Turbulent Kinetic Energy Generation Research Articles

Dynamics of Sheared Convective Boundary Layer Entrainment. Part II: Evaluation of Bulk Model Predictions of Entrainment Flux

Abstract Several bulk model–based entrainment parameterizations for the atmospheric convective boundary layer (CBL) with wind shear are reviewed and tested against large-eddy simulation (LES) data to evaluate their ability to model one of the basic integral parameters of convective entrainment—the entrainment flux ratio. Test results indicate that many of these parameterizations fail to correctly reproduce entrainment flux in the presence of strong shear because they underestimate the dissipation of turbulence kinetic energy (TKE) produced by shear in the entrainment zone. It is also found that surface shear generation of TKE may be neglected in the entrainment parameterization because it is largely balanced by dissipation. However, the surface friction has an indirect effect on the entrainment through the modification of momentum distribution in the mixed layer and regulation of shear across the entrainment zone. Because of this effect, parameterizations that take into account the surface friction velocity but exclude entrainment zone shear may sufficiently describe entrainment when wind shear in the free atmosphere above the CBL is small. In this case, the surface shear acts as a proxy for the entrainment zone shear. Such parameterizations can be most useful if applied in situations where atmospheric data are insufficient for calculating entrainment zone shear. The importance of modeling a Richardson-number-limited, finite-depth entrainment zone is evidenced by the relatively accurate entrainment flux predictions by models that explicitly account for effects of entrainment zone shear, but predictions by these models are often adversely affected by the underestimation of TKE dissipation in the entrainment zone.

The Effect of Real Turbine Roughness With Pressure Gradient on Heat Transfer

Experimental measurements of heat transfer (St) are reported for low speed flow over scaled turbine roughness models at three different freestream pressure gradients: adverse, zero (nominally), and favorable. The roughness models were scaled from surface measurements taken on actual, in-service land-based turbine hardware and include samples of fuel deposits, TBC spallation, erosion, and pitting as well as a smooth control surface. All St measurements were made in a developing turbulent boundary layer at the same value of Reynolds number Rex≅900,000. An integral boundary layer method used to estimate cf for the smooth wall cases allowed the calculation of the Reynolds analogy 2St/cf. Results indicate that for a smooth wall, Reynolds analogy varies appreciably with pressure gradient. Smooth surface heat transfer is considerably less sensitive to pressure gradients than skin friction. For the rough surfaces with adverse pressure gradient, St is less sensitive to roughness than with zero or favorable pressure gradient. Roughness-induced Stanton number increases at zero pressure gradient range from 16–44% (depending on roughness type), while increases with adverse pressure gradient are 7% less on average for the same roughness type. Hot-wire measurements show a corresponding drop in roughness-induced momentum deficit and streamwise turbulent kinetic energy generation in the adverse pressure gradient boundary layer compared with the other pressure gradient conditions. The combined effects of roughness and pressure gradient are different than their individual effects added together. Specifically, for adverse pressure gradient the combined effect on heat transfer is 9% less than that estimated by adding their separate effects. For favorable pressure gradient, the additive estimate is 6% lower than the result with combined effects. Identical measurements on a “simulated” roughness surface composed of cones in an ordered array show a behavior unlike that of the scaled “real” roughness models. St calculations made using a discrete-element roughness model show promising agreement with the experimental data. Predictions and data combine to underline the importance of accounting for pressure gradient and surface roughness effects simultaneously rather than independently for accurate performance calculations in turbines.

Local Dynamic Similarity Model of Cross-Ventilation Part 1 - Theoretical Framework

A new model has been proposed for evaluating the discharge coefficient and flow angle at an inflow opening for cross-ventilation. This model is based on the fact that the cross-ventilation flow structure in the vicinity of an inflow opening creates dynamic similarity under the condition that the ratio of the cross-ventilation driving pressure to the dynamic pressure of cross flow at the opening is consistent. It was confirmed, from a wind tunnel experiment, that the proposed model can be applied regardless of wind direction and opening position. Change of pressure along the stream tube of a cross-ventilated flow was estimated from the results of Large Eddy Simulation, and was set as the basis of model preparation. It was found that the static pressure at the opening was exhausted by the flow‘s acceleration and by turbulent kinetic energy generation during this stage.

