scholarly journals Predicting fully-developed channel flow with zero-equation model

2021 ◽  
Vol 9 ◽  
pp. 17-22
Author(s):  
Md Mizanur Rahman ◽  
Khalid Hasan ◽  
Wenchang Liu ◽  
Xinming Li
Keyword(s):  
Eddy Viscosity ◽  
Viscosity Ratio ◽  
Layer Structure ◽  
Equation Model ◽  
Physical Parameters ◽  
Turbulent Dissipation ◽  
Flow Domain ◽  
Length Variable ◽  
Structural Ensemble ◽  
Wall Bounded Turbulence

A new zero-equation model (ZEM) is devised with an eddy-viscosity formulation using a stress length variable which the structural ensemble dynamics (SED) theory predicts. The ZEM is distinguished by obvious physical parameters, quantifying the underlying flow domain with a universal multi-layer structure. The SED theory is also utilized to formulate an anisotropic Bradshaw stress-intensity factor, parameterized with an eddy-to-laminar viscosity ratio. Bradshaw’s structure function is employed to evaluate the kinetic energy of turbulence k and turbulent dissipation rate epsilon  . The proposed ZEM is intrinsically plausible, having a dramatic impact on the prediction of wall-bounded turbulence. 

scholarly journals Precise drag prediction of airfoil flows by a new algebraic model

2019 ◽  
Vol 36 (1) ◽  
pp. 35-43 ◽  
Author(s):  
Meng-Juan Xiao ◽  
Zhen-Su She
Keyword(s):  
Prediction Accuracy ◽  
Eddy Viscosity ◽  
Layer Structure ◽  
Algebraic Model ◽  
Simulation Data ◽  
Clear Physical Meaning ◽  
Order Of Magnitude ◽  
Drag Prediction ◽  
Structural Ensemble ◽  
Magnitude Improvement

AbstractWe report the results of accurate prediction of lift ($$C_L$$CL) and drag ($$C_D$$CD) coefficients of two typical airfoil flows (NACA0012 and RAE2822) by a new algebraic turbulence model, in which the eddy viscosity is specified by a stress length (SL) function predicted by structural ensemble dynamics (SED) theory. Unprecedented accuracy of the prediction of $$C_D$$CD with error of a few counts (one count is $$10^{-4}$$10-4) and of $$C_L$$CL with error under 1%-2% are uniformly obtained for varying angles of attack (AoA), indicating an order of magnitude improvement of drag prediction accuracy compared to currently used models (typically around 20 to 30 counts). More interestingly, the SED-SL model is distinguished with fewer parameters of clear physical meaning, which quantify underlying turbulent boundary layer (TBL) with a universal multi-layer structure, and is thus promising to be more easily generalizable to complex TBL. The use of the new model for the calibration of flow condition in experiment and the extraction of flow physics from numerical simulation data of aeronautic flows are discussed.

Algebraic Anisotropic Eddy-Viscosity Modeling for Application to Turbulent Film Cooling Flows

2011 ◽  
Author(s):  
Xueying Li ◽  
Jing Ren ◽  
Hongde Jiang
Keyword(s):  
Flow Field ◽  
Film Cooling ◽  
Eddy Viscosity ◽  
Viscosity Ratio ◽  
Equation Model ◽  
Wall Region ◽  
Mean Flow ◽  
Film Cooling Effectiveness ◽  
Jet In Crossflow ◽  
Comparison Of The Results

Under-predicting the spanwise spreading of film cooling is a big problem in the film cooling computation. This is mainly due to the incorrect simulation of the spanwise transport of the jet in crossflow by conventional isotropic eddy viscosity turbulent models. An improved algebraic anisotropic eddy viscosity method including both the influence of the wall and the strain of the mean flow field to the anisotropic ratio has been raised by the authors in the paper, referred to as Algebraic Anisotropic Eddy Viscosity (AAEV) method. An equation derived from the algebraic Reynolds stress transport equations is applied to compute the anisotropic eddy-viscosity ratio. The variation of the anisotropic eddy-viscosity ratio is a function of both the dimensionless wall distance and the local mean flow field. This method is applied to the two layer k-ε model with a one-equation model in near-wall region to form a new turbulent model- AAEV k-ε model. The new model is tested for the computation of a flat plate film cooling flow with an inclined row of streamwise injected jets. Comparison of the results between the AAEV k-ε model and two-layer k-ε model with the measured adiabatic film-cooling effectiveness distributions indicates that the AAEV k-ε model can correctly predict the spanwise spreading of the film and reduce the strength of the secondary vortices.

scholarly journals Predictions of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions Using an Intermittency Transport Equation

2003 ◽  
Vol 125 (3) ◽  
pp. 455-464 ◽  
Author(s):  
Y. B. Suzen ◽  
P. G. Huang ◽  
Lennart S. Hultgren ◽  
David E. Ashpis
Keyword(s):  
Transport Equation ◽  
Boundary Layers ◽  
Eddy Viscosity ◽  
Reynolds Numbers ◽  
Low Pressure ◽  
Equation Model ◽  
Intermittent Behavior ◽  
Low Pressure Turbine ◽  
Transitional Boundary Layer ◽  
Intermittency Factor

