R. Seban
Keyword(s):  
Temperature Distribution ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Thermal Convection ◽  
Equation Model ◽  
Experimental Results ◽  
Mixing Length ◽  
Mean Temperature ◽  
The Mean ◽  
The One

The one-equation model of turbulence is applied to the turbulent thermal convection between horizontal plates maintained at constant temperatures. A pseudo-three-layer model is used consisting of a conduction sublayer adjacent to the plates, a turbulent region within which the mixing length increases linearly, and a turbulent core within which the mixing length is a constant. It is assumed that the Nusselt number varies with the Rayleigh number to the one-third power. As a result, the steady-state distributions of the turbulent kinetic energy and the mean temperature are obtrained and presented in closed forms. These results include the effects of Prandtl number. The predictions are compared with the available experimental results for different Prandtl and Rayleigh numbers. Also included are the predictions of Kraichnan, which are based on a less exact analysis. The results of the one-equation model are in fair agreement with the experimental results for the distribution of the turbulent kinetic energy and the mean temperature distribution. The predictions of Kraichnan are in better agreement with the experimental results for the mean temperature distribution.

scholarly journals Full-Coverage Film-Cooling: A One-Equation Model of Turbulence for the Calculation of the Full-Coverage and the Recovery-Region Hydrodynamics

1985 ◽  
Author(s):  
S. Yavuzkurt
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Film Cooling ◽  
Plate Boundary ◽  
Cross Flow ◽  
Equation Model ◽  
Mixing Length ◽  
Two Dimensional ◽  
Mean Velocity ◽  
Full Coverage

A one-equation model (mixing-length and turbulent kinetic energy) of turbulence is used for the calculation of the full-coverage and recovery region hydrodynamics over a full-coverage film-cooled surface. The model requires a detailed description of the form and dynamics of the complex mixing-length profile encountered in this type of flow structure. This is achieved through extensive use of experimental input and physical interpretation of the data by combining equations for simple flow structures such as two-dimensional turbulent flat plate boundary layers and jets-in-cross flow. The one-equation model is used in a two-dimensional finite difference boundary layer code giving successful predictions of the spanwise averaged mean velocity and turbulent kinetic energy profiles between injection rows in the full coverage region and also in the recovery region for two blowing ratios (Ujet/U∞ = 0.4, 0.9).

Mean Temperature Difference Charts for Air Coolers

1983 ◽  
Vol 105 (3) ◽  
pp. 592-597 ◽  
Author(s):  
A. Pignotti ◽  
G. O. Cordero
Keyword(s):  
Heat Transfer ◽  
Heat Capacity ◽  
Temperature Difference ◽  
Optimization Technique ◽  
Independent Variables ◽  
Mean Temperature ◽  
Air Cooler ◽  
The Mean ◽  
The One ◽  
Water Ratio

Computer generated graphs are presented for the mean temperature difference in typical air cooler configurations, covering the combinations of numbers of passes and rows per pass of industrial interest. Two sets of independent variables are included in the graphs: the conventional one (heat capacity water ratio and cold fluid effectiveness), and the one required in an optimization technique of widespread use (hot fluid effectiveness and the number of heat transfer units). Flow arrangements with side-by-side and over-and-under passes, frequently found in actual practice, are discussed through examples.

scholarly journals Diurnal Dynamics of the Umov Kinetic Energy Density Vector in the Atmospheric Boundary Layer from Minisodar Measurements

Atmosphere ◽  
2021 ◽  
Vol 12 (10) ◽  
pp. 1347
Author(s):  
Alexander Potekaev ◽  
Nikolay Krasnenko ◽  
Liudmila Shamanaeva
Keyword(s):  
Energy Density ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Energy Flux ◽  
Wind Effect ◽  
Kinetic Energy Density ◽  
Near Surface ◽  
Density Vector ◽  
The Mean ◽  
Umov Vector

