A Quasi-Realizable Cubic Low-Reynolds Eddy-Viscosity Turbulence Model with a New Dissipation Rate Equation

A non-linear relationship of the Reynolds stresses in function of the strain rate and vorticity tensors, with terms up to third order, is developed. Anisotropies in the normal stresses, influence from streamline curvature or rotation of the reference frame, and swirl effects are accounted for. The relationship is linked to ak–ε model with a modified transport equation for the dissipation rate. A new low-Reynolds source term is introduced and a model parameter is written in terms of dimensionless rate-of-strain and vorticity. The model is checked on different realizability constraints. It is shown that practically all constraints are fulfilled. The model is numerically tested on a fully developed channel and pipe flow, both stationary and rotating. The plane jet–round jet anomaly is addressed. Finally, the model is applied to the flow over a backward-facing step. Results are compared with a linear low-Reynolds k–ε model and the shear stress transport model. This revised version was published online in July 2006 with corrections to the Cover Date.     

Assessment of Turbulence Models for Predicting the Interaction Region in a Wall Jet by Reference to LES Solution and Budgets

Highly-resolved LES and experimental data for a plane wall jet are used to study the characteristics of turbulence-closure proposals, mainly within the framework of second-moment-transport modelling. The study is motivated by the observed importance of diffusive Reynolds-stress transport in the interaction region between the outer shear layer and the near-wall layer of the wall jet, which gives the near-wall flow characteristics that are very different from those of a conventional boundary layer. Comparisons are presented for mean-flow quantities, second moments and budgets. Also included are a priori studies of approximations for the pressure-velocity interaction, pressure-fluctuation-driven transport and turbulent transport of the Reynolds stresses by triple correlations, the last observed to contribute significantly to the stress budgets. The study reveals major defects in the closure approximations for the pressure-velocity interaction terms, especially in the near-wall region. These defects result in a poor representation by the particular second-moment closures investigated of even the integral and mean-flow characteristics of the wall jet.     

Fractal-Generated Turbulence in Opposed Jet Flows

The opposed jet configuration presents a canonical geometry suitable for the evaluation of calculation methods seeking to reproduce the impact of strain and re-distribution on turbulent transport in reacting and non-reacting flows. The geometry has the advantage of good optical access and, in principle, an absence of complex boundary conditions. Disadvantages include low frequency flow motion at high nozzle separations and comparatively low turbulence levels causing bulk strain to exceed the turbulent contribution at small nozzle separations. In the current work, fractal generated turbulence has been used to increase the turbulent strain and velocity measurements for isothermal flows are reported with an emphasis on the axis, stagnation plane and the distribution of mean and instantaneous strain rates. Energy spectra were also determined. The instrumentation comprised hot-wire anemometry and particle image velocimetry with the flows to both nozzles seeded with 1  $\upmu$ m silicon oil droplets providing a relaxation time of ? 3 $\upmu$ s. It is shown that fractal grids increase the turbulent Reynolds number range from 48–125 to 109–220 for bulk velocities from 4 to 8 m/s as compared to conventional perforated plate turbulence generators. Low frequency motion of the order 10 Hz could not be completely eliminated and probability density functions were determined for the location of the stagnation plane. Results show that the fluctuation in the position of the stagnation plane is of the order of the integral length scale, which was determined to be 3.1±0.1 mm at the nozzle exits through the use of hot-wire anemometry. Flow statistics close to the fractal plate located upstream of the nozzle exit were also determined using a transparent glass nozzle.     

Jet Outflow from a Small Hole in a Plane

On the basis of the method of matched asymptotic expansions, the problem of the outflow of a nonswirling axisymmetric laminar jet from a hole in a plane is solved for large Reynolds numbers. Since directly matching the leading terms of the asymptotic expansions for the axial boundary layer and the main flow region is impossible, the problem is solved by introducing an intermediate region. In the axial region the solution is the Schlichting solution [1] for an axisymmetric jet in the boundary-layer approximation, in the intermediate region the solution is found analytically, and in the main flow region the problem is reduced to that of viscous flow induced by a sink line in the presence of a transverse wall [2].     

