Second-order moment modeling of dispersed two-phase turbulence—Part 1: USM, k-ɛ-k p, and non-linear k-ɛ-k p two-phase turbulence models

2011 ◽  
Vol 54 (6) ◽  
pp. 1098-1107 ◽  
Author(s):  
LiXing Zhou
Keyword(s):  
Turbulence Models ◽  
Second Order ◽  
Order Moment ◽  
Two Phase ◽  
Non Linear

scholarly journals Method for Measuring the Second-Order Moment of Atmospheric Turbulence

Atmosphere ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 564
Author(s):  
Hong Shen ◽  
Longkun Yu ◽  
Xu Jing ◽  
Fengfu Tan
Keyword(s):  
Atmospheric Turbulence ◽  
Weighting Function ◽  
Structure Constant ◽  
Turbulence Models ◽  
Second Order ◽  
Index Structure ◽  
Order Moment ◽  
Site Testing ◽  
Optical Effects ◽  
Novel Method

The turbulence moment of order m (μm) is defined as the refractive index structure constant Cn2 integrated over the whole path z with path-weighting function zm. Optical effects of atmospheric turbulence are directly related to turbulence moments. To evaluate the optical effects of atmospheric turbulence, it is necessary to measure the turbulence moment. It is well known that zero-order moments of turbulence (μ0) and five-thirds-order moments of turbulence (μ5/3), which correspond to the seeing and the isoplanatic angles, respectively, have been monitored as routine parameters in astronomical site testing. However, the direct measurement of second-order moments of turbulence (μ2) of the whole layer atmosphere has not been reported. Using a star as the light source, it has been found that μ2 can be measured through the covariance of the irradiance in two receiver apertures with suitable aperture size and aperture separation. Numerical results show that the theoretical error of this novel method is negligible in all the typical turbulence models. This method enabled us to monitor μ2 as a routine parameter in astronomical site testing, which is helpful to understand the characteristics of atmospheric turbulence better combined with μ0 and μ5/3.

Simulation of Swirling Gas-Particle Flows Using Different Time Scales for the Closure of Two-Phase Velocity Correlation in the Second-Order Moment Two-Phase Turbulence Model1

2003 ◽  
Vol 125 (2) ◽  
pp. 247-250 ◽  
Author(s):  
Y. Yu ◽  
L. X. Zhou ◽  
C. G. Zheng ◽  
Z. H. Liu
Keyword(s):  
Phase Velocity ◽  
Time Scale ◽  
Second Order ◽  
Order Moment ◽  
Velocity Correlation ◽  
Two Phase ◽  
Fluctuation Velocity ◽  
Particle Flows ◽  
Measured Particle ◽  
Different Time Scales

Three different time scales—the gas turbulence integral time scale, the particle relaxation time, and the eddy interaction time—are used for closing the dissipation term in the transport equation of two-phase velocity correlation of the second-order moment two-phase turbulence model. The mass-weighted averaged second-order moment (MSM) model is used to simulate swirling turbulent gas-particle flows with a swirl number of 0.47. The prediction results are compared with the PDPA measurement results taking from references. Good agreement is obtained between the predicted and measured particle axial and tangential time-averaged velocities. There is some discrepancy between the predicted and measured particle axial and tangential fluctuation velocities. The results indicate that the time scale has an important effect. It is found that the predictions using the eddy interaction time scale give the right tendency—for example, the particle tangential fluctuation velocity is smaller than the gas tangential fluctuation velocity, as that given by the PDPA measurements.

Second-order moment model for dense two-phase turbulent flow of Bingham fluid with particles

2006 ◽  
Vol 27 (10) ◽  
pp. 1373-1381
Author(s):  
Zhuo-xiong Zeng ◽  
Li-xing Zhou ◽  
Zhi-he Liu
Keyword(s):  
Turbulent Flow ◽  
Bingham Fluid ◽  
Second Order ◽  
Order Moment ◽  
Two Phase

Nonlocal Convective PBL Model Based on New Third- and Fourth-Order Moments

2005 ◽  
Vol 62 (7) ◽  
pp. 2189-2204 ◽  
Author(s):  
Y. Cheng ◽  
V. M. Canuto ◽  
A. M. Howard
Keyword(s):  
Fourth Order ◽  
Potential Temperature ◽  
Turbulence Models ◽  
Second Order ◽  
Order Moment ◽  
Third Order ◽  
Mean Velocity ◽  
Eddy Simulation ◽  
Analytic Expressions ◽  
Aircraft Data

Abstract The standard approach to studying the planetary boundary layer (PBL) via turbulence models begins with the first-moment equations for temperature, moisture, and mean velocity. These equations entail second-order moments that are solutions of dynamic equations, which in turn entail third-order moments, and so on. How and where to terminate (close) the moments equations has not been a generally agreed upon procedure and a variety of models differ precisely in the way they terminate the sequence. This can be viewed as a bottom-up approach. In this paper, a top-down procedure is suggested, worked out, and justified, in which a new closure model is proposed for the fourth-order moments (FOMs). The key reason for this consideration is the availability of new aircraft data that provide for the first time the z profile of several FOMs. The new FOM expressions have nonzero cumulants that the model relates to the z integrals of the third-order moments (TOMs), giving rise to a nonlocal model for the FOMs. The new FOM model is based on an analysis of the TOM equations with the aid of large-eddy simulation (LES) data, and is verified by comparison with the aircraft data. Use of the new FOMs in the equations for the TOMs yields a new TOM model, in which the TOMs are damped more realistically than in previous models. Surprisingly, the new FOMs with nonzero cumulants simplify, rather than complicate, the TOM model as compared with the quasi-normal (QN) approximation, since the resulting analytic expressions for the TOMs are considerably simpler than those of previous models and are free of algebraic singularities. The new TOMs are employed in a second-order moment (SOM) model, a numerical simulation of a convective PBL is run, and the resulting mean potential temperature T, the SOMs, and the TOMs are compared with several LES data. As a final consistency check, T, SOMs, and TOMs are substituted from the PBL run back into the FOMs, which are again compared with the aircraft data.

A Nonlinear k-ε-kp Two-Phase Turbulence Model

2003 ◽  
Vol 125 (1) ◽  
pp. 191-194 ◽  
Author(s):  
L. X. Zhou ◽  
H. X. Gu
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulence Model ◽  
Computation Time ◽  
Second Order ◽  
Phase Correlation ◽  
Order Moment ◽  
Reynolds Stresses ◽  
Two Phase ◽  
Particle Flows

Nonlinear relationships of two-phase Reynolds stresses with the strain rates together with the transport equations of gas and particle turbulent kinetic energy and the two-phase correlation turbulent kinetic energy are proposed as the nonlinear k-ε-kp turbulence model. The proposed model is applied to simulate swirling gas-particle flows. The predicted two-phase time-averaged velocities and Reynolds stresses are compared with the PDPA measurements and those predicted using the second-order moment model. The results indicate that the nonlinear k-ε-kp model has the modeling capability near to that of the second-order moment model, but the former can save much computation time than the latter.

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