A similarity hypothesis for shallow‐cumulus transports

AbstractA similarity theory for cumulus convection is proposed, and applied to the problem of cumulus transports, using data from several large‐eddy simulations to test the theory. the parameters in the similarity hypothesis include the cloud‐base mass flux, the buoyancy of a parcel undergoing reversible ascent, through the cloud layer and the depth of the cloud layer. Using arguments based on the turbulence kinetic‐energy budget a velocity‐scale is derived, in addition to the conventional Convective Available Potential Energy scale. This new scale is analogous to the convective velocity‐scale used in boundary‐layer theories, but incorporates the effects of latent‐heat release. the ratio between the cloud‐base mass flux and the velocity‐scale is found to be a key parameter in describing cumulus convection.It is shown that the similarity hypothesis can be applied to mass‐flux schemes to determine the fractional entrainment rate. For this the entrainment rate is assumed to be related to the rate of generation of turbulent kinetic energy in the cloud ensemble. the resulting scaling is tested against fractional entrainment rates diagnosed from the large‐eddy simulations.

Interaction between a spatially growing turbulent boundary layer and embedded streamwise vortices

The interaction between a zero-pressure-gradient turbulent boundary layer and a pair of strong, common-flow-down, streamwise vortices with a sizeable velocity deficit is studied by large-eddy simulation. The subgrid-scale stresses are modelled by a localized dynamic eddy-viscosity model. The results agree well with experimental data. The vortices drastically distort the boundary layer, and produce large spanwise variations of the skin friction. The Reynolds stresses are highly three-dimensional. High levels of kinetic energy are found both in the upwash region and in the vortex core. The two secondary shear stresses are significant in the vortex region, with magnitudes comparable to the primary one. Turbulent transport from the immediate upwash region is partly responsible for the high levels of turbulent kinetic energy in the vortex core; its effect on the primary stress 〈u′v′〉 is less significant. The mean velocity gradients play an important role in the generation of 〈u′v′〉 in all regions, while they are negligible in the generation of turbulent kinetic energy in the vortex core. The pressure-strain correlations are generally of opposite sign to the production terms except in the vortex core, where they have the same sign as the production term in the budget of 〈u′v′〉. The results highlight the limitations of the eddy-viscosity assumption (in a Reynolds-averaged context) for flows of this type, as well as the excessive diffusion predicted by typical turbulence models.

Bubble interaction in low-viscosity liquids

An experimental study investigated how freely rising ellipsoidal bubbles approach each other, make contact and coalesce or breakup. Pulsed planar swarms of 10–20 bubbles with Eötvös numbers from 6.0 to 27.5 were released simultaneously in aqueous solutions of 0–48 wt% sugar with Morton numbers from 3.2 × 10 −11 to 3.7 × 10 −6. Bubble interaction was recorded by a video camera following the rising bubbles. Essentially, all coalescence and breakup events occurred after, not during, wake-induced collisions by a complex process related to the bubble vortex shedding cycle. This same process was also found in multi-bubble clusters and may account for excess turbulent kinetic energy generation in bubbly flow.

An equilibrium model for the coupled ocean‐atmosphere boundary layer in the tropics

A coupled model is used to study the equilibrium state of the ocean‐atmosphere boundary layer in the tropics. The atmospheric model is a one‐dimensional thermodynamic model for a partially mixed, partly cloudy convective boundary layer (CBL), including the effects of cloud‐top subsidence, surface momentum and heat (latent and sensible) fluxes, and realistic radiative transfer for both shortwaves and longwaves (Betts and Ridgway, 1988; 1989). The oceanic model is a thermodynamic model for a well‐mixed layer, with a closure constraint based on a one‐dimensional turbulent kinetic energy (TKE) equation following Kraus and Turner (1967). Results of several sets of experiments are reported in this paper. In the first two sets of experiments, with sea surface temperature (SST) specified, we solve the equilibrium state of the coupled system as a function of SST for a given surface wind (case 1) and as a function of surface wind for a given SST (case 2). In both cases the depth of the CBL and the ocean mixed layer (OML) increases and the upwelling below the OML decreases, corresponding to either increasing SST or increasing surface wind. The deepening of the equilibrium CBL is primarily linked to the increase of CBL moisture with increasing SST and surface wind. The increase of OML depth and decrease of upwelling are due to a decrease of net downward heat flux with increasing SST and the generation of TKE by increasing wind. In another two sets of experiments, we solve for the coupled ocean‐atmosphere model iteratively as a function of surface wind for a fixed upwelling (case 3) and a fixed OML depth (case 4). SST falls with increasing wind in both cases, but the fall is steeper in case 4, because the OML depth is fixed, whereas in case 3 the depth is allowed to deepen and the cooling is spread over a larger mass of water. The decrease of evaporation with increasing wind in case 4 leads to a very dry and shallow CBL. Results of further experiments with surface wind and SST (upwelling) prescribed as a function of longitude similar to the observed values across the Pacific show that the model gives realistic gradients of mixed‐layer depth and upwelling (SST). This work suggests that the equilibrium state of the coupled system is very sensitive to the coupling of the boundary layers. Special efforts are needed to incorporate physical processes in the CBL and OML in coupled models.