The diurnal hourly dynamics of the kinetic energy flux density vector, called the Umov vector, and the mean and turbulent components of the kinetic energy are estimated from minisodar measurements of wind vector components and their variances in the lower 200-meter layer of the atmosphere. During a 24-hour period of continuous minisodar observations, it was established that the mean kinetic energy density dominated in the surface atmospheric layer at altitudes below ~50 m. At altitudes from 50 to 100 m, the relative contributions of the mean and turbulent wind kinetic energy densities depended on the time of the day and the sounding altitude. At altitudes below 100 m, the contribution of the turbulent kinetic energy component is small, and the ratio of the turbulent to mean wind kinetic energy components was in the range 0.01–10. At altitudes above 100 m, the turbulent kinetic energy density sharply increased, and the ratio reached its maximum equal to 100–1000 at altitudes of 150–200 m. A particular importance of the direction and magnitude of the wind effect, that is, of the direction and magnitude of the Umov vector at different altitudes was established. The diurnal behavior of the Umov vector depended both on the time of the day and the sounding altitude. Three layers were clearly distinguished: a near-surface layer at altitudes of 5–15 m, an intermediate layer at altitudes from 15 m to 150 m, and the layer of enhanced turbulence above. The feasibility is illustrated of detecting times and altitudes of maximal and minimal wing kinetic energy flux densities, that is, time periods and altitude ranges most and least favorable for flights of unmanned aerial vehicles. The proposed novel method of determining the spatiotemporal dynamics of the Umov vector from minisodar measurements can also be used to estimate the effect of wind on high-rise buildings and the energy potential of wind turbines.

On the structure of shear stress and turbulent kinetic energy flux across the roughness layer of a gravel-bed channel flow

2009 ◽  
Vol 638 ◽  
pp. 423-452 ◽  
Author(s):  
EMMANUEL MIGNOT ◽  
D. HURTHER ◽  
E. BARTHELEMY
Keyword(s):  
Shear Stress ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Channel Flow ◽  
Mean Flow ◽  
Local Flow ◽  
Gravel Bed ◽  
Wall Flows ◽  
The Mean ◽  
Conditional Statistics

This study examines the structure of shear stress and turbulent kinetic energy (TKE) flux across the roughness layer of a uniform, fully rough gravel-bed channel flow (ks+ ≫ 100, δ/k = 20) using high-resolution acoustic Doppler velocity profiler measurements. The studied gravel-bed roughness layer exhibits a complex random multi-scale roughness structure in strong contrast with conceptualized k- or d-type roughness in standard rough-wall flows. Within the roughness layer, strong spatial variability of all time-averaged flow quantities are observed affecting up to 40% of the boundary layer height. This variability is attributed to the presence of bed zones with emanating bed protuberances (or gravel clusters) acting as local flow obstacles and bed zones of more homogenous roughness of densely packed gravel elements. Considering the strong spatial mean flow variability across the roughness layer, a spatio-temporal averaging procedure, called double averaging (DA), has been applied to the analysed flow quantities. Three aspects have been addressed: (a) the DA shear stress and DA TKE flux in specific bed zones associated with three classes of velocity profiles as previously proposed in Mignot, Barthélemy & Hurther (J. Fluid Mech., vol. 618, 2009, p. 279), (b) the global and per class DA conditional statistics of shear stress and associated TKE flux and (c) the contribution of large-scale coherent shear stress structures (LC3S) to the TKE flux across the roughness layer. The mean Reynolds and dispersive shear structure show good agreement between the protuberance bed zones associated with the S-shape/accelerated classes and recent results obtained in standard k-type rough-wall flows (Djenidi et al., Exp. Fluids, vol. 44, 2008, p. 37; Pokrajac, McEwan & Nikora, Exp. Fluids, vol. 45, 2008, p. 73). These gravel-bed protuberances act as local flow obstacles inducing a strong turbulent activity in their wake regions. The conditional statistics show that the Reynolds stress contribution is fairly well distributed between sweep and ejection events, with threshold values ranging from H = 0 to H = 8. However, the TKE flux across the roughness layer primarily results from the residual shear stress between ejection and sweep of very high magnitude (H = 10–20) and of small turbulent scale. Although LC3S are seen to penetrated the interfacial roughness layer, their TKE flux contribution is found to be negligible compared to the very energetic small-scale sweep events. These sweeps are dominantly produced in the bed zones of local gravel protuberances where the velocity profiles are inflexional of S-shape type and the mean flow properties are of mixing-layer flow type as previously shown in Mignot et al. (2009).

