scholarly journals Scaling Behavior of a Turbulent Kinetic Energy Closure Scheme for the Stably Stratified Atmosphere: A Steady-State Analysis

2020 ◽  
Vol 77 (9) ◽  
pp. 3161-3170
Author(s):  
Michael MacDonald ◽  
João Teixeira
Keyword(s):  
Steady State ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Present Model ◽  
Scaling Behavior ◽  
Mixing Length ◽  
Closure Scheme ◽  
Tke Closure ◽  
The Stability ◽  
Unique Steady State

Abstract We present a turbulent kinetic energy (TKE) closure scheme for the stably stratified atmosphere in which the mixing lengths for momentum and heat are not parameterized in the same manner. The key difference is that, while the mixing length for heat tends toward the stability independent mixing length for momentum in neutrally stratified conditions, it tends toward one based on the Brunt–Väisälä time scale and square root of the TKE in the limit of large stability. This enables a unique steady-state solution for TKE to be obtained, which we demonstrate would otherwise be impossible if the mixing lengths were the same. Despite the model’s relative simplicity, it is shown to perform reasonably well with observational data from the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99) using commonly employed model constants. Analyzing the scaling behavior of the nondimensional velocity and potential temperature gradients, or of the stability (correction) functions, reveals that for large stability the present model scales in the same manner as the first-order operational scheme of Viterbo et al. Alternatively, it appears as a blend of two cases of the TKE closure scheme of Baas et al. Critically, because a unique steady-state TKE can be obtained, the present model avoids the nonphysical behavior identified in one of the cases of Baas et al.

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.

Prediction of Turbulent Source Flow Between Corotating Disks With an Anisotropic Two-Equation Turbulence Model

1988 ◽  
Vol 110 (2) ◽  
pp. 187-194 ◽  
Author(s):  
S. A. Shirazi ◽  
C. R. Truman
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulence Model ◽  
Ad Hoc ◽  
Low Reynolds Number ◽  
Wall Region ◽  
Mixing Length ◽  
Mean Flow ◽  
Low Reynolds

An anisotropic form of a low-Reynolds-number two-equation turbulence model has been implemented in a numerical solution for incompressible turbulent flow between corotating parallel disks. Transport equations for turbulent kinetic energy and dissipation rate were solved simultaneously with the governing equations for the mean-flow variables. Comparisons with earlier mixing-length predictions and with measurements are presented. Good agreement between the present predictions and the measurements of velocity components and turbulent kinetic energy was obtained. The low-Reynolds-number two-equation model was found to model adequately the near-wall region as well as the effects of rotation and streamline divergence, which required ad hoc assumptions in the mixing-length model.

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).

scholarly journals A Scale-Adaptive Turbulent Kinetic Energy Closure for the Dry Convective Boundary Layer

2018 ◽  
Vol 75 (2) ◽  
pp. 675-690 ◽  
Author(s):  
Marcin J. Kurowski ◽  
João Teixeira
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Convective Boundary Layer ◽  
Mixing Length ◽  
Subgrid Scale ◽  
Convective Boundary ◽  
Continuous Transition ◽  
Simple Method ◽  
Grid Length

Abstract A pragmatic scale-adaptive turbulent kinetic energy (TKE) closure is proposed to simulate the dry convective boundary layer for a variety of horizontal grid resolutions: from 50 m, typical of large-eddy simulation models that use three-dimensional turbulence parameterizations/closures, up to 100 km, typical of climate models that use one-dimensional turbulence and convection parameterizations/closures. Since parameterizations/closures using the TKE approach have been frequently used in these two asymptotic limits, a simple method is proposed to merge them with a mixing-length-scale formulation for intermediate resolutions. This new scale-adaptive mixing length naturally increases with increasing grid length until it saturates as the grid length reaches mesoscale-model resolution. The results obtained using this new approach for dry convective boundary layers are promising. The mean vertical profiles of potential temperature and heat flux remain in good agreement for different resolutions. A continuous transition (in terms of resolution) across the gray zone is illustrated through the partitioning between the model-resolved and the subgrid-scale transports as well as by documenting the transition of the subgrid-scale TKE source/sink terms. In summary, a natural and continuous transition across resolutions (from 50 m to 100 km) is obtained, for dry convection, using exactly the same atmospheric model for all resolutions with a simple scale-adaptive mixing-length formulation.

