Bassam A. Younis

A second-moment closure study of rotating channel flow

The second-moment closure applied by Gibson & Launder (1978) to buoyant turbulent flows is here employed without modification to compute the effects of Coriolis forces on fully-developed flow in a rotating channel. The augmentation of turbulent transport on the pressure surface of the channel and its damping on the suction surface seem to be well captured by the computations, provided the flow near the suction surface remains turbulent. The rather striking alteration in shape of the mean velocity profile that occurs as the Rossby number is increased from 0.06 to 0.2 is shown to be explicable in terms of the modification to the intensity of the turbulent velocity fluctuations normal to the plate; for the larger value of Rossby number these fluctuations become larger than those in the flow direction causing what at low spin rates is a source of shear stress to become a sink.

Calculation of swirling jets with a Reynolds stress closure

The transport equations for the Reynolds stresses are closed by modeling the turbulence and mean‐strain parts of the pressure‐strain‐rate correlation. The model constants are determined from simple relationships deduced from measurements in rectilinear and longitudinally curved shear flows. It is found that the effects of complex strain fields are more correctly predicted when the influence of the mean‐strain part is reduced from levels indicated by rapid distortion theory, and the turbulence part is adjusted to conform approximately with the measured rates of return to isotropy. The case of the swirling jet is used to illustrate the improved performance of the model.

Calculation of turbulent boundary layers on curved surfaces

Published data from boundary layers on convex surfaces are used to assess the performance of a calculation method based on the solution of modeled transport equations for the Reynolds’ stresses and the dissipation rate of turbulence energy. For flows with large curvature, the model closely reproduces the suppression of turbulence and the diminished growth rate and skin friction. The recovery of flow distorted by curvature is also predicted with results broadly in accord with the measurements.

A rational model for the turbulent scalar fluxes

The paper reports on an alternative approach to modelling the turbulent scalar fluxes that arise from time averaging the transport equation for a scalar. In this approach, a functional relationship between these fluxes and various tensor quantities is constructed with guidance from the exact equations governing the transport of fluxes. Results from tensor representation theory are then used to obtain an explicit relationship between the fluxes and the terms in the assumed functional relationship. Where turbulence length– and time–scales are implied, these are determined from two scalar quantities: the turbulence kinetic energy and its rate of dissipation by viscous action. The general representation is then reduced by certain justifiable assumptions to yield a practical model for the turbulent scalar fluxes that is explicit and algebraic in these quantities and one that correctly reflects their dependence on the gradients of mean velocity and on the details of the turbulence. Examination of alternative algebraic models shows most to be subsets of the present proposal. The new model is calibrated using results from large–eddy simulations (LESs) of homogeneous turbulence with passive scalars and then assessed by reference to benchmark data from heated turbulent shear flows. The results obtained show the model to correctly predict the anisotropy of the turbulent diffusivity tensor. The asymmetric nature of this tensor is also recovered, but only qualitatively, there being significant quantitative differences between the model predictions and the LES results. Finally, comparisons with data from benchmark two–dimensional free shear flows show the new model to yield distinct improvements over other algebraic scalar–flux closures.

Analysis and modelling of turbulent flow in an axially rotating pipe

The analysis and modelling of the structure of turbulent flow in a circular pipe subjected to an axial rotation is presented. Particular attention is paid to determining the terms in various turbulence closures that generate the two main physical features that characterize this flow: a rotationally dependent axial mean velocity and a rotationally dependent mean azimuthal or swirl velocity relative to the rotating pipe. It is shown that the rst feature is well represented by two-dimensional explicit algebraic stress models but is irreproducible by traditional two-equation models. On the other hand, three-dimensional frame-dependent models are needed to predict the presence of a mean swirl velocity. The latter is argued to be a secondary eect which arises from a cubic nonlinearity in standard algebraic models with conventional nearwall treatments. Second-order closures are shown to give a more complete description of this flow and can describe both of these features fairly well. In this regard, quadratic pressure{strain models perform the best overall when extensive comparisons are made with the results of physical and numerical experiments. The physical signicance of this problem and the implications for future research in turbulence are discussed in detail.