Mean Flow and Turbulence Measurements in a Turbulent Free Cruciform Jet

The results of measurements of all three components of the mean velocity vector, the Reynolds normal and primary shear stresses and the mean static pressure in a turbulent free jet, issuing from a sharp-edged cruciform orifice, are presented in this paper. The measurements were made with an x-array hot-wire probe and a pitot-static tube in the near flow field of the jet. The Reynolds number, based upon the equivalent diameter of the orifice, was 1.70 × 10⁵. In addition to the quantities measured directly, the mean streamwise centreline velocity decay, the jet half-velocity widths, the jet spreading rate, the mean streamwise vorticity, the mass entrainment rate, the integral momentum flux and the one-dimensional energy spectra have been derived from the measured data. The results show that the mean streamwise centreline velocity decay rate of the cruciform jet is higher than that of a round jet issuing from an orifice with the same exit area as that of the cruciform orifice. The mean streamwise velocity field changed shape continuously from a cruciform close to the orifice exit plane to circular at 12 and half equivalent diameters downstream. The mean streamwise vorticity field, up to about three equivalent diameters downstream of the orifice exit plane, consists of four pairs of counter-rotating cells, which are aligned with the four edges in the centre of the cruciform orifice.     

Application of a Synthetic Jet to Control Boundary Layer Separation under Ultra-High-Lift Turbine Pressure Distribution

The transition and separation processes of the boundary layer developing on a flat plate under a prescribed adverse pressure gradient typical of Ultra-High-Lift low-pressure turbine profiles have been investigated, with and without the application of a synthetic jet (zero net mass flow rate jet). A mechanical piston has been adopted to produce an intermittent flow with zero net mass flow rate. The capability of the device to suppress or reduce the large laminar separation bubble occurring under steady inflow condition at low Reynolds numbers has been experimentally investigated by means of hot-wire measurements. Wall static pressure measurements complement the hot-wire time-resolved velocity results. The paper reports the investigations performed for both steady and controlled conditions. The active device is able to control the laminar separation bubble induced at low Reynolds number conditions by the strong adverse pressure gradient. An overall view of the time-dependent evolution of the controlled boundary layer is provided by the phase-locked ensemble averaging technique, triggered at the synthetic jet frequency. The separated flow transition process, which is detected for the uncontrolled condition, is modified by the synthetic jet in different ways during the blowing and suction phases. Overall, the phase-locked velocity distributions show a reduced separated flow region for the whole jet cycle as compared to the uncontrolled condition. The phase-locked distributions of the random unsteadiness allow the identification of vortical structures growing along the shear layer mainly during the blowing phase.     

Wall-Distance-Free Turbulence Models Applied to Incompressible Flows

Abstract

A comparative study of low-Re wall-distance-free (WDF) turbulence models in incompressible flows is presented. The study includes the WDF k-? and the three-equation WDF k-?-γ as well as two k-? models which invoke the distance from the wall. The models are implemented in conjunction with a characteristics-based method and an implicit unfactored scheme. Comparison with direct-numerical-simulation data reveals that the WDF models provide much more accurate results for the dissipation rate, especially in the near wall region. A grid refinement study further reveals that the models which explicitly involve the distance from the wall cannot capture the correct turbulence dissipation rate behaviour in the near-wall region even on the finest grid, where grid-independent solution is achieved. However, the low-Re WDF models require slightly more iterations than the other k - ? models to converge. Results are presented for channel, flat plate and backward-facing step flows.     

Turbulence Resolution Scale Dependence in Large-Eddy Simulations of a Jet Flame

The explicit dependence of LES fields on the turbulence resolution scale Δ implies that LES statistics usually vary with Δ and exhibit different convergence behaviors for different types of statistics, flow variables and subgrid LES models. The present work compares the performance of two popular subgrid models—the dynamic Smagorinsky model and the Vreman model—based on the convergence of their LES statistics with respect to Δ for a piloted methane-air (Sandia D) flame. The Δ-dependence of the LES statistics is studied based on five grids with progressively increased resolution ranging from 3 × 10⁵ to about 10.4 × 10⁶ cells. The simulation results show that the resolved velocity statistics converge for the finest grids with some weak Δ-dependence observed in the variance fields. The mixture fraction statistics are found to be more sensitive to the turbulence resolution scale upstream in the flame signifying the importance of the estimation of the Δ-invariant LES statistics at the DNS limit. For the considered flame the Vreman subgrid model exhibits good performance with the statistics being very close to those given by the dynamic Smagorinsky model, and being rather insensitive to a choice of the model constant.     

