Near-wall Reynolds Stress Model Research Articles

Secondary flow and thermal field dynamics in a T-junction with an upstream elbow: A POD-aided, eddy-sensitized Reynolds-stress modeling study

The thermal mixing of the flow-crossing streams in a T-shaped pipe junction configuration with the main branch inflow forming an elbow is presently simulated by applying a RANS-based eddy-resolving model of turbulence. The low-temperature main stream enters the T-junction with a Reynolds number of Rem=107893 after passing through a 90o-turned elbow located upstream. The high temperature branch stream is injected perpendicularly into the main stream at a Reynolds number of Rem=5422. A significant difference between the flow velocities of the two streams leads to the formation of a characteristic mixing process resembling a reattached jet configuration. Of particular interest is the interference of the branch flow with the main flow characterized by secondary vortices – the so – called Dean vortices, that are convected from the curved main inlet generating a low-rank mixing structures in its wake. The reference LES-based (Large-Eddy Simulation) database is provided by Tunstall et al. (2016). The computational framework relying on the scale-adaptive turbulence modeling approach, introduced principally by Menter and Egorov (2010), is used to simulate the dynamics of large-scale turbulent structures with moderate spatial and temporal resolution requirements. The motion of unresolved subscale structures is described by an appropriately sensitized differential near-wall Reynolds stress model according to Jakirlić and Maduta (2015). In addition, Proper-Orthogonal Decomposition (POD) is used to analyze the prevailing flow and thermal field mechanisms. The results obtained show a reasonable level of agreement with the LES reference, both from the standpoint of first-order statistics and spectral reproduction of the dynamics of coherent structures.

Eddy-resolving Reynolds-stress modelling of thermal mixing in cross-stream type T-junction configurations

The present work is concerned with the numerical simulation study of turbulent thermal mixing involving hot main and cold branch streams at high Reynolds numbers in two T-junction configurations that differ in flow rate ratio. This results in two topologically very different flow scenarios, classified as “wall-jet” and “impinging-jet” mixing processes. The underlying reference database originates from the well-known experimental WATLON study[16], dealing with the phenomena of thermal stripping in piping systems, and provides details on the configuration geometry and the associated boundary and operating conditions. The turbulence model used, implemented in the finite-volume-based numerical code OpenFOAM® [30], is a near-wall Reynolds stress model formulation appropriately sensitized by applying the scale-adaptive modeling strategy to enable its eddy-resolving capability [14]. The flow analysis includes the first- and second-order statistics, including both the flow and thermal fields, with the model results closely following the experimental reference. This refers to the global flow topology in terms of the flow separation pattern, both in terms of its shape and size, as well as to the individual mean velocity and temperature profiles and their fluctuating components. In addition, the spectral features of the flow are studied in detail using the proper orthogonal decomposition (POD) method to identify the low-rank structures whose frequency signatures contribute most to the phenomena of thermal stripping phenomena.

Leading edge vortex formation and detachment on a flat plate undergoing simultaneous pitching and plunging motion: Experimental and computational study

This study focuses on the formation and detachment of a leading edge vortex (LEV) appearing on an airfoil when its effective angle of attack is dynamically changed, inducing additional forces and moments on the airfoil. Experimental measurements of the time-resolved velocity field using Particle Image Velocimetry (PIV) are complemented by a computational study using an URANS (Unsteady Reynolds-Averaged Navier–Stokes) framework. In this framework a transition-sensitive Reynolds-stress model of turbulence, proposed by Maduta et al. (2018), which combines the near-wall Reynolds-Stress model by Jakirlic and Maduta (2015) and a phenomenological transition model governing the pre-turbulent kinetic energy by Walters and Cokljat (2008), is employed. Combined pitching and plunging kinematics of the investigated flat plate airfoil enable the effective inflow angle to be arbitrarily prescribed. A qualitative assessment of flow fields and a quantitative comparison of LEV characteristics in terms of its center position and circulation as well as an investigation of the mechanism causing the vortex to stop accumulating circulation revealed close agreement between the experimental and simulation results. Further considerations of the lift contribution from the pressure and suction side of the airfoil to the overall lift indicates that the qualitative lift evolution is reproduced even if the pressure side contribution is neglected. This reveals important characteristics of such airfoil dynamics, which can be exploited in future experimental studies, where direct aerodynamic force and moment measurements are greatly inhibited by dominating inertial forces.