A new transport equation for the intermittency factor was proposed to predict separated and transitional boundary layers under low-pressure turbine airfoil conditions. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, μt, with the intermittency factor, γ. Turbulent quantities are predicted by using Menter’s two-equation turbulence model (SST). The intermittency factor is obtained from a transport equation model, which not only can reproduce the experimentally observed streamwise variation of the intermittency in the transition zone, but also can provide a realistic cross-stream variation of the intermittency profile. In this paper, the intermittency model is used to predict a recent separated and transitional boundary layer experiment under low pressure turbine airfoil conditions. The experiment provides detailed measurements of velocity, turbulent kinetic energy and intermittency profiles for a number of Reynolds numbers and freestream turbulent intensity conditions and is suitable for validation purposes. Detailed comparisons of computational results with experimental data are presented and good agreements between the experiments and predictions are obtained.

Depth Dependence of Physical Parameters Associated with Convection in the Solar Atmosphere

1971 ◽  
Vol 2 (1) ◽  
pp. 50-51
Author(s):  
B. E. Waters
Keyword(s):  
Steady State ◽  
Rayleigh Number ◽  
Eddy Viscosity ◽  
Convection Zone ◽  
Finite Amplitude ◽  
Physical Parameters ◽  
Solar Granulation ◽  
Solar Convection Zone ◽  
Solar Convection ◽  
Convective Phenomenon

It has been often suggested that the solar granulation is essentially a turbulent convective phenomenon. It is then worthwhile to investigate steady state, finite-amplitude convection in the outer layers of the solar convection zone. On the basis that the convection zone is turbulent, we will define an eddy viscosity; and for the present we will consider only the first 300 km of the convection zone. This value is predicted by van der Borght using an asymptotic analysis of convection at high Rayleigh number—provided we assume the horizontal dimension of the cellular pattern to be ˜1000 km.

Deformation and breakup of a viscoelastic drop in a Newtonian matrix under steady shear

2007 ◽  
Vol 584 ◽  
pp. 1-21 ◽  
Author(s):  
NISHITH AGGARWAL ◽  
KAUSIK SARKAR
Keyword(s):  
Steady State ◽  
Viscosity Ratio ◽  
Equation Model ◽  
Deborah Number ◽  
Steady Shear ◽  
Drop Deformation ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
Critical Capillary Number ◽  
Viscous Stresses

The deformation of a viscoelastic drop suspended in a Newtonian fluid subjected to a steady shear is investigated using a front-tracking finite-difference method. The viscoelasticity is modelled using the Oldroyd-B constitutive equation. The drop response with increasing relaxation time λ and varying polymeric to the total drop viscosity ratio β is studied and explained by examining the elastic and viscous stresses at the interface. Steady-state drop deformation was seen to decrease from its Newtonian value with increasing viscoelasticity. A slight non-monotonicity in steady-state deformation with increasing Deborah number is observed at high Capillary numbers. Transient drop deformation displays an overshoot before settling down to a lower value of deformation. The overshoot increases with increasing β. The drop shows slightly decreased alignment with the flow with increasing viscoelasticity. A simple ordinary differential equation model is developed to explain the various behaviours and the scalings observed numerically. The critical Capillary number for drop breakup is observed to increase with Deborah number owing to the inhibitive effects of viscoelasticity, the increase being linear for small Deborah number.

Impact of turbulence on cloud microphysics of water droplets population

2020 ◽  
Author(s):  
Mina Golshan ◽  
Mattia Tomatis ◽  
Shahbozbek Abdunabiev ◽  
Federico Fraternale ◽  
Marco Vanni ◽  
...  
Keyword(s):  
Dissipation Rate ◽  
Droplet Size Distribution ◽  
Liquid Water Content ◽  
Cloud Microphysics ◽  
Equation Model ◽  
Collision Kernel ◽  
Physical Parameters ◽  
Vapor Density ◽  
Air Interface ◽  
Number Of Particles

<p>This work focuses on the turbulent shearless mixing structure of a cloud/clear air interface with physical parameters typical of cumulus warm clouds. We investigate the effect of turbulence on the droplet size distribution, in particular, we focus on the distribution's broadening and on the collision kernel. We performed numerical experiments via Direct Numerical Simulations(DNS) of turbulent interfaces subject to density stratification and vapor density  fluctuation. Specifically, an initial supersaturation around 2 % and a dissipation rate of turbulent kinetic energy of 100 cm<sup>2</sup>/s<sup>3</sup> are set in the DNSs. Taylor's Reynolds number is between 150 and 300. The total number of particles is around 5-10 millions, matching an initial liquid water content of 0.8 g/m<sup>3</sup>. Through these experiments, we provide a measure of the collision kernel and compare it with literature models [Saffman & Turner,1955], which is then included in a drops Population Balance Equation model (PBE). The PBE includes both processes of drops growth by condensation/evaporation and aggregation.</p>

scholarly journals Coherent structures in a swirl injector at Re  = 4800 by nonlinear simulations and linear global modes

