Turbulent Kinetic Energy Model Research Articles

Short time-scale analysis of the NW Mediterranean ecosystem during summer–autumn transition: A 1D modelling approach

Modelling was used as a tool to better understand the physical and biological processes observed during the multidisciplinary cruise DYNAPROC 2 (DYNAmic of rapid PROCesses in the water column), which took place in the Ligurian Sea in September–October 2004. The aim of the cruise was to study the short time-scale physical and biological processes that occur when the ecosystem switches from summer oligotrophy to autumnal mesotrophy. In this study, we have tested two 1D physical–biological coupled models. The first was a classical model in which surface layer dynamics were obtained using the turbulent kinetic energy model of Gaspar [Gaspar et al., 1990]. The simulated food-web took into account ten state variables: three nutrients, three classes of phytoplankton, two classes of zooplankton and two types of detritus. The second model (called IDA, Isopycnals Depth Adjustment) was based on the initial one but it took into account the measured variations of isopycnals depths. The results showed that the IDA model most efficiently reproduced the observed ecosystem dynamics. We have therefore used the IDA model to show that physical processes observed during the cruise had a major effect on biological compartment, mainly on nano- and picophytoplankton.

On the Turbulence in the Upper Part of the Low-Level Jet: An Experimental and Numerical Study

The characteristics of low-level jets (LLJ) observed at the “Centro de Investigacion de la Baja Atmosfera” (CIBA) site in Spain are analysed, focussing on the turbulence generated in the upper part of the jet, a feature that is still to be thoroughly understood. During the Stable Boundary Layer Experiment in Spain (SABLES) 1998, captive balloon soundings were taken intensively, and their analyses have highlighted the main characteristics of the jet’s wind and temperature structure, leading to a composite profile. There are indications that the turbulence has a minimum at the level of the wind maximum, with elevated turbulence in a layer at a height between two and three times that of the LLJ maximum, but no direct measurements of turbulence were available at these heights. In September 2001, a 100-m tower at the same site was re-instrumented to give turbulence measurements up to 96.6 m above ground level. All occurrences of LLJ below this height between September 2002 and June 2003 have been selected and significant turbulence above the LLJ has been found. Simulations with a single-column turbulence kinetic energy model have been made in order to further investigate the generation of elevated turbulence. The results correlate well with the measurements, showing that in the layer above the LLJ, where there is significant shear and weakly stable stratification, conditions are conducive to the development of turbulence.

Large eddy simulations for studying tunnel smoke ventilation

Computational fluid dynamics are applied to simulate the smoke movement in a ventilated tunnel fire through large eddy simulation (LES). Several scenarios with different ventilation rates are considered by taking the fire as a volumetric heat source. Results predicted by LES are compared with those from a turbulent kinetic energy; thermal conductivity-dissipation of the turbulent kinetic energy model. These include temperature fields, flame shape and the smoke movement pattern. It is found that thermal stratification and smoke backflow can be predicted successfully by LES. The possibility of applying LES as an engineering tool to smoke management system design in tunnels is discussed. (A) Reprinted with permission from Elsevier.

Structure of subfilter-scale fluxes in the atmospheric surface layer with application to large-eddy simulation modelling