Calculation of turbulent buoyant plumes with a Reynolds stress and heat flux transport closure

Abstract A differential Reynolds stress and heat flux closure is adopted for modelling the turbulent transport of heat and momentum in vertical buoyant free plumes. Modelled transport equations are solved for the turbulent stresses and heat fluxes, the turbulence energy dissipation rate, and the mean-square temperature fluctuations. Closure at this level permits the turbulent transport processes to be treated more exactly than with Boussinesq-type two-equation models which are based on the notion of an effective viscosity and diffusivity. The solution of a transport equation for the thermal dissipation rate, which avoids the need to empirically prescribe the ratio of the thermal and mechanical time scales, is also investigated. The model is applied to the calculation of both self-similar plumes and forced plumes. The results are compared with existing experimental data and are found to be in reasonable agreement with the measured behaviour.

On the prediction of turbulent flows around full-scale buildings

Data from tests on a full-scale, single-span high eaves commercial glasshouse are used to quantify the uncertainties associated with the use of computational fluid dynamics to obtain wind load predictions for full-scale structures. It is demonstrated that the widely used assumption of two-dimensional flow field in the mid-span leads to serious overestimation of the suction pressures over the roof and on the leeward wall. It is further shown that the use of a Reynolds-stress closure enables the capture of flow reversal downstream of the windward eaves. In contrast, the industry-standard k–e model is found to predict no flow separation, contrary to the experimental observation. Finally, guidelines are suggested for suitable mesh distributions and for the efficient sizing of the computational domain relative to the buildings dimensions.

Towards a Rational Model for the Triple Velocity Correlations of Turbulence

The purpose of this paper is to present a rational approach to modelling the triple velocity correlations that appear in the transport equations for the Reynolds stresses. All existing models of these correlations have largely been formulated on phenomenological grounds and are defective in one important aspect: they all neglect to allow for the dependence of these correlations on the local gradients of mean velocity. The mathematical necessity for this dependence will be demonstrated in the paper. The present contribution lies in the novel use of group representation theory to determine the most general tensorial form of these correlations in terms of all the secondand third-order tensor quantities which appear in the exact equations that govern their evolution. The requisite representation did not exist in the literature and had therefore to be developed specifically for this purpose. The outcome of this work is a mathematical framework for the construction of algebraic, explicit and rational models for the triple velocity correlations that are theoretically consistent and include all the correct dependencies. Previous models are reviewed, and all are shown to be incomplete subsets of this new representation, even to lowest order.

On consistency conditions for rotating turbulent flows

Consistency conditions for the prediction of turbulent flows in a rotating frame are examined. It is shown that the dissipation rate should vanish along with the eddy viscosity in the limit of rapid rotations. The latter result is also true when the eddy viscosity is anisotropic and formally follows from the explicit algebraic stress approximation as well as from a phenomenological treatment. The former result has been built into the modeled dissipation rate equation of recent turbulence models where the second result has been violated. In fact, some of these models have the eddy viscosity going to infinity while the dissipation rate vanishes, leading to an inconsistency. For consistency, both of these conditions must be satisfied. The implications of these results for turbulence modeling are thoroughly discussed.

Large-Eddy Simulations and Heat-Flux Modeling in a Turbulent Impinging Jet

This article documents the results of an investigation into aspects of the simulation and modeling of turbulent jets that impinge orthogonally on a target surface. The focus is on the case of a jet which issues from a circular pipe into stagnant surrounding at the relatively high value of Reynolds number of 23,000 (based on nozzle diameter and bulk velocity) for which experimental data are available. Large-eddy simulations were performed to obtain details of the mean flows and the turbulence fields including distributions of all components of the turbulent heat fluxes. The outcome of these simulations were used to assess three alternative models for the turbulent heat fluxes which differ from the conventional Fouriers Law by not being based on the assumption of proportionality between the eddy and thermal diffusivities via a constant Prandtl number. It was found that only one of the models considered succeeds in representing the effects on the heat fluxes of the complex strain field associated with the stagnation region and the subsequent development into the wall-jet region. The reasons for this outcome are discussed.