scholarly journals A Budget-Based Turbulence Length Scale Diagnostic

2021 ◽  
Author(s):  
Ivan Bastak Duran ◽  
Juerg Schmidli ◽  
Stephanie Reilly
Keyword(s):  
Ad Hoc ◽  
Weather Prediction ◽  
Strong Dependence ◽  
Length Scale ◽  
Boundary Layer Turbulence ◽  
Eddy Simulation ◽  
Budget Equation ◽  
Turbulence Length ◽  
Core Idea ◽  
Turbulence Length Scale

<p>The most frequently used boundary-layer turbulence parameterization in numerical weather prediction (NWP) models are turbulence kinetic energy (TKE) based schemes. However, these parameterizations suffer from a potential weakness, namely the strong dependence on an ad-hoc quantity, the so-called turbulence length scale. The physical interpretation of the turbulence length scale is difficult and hence it cannot be directly related to measurements or large eddy simulation (LES) data. Consequently, formulations for the turbulence length scale in basically all TKE schemes are based on simplified assumptions and are model-dependent. A good reference for the independent evaluation of the turbulence length scale expression for NWP modeling is missing. We propose a new turbulence length scale diagnostic which can be used in the gray zone of turbulence without modifying the  underlying TKE turbulence scheme. The new diagnostic is based on the TKE budget: The core idea is to encapsulate the sum of the molecular dissipation  and the cross-scale TKE transfer into an effective dissipation, and associate it with the new turbulence length scale. This effective dissipation can then be calculated as a residuum in the TKE budget equation (for horizontal sub-domains of different sizes) using LES data. Estimation of the scale dependence of the diagnosed turbulence length scale using this novel method is presented for several idealized cases.</p>

scholarly journals A Budget-Based Turbulence Length Scale Diagnostic

Atmosphere ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 425 ◽  
Author(s):  
Ivan Bašták Ďurán ◽  
Juerg Schmidli ◽  
Ritthik Bhattacharya
Keyword(s):  
Ad Hoc ◽  
Weather Prediction ◽  
Strong Dependence ◽  
Length Scale ◽  
Boundary Layer Turbulence ◽  
Eddy Simulation ◽  
Budget Equation ◽  
Turbulence Length ◽  
Core Idea ◽  
Turbulence Length Scale

The most frequently used boundary-layer turbulence parameterization in numerical weather prediction (NWP) models are turbulence kinetic energy (TKE) based-based schemes. However, these parameterizations suffer from a potential weakness, namely the strong dependence on an ad-hoc quantity, the so-called turbulence length scale. The physical interpretation of the turbulence length scale is difficult and hence it cannot be directly related to measurements or large eddy simulation (LES) data. Consequently, formulations for the turbulence length scale in basically all TKE schemes are based on simplified assumptions and are model-dependent. A good reference for the independent evaluation of the turbulence length scale expression for NWP modeling is missing. Here we propose a new turbulence length scale diagnostic which can be used in the gray zone of turbulence without modifying the underlying TKE turbulence scheme. The new diagnostic is based on the TKE budget: The core idea is to encapsulate the sum of the molecular dissipation and the cross-scale TKE transfer into an effective dissipation, and associate it with the new turbulence length scale. This effective dissipation can then be calculated as a residuum in the TKE budget equation (for horizontal sub-domains of different sizes) using LES data. Estimation of the scale dependence of the diagnosed turbulence length scale using this novel method is presented for several idealized cases.

scholarly journals A Budget-Based Turbulence Length Scale Diagnostic

2021 ◽  
Author(s):  
Stephanie Reilly ◽  
Ivan Bašták Ďurán ◽  
Juerg Schmidli
Keyword(s):  
Dissipation Rate ◽  
General Circulation ◽  
Energy Production ◽  
Ad Hoc ◽  
Weather Prediction ◽  
Strong Dependence ◽  
Length Scale ◽  
Gray Zone ◽  
Turbulence Length ◽  
Turbulence Length Scale