Effects of radiation on clouds

The effects of radiation on the growth of individual cloud particles and on the structure of clouds are reviewed. It is shown that the rate of growth of both water drops and ice crystals may be changed significantly by effects of radiation either near the edges of cloud sheets or below cloud, although the overall effect on particle size depends on the period spent in such regions. Sub-cloud evaporation of ice particles may be reduced by radiative cooling of the crystals giving rise to persistent fall streaks. The role of radiative transfer in the formation of radiation fog is well established. It is shown, however, that the nature of the radiative process is crucial in explaining the observed distribution of liquid water in fogs. The way in which radiation fogs may be dissipated due to changes in the radiation balance are also described. Layer clouds contain regions of radiative flux divergence which give rise to localised heating or cooling. In low-level water clouds and in some higher-level ice clouds this gives rise to destabilisation of the cloud layer leading to the generation of turbulent kinetic energy. This may be enhanced by evaporation of cloud particles into air entrained into the cloud layer. The sensitivity of the cloud structure to the radiative processes may give rise to a pronounced diurnal variation in the structure and to a dependence of the structure on latitude. The turbulent motions generated, in part, by radiative processes feed back on the cloud particle size distribution either by increasing the time spent in the cloud by a small fraction of the particles or by modifying the coupling between those clouds regions in which particles form with those regions where growth occurs. The review brings together theoretical studies and observations. It is concluded that while the effects of radiation on the evolution of stratocumulus cloud sheets are comparatively well understood, some details remain unresolved. However, cirrus clouds are less fully understood owing to the limited observations and the greater coupling between radiative, dynamical and microphysical processes.

UNDERSTANDING THE PHYSICAL STRUCTURE OF SOUTHERN AFRICA'S STANDING WATERS

SUMMARY An examination of the nature of the stratification in polymictic and monomictic Southern African reservoirs is presented. Wind stirring is the principal mode of heat transfer during spring heating. In high summer radiation from stable heated surface layers is responsible for the generation of turbulent kinetic energy (TKE) as a consequence of cascading of high density water downwards to neutral density levels. Entrainment of warm layers by inflow gradients in the reservoirs of the summer rainfall regions of the subcontinent is a further important mechanism setting up TKE in the epilimnion. It may become dominant during periods of high river inflow and often precedes autumnal turnover.

Large-Eddy Simulation of a Stratus-Topped Boundary Layer. Part II: Implications for Mixed-Layer Modeling

Abstract Two sets of large-eddy simulation data were used to study some of the assumptions about the cloud-topped boundary layer (CTBL) structure which are used in mixed-layer models. The roles of buoyant production and cloud-top radiative cooling in turbulent kinetic energy generation were examined. The buoyant production in the turbulent kinetic energy (TKE) budgets was partitioned into production and consumption components by grouping the warm-rising and cold-sinking parcels and the warm-sinking and cold-rising parcels, separately. The results indicate that the ratio of the consumption part of the buoyant production to the sum of the shear production and the production part of the buoyant production is 0.15 for the clear convective mixed layer, and 0.22 for the CTBL. Almost all mixed-layer models use the experimentally (from either direct measurement or tank experiment) obtained ratio of the buoyancy flux at the top of the clear convective boundary layer to the flux at the surface for their entrainment...

Conditional Instability of the First Kind Upside-Down

It is shown that entrainment leads to the generation of turbulence kinetic energy in a stratocumulus layer when the virtual temperature jump at the cloud top is weaker than a critical value. The critical value increases as the relative humidity of the air above the cloud top decreases. This result is interpreted as a criterion for the instability of the layer cloud to penetrative downdrafts. The role of the instability in determining the subtropical and tropical distributions of boundary-layer cloudiness is assessed.