2016 ◽  
Vol 792 ◽  
pp. 620-657 ◽  
Author(s):  
O. Tammisola ◽  
M. P. Juniper
Keyword(s):  
Shear Layer ◽  
Vortex Core ◽  
Eddy Viscosity ◽  
Vortex Breakdown ◽  
Turbulent Viscosity ◽  
Fuel Injector ◽  
Mean Flow ◽  
Turbulent Dissipation ◽  
Precessing Vortex Core ◽  
Global Modes

The large-scale coherent motions in a realistic swirl fuel-injector geometry are analysed by direct numerical simulations (DNS), proper orthogonal decomposition (POD), and linear global modes. The aim is to identify the origin of instability in this turbulent flow in a complex internal geometry. The flow field in the nonlinear simulation is highly turbulent, but with a distinguishable coherent structure: the precessing vortex core (a spiralling mode). The most energetic POD mode pair is identified as the precessing vortex core. By analysing the fast Fourier transform (FFT) of the time coefficients of the POD modes, we conclude that the first four POD modes contain the coherent fluctuations. The remaining POD modes (incoherent fluctuations) are used to form a turbulent viscosity field, using the Newtonian eddy model. The turbulence sets in from convective shear layer instabilities even before the nonlinear flow reaches the other end of the domain, indicating that equilibrium solutions of the Navier–Stokes are never observed. Linear global modes are computed around the mean flow from DNS, applying the turbulent viscosity extracted from POD modes. A slightly stable discrete $m=1$ eigenmode is found, well separated from the continuous spectrum, in very good agreement with the POD mode shape and frequency. The structural sensitivity of the precessing vortex core is located upstream of the central recirculation zone, identifying it as a spiral vortex breakdown instability in the nozzle. Furthermore, the structural sensitivity indicates that the dominant instability mechanism is the Kelvin–Helmholtz instability at the inflection point forming near vortex breakdown. Adjoint modes are strong in the shear layer along the whole extent of the nozzle, showing that the optimal initial condition for the global mode is localized in the shear layer. We analyse the qualitative influence of turbulent dissipation in the stability problem (eddy viscosity) on the eigenmodes by comparing them to eigenmodes computed without eddy viscosity. The results show that the eddy viscosity improves the complex frequency and shape of global modes around the fuel-injector mean flow, while a qualitative wavemaker position can be obtained with or without turbulent dissipation, in agreement with previous studies. This study shows how sensitivity analysis can identify which parts of the flow in a complex geometry need to be altered in order to change its hydrodynamic stability characteristics.

EXISTENCE AND POSITIVITY RESULTS FOR THE φ−θ AND A MODIFIED k−ε TWO-EQUATIONTURBULENCE MODELS

1993 ◽  
Vol 03 (02) ◽  
pp. 195-215 ◽  
Author(s):  
ROGER LEWANDOWSKI ◽  
BIJAN MOHAMMADI
Keyword(s):  
Numerical Analysis ◽  
Turbulence Model ◽  
Eddy Viscosity ◽  
Equation Model ◽  
Point Of View ◽  
Complete Model ◽  
Change Of Variables ◽  
Nonlinear Viscosity ◽  
The Right ◽  
The Impact

In this work, we consider the k−ε two-equation turbulence model from the point of view of mathematical and numerical analysis. We introduce a new equivalent two-equation model based on a new set of variables. In the first part, we study this model with a constant eddy viscosity. In this model, the coupling between the equations is done only through the right-hand side. In the second part, we consider the complete model with a nonlinear viscosity. Finally, the impact of this new change of variables on the numerical computations with the k−ε model is shown and a robust algorithm which preserves the positivity of the variables is given.

The relaxation of a turbulent boundary layer in an adverse pressure gradient

1989 ◽  
Vol 200 ◽  
pp. 367-387 ◽  
Author(s):  
Andrew D. Cutler ◽  
James P. Johnston
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Eddy Viscosity ◽  
Layer Structure ◽  
Adverse Pressure Gradient ◽  
Great Sensitivity ◽  
A Value ◽  
Gradient Parameter ◽  
Self Similar

The relaxation of a reattached turbulent boundary layer downstream of a wall fence has been investigated. The boundary layer has an adverse pressure gradient imposed upon it which is adjusted in an attempt to bring the boundary layer into equilibrium. This is done by adjusting the pressure gradient so as to bring the Clauser parameter (G) down to a value of about 11.4 and then maintain it constant. In the region from the reattachment point to 2 or 3 reattachment lengths downstream, the boundary layer recovers from the initial major effects of reattachment. Farther downstream (where G is constant) the pressure-gradient parameter changes very slowly and profiles of non-dimensionalized eddy viscosity appear self-similar. However, pressure gradient and eddy viscosity are both roughly twice as large as expected on the basis of previous studies of equilibrium turbulent boundary layers. It is not known whether equilibrium has been achieved in this downstream region. This is another illustration of the great sensitivity of boundary-layer structure to perturbations.

Sign in / Sign up

Export Citation Format

Share Document