On the interactions between large-scale structure and fine-grained turbulence in a free shear flow I. The development of temporal interactions in the mean

1976 ◽  
Vol 352 (1669) ◽  
pp. 213-247 ◽  
Keyword(s):  
Energy Transfer ◽  
Kinetic Energy ◽  
Shear Layer ◽  
Turbulent Kinetic Energy ◽  
Viscous Dissipation ◽  
Mean Flow ◽  
Fine Grained ◽  
Large Eddy ◽  
The Mean ◽  
Three Components

In this problem a mean turbulent shear layer originally exists, homogeneous in the streamwise direction, formed perhaps by previous instabilities, but in equilibrium with the fine-grained turbulence. At a given time, a large eddy of a fixed horizontal wavenumber is initiated. We study the subsequent time development of the non-equilibrium interactions between the three components of flow as they adjust towards ultimate simultaneous equilibrium, using the integrated energy-balance conservation equations to derive the amplitude equations. This necessarily involves the usual averaging procedure and a conditional or phase-averaging procedure by which the large structure motion is educed from the total fluctuations. In general, the mean flow growth is due to the energy transfer to both fluctuating components, the large eddy gains energy from the mean motion and exchanges energy with the fine-grained turbulence, while the fine-grained turbulence gains energy from the mean flow and exchanges with the large eddy and converts its energy to heat through viscous dissipation of the smallest scales. The closure problem is obtained via the shape assumptions which enter into the interaction integrals. The situation in which the fine-grained turbulent kinetic energy production and viscous dissipation are in local balance is considered, the displacement from equilibrium being due only to the energy transfer from the large eddy. The large eddy shape is taken to be two-dimensional, instability-wavelike, with its vorticity axis perpendicular to the direction of the mean outer stream. Prior to averaging, detailed but approximate calculations of the wave-induced turbulent Reynolds stresses are obtained; the product of these stresses with the appropriate large-eddy rates of strain give the energy transfer mechanism between the two disparate scales of fluctuations. Coupled, nonlinear amplitude or energy density equations for the three components of motion are obtained, the coefficients of which are the interaction integrals guided by the shape assumptions. It is found that for the special case of parallel flow, the energy of the large eddy first undergoes a hydrodynamic-instability type of amplification but eventually decays due to the energy transfer to the fine-grained turbulence, while the turbulent kinetic energy is displaced from an original level of equilibrium to a new one because of the ability of the large eddy to negotiate an indirect energy transfer from the mean flow. For the growing shear layer, approximate considerations show that if the mechanism of energy transfer from the large to the small scale is eventually weakened by the shear layer growth compared to the large-eddy production mechanism so that the amplification and decay process repeats, ‘bursts’ of the remnant of the same large eddy will occur repeatedly until an ultimate equilibrium is reached among the three interacting components of motion. However, for the large eddy whose wavenumber corresponds to that of the initially most amplified case, the ‘bursting’ phenomenon is much less pronounced and equilibrium is very nearly reached at the end of the very first ‘burst’.

scholarly journals Tables of the variation, through a cycle of nine years, of the mean height of the barometer, mean temperature, and depth of rain, as connected with the prevailing winds, influenced in their direction by the occurrence of the lunar apsides, with some concluding observations on the result

1843 ◽  
Vol 4 ◽  
pp. 226-227
Keyword(s):  
The Other ◽  
Mean Temperature ◽  
The Mean ◽  
The One