<p>The most frequently used boundary-layer turbulence parameterization in numerical weather prediction (NWP) and general circulation (GC) models are turbulence kinetic energy (TKE) based schemes. However, these parameterizations suffer from a potential weakness, namely the strong dependence on an ad-hoc quantity, the so-called turbulence length scale. The turbulence length scale is used to parameterize the molecular dissipation of TKE and is required to calculate the turbulence exchange coefficients. Traditional turbulence length scale formulations are designed for scales that are located above the energy production range of the turbulence spectra, hence the transfer of TKE across scales is not considered. However, as computational power increase, there is an increase in the potential for simulating turbulence at resolutions that are within the energy production range of turbulence. This is a gray zone problem. In order to represent turbulence processes accurately at these resolutions, the transfer of TKE across scales needs to be accounted for. For this purpose, a new turbulence length scale diagnostic, that can be used in the development of new turbulence length scale formulations, has been developed.  The new diagnostic uses the budget of TKE and the budgets of scalar variances to estimate the effective dissipation rate, which encapsulate the sum of the molecular dissipation and the cross-scale TKE transfer. The effective dissipation rate is then associated with the new scale-dependent turbulence length scale. Several idealized LES cases, simulated with the MicroHH model, are used to diagnose the turbulence length scale. It has been found that in the gray zone of turbulence the new turbulence length scale strongly depends on the horizontal grid spacing, and that this scale-dependence is also height-dependent. The new diagnostic is used for the evaluation of existing turbulence length scale formulations.</p>

A Framework for Simulating the Tropical-Cyclone Boundary Layer Using Large-Eddy Simulation and Its Use in Evaluating PBL Parameterizations

2021 ◽  
Author(s):  
Xiaomin Chen ◽  
George H. Bryan ◽  
Jun A. Zhang ◽  
Joseph J. Cione ◽  
Frank D. Marks
Keyword(s):  
Boundary Layer ◽  
Tropical Cyclone ◽  
Large Eddy Simulation ◽  
Momentum Flux ◽  
Intensity Change ◽  
Length Scale ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Turbulence Length ◽  
Turbulence Length Scale

AbstractBoundary layer turbulent processes affect tropical cyclone (TC) structure and intensity change. However, uncertainties in the parameterization of the planetary boundary layer (PBL) under high-wind conditions remain challenging, mostly due to limited observations. This study presents and evaluates a framework of numerical simulation that can be used for a small-domain [O(5 km)] large-eddy simulation (LES) and single-column modeling (SCM) to study the TC boundary layer. The framework builds upon a previous study that uses a few input parameters to represent the TC vortex and adds a simple nudging term for temperature and moisture to account for the complex thermodynamic processes in TCs. The reference thermodynamic profiles at different wind speeds are retrieved from a composite analysis of dropsonde observations of mature hurricanes. Results from LES show that most of the turbulence kinetic energy and vertical momentum flux is associated with resolved processes when horizontal grid spacing is O(10 m). Comparison to observations of turbulence variables such as momentum flux, effective eddy viscosity, and turbulence length scale show that LES produces reasonable results but highlight areas where further observations are necessary. LES results also demonstrate that compared to a classic Ekman-type boundary layer, the TC boundary layer is shallower, develops steady conditions much quicker, and exhibits stronger wind speed near the surface. The utility of this framework is further highlighted by evaluating a first-order PBL parameterization, suggesting that an asymptotic turbulence length scale of 40 m produces a good match to LES results.

Tooth Thickness Effect on the Performance of Gas Labyrinth Seals

1992 ◽  
Vol 114 (4) ◽  
pp. 790-795 ◽  
Author(s):  
D. L. Rhode ◽  
R. I. Hibbs
Keyword(s):  
Finite Difference ◽  
Computer Code ◽  
Thickness Effect ◽  
Turbulence Energy ◽  
Length Scale ◽  
Labyrinth Seals ◽  
Cpu Time ◽  
Reservoir Conditions ◽  
Turbulence Length ◽  
Turbulence Length Scale

A previously validated finite difference computer code was revised to allow the specification of upstream and downstream reservoir conditions as boundary conditions, whereas the domain extends only from the seal inlet to outlet plane. As a result of this special revision, the required execution CPU time is approximately only one hour on a VAX 8650 computer for three-cavity, straight-through seals. A parametric study focusing on tooth thickness showed that streamwise swirl development was only slightly higher for the thickest tooth. Further, for straight-through seals it was found that leakage is almost independent of tooth thickness and that the second cavity yields a definite increase in turbulence energy and turbulence length scale over the first cavity.

