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SUMMARYThe present numerical study is focused on testing two different modeling approaches to simulate a large turbulent buoyant helium plume, in particular the near-field region. First, buoyancy-corrected k-models are applied in Reynolds-averaged Navier-Stokes (RANS) calculations, then large eddy simulation (LES) using a standard Smagorinsky model is examined. Good results are produced using the buoyancy-corrected models, in particular, excellent agreement is achieved for the radial profiles of the streamwise velocity. However, the predictions are very sensitive to the choice of the buoyancy constant, C 3 , in the models. The present LES calculations show that the puffing frequency is accurately predicted. Predictions for the time-averaged velocities are within experimental uncertainty at all locations. The predicted plume concentrations are in good agreement at the base of the plume, but the centerline values are overpredicted farther downstream. The higher-order statistics are best predicted with the finest mesh. A sensitivity analysis on grid refinement, values of the Smagorinsky constant and the Schmidt number are included.

SummaryThe current paper is focused on investigating a Jacobian‐free Newton–Krylov (JFNK) method to obtain a fully implicit solution for two‐phase flows. In the JFNK formulation, the Jacobian matrix is not directly evaluated, potentially leading to major computational savings compared with a simple Newton's solver. The objectives of the present paper are as follows: (i) application of the JFNK method to two‐fluid models; (ii) investigation of the advantages and disadvantages of the fully implicit JFNK method compared with commonly used explicit formulations and implicit Newton–Krylov calculations using the determination of the Jacobian matrix; and (iii) comparison of the numerical predictions with those obtained by the Canadian Algorithm for Thermaulhydraulics Network Analysis 4. Two well‐known benchmarks are considered, the water faucet and the oscillating manometer.An isentropic two‐fluid model is selected. Time discretization is performed using a backward Euler scheme. A Crank–Nicolson scheme is also implemented to check the effect of temporal discretization on the predictions. Advection Upstream Splitting Method+ is applied to the convective fluxes. The source terms are discretized using a central differencing scheme. One explicit and two implicit formulations, one with Newton's solver with the Jacobian matrix and one with JFNK, are implemented. A detailed grid and model parameter sensitivity analysis is performed.For both cases, the JFNK predictions are in good agreement with the analytical solutions and explicit profiles. Further, stable results can be achieved using high CFL numbers up to 200 with a suitable choice of JFNK parameters. The computational time is significantly reduced by JFNK compared with the calculations requiring the determination of the Jacobian matrix. Copyright © 2015 John Wiley & Sons, Ltd.

A new method for calculating the conditional scalar dissipation rate ͗N͉͘ is derived from the probability density function ͑pdf͒ transport equation for the conserved scalar Z. Two different formulations are obtained. One is the result of direct integration of the pdf transport equation and the second is further developed assuming a two-parameter presumed form for the pdf. A linear model is used for the conditional velocity. The model is compared with a direct numerical simulation ͑DNS͒ of inhomogeneous turbulent mixing. The results are in very good agreement with the DNS and perform better than Girimaji's model which is based on homogeneous flow properties. Further validation with some experimental data would be useful. The new method has also the potential of being easily implemented in a finite-volume computational fluid dynamics code.