From the Tables here given, the author draws the following conclusions:— 1 The barometer is higher under the lunar apogee, than under the perigee; the mean height in the former case being 29·84517, and in the latter, 29·75542. 2. The mean temperature is lower under the apogee than under the perigee; that of the former being 48°·7126, and of the latter, 49°·0356. The mean of the whole year was 48°·7126. 3. The rain of the weeks following the apsis exceeds that under the perigee; but with two striking exceptions in the annual result of nine years, the one in the wettest, and the other in the driest year of the cycle.

scholarly journals The streamwise turbulence intensity in the intermediate layer of turbulent pipe flow

2015 ◽  
Vol 774 ◽  
pp. 324-341 ◽  
Author(s):  
J. C. Vassilicos ◽  
J.-P. Laval ◽  
J.-M. Foucaut ◽  
M. Stanislas
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Intermediate Layer ◽  
High Reynolds Number ◽  
Logarithmic Derivative ◽  
Turbulent Pipe Flow ◽  
Mean Flow ◽  
The Mean ◽  
High Reynolds

The spectral model of Perryet al. (J. Fluid Mech., vol. 165, 1986, pp. 163–199) predicts that the integral length scale varies very slowly with distance to the wall in the intermediate layer. The only way for the integral length scale’s variation to be more realistic while keeping with the Townsend–Perry attached eddy spectrum is to add a new wavenumber range to the model at wavenumbers smaller than that spectrum. This necessary addition can also account for the high-Reynolds-number outer peak of the turbulent kinetic energy in the intermediate layer. An analytic expression is obtained for this outer peak in agreement with extremely high-Reynolds-number data by Hultmarket al. (Phys. Rev. Lett., vol. 108, 2012, 094501;J. Fluid Mech., vol. 728, 2013, pp. 376–395). Townsend’s (The Structure of Turbulent Shear Flows, 1976, Cambridge University Press) production–dissipation balance and the finding of Dallaset al. (Phys. Rev. E, vol. 80, 2009, 046306) that, in the intermediate layer, the eddy turnover time scales with skin friction velocity and distance to the wall implies that the logarithmic derivative of the mean flow has an outer peak at the same location as the turbulent kinetic energy. This is seen in the data of Hultmarket al. (Phys. Rev. Lett., vol. 108, 2012, 094501;J. Fluid Mech., vol. 728, 2013, pp. 376–395). The same approach also predicts that the logarithmic derivative of the mean flow has a logarithmic decay at distances to the wall larger than the position of the outer peak. This qualitative prediction is also supported by the aforementioned data.

Large Eddy Simulation of Cylindrical Jet Breakup and Correlation of Simulation Results With Experimental Data

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Shashank S. Moghe ◽  
Scott M. Janowiak
Keyword(s):  
Experimental Data ◽  
Kinetic Energy ◽  
Large Eddy Simulation ◽  
Turbulent Kinetic Energy ◽  
Experimental Results ◽  
Eddy Simulation ◽  
Jet Breakup ◽  
Large Eddy ◽  
Oil Jet ◽  
Piston Cooling

Modern engines with increasing power densities have put additional demands on pistons to perform in incrementally challenging thermal environments. Piston cooling is therefore of paramount importance for engine component manufacturers. The objective of this computational fluid dynamics (CFD) study is to identify the effect of a given piston cooling nozzle (PCN) geometry on the cooling oil jet spreading phenomenon. The scope of this study is to develop a numerical setup using the open-source CFD toolkit OpenFoam® for measuring the magnitude of oil jet spreading and comparing it to experimental results. Large eddy simulation (LES) turbulence modeling is used to capture the flow physics that affects the inherently unsteady jet breakup phenomenon. The oil jet spreading width is the primary metric used for comparing the numerical and experimental results. The results of simulation are validated for the correct applicability of LES by evaluating the fraction of resolved turbulent kinetic energy (TKE) at various probe locations and also by performing turbulent kinetic energy spectral analysis. CFD results appear promising since they correspond to the experimental data within a tolerance (of ±10%) deemed satisfactory for the purpose of this study. Further generalization of the setup is underway toward developing a tool that predicts the aforementioned metric—thereby evaluating the effect of PCN geometry on oil jet spreading and hence on the oil catching efficiency (CE) of the piston cooling gallery. This tool would act as an intermediate step in boundary condition formulation for the simulation determining the filling ratio (FR) and subsequently the heat transfer coefficients (HTCs) in the piston cooling gallery.