In the atmospheric surface layer, the wavelength of the peak in the vertical velocity spectrum $\Lambda_w$ decreases with increasing stable stratification and proximity to the surface and this dependence constrains our ability to perform high-Reynolds-number large-eddy simulation (LES). Near the ground, the LES filter cutoff $\Delta_f$ is comparable to or larger than $\Lambda_w$ and as a result the subfilter-scale (SFS) fluxes in LES are always significant and their contribution to the total flux grows with increasing stability. We use the three-dimensional turbulence data collected during the Horizontal Array Turbulence Study (HATS) field program to construct SFS fluxes and variances that are modelled in LES codes. Detailed analysis of the measured SFS motions shows that the ratio $\Lambda_w/\Delta_f$ contains the essential information about stratification, vertical distance above the surface, and filter size, and this ratio allows us to connect measurements of SFS variables with LES applications. We find that the SFS fluxes and variances collapse reasonably well for atmospheric conditions and filter widths in the range $\Lambda_w/\Delta_f = [0.2,15]$ . The SFS variances are anisotropic and the SFS energy is non-inertial, exhibiting a strong dependence on the stratification, large-scale shear, and proximity to the surface. SFS flux decomposition into modified-Leonard, cross-, and Reynolds terms illustrates that these terms are of comparable magnitude and scale content at large $\Lambda_w/\Delta_f$ . As $\Lambda_w/\Delta_f \rightarrow 0$ , the SFS flux approaches the-ensemble-average flux and is dominated by the Reynolds term. Backscatter of energy from the SFS motions to the resolved fields is small in the bulk of the surface layer, less than 20% for $\Lambda_w/\Delta_{f} . A priori testing of typical SFS models using the HATS dataset shows that the turbulent kinetic energy and Smagorinsky model coefficients $C_k$ and $C_s$ depend on $\Lambda_w/\Delta_f$ and are smaller than theoretical estimates based on the assumption of a sharp spectral cutoff filter in the inertial range. $C_k$ and $C_s$ approach zero for small $\Lambda_w/\Delta_f$ . Much higher correlations between measured and modelled SFS fluxes are obtained with a mixed SFS model that explicitly includes the modified-Leonard term. The eddy-viscosity model coefficients still retain a significant dependence on $\Lambda_w/\Delta_f$ with the mixed model. A dissipation model of the form $\epsilon = C_\epsilon E_s^{3/2}/\Delta_f$ is not universal across the range of $\Lambda_w/\Delta_f$ typical of atmospheric LES applications. The inclusion of a shear-stability-dependent length scale (Canuto & Cheng 1997) captures a large fraction of the variation in the eddy-viscosity and dissipation model coefficients.

Application of Two Turbulence Closure Schemes in the Modelling of Tidal Currents and Salinity in the Hooghly Estuary

This paper has two purposes. The first is to study the circulation and salinity in Hooghly Estuary, along the east coast of India and the second is to compare the performance of two turbulence closure schemes by modelling it. A breadth averaged numerical model using a sigma co-ordinate system in the vertical is briefly described. Vertical diffusion of momentum and salt are parameterized by a simple first-order turbulent closure or by a one equation model for turbulent kinetic energy (TKE) which uses a specified mixing length. The results are compared with the available neap and spring tide observations along the estuary for both low and high discharge periods.The computed elevations and currents are in reasonable agreement with the observations showing no major differences in vertical current profiles by both the turbulent schemes. However, there is a slight under-prediction of bottom currents. The salinity profiles predicted by TKE model show better matching with observations. Statistical tests are also conducted to study the comparative performance of the turbulent closure schemes. The maintenance of two layer structure in residual currents and salt variability are also studied by using the model.

Large-Eddy Simulations of Radiatively Driven Convection: Sensitivities to the Representation of Small Scales

Large-eddy simulations of a smoke cloud are examined with respect to their sensitivity to small scales as manifest in either the grid spacing or the subgrid-scale (SGS) model. Calculations based on a Smagorinsky SGS model are found to be more sensitive to the effective resolution of the simulation than are calculations based on the prognostic turbulent kinetic energy (TKE) SGS model. The difference between calculations based on the two SGS models is attributed to the advective transport, diffusive transport, and/or time-rate-of-change terms in the TKE equation. These terms are found to be leading order in the entrainment zone and allow the SGS TKE to behave in a way that tends to compensate for changes that result in larger or smaller resolved scale entrainment fluxes. This compensating behavior of the SGS TKE model is attributed to the fact that changes that reduce the resolved entrainment flux (viz., values of the eddy viscosity in the upper part of the PBL) simultaneously tend to increase the buoyant production of SGS TKE in the radiatively destabilized portion of the smoke cloud. Increased production of SGS TKE in this region then leads to increased amounts of transported, or fossil, SGS TKE in the entrainment zone itself, which in turn leads to compensating increases in the SGS entrainment fluxes. In the Smagorinsky model, the absence of a direct connection between SGS TKE in the entrainment and radiatively destabilized zones prevents this compensating mechanism from being active, and thus leads to calculations whose entrainment rate sensitivities as a whole reflect the sensitivities of the resolved-scale fluxes to values of upper PBL eddy viscosities.

