Turbulence modeling in ocean circulation problems

Haline stratification in the Rhine-Meuse freshwater plume: a three-dimensional model sensitivity analysis

Improving the Turbulence Coupling between High Resolution Numerical Weather Prediction Models and Lagrangian Particle Dispersion Models

The parameterization for transilient turbulence coefficients suggested by Stull and Driedonks (SD. 1987) is tested against the large-eddy simulations (LES) of Ebert et al. (ESS, 1989) for the special case of an idealized convective boundary layer. The SD parameterization is based on a nonlocal approximation to the turbulence kinetic energy (TKE) equation, and requires turbulent exchange (i.e., the matrix of transilient mixing coefficients is assumed to be symmetric) and dominance of the smaller eddies (i.e., elements closer to the main diagonal of the matrix are greater). Measurements from the LES model, however, show that the transilient matrix is asymmetric in convective situations, with larger eddies dominating. Mean-state conditions such as the deep convective mixing and mixed-layer growth are satisfactorily described by the parameterization, but the surface layer is too deep and the entrainment zone thickness is poorly defined. Turbulence properties such as skewed vertical velocity distributions are not possible within the constraint of a symmetric matrix, and partial convective overturning is also not possible because of the restriction that small eddies dominate. Future improved parametcrizations might continue to be based on the TKE equation, but should allow transilient matrix asymmetry.

The slurry column reactor has the most promising prospect in FT synthesis. In this paper, the gas distributor developed for slurry column rector was analyzed to find an improved gas distributor with small energy consumption, good distribution performance and the good characteristics of preventing backflow. A novel gas distributor which is employed in the slurry column reactor was proposed and multiphase flow patterns were numerically studied. The single phase flow patterns of the new slurry column gas distributor were simulated and the smaller preventing-backflow ball was found out. When connect the upper and lower two openings to form one opening, there is lower pressure drop in the gas distributor, unevenness also reduced accordingly. The overall gas holdup was consistent with the experimental data. The performance of the preventing-backflow ball was also studied in this paper. Some design requirements were put forward in order to stroke the liquid flow back.

After a careful consideration of the laws of generation, advection, diffusion and dissipation of turbulent kinetic energy proposed by Prandtl (1945) and Emmons (1954), equations of motion and turbulent kinetic energy for the vortex flow near a solid end wall are established. These equations are then evaluated by a numerical procedure. Care is taken to specify boundary conditions such that satisfactory matching of the solution with the main vortex is assured. The agreement between the predicted mean velocity distribution and the experimental data is remarkably good. In addition, several interesting characteristics are predicted by the theory: (i) the vertical distribution of horizontal velocity is oscillatory in the inner region, whilst it is of the ordinary boundary-layer type in the outer region; (ii) the maximum velocity in the boundary layer can exceed that in the main vortex by a considerable amount and (iii) the minimum pressure of the vortex does not occur in the vortex-core root as has been generally believed.

A statistical formalism overcoming some conceptual and practical difficulties arising in existing two‐phase flow (2 PHF) formulations and modelling techniques is introduced. Basic theorems for the case of dispersed 2 PHF are presented. Phase interaction terms with a clear physical meaning enter the equations and this formalism provides some guidelines to avoid closure assumptions or to close those terms rationally. Continuous phase averaged continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations can be rigorously and systematically obtained with this methodology in a single step. These equations display a structure similar to that for single‐phase flows. It is also assumed that the dispersed phase is well described by a "Boltzmann‐type" equation and Eulerian "continuity", momentum and fluctuating kinetic energy equations for the dispersed phase are obtained. A k‐ε turbulence model for the continuous phase is used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of momentum and kinetic energy. Closure assumptions are proposed for the phase interaction terms. This model is then used to predict the behaviour of an axisymmetric turbulent jet of air laden with solid particles varying in sizes and concentrations. Numerical results compare reasonably well with available experimental data.

