A FEniCS-based programming framework for modeling turbulent flow by the Reynolds-averaged Navier-Stokes equations

Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier-Stokes models, discretized by finite element methods. The novel implementation makes use of Python and the FEniCS package, the combination of which leads to compact and reusable code, where model- and solver-specific code resemble closely the mathematical formulation of equations and algorithms. The presented ideas and programming techniques are also applicable to other fields that involve systems of nonlinear partial differential equations. We demonstrate the framework in two applications and investigate the impact of various linearizations on the convergence properties of nonlinear solvers for a Reynolds-averaged Navier-Stokes model. © 2011 Elsevier Ltd.

RANS-URANS in axial compressor, a design methodology

Turbomachinery flows are inherently unsteady. Until now during the design process, unsteadiness has been neglected, with resort merely to steady numerical simulations. Despite the assumption involved, the results obtained with steady simulations have been used with success. One of the questions arising in recent years is can unsteady simulations be used to improve the design of turbomachines? In this work the numerical simulation of a multi-stage axial compressor is carried out. Comparison of Reynolds averaged Navier-Stokes (RANS) and unsteady Reynolds averaged Navier-Stokes (URANS) calculation shows that the unsteadiness affects pressure losses and the prediction of stall limit. The unsteady inflow due to the wake passing mainly modifies the losses and whirl angle near the endwalls. The computational cost of the fully unsteady compared with a steady simulation is about four times in terms of mesh dimension and two orders of magnitude as number of iterations. A mixed RANS-URANS solution has been proposed to give the designer the possibility to simulate an unsteady stage embedded in a steady-state simulation. This method has been applied to the simulation of a four-stage axial compressor rig. The mixed RANS-URANS approach has been developed using sliding and mixing planes as interface conditions. The rotor-stator interaction has been captured physically while reducing the computational time and mesh size.

Normal shock boundary layer control with various vortex generator geometries

Various vortex generators which include ramp, split-ramp and a new hybrid concept "ramped-vane" are investigated under normal shock conditions with a diffuser at Mach number of 1.3. The dimensions of the computational domain were designed using Reynolds Average Navier-Stokes studies to be representative of the flow in an external-compression supersonic inlet. Using this flow geometry, various vortex generator concepts were studied with Implicit Large Eddy Simulation. In general, the ramped-vane provided increased vorticity compared to the other devices and reduced the separation length downstream of the device centerline. In addition, the size, edge gap and streamwise position respect to the shock were studied for the ramped-vane and it was found that a height of about half the boundary thickness and a large trailing edge gap yielded a fully attached flow downstream of the device. This ramped-vane also provided the largest reduction in the turbulent kinetic energy and pressure fluctuations. Additional benefits include negligible drag while the reductions in boundary layer displacement thickness and shape factor were seen compared to other devices. © 2010 by Sang Lee.

Normal shock boundary layer control with various vortex generator geometries

Various vortex generators which include ramp, split-ramp and a new hybrid concept "ramped-vane" are investigated under normal shock conditions with a diffuser at Mach number of 1.3. The dimensions of the computational domain were designed using Reynolds Average Navier-Stokes studies to be representative of the flow in an external-compression supersonic inlet. Using this flow geometry, various vortex generator concepts were studied with Implicit Large Eddy Simulation. In general, the ramped-vane provided increased vorticity compared to the other devices and reduced the separation length downstream of the device centerline. In addition, the size, edge gap and streamwise position respect to the shock were studied for the ramped-vane and it was found that a height of about half the boundary thickness and a large trailing edge gap yielded a fully attached flow downstream of the device. This ramped-vane also provided the largest reduction in the turbulent kinetic energy and pressure fluctuations. Additional benefits include negligible drag while the reductions in boundary layer displacement thickness and shape factor were seen compared to other devices. © 2011 Elsevier Ltd.

Effects of Lewis number on scalar variance transport in premixed flames

The influences of differential diffusion rates of heat and mass on the transport of the variances of Favre fluctuations of reaction progress variable and non-dimensional temperature have been studied using three-dimensional simplified chemistry based Direct Numerical Simulation (DNS) data of statistically planar turbulent premixed flames with global Lewis number ranging from Le = 0.34 to 1.2. The Lewis number effects on the statistical behaviours of the various terms of the transport equations of variances of Favre fluctuations of reaction progress variable and non-dimensional temperature have been analysed in the context of Reynolds Averaged Navier Stokes (RANS) simulations. It has been found that the turbulent fluxes of the progress variable and temperature variances exhibit counter-gradient transport for the flames with Lewis number significantly smaller than unity whereas the extent of this counter-gradient transport is found to decrease with increasing Lewis number. The Lewis number is also shown to have significant influences on the magnitudes of the chemical reaction and scalar dissipation rate contributions to the scalar variance transport. The modelling of the unclosed terms in the scalar variance equations for the non-unity Lewis number flames have been discussed in detail. The performances of the existing models for the unclosed terms are assessed based on a-priori analysis of DNS data. Based on the present analysis, new models for the unclosed terms of the active scalar variance transport equations are proposed, whenever necessary, which are shown to satisfactorily capture the behaviours of unclosed terms for all the flames considered in this study. © 2010 Springer Science+Business Media B.V.