Computational modeling of gas/particle flow in a riser

AbstractAxial solid velocity, solid volume fraction, and solid shear viscosity were computed in the riser of a circulating fluidized‐bed reactor using a two‐phase 2‐D computational fluid dynamic model. The time‐averaged model predictions agree well with the experimental data of Miller and Gidaspow (1992). The model predicts a core‐annulus flow in the riser, similar to that found experimentally. The maximum velocity in the core agrees well with the measurements, but the downflow in the annulus is somewhat overpredicted. The solid volume fractions profiles agree well in both core and annulus, with discrepancy in the core at the level close to the inlet. The radial profile of solid shear viscosity computed by the turbulent kinetic energy model is ten times lower in the core than that found experimentally, but with a linear function of solid volume fraction in the measurement, the computed profile agrees well with experiments.

Jet inflow simulation and its downwash effect on lifting surfaces

SummaryA turbulent hot jet is calculated and its entrainment effect is modelled by a line sink with the objective of estimating the downwash effect on rectangular lifting surfaces of various aspect ratios. The line sink density is determined by numerical solution of the free shear layer equations with a turbulent kinetic energy model. The ‘incompressible equivalent jet’ concept is verified within the context of practical engineering calculations.

Turbulence modelling in pipe flow

A one equation turbulent kinetic energy model, similar to that proposed by Prandtl is examined with reference to fully developed pipe flow. Its use required the formulation of two length scales occuring in the model. These are obtained. Existing proposals are not directly applicable in the present situation. Computed results are then compared with existing experimental data. The purpose of the present study is to throw more light on the modelled turbulent kinetic energy equation.

Turbulence modeling in a hypersonic inlet

A study is conducted to analyze the performance of different turbulence models when applied to flow through a Mach 7.4 hypersonic inlet. The analysis, which is two-dimensional, is done by comparing computational results from a Parabolized Navier-Stokes code and a full Navier-Stokes code with experimantal data. The McDonaldCamarate (MC) and Baldwin-Lomax (BL) models were the two zero-equation models used in the study. The Turbulent Kinetic Energy (TKE) model was chosen as a representative higher-order model. The MC model, when run with user-specified transition of the boundary layer, provides a solution that compares excellently with the data. The BL model predicts separation of flow in the inlet, which contradicts experimental findings. The TKE model does not perform any better than the MC and BL models, despite the fact that it is a higher-order turbulence model.

Numerical solutions of scramjet nozzle flows

The accurate prediction of nozzle flows for ramjets and scramjets is important for design and system performance analysis. The problem is made complex by the presence of strongly nonuniform entrance profiles, especially for scramjets (which have no throat at the end of the combustor). Thus, turbulent mixing and, often, chemical reactions can be expected to be under way during the expansion process. The rapid expansion common in nozzles implies substantial radial pressure gradients. Taken together, these requirements lead to the necessity of utilizing the full Navier-Stokes equations for a compressible, multicomponent, turbulent flow with finite-rate chemistry. For this work, the unsplit, explicit, MacCprmack unsteady/finite-difference method was used to solve the equations of motion. Turbulence transport is represented with a turbulent kinetic energy model. Chemistry is treated at this time by either frozen equilibrium or a simple, global finite-rate model. Calculations are presented for a typical scramjet case where the effects of nonuniform inflow profiles on the nozzle flowfield and performance are shown for different nozzle designs.