Reynolds stress modelling of wake interference of two cylinders in tandem: Conventional vs. eddy-resolving closure

A differential, near-wall Reynolds stress model (RSM) employed in Unsteady RANS (Reynolds-Averaged Navier–Stokes) framework, coupled with the equation governing the inverse turbulent time scale relying on the so-called 'homogeneous dissipation' rate (ωh=ɛh/k), was applied to two in-line tandem-cylinder flow configurations. The configurations differ with respect to the distance between cylinders, with the consequence of a differently characterized wake structure. The reference experimental database has been provided by Jenkins et al. (2005, 2006) and Neuhart et al. (2009). Complementary to the ‘conventional’ Reynolds stress model based on the Jakirlic and Hanjalic's (2002) formulation, its version sensitized appropriately to account for the turbulent unsteadiness by a selective enhancement of its production in line with the SAS (Scale-adaptive Simulation) proposal (Menter and Egorov, 2010), formulated recently by Jakirlic and Maduta (2015), was also applied. This eddy-resolving RSM formulation has been shown to be capable of returning all important mean flow and turbulence features of the configurations considered, including also the intermittent shedding behaviour of the flow in the gap between cylinders related to the long-distance case. The model's inherent capability of capturing the turbulence unsteadiness resulted consequently in the correctly predicted mean flow and turbulence fields, unlike the conventional URANS RSM model which could reasonably well return only the mean surface pressure distribution.

Extending the bounds of ‘steady’ RANS closures: Toward an instability-sensitive Reynolds stress model

The incapability of the conventional Unsteady RANS (Reynolds–Averaged Navier Stokes) models to adequately capture turbulence unsteadiness presents the prime motivation of the present work, which focuses on formulating an instability-sensitive, eddy-resolving turbulence model on the Second-Moment Closure level. The model scheme adopted, functioning as a ‘sub-scale’ model in the Unsteady RANS framework, represents a differential near-wall Reynolds stress model formulated in conjunction with the scale-supplying equation governing the homogeneous part of the inverse turbulent time scale ωh (ωh=ɛh/k). The latter equation was straightforwardly obtained from the model equation describing the dynamics of the homogeneous part of the total viscous dissipation rate ɛ, defined as ɛh=ɛ−0.5ν∂2k/(∂xj∂xj) (Jakirlic and Hanjalic, 2002), by applying the derivation rules to the expression for ωh. The model capability to account for vortex length and time scales variability was enabled through an additional term in the corresponding length-scale determining equation, providing a selective enhancement of its production, pertinent particularly to the highly unsteady separated shear layer region, modeled in terms of the von Karman length scale (comprising the second derivative of the velocity field) in line with the SAS (Scale-Adaptive Simulation) proposal (Menter and Egorov, 2010). The present model formulation, termed as SRANS model (Sensitized RANS), does not comprise any parameter depending explicitly on grid spacing. The predictive capabilities of the newly proposed length-scale determining model equation, solved in conjunction with Jakirlic and Hanjalic’s (2002) Reynolds stress model equation, are presently demonstrated by computing the flow configurations of increasing complexity featured by boundary layer separation from sharp-edged and continuous curved surfaces: backward-facing step flow, flow over a wall-mounted fence, flow over smoothly contoured periodically arranged hills and flow in a 3-D diffuser. The model performances are also assessed in capturing the natural decay of the homogeneous isotropic turbulence and the near-wall Reynolds stress anisotropy in a plane channel. In most cases considered the fluctuating velocity field was obtained starting from steady RANS results.

Linear-Stability-Based Transition Modeling for Aerodynamic Flow Simulations with a Near-Wall Reynolds-Stress Model

An extended e^N-based modeling approach for Tollmien–Schlichting-type transition in aerodynamic flow simulations with the low-Re epsilon^h-Reynolds-stress model is presented. Instead of simply activating the turbulence production terms at the transition location (point-transition approach), the method incorporates the otherwise neglected Reynolds-stress contributions by the fluctuations of the Tollmien–Schlichting waves and provides them as local input for the turbulence model at the transition point. The shapes of the Reynolds-stress profiles are derived from linear stability analysis within the e^N method, whereas their absolute magnitudes are calibrated with the aid of direct numerical simulation data of a transitional boundary layer with adverse-pressure gradient. The dissipationrate input is adjusted to theoretically match the amplification rate of the fluctuations but requires a correction to account for the low-Re damping in the epsilon^h-Reynolds-stress model. The paper describes the general modeling ideas and the implementation in the flow solver. Aspects of the numerical discretization and a verification for threedimensional flows are addressed as well. Besides a basic validation for the adverse-pressure-gradient boundary layer, simulations of the SD7003 airfoil flow comprising a laminar separation bubble are presented, which yield very good agreement with measurements. Results of a transitional flat-plate flow are, however, impaired by the lack of intermittency modeling. Finally, the method is applied to a flowthrough nacelle near stall conditions in order to prove its ability to compute consistent transitional behavior in complex three-dimensional flows.