Numerical Simulation of Gas-Particle Turbulent Flow Using kg-εg -kp-εp-kpg-θ Turbulence Model

2012 ◽  
Vol 204-208 ◽  
pp. 4327-4331 ◽  
Author(s):  
Zhuo Xiong Zeng ◽  
Feng Xue ◽  
Yi Hua Xu
Keyword(s):  
Kinetic Energy ◽  
Phase Velocity ◽  
Turbulent Kinetic Energy ◽  
Turbulence Model ◽  
Present Model ◽  
Particle Interaction ◽  
Particle Collision ◽  
Sudden Expansion ◽  
Velocity Correlation ◽  
Two Phase

kg-εg-kp-εp-kpg-θ turbulence model is proposed which considers particle-particle collision and gas-particle turbulence. This model includes turbulent kinetic energy equation, turbulent kinetic energy dissipation rate equation, particle pseudo-temperature transportation equation and the two-phase velocity correlation transport equation. To close the turbulence model, algebraic expressions of two-phase Reynolds stresses and two-phase velocity correlation variable are established which considered both gas-particle interaction and anisotropy. This model is used to simulate gas-particle in swirling sudden-expansion chamber. Comparing with kg-εg-kp-εp-θ model which is simply closed using a semi-empirical dimensional analysis, the present model has better predicted capability. It is shown that the present model gives simulation results in much better agreement with the experimental results than the kg-εg-kp-εp-θ model.

The Stability of Steady-State Depth Distributions of Marine Phytoplankton

1974 ◽  
Vol 108 (963) ◽  
pp. 679-687 ◽  
Author(s):  
W. O. Criminale, ◽  
D. F. Winter
Keyword(s):  
Steady State ◽  
Marine Phytoplankton ◽  
The Stability ◽  
Depth Distributions

scholarly journals Steady-state $$\dot{V}{\text{O}}_{2}$$ above MLSS: evidence that critical speed better represents maximal metabolic steady state in well-trained runners

2021 ◽  
Author(s):  
Rebekah J. Nixon ◽  
Sascha H. Kranen ◽  
Anni Vanhatalo ◽  
Andrew M. Jones
Keyword(s):  
Steady State ◽  
Critical Speed ◽  
Lactate Concentration ◽  
Practical Interest ◽  
Blood Lactate Concentration ◽  
Distance Runners ◽  
Severe Intensity ◽  
The Stability ◽  
Trained Runners ◽  
Over Time

AbstractThe metabolic boundary separating the heavy-intensity and severe-intensity exercise domains is of scientific and practical interest but there is controversy concerning whether the maximal lactate steady state (MLSS) or critical power (synonymous with critical speed, CS) better represents this boundary. We measured the running speeds at MLSS and CS and investigated their ability to discriminate speeds at which $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 was stable over time from speeds at which a steady-state $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 could not be established. Ten well-trained male distance runners completed 9–12 constant-speed treadmill tests, including 3–5 runs of up to 30-min duration for the assessment of MLSS and at least 4 runs performed to the limit of tolerance for assessment of CS. The running speeds at CS and MLSS were significantly different (16.4 ± 1.3 vs. 15.2 ± 0.9 km/h, respectively; P < 0.001). Blood lactate concentration was higher and increased with time at a speed 0.5 km/h higher than MLSS compared to MLSS (P < 0.01); however, pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 did not change significantly between 10 and 30 min at either MLSS or MLSS + 0.5 km/h. In contrast, $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 increased significantly over time and reached $$\dot{V}{\text{O}}_{2\,\,\max }$$ V ˙ O 2 max at end-exercise at a speed ~ 0.4 km/h above CS (P < 0.05) but remained stable at a speed ~ 0.5 km/h below CS. The stability of $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 at a speed exceeding MLSS suggests that MLSS underestimates the maximal metabolic steady state. These results indicate that CS more closely represents the maximal metabolic steady state when the latter is appropriately defined according to the ability to stabilise pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 .

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