Assessment of computational fluid dynamics and experimental data for shock boundary-layer interactions

A workshop on the computational fluid dynamics (CFD) prediction of shock boundary-layer interactions (SBLIs) was held at the 48th AIAA Aerospace Sciences Meeting. As part of the workshop, numerous CFD analysts submitted solutions to four experimentally measured SBLIs. This paper describes the assessment of the CFD predictions. The assessment includes an uncertainty analysis of the experimental data, the definition of an error metric, and the application of that metric to the CFD solutions. The CFD solutions provided very similar levels of error and, in general, it was difficult to discern clear trends in the data. For the Reynolds-averaged Navier-Stokes (RANS) methods, the choice of turbulence model appeared to be the largest factor in solution accuracy. Scale-resolving methods, such as large-eddy simulation (LES), hybrid RANS/LES, and direct numerical simulation, produced error levels similar to RANS methods but provided superior predictions of normal stresses. Copyright © 2012 by Daniella E. Raveh and Michael Iovnovich.

A presumed joint pdf model for turbulent combustion with varying equivalence ratio

Modeling of the joint probability density function of the mixture fraction and progress variable with a given covariance value is studied. This modeling is validated using experimental and direct numerical simulation (DNS) data. A very good agreement with experimental data of turbulent stratified flames and DNS data of a lifted hydrogen jet flame is obtained. The effect of using this joint pdf modeling to calculate the mean reaction rate with a flamelet closure in Reynolds averaged Navier-Stokes (RANS) calculation of stratified flames is studied. The covariance effect is observed to be large within the flame brush. The results obtained from RANS calculations using this modeling for stratified jet- and rod-stabilized V-flames are discussed and compared to the measurements as a posteriori validation for the joint probability density function model with the flamelet closure. The agreement between the computed and measured values of flame and turbulence quantities is found to be good. © 2012 Copyright Taylor and Francis Group, LLC.

LES of heat transfer in electronics

Numerical methods based on the Reynolds Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES) equations are applied to the thermal prediction of flows representative of those found in and around electronics systems and components. Low Reynolds number flows through a heated ribbed channel, around a heated cube and within a complex electronics system case are investigated using linear and nonlinear LES models, hybrid RANS-LES and RANS-Numerical-LES (RANS-NLES) methods. Flow and heat transfer predictions using these techniques are in good agreement with each other and experimental data for a range of grid resolutions. Using second order central differences, the RANS-NLES method performs well for all simulations. © 2011 Elsevier Inc.

Strategies for modeling turbulent flows in electronics

Hybrid methods based on the Reynolds Averaged Navier Stokes (RANS) equations and the Large Eddy Simulation (LES) formulation are investigated to try and improve the accuracy of heat transfer and surface temperature predictions for electronics systems and components. Two relatively low Reynolds number flows are studied using hybrid RANS-LES, RANS-Implicit-LES (RANS-ILES) and non-linear LES models. Predictions using these methods are in good agreement with each other, even using different grid resolutions. © 2008 IEEE.

A single-Stream jet noise prediction model for a family of chevron nozzles

This study develops a single-stream jet noise prediction model for a family of chevron nozzles. An original equation is proposed for the fourth-order space-time cross-correlations. They are expressed in flow parameters such as streamwise circulation and turbulent kinetic energy. The cross-correlations based on a Reynolds Averaged Navier-Stokes (RANS) flowfield showed a good agreement with those based on a Large Eddy Simulation (LES) flowfield. This proves that the proposed equation describes the cross-correlations accurately. With this novel source description, there is an excellent agreement between our model's far-field noise predictions and measurements1 for a wide range of frequencies and radiation angles. Our model captures the spectral shape, amplitude and peak frequency very well. This establishes that our model holds good for a family of chevron nozzles. As our model provides quick and accurate predictions, a parametric study was performed to understand the effects of a chevron nozzle geometry on jet noise and thrust loss. Chevron penetration is the underpinning factor for jet noise reduction. The reduction of jet noise per unit thrust loss decreases linearly with chevron penetration. The number of chevrons also has a considerable effect on jet noise.

Hybrid LES - RANS of complex geometry jets

Large eddy simulation (LES) type studies are made of a realistic geometry coaxial nozzle with a pylon. For the LES, since the solver being used tends towards having dissipative qualities, the subgrid scale (SGS) model is omitted, giving Numerical LES (NLES). To overcome near wall streak resolution problems a near wall RANS (Reynolds averaged Navier Stokes) model is used giving a hybrid NLES-RANS approach.The pylon is shown to influence the flow development, having a significant impact on peak turbulence levels and spreading rates. The results show that real geometry effects are influential and should be taken into account when moving towards real engine simulations. If their effects are ignored then, based on the studies here, key turbulence parameters will have significant error.

Zonal RANS-LES modeling for turbines in aeroengines

The cost of large-eddy simulation (LES) modeling in various zones of gas turbine aeroengines is outlined. This high cost clearly demonstrates the need to perform hybrid Reynolds-averaged Navier-Stokes-LES (RANS-LES) over the majority of engine zones because the Reynolds number is too high for pure LES. The RANS layer is used to cover over the fine streaks found in the inner part of the boundary layer. The hybrid strategy is applied to various engine zones, which is shown to typically give much greater predictive accuracy than pure RANS simulations. However, the cost estimates show that the RANS layer should be disposed within the low-pressure turbine zone. Also, the nature of the flow physics in this zone makes LES most sensible. © 2012 by Begell House, Inc.