Improved Prediction of Turbomachinery Flows Using Near-Wall Reynolds-Stress Model

In this paper an assessment of the improvement in the prediction of complex turbomachinery flows using a new near-wall Reynolds-stress model is attempted. The turbulence closure used is a near-wall low-turbulence-Reynolds-number Reynolds-stress model, that is independent of the distance-from-the-wall and of the normal-to-the-wall direction. The model takes into account the Coriolis redistribution effect on the Reynolds-stresses. The five mean flow equations and the seven turbulence model equations are solved using an implicit coupled OΔx3 upwind-biased solver. Results are compared with experimental data for three turbomachinery configurations: the NTUA high subsonic annular cascade, the NASA_37 rotor, and the RWTH 1 1/2 stage turbine. A detailed analysis of the flowfield is given. It is seen that the new model that takes into account the Reynolds-stress anisotropy substantially improves the agreement with experimental data, particularily for flows with large separation, while being only 30 percent more expensive than the k−ε model (thanks to an efficient implicit implementation). It is believed that further work on advanced turbulence models will substantially enhance the predictive capability of complex turbulent flows in turbomachinery.

A near-wall reynolds stress model for backward-facing step flows

A near-wall Reynolds stress model has been used in numerical computations for two-dimensional, incompressible turbulent flows over backward-facing steps. Numerical results are compared with Direct Numerical Simulation data as well as experimental data for flow quantities such as the skin friction, wall pressure,U-velocity and the Reynolds stress. Budgets of the transport equations for theU-velocity, turbulence kinetic energy,k and the Reynolds shear stress,— $$\overline {uv} $$ are also calculated and compared with the Direct Numerical Simulation data. The comparison reveals that the near-wall Reynolds stress model predicts the reattachment length fairly accurately. The near-wall Reynolds stress model also predicts the development of the boundary layer downstream of the reattachment point correctly when the Reynolds number is low. However, the model generally predicts a weak separation bubble and a slowly developing boundary layer when the Reynolds number is high.

Near-wall two-equation and Reynolds-stress modeling of backstep flow

Most near-wall two-equation turbulence models fail to predict the wall shear stress along the step wall of a plane backstep flow and the error could become very large downstream of the reattachment point. This failure was usually attributed to the use of an eddy viscosity damping function that depends on the wall friction velocity and the fact that the near-wall correction depends on the wall normal coordinate. The present paper examines the underlying reasons for this failure and suggests that the major cause is the lack of asymptotic consistency in the near-wall region. Several asymptotically consistent models are analysed and their predictions are compared with direct numerical simulations (DNS), with conventional model results and with Reynolds-stress model calculations. Three Reynolds-stress models are compared; two of which do not depend on wall normals. It is shown that asymptotically consistent models with or without dependence on wall normal coordinate and with a damping function not dependent on friction velocity give fairly accurate predictions of the plane backstep flow considered. Furthermore, these calculations are in good agreement with that given by a near-wall Reynolds-stress model with no damping functions. In many respects, the predictions agree better with DNS data than those given by the Reynolds-stress models. The presence of wall normals does not significantly affect the performance of the Reynolds-stress model for this particular flow.

Turbulence-driven secondary flows in a curved pipe

If the torque exerted on a fluid element and the source of streamwise vorticity generation are analyzed, a turbulence-driven secondary flow is found to be possible in a curved pipe. Based on this analysis, it is found that the secondary flow is primarily induced by high anisotropy of the cross-stream turbulent normal stresses near the outer bend (furthest from the center of curvature of the bend). This secondary flow appears as a counterrotating vortex pair embedded in a Dean-type secondary motion. Recent hot-wire measurements provide some evidence for the existence of this vortex pair. To verify the formation and extent of this turbulence-driven vortex pair further, a near-wall Reynolds-stress model is used to carry out a detailed numerical investigation of a curved-pipe flow. The computation is performed specifically for a U-bend with a full developed turbulent flow at the bend entrance and a long straight pipe attached to the exit. Numerical results reveal that there are three vortex pairs in a curved pipe. The primary one is the Dean-type vortex pair. Another pair exists near the pipe core and is a consequence of local pressure imbalance. A third pair is found near the outer bend and is the turbulence-driven secondary flow. It starts to appear around 60° from the bend entrance, grows to a maximum strength at the bend exit, and disappears altogether at about seven pipe diameters downstream of the bend. On the other hand, calculations of developing laminar curved-pipe flows covering a range of pipe-to-bend curvature ratios, Reynolds number, and different inlet conditions fail to give rise to a third cell near the outer bend. Therefore, experimental and numerical evidence together lend support to the formation of a pair of turbulence-driven secondary cells in curved-pipe flows.