Turbulence Models for High-speed, Rough-Wall Boundary Layers

7 <5 Three distinct approaches have been investigated for the calculation of heat, momentum, and mass transfer in rough-wall turbulent boundary layers. Emphasis is placed on the high-speed flow regime. Of particular interest is the turbulent kinetic energy model, which has been modified to incorporate a two-phase flow concept such that the formulation allows explicit consideration of the effects of roughness shape, pattern, and density. The assessment consists of comparisons between numerical results and experimental data. These preliminary results suggest the following: 1) a local roughness-induced heating reduction is possible in high-speed flow; 2) the specification of nominal roughness height alone is not sufficient to define the rough-wall geometry characteristics; and 3) a strong Mach number effect on rough-wall heat transfer and shear stress distributions may exist. More accurate and complete data are needed in the high-speed regime to verify advanced numerical models of the type considered herein, which are required to adequately predict high-speed rough-wall boundary-layer behavior.

Numerical Prediction of Mean and Fluctuating Velocities for Jet-Flap Flows

A method is developed to predict the flow characteristics in the near wake region of a jet over a finite chord wing surface of an upper surface blown flap. Transition distributions of mean flow and select fluctuating velocity correlations, within the region immediately downstream of a sharp-edged terminus of a slot nozzle-jet flap, are established using a parabolized form of the time-averaged steady flow Navier-Stokes equations closed with a turbulence kinetic energy model. Numerical solutions, obtained using a finite-element algorithm are presented which quantize the localized large mean flow accelerations and resultant peaks in the distribution of turbulence kinetic energy in the near wake region. Results are verified by comparison to experiment.

Oceanic Thermal Response to Strong Atmospheric Forcing II. The Role of One-Dimensional Processes

The oceanic response to individual atmospheric forcing events during September to December is studied using ocean weather ship observations supplemented by simulations with a bulk turbulent kinetic energy model. A total of 49 cases with durations of 10–30 days and including one or more impulsive increases in wind speed were selected from three ocean weather ship records. A characteristic response of rapid deepening and cooling of the ocean mixed layer is round as extratropical cyclones pass. Periods between storms tend to exhibit little deepening, or even layer retreat, if the net heat flux at the surface is downward. The success in simulating a major fraction of the upper ocean response during strong forcing events with the use of the bulk turbulent kinetic energy model suggests that one-dimensional mixing processes play an important role. The successful simulation of the mixed layer response permits an inference of the heat fluxes and potential energy changes in the column when observations are missing during some events. During the early cooling season the heat flux at the base of the mixed layer can be 10 times the magnitude of the surface heat flux. Strong forcing events at OWS Papa tend to increase the potential energy, whereas the relatively greater surface heat flux contribution at OWS November and Victor results in a potential energy decrease.

Radiative Effects of Elevated Pollutant Layers

Abstract A one-dimensional transport model was developed to study the effects of radiative participation of elevated pollutant layers. Special features of the model include a turbulent kinetic energy model and a two-stream solar radiation model. Pollutants were assumed to consist of aerosols and pollutant gases. Aerosols were allowed to scatter and absorb energy in the solar spectrum while pollutant gases were assumed to interact only with thermal radiation. The results of the simulations conducted with the model showed that elevated layers of pollutants could control mixed-layer expansion by modifying the stability of the capping stable layer. Cooling associated with gaseous pollutants generally helped the growth of the mixed layer, while solar heating induced by pollutants hindered mixed-layer growth by creating sharp inversions. By affecting mixed-layer growth, radiative participation by pollutants also modified pollutant dispersal from the elevated pollutant layer. These results have important implica...

Efficient Computation of "Stiff" Chemically Reacting Flow in Turbulent Free Jets

The chemically reacting flow in axisymmetric, turbulent free jets is solved numerically by a second-order accurate finite-difference scheme that is unconditionally stable with respect to the chemical rates. The transport properties are obtained from the turbulent kinetic energy model of turbulence. The momentum, energy, and turbulence model equations are solved by an explicit differencing scheme, whereas a hybrid expolcit/implicit scheme is used to solve the species conservation equations. High computational efficiency is attained by solving the equations in a natural coordinate system, and by employing the chemical element conservation principles to minimize the order of the matrix inverted to obtain the species concentrations. The scheme computes reacting jet flows in one-fifth the computer time required by any previously reported scheme.