Turbulent Kinetic Energy Values Research Articles

The Numerical Solution of the Mellor-Yamada Level 2.5 Turbulent Kinetic Energy Equation in the Eta Model

Abstract A new method is presented for obtaining the numerical solution of the production-dissipation component of the turbulent kinetic energy equation that arises in the Mellor-Yamada level 2.5 turbulent closure model. The development of this new method was motivated by the occasional appearance of large temporal oscillations in the solution provided by a previously used method. Analysis of the equation revealed that the solution should tend toward a stationary asymptotic value, which is the equilibrium value of turbulent kinetic energy for the level 2, Mellor-Yamada model. Failure to identify the correct asymptotic value in the formalism underlying the numerical solution of the equation allows the solution to overshoot the equilibrium. Repeated overshooting gives rise to an oscillation in the solution from one time step to the next. The new method prevents this from happening. Idealized cases are used to demonstrate the performance of the new method. It has been incorporated into the eta coordinate, nu...

Finite analytic solution of a two-dimensional sea breeze on a regular grid

A turbulent, two-dimensional sea breeze model is solved by the finite analytic method on a regular grid using the momentum weighted interpolation method. A k-ε turbulence model is used to simulate the turbulent aspects of the planetary boundary layer. The spatial structure of the model circulation, including inflow depth and penetration, were in close agreement with observational studies. The magnitude of the mean horizontal speed reached a maximum of 3.4 ms −1, somewhat less than those reported in many observational studies. However, the magnitude of the vertical velocity reached a maximum of 0.7 ms −1, similar to speeds observed in experimental studies. Model results for quantities of turbulent kinetic energy, dissipation of turbulent kinetic energy, and turbulent viscosity showed very close agreement with those measured in experimental studies. The maximum value of turbulent kinetic energy was nearly 2 m 2s −2, while the rate of dissipation of turbulent kinetic energy reached a maximum value of 11.8 cm 2s −3. The turbulent viscosity attained values of nearly 100 m 2s −1.

Mean velocity and turbulence fields inside a β=0.50 orifice flowmeter

AbstractThe flow field inside an orifice flowmeter with a beta ratio of 0.50 operating at a Reynolds number of 91,100 has been studied using a three‐color, 3‐D laser Doppler anemometer system. Mean velocity measurements show large radial velocities leading into the orifice, the fluid separating from the orifice plate at the throat, the presence of a vena contracta farther downstream, flow reattachment to the pipe wall 5.3 pipe radii (R) downstream, the presence of a small upstream recirculation zone, and both a primary and secondary recirculation zone downstream of the orifice plate. The static wall pressure distribution attains a minimum pressure at 1.5 R, which does not coincide with the location of the vena contracta (0.75 R). Distributions of the entire Reynolds stress tensor are presented along with calculated values of turbulence kinetic energy, turbulence kinetic energy production, vorticity, and turbulence induced accelerations. These data are analyzed to interpret the complex turbulent flow field.

Experimental Study of an Embedded Longitudinal Vortex Interacting with a Three-Dimensional Turbulent Boundary Layer. 3rd Report, Triple Products and Production Mechanism.

The present research is undertaken to further the physical understanding of the behavior of an embedded vortex in a three-dimensional turbulent boundary layer. The vectors of instantaneous transport of turbulent kinetic energy are large above the vortex and in the downwash region, in Case 2. The production terms are mainly contributed to the values of V2 and W2. Then these profiles show an elliptic shape centered on the peak vorticity point. Both the production and advection terms of turbulent kinetic energy fall rapidly between the first and second measurement stations. In Case 2, a region of high production develops in the upwash region. The contribution of production and advection results in a uniform high value of turbulent kinetic energy in the entire region above the vortex.

On the prediction of local flow structures in internal loop and bubble column reactors using a two-fluid model

In the petrochemical and in particular in the biochemical industry multiphase reactors of the internal draft tube and bubble column type are used in increasing numbers. For design and scaleup a detailed knowledge of the flow structure within these reactors is necessary. This work is a continuation and expansion of our two fluid model programme ( Torvik and Svendsen, 1990; Svendsen et al. 1992). The assumption of the turbulent length scale being proportional to the bubble size is used to develop a relationship for the determination of Sauter Mean bubble Diameter as a function of the local values of turbulent kinetic energy and energy dissipation. The drag formulation has also been changed to take into account the spatially varying bubble diameters. Comparisons between simulated and experimental values of local liquid velocity and local gas holdup are found to be in very good agreement. Changes in the bubble size distribution has also been shown to give responses in fluid velocities and gas holdup in qualitative agreement with that expected from experimental measurements. Discrepancies in bubble size and gas volumetric velocities were observed in the reverse flow region close to the column walls and has been attributed to experimental uncertainties and to the lateral forces, the drag coefficient and the bubble-liquid momentum transfer being functions of the bubble size. The experiments were performed with the air/water system in an ordinary bubble column and an internal loop reactor, both with largest inner diameter 0.288m using the five point conductivity method (FPC).