The issue of fiber suspension flow has received great substantial attention in the last decades. In contrast with the abundant researches of normal size fiber suspensions flow, this paper is devoted to the small size fiber suspension composed of water and polyarmide fiber where Brownian motion plays an important role and thus cannot be neglected. The spatial distribution and orientation of fiber, streamwise mean velocity profile, turbulent kinetic energy, Reynolds stress and rheological property of fiber suspension in a turbulent channel flow are obtained and analyzed both numerically and experimentally. To simulate the small fiber suspension flow well, the well-known Reynolds averaged Navier-Stokes (N-S) equation governing the suspension flow is modified in consideration of the effect of fibers on base flow. The equation describing the probability density functions for fiber orientation is derived in view of the rotary Brownian diffusion. The general dynamic equation for fibers is reshaped in the effect of spatial Brownian diffusion. For the sake of the closure of the N-S equation, the turbulence kinetic energy and turbulence dissipation rate equations with fiber term are employed. The conditional finite difference method is adopted to discrete these partial differential equations. And the diffusion term and convective term are discretized by the central finite differences and the second-order upwind finite difference schemes, respectively. The second and fourth-order orientation tensors are integrated by the Simpson formula. Experiment is also performed to validate some numerical results. The results show that most fibers tend to align parallelly to the flow direction in the flow, especially in regions near the wall. Such a phenomenon is more obvious with the decreases of Reynolds number and fiber concentration, and with the increase of fiber aspect ratio. Fiber volume fraction distribution is non-uniform across the channel, and becomes more uniform with increasing Reynolds number, and with reducing fiber aspect ratio. The changes of fiber orientation distribution and spatial distribution are not sensitive to fiber aspect ratio for 5. Streamwise mean velocity profile in fiber suspension has a steeper slope than that in single phase flow, and the steepness increases as the fiber concentration and fiber aspect ratio increase, and as the Reynolds number decreases. The presence of fiber will reduce the turbulence kinetic energy and Reynolds stress. The effect of fiber on the turbulence suppression becomes more obvious with the increases of fiber concentration and aspect ratio, and with the decrease of Reynolds number. The first normal stress difference is less than 0.05 and much less than the shear stress. From the wall to the center of the channel, the shear stress increases while the first normal stress difference decreases. Both the shear stress and the first normal stress difference increase with increasing fiber concentration and aspect ratio. Shear stress increases while the first normal stress difference decreases with increasing Reynolds number. The effects of fiber concentration on the shear stress and the first normal stress difference are larger than the fiber aspect ratio.

A numerical model for the computation of the wind field, air temperature and humidity in the atmospheric boundary layer including the urban canopy layer was developed for urban and architectural planning. The model is a k-ε type used widely in the environmental engineering. The ensemble-spatial averaged three-dimensional Reynolds equations, equation of continuity, turbulent kinetic energy (Adequation) and turbulent energy dissipation equation (ε-equation) are solved together with equations of heat and moisture transfer in the air. Inside the urban canopy layer, effects of buildings and other urban structures on the momentum transfer are modeled by introducing a form drag force, and volumes of them are accounted for by a spatial averaging procedure. The values of the coefficient for eddy viscosity evaluation C_μ and turbulent Prandtl number P_<rt> are defined as the atmospheric stability function and compared with Level 2.5 model. Numerical results by the new model show that the flow behavior of the air in the urban canopy layer is extremely affected by the existence of buildings and thermal stratification.

A review of the past work done on free stream turbulence (FST) as applied to gas turbine heat transfer and its implications for future studies are presented. It is a comprehensive approach to the results of many individual studies in order to derive the general conclusions that could be inferred from all rather than discussing the results of each individual study. Three experimental and four modeling studies are reviewed. The first study was on prediction of heat transfer for film cooled gas turbine blades. An injection model was devised and used along with a 2-D low Reynolds number k-epsilon model of turbulence for the calculations. Reasonable predictions of heat transfer coefficients were obtained for turbulence intensity levels up to 7%. Following this modeling study a series of experimental studies were undertaken. The objective of these studies was to gain a fundamental understanding of mechanisms through which FST augments the surface heat transfer. Experiments were carried out in the boundary layer and in the free stream downstream of a gas turbine combustor simulator, which produced initial FST levels of 25.7% and large length scales (About 5-10 cm for a boundary layer 4-5 cm thick). This result showed that one possible mechanism through which FST caused an increase in heat transfer is by increasing the number of ejection events. In a number of modeling studies several well-known k-epsilon models were compared for their predictive capability of heat transfer and skin friction coefficients under moderate and high FST. Two data sets, one with moderate levels of FST (about 7%) and one with high levels of FST (about 25%) were used for this purpose. Although the models did fine in their predictions of cases with no FST (baseline cases) they failed one by one as FST levels were increased. Under high FST (25.7% initial intensity) predictions of Stanton number were between 35-100% in error compared to the measured values. Later a new additional production term indicating the interaction between the turbulent kinetic energy (TKE) and mean velocity gradients was introduced into the TKE equation. The predicted results of skin friction coefficient and Stanton number were excellent both in moderate and high FST cases. In fact these model also gave good predictions of TKE profiles whereas earlier unmodified models did not predict the correct TKE profiles even under moderate turbulence intensities. Although this new production term seems to achieve the purpose, it is the authors' belief that it is diffusion term of the TKE equation, which needs to be modified in order to fit the physical events in high FST boundary layer flows. The results of these studies are currently being used to come up with new diffusion model for the TKE equation.