Symmetry Breaking and Turbulence in Perturbed Plane Couette Flow

Perturbed plane Couette flow containing a thin spanwise-oriented ribbon undergoes a subcritical bifurcation at Re≈230 to a steady three-dimensional state containing streamwise vortices. This bifurcation is followed by several others giving rise to a fascinating series of stable and unstable steady states of different symmetries and wavelengths. First, the backwards-bifurcating branch reverses direction and becomes stable near Re≈200. Then the spanwise reflection symmetry is broken, leading to two asymmetric branches which are themselves destabilized at Re≈420. Above this Reynolds number, time evolution leads first to a metastable state whose spanwise wavelength is halved and then to complicated time-dependent behavior. These features are in agreement with experiments. Received 15 December 2001 and accepted 29 March 2002 Published online: 2 October 2002 Communicated by H.J.S. Fernando     

Compressibility Effectsy in One-Equation Turbulence Models

Fluid Dynamics - The one-equation turbulence models by Spalart and Allmaras (SA) and Sekundov et al. (Nut-92) are tested against two compressible two-dimensional flows, namely, the turbulent...     

Flow Separation and Turbulence in Jet Pumps for Thermoacoustic Applications

The effect of flow separation and turbulence on the performance of a jet pump in oscillatory flows is investigated. A jet pump is a static device whose shape induces asymmetric hydrodynamic end effects when placed in an oscillatory flow. This will result in a time-averaged pressure drop which can be used to suppress acoustic streaming in closed-loop thermoacoustic devices. An experimental setup is used to measure the time-averaged pressure drop as well as the acoustic power dissipation across two different jet pump geometries in a pure oscillatory flow. The results are compared against published numerical results where flow separation was found to have a negative effect on the jet pump performance in a laminar flow. Using hot-wire anemometry the onset of flow separation is determined experimentally and the applicability of a critical Reynolds number for oscillatory pipe flows is confirmed for jet pump applications. It is found that turbulence can lead to a reduction of flow separation and hence, to an improvement in jet pump performance compared to laminar oscillatory flows.     

Improved Unsteady RANS Models Applied to Jet Transverse to a Pipe Flow

An unsteady RANS model is developed in order to simulate the complex situations involving both free and bounded flows. This model tuned to catch coherent flow structures is developed both in the k-ε and k-l approaches. The full 3D geometry of a round jet exiting from a reservoir into a pipe has been computed. Periodic conditions are applied in order to compare with an experiments consisting of eight jets exiting in a cross pipe flow. Improvement has been obtained with this URANS turbulence model compared to RANS and good agreement compared with experiment has been obtained. Unsteady phenomena are reproduced by the model and provide more insight into the physical properties of the flow and of the transport of a passive scalar.     

Predicting Noninertial Effects with Linear and Nonlinear Eddy-Viscosity, and Algebraic Stress Models

Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coroiolis-modified eddy-viscosity model, a realizable nonlinear eddy-viscosity model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the validation of the turbulence models. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.     

Effect of Strong External Turbulence on a Wall Jet Boundary Layer

The initial stage of the development of a wall jet under the influence of strong external turbulence has been studied in a novel shear-flow mixing-box experiment. A fully developed channel flow of depth h (40 mm) enters along the top wall of a cuboidal box of height 11 h in which a combination of oscillatory and turbulent velocity fluctuations are generated by a vertical oscillating grid at the midplane 5 h below the wall. When the ratio of the rms grid-generated velocity fluctuations, , to the local mean velocity inside the wall jet layer, u, is greater than about 0.1, significant changes are observed in the mean shear profile and in the eddy structure of the wall jet. The wall jet thickness increases by approximately 25% but the maximum velocity decreases by less than 10% compared to the case without the external turbulence. Fluctuations of the streamwise velocity component increase as expected in the outer part of the wall jet, but the most significant result is the increase by 70% of the fluctuations in the boundary layer close to the wall. CFD simulations using the k-ɛ RNG of the FLUENT CFD Code do not properly model the effect of the large scale external turbulence in this experiment. However, an artificial method, which introduces a series of small inlet/outlet jets to represent external turbulence, approximately simulates the overall effects of the oscillating grid on the wall jet, but does not simulate the amplification of the near wall turbulence. F. T. M. Nieuwstadt: Rest in peace (1946–2005).     