Turbulence Modeling for Secondary Flow Prediction in a Turbine Cascade

Predictions of secondary flow in an axial turbine cascade have been made using three different turbulence models: mixing length, a one-equation model and a k–ε mixing length hybrid model. The results are compared with results from detailed measurements, not only by looking at mean flow velocities and total pressure loss, but also by assessing how well turbulence quantities are predicted. It is found that the turbulence model can have a big influence on the mean flow results, with the mixing length model giving generally the best mean flow. None of the models give good predictions of the turbulent shear stresses in the vortex region, although the k–ε model gives quite good turbulent kinetic energy values. The one-equation model is the only one to contain a transition criterion. The importance of such a criterion is illustrated, but the present one needs development to give reliable predictions in the complex flow within a blade passage.

Atmospheric Simulations of Extreme Surface Heating Episodes on Simple Hills

A two-dimensional nonhydrostatic atmospheric model was used to simulate the circulation patterns (wind and vorticity) and turbulence energy fields associated with lines of extreme surface heating on simple two-dimensional hills. Heating-line locations and ambient crossflow conditions were varied to qualitatively determine the impact of terrain geometry on the development of buoyancy-induced horizontal roll vortices and their turbulence structures. The model simulations indicate that the type of induced circulation that develops near a line of extreme surface heating on a simple hill is very dependent on the location of the heating line. Heating lines located on the crests of simple hills produced symmetric horizontal roll vortices with large values of turbulent kinetic energy. Symmetric vortices did not develop over heating lines located on the slopes of the hills. The introduction ofa light ambientcrossflowradically changed the circulation and turbulence structures. Simulated vorticity and turbulence energy values over a heating line located on the windward slope were very different than those observed over heating lines located on the crest or leeward slope. A low-level vortex developed just downwind of the windward-slope heating line when a light ambient crossflow was introduced, and this vortex became stronger as the steepness of the hill was increased. Although field dataare not available toconfirm the model results, the simulations suggest that terrain effects play an important role in the development and destruction of vortices near lines of extreme surface heating, especially when a light ambient crossflow is introduced. These effects have implications for fire-fighter safety in actual wildland fire episodes.

Large-eddy simulations of the effects of hilly terrain on the convective boundary layer

Large-eddy simulations of the convective boundary layer are compared over hilly versus flat surfaces. Moderate values for the height and horizontal spacing of the hills were selected. Thermally-direct hill-valley circulations are induced by the uneven terrain, accounting for a significant fraction of the resolved energy in the boundary-layer eddies. The probability of upward eddy motion reaches up to 70% over the hilltops and down to 15% over the valleys. Above-average values of both subgrid scale turbulent kinetic energy and upward eddy heat transport are found above the higher terrain. Horizontal spectra of vertical motion are strongly biased toward the horizontal scales of the terrain. Vertical profiles of atmospheric variables obtained by horizontal averaging, however, exhibit no significant differences between hilly and flat terrain simulations.

