Recent Mathematical Models for Turbulent Flow in Saturated Rigid Porous Media

2001 ◽  
Vol 123 (4) ◽  
pp. 935-940 ◽  
Author(s):  
Marcelo J. S. de Lemos ◽  
Marcos H. J. Pedras
Keyword(s):  
Kinetic Energy ◽  
Mathematical Models ◽  
Time Integration ◽  
Turbulence Models ◽  
Volume Averaging ◽  
Turbulence Kinetic Energy ◽  
Time Space ◽  
Interfacial Surface ◽  
Flow Through ◽  
Double Decomposition

Turbulence models proposed for flow through permeable structures depend on the order of application of time and volume average operators. Two developed methodologies, following the two orders of integration, lead to different governing equations for the statistical quantities. The flow turbulence kinetic energy resulting in each case is different. This paper reviews recently published mathematical models developed for such flows. The concept of double decomposition is discussed and models are classified in terms of the order of application of time and volume averaging operators, among other peculiarities. A total of four major classes of models are identified and a general discussion on their main characteristics is carried out. Proposed equations for turbulence kinetic energy following time-space and space-time integration sequences are derived and similar terms are compared. Treatment of the drag coefficient and closure of the interfacial surface integrals are discussed.

scholarly journals The influence of boundary condition functions on the quality of the solution and its sensitivity to coefficients of k-ε turbulence models

2011 ◽  
Vol 8 (1) ◽  
pp. 015-026
Author(s):  
Ewa Błazik-Borowa
Keyword(s):  
Boundary Condition ◽  
Kinetic Energy ◽  
Boundary Conditions ◽  
Input Data ◽  
Turbulence Models ◽  
Turbulence Kinetic Energy ◽  
Flow Parameters ◽  
Measurement Results ◽  
Calculation Results

The paper is devoted to the problem of boundary conditions influence on the quality of the solution obtained with use of k-ε turbulence models. There are calculation results for different boundary conditions and two methods: standard k-ε and RNG k-ε in the paper. The flow parameters obtained from the calculation are compared with our own measurement results. Moreover, the influence of input data on the inflow edge on sensitivity coefficients is shown and analysed in the paper. The research is performed for components of velocity and turbulence kinetic energy.

scholarly journals Optimization of Fluent Turbulence Models for Annular Diffuser

2020 ◽  
Vol 6 (6) ◽  
pp. 57-60
Author(s):  
Nagendra Kumar Sharma
Keyword(s):  
Kinetic Energy ◽  
Mathematical Models ◽  
Flow Characteristics ◽  
Turbulence Models ◽  
Cfd Analysis ◽  
Mechanical Device ◽  
Engineering Structures ◽  
Flowing Fluid ◽  
Characteristic Quantity ◽  
Annular Diffuser

A diffuser is a mechanical device used for converting the kinetic energy of flowing fluid into pressure energy. As the flow advances through the diffuser there is ongoing retardation of the flow resulting in conversion of kinetic energy into pressure energy. This is known as diffusion. Diffuser constitutes an essential part in turbo machinery and engineering structures. The present study aims at CFD analysis for the prediction of flow characteristics using various mathematical models. The annular diffuser considered in the present case has both the hub and casings are diverging with equal angles and hub angle keeping constant as 10°. The characteristic quantity such as velocity profiles at various sections and flow patterns have been presented for studying. Standard turbulence models are studied in the present study.

A Study of Some Turbulence Models for Flow and Heat Transfer in Ducts of Annular Cross-Section

1981 ◽  
Vol 103 (1) ◽  
pp. 146-152 ◽  
Author(s):  
Mujeeb R. Malik ◽  
R. H. Pletcher
Keyword(s):  
Heat Transfer ◽  
Kinetic Energy ◽  
Turbulence Modeling ◽  
Turbulence Models ◽  
Thermal Conditions ◽  
Turbulence Kinetic Energy ◽  
Flow And Heat Transfer ◽  
Overall Performance ◽  
Transfer Parameters ◽  
Difference Calculation

A variable property finite-difference calculation procedure is used to predict turbulent flow and heat transfer parameters in annular passages. Predictions from several turbulence models are compared with measurements over a range of flow and thermal conditions. Of the models considered, one utilizing transport equations for turbulence kinetic energy and characteristic mixing length scale gave the best overall performance. The inclusion of turbulence kinetic energy in the turbulence modeling was found not to be crucial for predicting isothermal flows or for predicting all parameters except the temperature distribution for flows with heat transfer at Reynold numbers greater than 110,000.

scholarly journals Study on the characteristics of the pressure fluctuations and their contribution to turbulence kinetic energy

2021 ◽  
pp. 105634
Author(s):  
Zhuorui Wei ◽  
Hongsheng Zhang ◽  
Yan Ren ◽  
Qianhui Li ◽  
Xuhui Cai ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Pressure Fluctuations ◽  
Turbulence Kinetic Energy

scholarly journals Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

2021 ◽  
Author(s):  
Javier Bonet ◽  
Antonio J. Gil
Keyword(s):  
Kinetic Energy ◽  
Crack Propagation ◽  
Mathematical Models ◽  
Linear Elasticity ◽  
Strain Energy ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Discontinuous Solutions ◽  
Linear Elasticity Theory ◽  
Intersonic Crack Propagation

AbstractThis paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.

Composited structure of shallow cumulus clouds

2021 ◽  
Author(s):  
Chris Holloway ◽  
Jian-Feng Gu ◽  
Bob Plant ◽  
Todd Jones
Keyword(s):  
Kinetic Energy ◽  
Vertical Velocity ◽  
Inversion Layer ◽  
Potential Temperature ◽  
Vertical Wind Shear ◽  
Theoretical Models ◽  
Turbulence Kinetic Energy ◽  
Cloud Base ◽  
Asymmetric Structures ◽  
Negatively Buoyant

<div> <div> <div> <div> <p>The normalized distributions of thermodynamic and dynamical variables both within and outside shallow clouds are investigated through a composite algorithm using large eddy simulation of the BOMEX case. The normalized magnitude is maximum near cloud center and decreases outwards. While relative humidity (RH) and cloud liquid water (<em>q<sub>l </sub></em>) decrease smoothly to match the environment, the vertical velocity, virtual potential temperature (<em>θ<sub>v </sub></em>) and potential temperature (<em>θ</em>) perturbations have more complicated behaviour towards the cloud boundary. Below the inversion layer, <em>θ<sub>v</sub></em> becomes <span>negative before the vertical velocity has turned from updraft to subsiding shell outside the cloud, indicating the presence of a transition zone where the updraft is negatively buoyant. Due to the downdraft outside the cloud and the enhanced horizontal turbulent mixing across the edge, the normalized turbulence kinetic energy (TKE) and horizontal turbulence kinetic energy (HTKE) decrease more slowly from the cloud center outwards than the thermodynamic variables. The distributions all present asymmetric structures in response to the vertical wind shear, with more negatively buoyant air, stronger downdrafts and larger TKE on the downshear side. We discuss several implications of the distributions for theoretical models and parameterizations. Positive buoyancy near cloud base is mostly due to </span><span>the virtual effect of water vapor, emphasising the role of moisture in triggering. The mean vertical velocity is found </span><span>to be approximately half the maximum vertical velocity within each cloud, providing a constraint on some models. Finally, products of normalized distributions for different variables are shown to be able to well represent the vertical heat and moisture fluxes, but they underestimate fluxes in the inversion layer because they do not capture cloud top downdrafts.</span></p> </div> </div> </div> </div>

Sign in / Sign up

Export Citation Format

Share Document