On the Effect of Dissipation on Seasonal Thermocline Models

This paper considers several parameterizations of dissipation in a Kraus-Turner (1967) seasonal mixed-layer model with no net annual surface buoyancy flux. By studying the behavior of the turbulent kinetic energy equation near the end of the cooling season it is determined for a given parameterization of dissipation whether or not the mixed layer deepens to infinite depth at the end of the cooling season. It is concluded that the following two conditions together form a sufficient condition for the maximum mixed-layer depth to be finite. First, the dissipation must be able to balance the wind generation of turbulent kinetic energy in the absence of a surface buoyancy flux. Second, the dissipation must exactly balance the turbulent kinetic energy generated by the wind and released by convection near the end of the cooling season. For two parameterizations of dissipation, cyclic solutions of the Kraus-Turner model are obtained. With the constant background dissipation used by Niiler (1977) the mixed-layer depth stays finite; whereas, with the parameterization of dissipation used by Kamenkovich and Khar'kov (1975) the mixed layer deepens to infinite depth at the end of the cooling season. It is also mentioned that with the parameterizations of dissipation used by Gill and Turner (1976) and Elsberry et al. (1976) the mixed layer deepens to infinite depth at the end of the cooling season. Finally, the potential usefulness of these findings for numerical ocean modeling is discussed.

Prediction of buoyancy controlled turbulent wall diffusion flames

A numerical model of a buoyancy dominated turbulent diffusion flame adjacent to an inert vertical surface is developed. The K-∈-g model of turbulence was modified to account for the generation of turbulent kinetic energy and dissipation due to buoyancy and describes the fluctuations of a conserved scalar quantity. The combustion model assumes infinitely fast reactions and the local burning rate is obtained by solving for the source term in the fuel species equation. Due to the lack of experimental flame data, results are compared to non-reacting flow experimental data with good agreement. Sample results for a propane-air flame are presented.

The role of buoyancy direction and radiation in turbulent diffusion flames on surfaces

A large-scale gas-supplied sintered-metal burner was used to study radiation and spatial orientation effects on steady turbulent fires over a range of mass transfer driving forces, B . Three principal burning modes are evident: (1) turbulent pool fires from θ =0° to θ =15°; (2) upward turbulent burning from θ ∼15° to θ ∼168°; and (3) cellular ceiling fires from θ ∼168° to θ =180°. Steady burning rates decrease rapidly with inclination from the horizontal within the pool regime, followed by a more gradual decreases with inclimation within the upward turbulent burning regime being minimum θ ∼168°, i.e., 12° from the horizontal ceiling orientation. This trend is ascribed to the decreasing direct gravitational generation of turbulent kinetic energy, causing a reduction in the turbulent flame thicknesses with their reduced radiant fluxes. Previous laminar burning studies showed opposite trends, with minimum burning rates in the “pool” orientation. Increased cellular flow mixing is accompanied by a sharp increase in burning rate as the fuel surface rotates from 168° to the horizontal ceiling fire. Radiometer comparison of outward and surface directed radiant flux for a vertical burning surface indicate at least 7% absorption by combustion products and intermediates near the surface. Radiation is found to exceed convective heat transfer to the fuel surface for B >1.0. At large B numbers the burning is increasingly radiation-dominated as convection decreases due to heat blockage.

Effect of Cooling Air on Swirl Combustor

This paper presents the numerical study of the turbulent swirling flow in a combustor and the effect of cooling air, which has practical applications in industrial furnaces and jet engines. Cooling air is used to protect the combustor wall from burnout, while allowing the combustion to occur at higher temperature. The governing differential equations using k - ε turbulence model closure are solved by a control-volume based iterative finite difference technique. Computations are done for constant vane angle type swirl generation at inlet. Different swirl numbers up to 1.5 are considered. To study the effect of cooling air on the combustor performance, calculations are repeated for two different velocities of the cooling air jet. The predicted distribution of the mean axial and tangential velocities, turbulence kinetic energy and streamline plots are discussed in the article. With the increase of swirl strength, secondary on-axis recirculation due to swirl is observed. The swirl produces larger turbulence kinetic energy and enhances mixing rate, thus require shorter combustor length. The interaction between the non-swirling cooling air and swirling core flow also increases the generation of turbulence kinetic energy and mixing rate. The capability of the computational model for predicting recirculating flows is tested by comparing the results with available experimental data and found to have reasonable matching.Journal of Mechanical Engineering Vol.37 June 2007 pp.1-9doi:10.3329/jme.v37i0.811

Heat transfer from turbulent separated flows

A power-law relation is derived between the Stanton number and the Reynolds number, expressing the law of heat transfer for a wall adjacent to a region of turbulent separated flow. The derivation is based on Prandtl's (1945) proposal for the laws of dissipation, diffusion and generation of turbulent kinetic energy. The constants appearing in these laws are determined by reference to experimental data for the hydrodynamic properties of the constant-stress and the linear-stress layers.The agreement between the resulting predictions and the experimental data of other workers is sufficiently good to suggest that the actual mechanism of heat transfer from separated flows has much in common with that which is postulated. Closer agreement can be expected only after the present one-dimensional analysis has been superseded by a two-dimensional one.