An Improved K-Epsilon Model for Near-Wall Turbulence and Comparison with Direct Numerical Simulation

An improved k-epsilon model for low Reynolds number turbulence near a wall is presented. The near-wall asymptotic behavior of the eddy viscosity and the pressure transport term in the turbulent kinetic energy equation is analyzed. Based on this analysis, a modified eddy viscosity model, having correct near-wall behavior, is suggested, and a model for the pressure transport term in the k-equation is proposed. In addition, a modeled dissipation rate equation is reformulated. Fully developed channel flows were used for model testing. The calculations using various k-epsilon models are compared with direct numerical simulations. The results show that the present k-epsilon model performs well in predicting the behavior of near-wall turbulence. Significant improvement over previous k-epsilon models is obtained

An approach for jointly modeling multivariate longitudinal measurements and discrete time-to-event data

In many medical studies, patients are followed longitudinally and interest is on assessing the relationship between longitudinal measurements and time to an event. Recently, various authors have proposed joint modeling approaches for longitudinal and time-to-event data for a single longitudinal variable. These joint modeling approaches become intractable with even a few longitudinal variables. In this paper we propose a regression calibration approach for jointly modeling multiple longitudinal measurements and discrete time-to-event data. Ideally, a two-stage modeling approach could be applied in which the multiple longitudinal measurements are modeled in the first stage and the longitudinal model is related to the time-to-event data in the second stage. Biased parameter estimation due to informative dropout makes this direct two-stage modeling approach problematic. We propose a regression calibration approach which appropriately accounts for informative dropout. We approximate the conditional distribution of the multiple longitudinal measurements given the event time by modeling all pairwise combinations of the longitudinal measurements using a bivariate linear mixed model which conditions on the event time. Complete data are then simulated based on estimates from these pairwise conditional models, and regression calibration is used to estimate the relationship between longitudinal data and time-to-event data using the complete data. We show that this approach performs well in estimating the relationship between multivariate longitudinal measurements and the time-to-event data and in estimating the parameters of the multiple longitudinal process subject to informative dropout. We illustrate this methodology with simulations and with an analysis of primary biliary cirrhosis (PBC) data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS339 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Customer Concerns about Uncertainty and Willingness to Pay in Leasing Solar Power Systems

Although solar power systems are considered as one of the most promising renewable energy sources, some uncertain factors as well as the high cost could be barriers which create customer resistance. Leasing instead of purchase, as one type of product service system, could be an option to reduce consumer concern on such issues. This study focuses on consumer concerns about uncertainty and willingness to pay for leasing solar power systems. Conjoint analysis method is used to find part worth utilities and estimate gaps of willingness to pay between attribute levels, including various leasing time lengths. The results show the part worth utilities an d relative importance of four major attributes, including leasing time. Among concerns about uncertainties, government subsidy, electricity price, reliability, and rise of new generation solar power systems were found to be significantly related to the additional willingness-to-pay for a shorter leasing time. Cluster analysis is used to identify two groups standing for high and low concerns about uncertainty. People with more concerns tend to pay more for a shorter lease time

A new time scale based k-epsilon model for near wall turbulence

A k-epsilon model is proposed for wall bonded turbulent flows. In this model, the eddy viscosity is characterized by a turbulent velocity scale and a turbulent time scale. The time scale is bounded from below by the Kolmogorov time scale. The dissipation equation is reformulated using this time scale and no singularity exists at the wall. The damping function used in the eddy viscosity is chosen to be a function of R(sub y) = (k(sup 1/2)y)/v instead of y(+). Hence, the model could be used for flows with separation. The model constants used are the same as in the high Reynolds number standard k-epsilon model. Thus, the proposed model will be also suitable for flows far from the wall. Turbulent channel flows at different Reynolds numbers and turbulent boundary layer flows with and without pressure gradient are calculated. Results show that the model predictions are in good agreement with direct numerical simulation and experimental data

A kappa-epsilon calculation of transitional boundary layers

A recently proposed kappa-epsilon model for low Reynolds number turbulent flows was modified by introducing a new damping function f(sub mu). The modified model is used to calculate the transitional boundary layer over a flat plate with different freestream turbulence levels. It is found that the model could mimic the transitional flow. However, the predicted transition is found to be sensitive to the initial conditions

A k-epsilon modeling of near wall turbulence

A k-epsilon model is proposed for turbulent bounded flows. In this model, the turbulent velocity scale and turbulent time scale are used to define the eddy viscosity. The time scale is shown to be bounded from below by the Kolmogorov time scale. The dissipation equation is reformulated using the time scale, removing the need to introduce the pseudo-dissipation. A damping function is chosen such that the shear stress satisfies the near wall asymptotic behavior. The model constants used are the same as the model constants in the commonly used high turbulent Reynolds number k-epsilon model. Fully developed turbulent channel flows and turbulent boundary layer flows over a flat plate at various Reynolds numbers are used to validate the model. The model predictions were found to be in good agreement with the direct numerical simulation data

Calculations of turbulent separated flows

A numerical study of incompressible turbulent separated flows is carried out by using two-equation turbulence models of the K-epsilon type. On the basis of realizability analysis, a new formulation of the eddy-viscosity is proposed which ensures the positiveness of turbulent normal stresses - a realizability condition that most existing two-equation turbulence models are unable to satisfy. The present model is applied to calculate two backward-facing step flows. Calculations with the standard K-epsilon model and a recently developed RNG-based K-epsilon model are also made for comparison. The calculations are performed with a finite-volume method. A second-order accurate differencing scheme and sufficiently fine grids are used to ensure the numerical accuracy of solutions. The calculated results are compared with the experimental data for both mean and turbulent quantities. The comparison shows that the present model performs quite well for separated flows

An improved k-epsilon model for near wall turbulence

An improved k-epsilon model for low Reynolds number turbulence near a wall is presented. In the first part of this work, the near-wall asymptotic behavior of the eddy viscosity and the pressure transport term in the turbulent kinetic energy equation are analyzed. Based on these analyses, a modified eddy viscosity model with the correct near-wall behavior is suggested, and a model for the pressure transport term in the k-equation is proposed. In addition, a modeled dissipation rate equation is reformulated, and a boundary condition for the dissipation rate is suggested. In the second part of the work, one of the deficiencies of the existing k-epsilon models, namely, the wall distance dependency of the equations and the damping functions, is examined. An improved model that does not depend on any wall distance is introduced. Fully developed turbulent channel flows and turbulent boundary layers over a flat plate are studied as validations for the proposed new models. Numerical results obtained from the present and other previous k-epsilon models are compared with data from direct numerical simulation. The results show that the present k-epsilon model, with added robustness, performs as well as or better than other existing models in predicting the behavior of near-wall turbulence

On the Basic Equations for the Second-order Modeling of Compressible Turbulence

Equations for the mean and the turbulence quantities of compressible turbulent flows are derived in this report. Both the conventional Reynolds average and the mass-weighted Favre average were employed to decompose the flow variable into mean and turbulent quantities. These equations are to be used later in developing second-order Reynolds stress models for high-speed compressible flows. A few recent advances in modeling some of the terms in the equation due to compressibility effects are also summarized