The Effects of Freestream Turbulence, Turbulence Length Scale, and Exit Reynolds Number on Turbine Blade Heat Transfer in a Transonic Cascade

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
J. S. Carullo ◽  
S. Nasir ◽  
R. D. Cress ◽  
W. F. Ng ◽  
K. A. Thole ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Turbine Blade ◽  
Surface Heat ◽  
Length Scale ◽  
Freestream Turbulence ◽  
Surface Heat Transfer ◽  
Mach Numbers ◽  
Turbulence Length ◽  
Turbulence Length Scale

This paper experimentally investigates the effect of high freestream turbulence intensity, turbulence length scale, and exit Reynolds number on the surface heat transfer distribution of a turbine blade at realistic engine Mach numbers. Passive turbulence grids were used to generate freestream turbulence levels of 2%, 12%, and 14% at the cascade inlet. The turbulence grids produced length scales normalized by the blade pitches of 0.02, 0.26, and 0.41, respectively. Surface heat transfer measurements were made at the midspan of the blade using thin film gauges. Experiments were performed at the exit Mach numbers of 0.55, 0.78, and 1.03, which represent flow conditions below, near, and above nominal conditions. The exit Mach numbers tested correspond to exit Reynolds numbers of 6×105, 8×105, and 11×105, based on true chord. The experimental results showed that the high freestream turbulence augmented the heat transfer on both the pressure and suction sides of the blade as compared with the low freestream turbulence case. At nominal conditions, exit Mach 0.78, average heat transfer augmentations of 23% and 35% were observed on the pressure side and suction side of the blade, respectively.

scholarly journals A √k-l Turbulence Model for Fluids Engineering Applications

2016 ◽  
Vol 3 (1) ◽  
pp. 40
Author(s):  
Uriel Goldberg
Keyword(s):  
Viscous Sublayer ◽  
Dirichlet Boundary Conditions ◽  
Length Scale ◽  
Time Step ◽  
Wall Distance ◽  
Q Model ◽  
Turbulence Length ◽  
Turbulence Length Scale ◽  
Wall Proximity ◽  
Mean Strain

A turbulence closure based on transport equations for the square-root of the kinetic energy of turbulence, q=k1/2 and the length-scale, , is proposed and tested. The model is topography parameter free (no wall distance needed), uses local wall proximity indicators instead, and is meant to be applicable to both wall-bounded and free shear flows. Solving directly for the turbulence length-scale, invoking Dirichlet boundary conditions for both q and  and the fact that q varies linearly across the viscous sublayer contribute to reduced sensitivity of this model to near-wall grid concentration (as long as the sublayer is resolved) and to less numerical stiffness, hence faster convergence. A variable Cm parameter is featured in this model to account for non-simple shear where mean strain and vorticity rates are different. Several cases, covering a wide variety of flows, are presented to demonstrate the model’s performance. Fluids engineers whose work involves complex 3D topologies, particularly with non-stationary grids which require re-computing wall distance arrays at each time-step (a heavy demand on time and budget) may appreciate the fact that no distance arrays are needed for the q-  model.

Darryl E. Metzger Memorial Session Paper: An Account of Free-Stream-Turbulence Length Scale on Laminar Heat Transfer

1995 ◽  
Vol 117 (3) ◽  
pp. 401-406 ◽  
Author(s):  
K. Dullenkopf ◽  
R. E. Mayle
Keyword(s):  
Heat Transfer ◽  
Free Stream ◽  
Dominant Frequency ◽  
Length Scale ◽  
Free Stream Turbulence ◽  
Laminar Boundary Layers ◽  
Session Paper ◽  
Turbulence Length ◽  
Effective Intensity ◽  
Turbulence Length Scale

The effect of length scale in free-stream turbulence is considered for heat transfer in laminar boundary layers. A model is proposed that accounts for an “effective” intensity of turbulence based on a dominant frequency for a laminar boundary layer. Assuming a standard turbulence spectral distribution, a new turbulence parameter that accounts for both turbulence level and length scale is obtained and used to correlate heat transfer data for laminar stagnation flows. The result indicates that the heat transfer for these flows is linearly dependent on the “effective” free-stream turbulence intensity.

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