EFFET DU CLIMAT SUR LA FLETRISSURE BACTERIENNE DE LA POMME DE TERRE ET RELATION AVEC LE CONTENU EN SUCRES DES TIGES

1976 ◽  
Vol 56 (3) ◽  
pp. 549-554 ◽  
Author(s):  
ROGER PAQUIN ◽  
H. GÉNÉREUX
Keyword(s):  
Sugar Content ◽  
Degree Days ◽  
Bacterial Ring Rot ◽  
Higher Plant ◽  
Disease Evolution ◽  
Ring Rot ◽  
Mean Temperature ◽  
Northern Regions ◽  
The Mean ◽  
The One

Potato cultivars resistant to bacterial ring rot, inoculated with Corynebacterium sepedonicum, were more infected in the northern regions (North Shore) than at La Pocatière (South Shore of St. Lawrence River) where the number of degree-days and mean temperatures are higher. Plant stems from the Northern regions had a higher total and reducing sugar content than those of La Pocatière and there was a significant correlation between sugar content and the mean temperature or the number of degree-days. However, the latter correlation is more significant than the one between the percentage of infected plants and the mean temperature or the number of degree-days in that region. The possible role of sugars in the disease evolution in the cool regions is discussed.

Pseudo-turbulent gas-phase velocity fluctuations in homogeneous gas–solid flow: fixed particle assemblies and freely evolving suspensions

2015 ◽  
Vol 770 ◽  
pp. 210-246 ◽  
Author(s):  
M. Mehrabadi ◽  
S. Tenneti ◽  
R. Garg ◽  
S. Subramaniam
Keyword(s):  
Kinetic Energy ◽  
Phase Velocity ◽  
Turbulent Kinetic Energy ◽  
Gas Phase ◽  
Reynolds Stress ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Particle Assemblies

Gas-phase velocity fluctuations due to mean slip velocity between the gas and solid phases are quantified using particle-resolved direct numerical simulation. These fluctuations are termed pseudo-turbulent because they arise from the interaction of particles with the mean slip even in ‘laminar’ gas–solid flows. The contribution of turbulent and pseudo-turbulent fluctuations to the level of gas-phase velocity fluctuations is quantified in initially ‘laminar’ and turbulent flow past fixed random particle assemblies of monodisperse spheres. The pseudo-turbulent kinetic energy $k^{(f)}$ in steady flow is then characterized as a function of solid volume fraction ${\it\phi}$ and the Reynolds number based on the mean slip velocity $\mathit{Re}_{m}$. Anisotropy in the Reynolds stress is quantified by decomposing it into isotropic and deviatoric parts, and its dependence on ${\it\phi}$ and $Re_{m}$ is explained. An algebraic stress model is proposed that captures the dependence of the Reynolds stress on ${\it\phi}$ and $Re_{m}$. Gas-phase velocity fluctuations in freely evolving suspensions undergoing elastic and inelastic particle collisions are also quantified. The flow corresponds to homogeneous gas–solid systems, with high solid-to-gas density ratio and particle diameter greater than dissipative length scales. It is found that for the parameter values considered here, the level of pseudo-turbulence differs by only 15 % from the values for equivalent fixed beds. The principle of conservation of interphase turbulent kinetic energy transfer is validated by quantifying the interphase transfer terms in the evolution equations of kinetic energy for the gas-phase and solid-phase fluctuating velocity. It is found that the collisional dissipation is negligible compared with the viscous dissipation for the cases considered in this study where the freely evolving suspensions attain a steady state starting from an initial condition where the particles are at rest.

Sign in / Sign up

Export Citation Format

Share Document