A numerical method based on turbulence statistics obtained by LES (Large Eddy Simulation) was proposed to predict time-mean temperature field of conjugate heat transfer problem in complex turbulent flows. For the evaluation of turbulent heat flux in the time-mean field, a state-of-art heat flux model was newly adopted to enhance the prediction capability of time-mean temperature fields. Turbulence kinetic energy was estimated by the approximate budget of transport equation for turbulence kinetic energy. It is confirmed that prediction of dissipation rate of turbulence kinetic energy was improved.

Heat transfer systems have been employed in numerous industrial and residential settings to convert and recover heat. One effective approach for enhancing heat transfer rates involves incorporating artificial roughness in the form of regularly spaced ribs on the heated surface. In this particular study, the researchers conducted numerical simulations to analyze the turbulent heat and flow properties within a rectangular duct of a solar air heater (SAH). The duct featured three different types of transverse rib shapes: equilateral‐triangular, trapezoidal, and square sectional ribs. The governing equations have been solved numerically using a finite‐volume technique via ANSYS FLUENT. For solving the transport equations of turbulent kinetic energy and its dissipation rate, the RNG k– turbulence model was utilized. At a broad range of Reynolds numbers (6000 ≤ Re ≤ 18,000), relative roughness height (), and a fixed relative roughness pitch (), the Nusselt number (), friction factor (), and thermal performance factor (TPF) have been examined. The maximal Nu was obtained for equilateral‐triangular ribs, while the minimum friction factor was seen for square sectional ribs. The highest TPF of 1.591 was achieved with equilateral‐triangular ribs at and e/Dh = 0.032. Contours of kinetic energy, turbulent intensity, velocity, and pressure produced significant findings for comprehending the SAH's physical phenomena.

The effects of an air-temperature inversion in the atmosphere and a seawater density jump in the ocean on the structure of the atmospheric and oceanic boundary layers are studied by use of a coupled model. The numerical model consists of a closed system of equations for velocities, turbulent kinetic energy, turbulent exchange coefficient, local turbulent length scale, and stratification expressions for both air and sea boundary layers. The effects of the temperature inversion and the density jump are incorporated into the equations of turbulent kinetic energy of the atmosphere and ocean by a parameterization. A series of numerical experiments was conducted to determine the effects of various strengths of the inversion layer and surface heat fluxes in the atmosphere and of the density-jump layer in the ocean on the structure of the interacting boundary layers.

The objective of this study is to analyze turbulent flow characteristics of turbulence modeling in Steam Curved Converging Diverging Nozzle. The three turbulence models have been conducted to simulate flow characteristics using k-ε standard, k-ε Renormalization Group (RNG), and Reynolds Stress Model (RSM). Fluid dynamics parameters such as pressure, velocity, and/or density have been analyzed graphically to know the more suitable model. The k- k-ε STD and RNG show give the similar profile of the turbulent kinetic energy (k) and energy dissipation rate (ε) that is differ with the RSM model. After throat position (position 0.67 m) the k-k-ε STD and RNG give the magnitude more than 1200 (m2/s2) for its turbulent kinetic energy and more than 3.2E06 (m2/s3) for its energy dissipation rate. The RSM model give the lowest values which far below 200 (m2/s2) for turbulent kinetic energy and below 2E05 (m2/s3) for energy dissipation rate. The turbulence modeling analysis of steam saturated flow in plane-curved nozzle present the increasing steam velocity about 3 Ma for 200 kPa steam inlet.

The wind turbulence intensity observed on a site have an influence the wind turbine energy production and the lifetime of the blades. It is therefore primordial to master this parameter for the optimization of the production. So therefore, this study is interested on the modelling of the wind turbulence intensity at 10 m above the ground on the coast of Benin. Four years of wind data measured on the site of Cotonou Port Authority (PAC) from 2011 to 2014 and recorded with a temporal resolution of 10 min were used. From the transport equation of turbulent kinetic energy followed by a numerical simulation based on the Nelder-Mead algorithm developed under the Matlab software, we proposed five new models for estimating the wind turbulence intensity. The results of the different simulations reveal that four of proposed models and based on the roughness, the speed of friction and the length of Obukhov better fit the data, during the periods of January, April, June, July, August, September and December. The estimators of the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE) vary from (0.02; 0.01) in December to (0.09; 0.07) in August. As for the model which is a function of roughness and the wind shear coefficient (expressed only according to the wind speed), it gives better performance whatever the time of the year and the atmosphere stability conditions. The estimations errors are included between (0.02; 0.01) obtained in December and (0.08; 0.06) observed in March. A comparative study between the existing models in the literature and the best model proposed in this study showed that only this model gives the best adjustment with the data. It can therefore be used on the sites where turbulence is influenced by the roughness and the atmosphere stability. Finally, from this model a new wind turbine design class has been proposed for the site of Cotonou. It takes into account the actual levels of turbulence observed and thus allow to optimize the energy production.

Comparison of turbulence models for bubble column reactors