Shear-thinning duct flow characteristics of relevance to stirred reactors

Improvements in the performance of stirred reactors operating with non-Newtonian fluids under turbulent flow conditions require detailed knowledge of their fluid-mechanic properties. The complexity of stirred vessel flows, the large variety of flow configurations, and possible non-Newtonian fluids indicate that such an undertaking should be preceded by an investigation aimed at selecting the fluids and to assess transitional Reynolds number and non-Newtonian effects in the flows with characteristics of relevance to the process of stirring tanks. Mean and turbulent velocity characteristics of the flow of aqueous solutions of CMC (carboxymethyl cellulose) in a 25.4 mm diam duct, with and without a 50% area blockage disk located on its axis, were measured with a laser velocimeter. The polymer solutions at concentrations of 0.1% to 0.4% by weight were weakly elastic and shear-thinning. Water and a viscous Newtonian fluid were also investigated for comparison. The pipe flow measurements encompassing a range of Reynolds numbers from 240 to 111 000 quantify the delay in transition from laminar to turbulent flow caused by shear-thinning, the suppression of turbulence fluctuations particularly in the radial and tangential directions, and the reduction in the drag coefficient. The baffle flow of Newtonian and non-Newtonian fluids was increasingly dependent on Reynolds numbers below 50 000 with the dampening of the normal Reynolds stresses also dependent on polymer concentration. At a Reynolds number 8000, the maximum values of turbulent kinetic energy with the 0.2% CMS and 0.4% CMC solutions were 35% and 45% lower than for water, respectively. Non-Newtonian effects are important in regions of low strain rates at low Reynolds numbers, and are represented by a decrease of turbulent diffusion and an increase of viscous diffusion, which would be enlarged by the effect of the elongational viscosity if higher than three times the viscometric viscosity. The performance of stirred vessel flows is likely to be impaired by the suppression of small-scale turbulence over the boundary layer of the blades and its possible early separation. A deterioration in the quality of micromixing is also likely to arise because of lower turbulence production in the shear layer of the jet emanating from the impeller. With strong shear-thinning fluids, the high viscosity in the large regions of low mean shear rate far from the impeller further contribute to turbulence suppression so that laminarizations of the flow may occur. However, the strong three-dimensionality of the mixer flow means that turbulence damping will occur for all Reynolds stresses rather than in preferential directions.

Flow of non-Newtonian fluids over a confined baffle

Measurements of wall pressure, and mean and r.m.s. velocities of the confined flow about a disk of 50 % area blockage have been carried out for two Newtonian fluids and four concentrations of a shear-thinning weakly elastic polymer in aqueous solution encompassing a Reynolds-number range from 220 to 138000. The flows of Newtonian and non-Newtonian fluids were found to be increasingly dependent on Reynolds numbers below 50000, with a decrease in the length of the recirculation region and dampening of the normal Reynolds stresses. At Reynolds numbers less than 25000, the recirculation bubble lengthened and all turbulence components were suppressed with increased polymer concentration so that, at a Reynolds number of 8000, the maximum values of turbulent kinetic energy were 35 and 45% lower than that for water, with 0.2% and 0.4% solutions of the polymer. Non-Newtonian effects were found to be important in regions of low local strain rates in low-Reynolds-number flows, especially inside the recirculation bubble and close to the shear layer, and are represented by both an increase in viscous diffusion and a decrease in turbulent diffusion to, respectively, 6% and 18% of the largest term of the momentum balance with a 0.4 % polymer solution at a Reynolds number of 7700. The asymmetry and unsteadiness of the flow at Reynolds numbers between 400 and 6000 is shown to be an aerodynamic effect which increases in range and amplitude with the more concentrated polymer solutions.

Investigation of turbulent transport in an axisymmetric sudden expansion

Simultaneous two-component laser velocimeter measurements were made in the incompressible turbulent flowfield following an axisymmetric sudden expansion. Mean velocities, Reynolds stresses, and triple products were measured and are presented at axial positions ranging from x/H = 0.2-14. A balance of the turbulent kinetic energy in the flow was performed. The production, convection, and diffusion of turbulent kinetic energy were computed directly from the experimental data using central differencing. A specially designed correction lens was employed to correct for optical aberrations introduced by the circular tube. This lens system allowed the accurate simultaneous measurement of axial and radial velocities in the test section. The experimental measurements were compared to predictions generated by a code that employed the k-epsilon turbulence model. Agreement was good for mean axial velocities, turbulent kinetic energy, and turbulent shear stresses. However, the modeled turbulent normal stresses where in poor agreement with the measured values. The modeled diffusion of turbulent kinetic energy was underpredicted in the region between the shear layer and the centerline of the flow giving lower values of turbulent kinetic energy downstream of the potential core than measured.

A numerical model of flow over sand waves in water of finite depth

Summary. A model of turbulent flow above sand waves in water of finite depth is described. Closure assumptions are based on an eddy viscosity proportional to the square root of the local value of turbulent kinetic energy and mixing length dependent upon distance from the lower boundary. Results are presented for some idealized cases to investigate the effects of wave slope, water depth, Froude number and wave shape. The implications of the model for the transport of sediment are discussed and the development of the wave investigated. It is found that the crest of the wave will become sharper for lower flow rates, as has been observed in the sea. Comparisons are made with recent measurements made over sand waves in the Columbia River.