The Interaction between a Compressible Synthetic Jet and a Laminar Hypersonic Boundary Layer

Numerical simulations have been performed of a synthetic jet interacting with a laminar hypersonic boundary layer. Two datum cases were also considered, no jet and steady jet. The simulations for the case of no jet are in agreement with available experimental data. Predicted flow features of the steady jet interaction are broadly consistent with previous studies. For the synthetic jet, the upstream and downstream separated regions are dramatically reduced in size, and the jet appears to lie closer to the surface, compared with the steady jet. It is also found that the synthetic jet induces a greater mixing rate than the steady jet. This revised version was published online in July 2006 with corrections to the Cover Date.     

Turbulence Models and Large Eddy Simulations Applied to Ascending Mixed Convection Flows

Coolant flows in the cores of current gas-cooled nuclear reactors consist of ascending vertical flows in a large number of parallel passages. Under post-trip conditions such heated turbulent flows may be significantly modified from the forced convection condition by the action of buoyancy, and the thermal-hydraulic regime is no longer one of pure forced convection. These modifications are associated primarily with changes to the turbulence structure. Flow laminarization may occur, and in that event heat transfer rates may be as low as 40% of those in the corresponding forced convection case. The present work is concerned with the modelling of such ??mixed?? convection flows in a vertical heated pipe. All fluid properties are assumed to be constant and buoyancy is accounted for within the Boussinesq approximation. Six different Eddy Viscosity Models (EVMs) are examined against experimental measurements and the direct numerical simulation (DNS) data of You et?al. (Int J Heat Mass Transfer 46:1613?C1627, 2003). The EVMs selected for study embody distinct physical refinements with respect to the parent high-Reynolds-number k-?? model. Large Eddy Simulations employing the classical Smagorinsky sub-grid-scale model are also presented. It is found that the early EVM scheme of Launder and Sharma (1974) is the turbulence model in the closest agreement with direct simulation results for the ratio of mixed-to-forced convection Nusselt number, Nu/Nu ₀; the model in the poorest accord with the DNS data is a k-??-SST formulation. However, in relation to comparisons with both numerical and experimental data for forced convection Nusselt number, Nu ₀, the present work reveals that some of the more recent models perform better than the Launder-Sharma scheme. No single scheme is in consistently close agreement with the numerical simulation flow profiles.     

Investigation of Advanced Turbulence Models for the Flow in a Generic Wing-Body Junction

The predictive performance of several turbulence models, among them formulations based on non-linear stress-strain relationships and on stress-transport equations, is examined in a collaborative university-industry study directed towards a generic wing-body junction. The geometry consists of a variation of the symmetric NACA 0020 aerofoil mounted on a flat plate, with the oncoming stream aligned with the aerofoil's symmetry plane. The dominant feature of this flow is a pronounced horseshoe vortex evolving in the junction region following separation ahead of the aerofoil's leading edge. This case is one of 6 forming a broad programme of turbulence-model validation by UMIST, Loughborough University, BAE Systems, Aircraft Research Association, Rolls-Royce plc and DERA. Key aspects of this collaboration were a high level of interaction between the partners, the use of common grids and boundary conditions, and numerical verifications aimed at maximizing confidence in the validity of the computational solutions. In total, 12 turbulence models were studied by four partners. Model performance is judged by comparing solutions with experimental data for pressure fields on the plane wall and around the aerofoil; for velocity, turbulence energy, shear stress and streamwise normal stress in the upstream symmetry plane; and for velocity, turbulence energy and shear stress in cross-flow planes downstream of the aerofoil leading edge. The emphasis of the study is on the structure of the horseshoe vortex and its effects on the forward flow. The main finding of the study is that, for this particular 3D flow, second-moment closure offers predictive advantages over the other models examined, especially in terms of the far-field structure of the horse-shoe vortex, although no model achieves close agreement with the experimental data in respect of both mean flow and turbulence quantities. This revised version was published online in July 2006 with corrections to the Cover Date.