Assessment of turbulence model performance: Large streamline curvature and integral length scales

For the flow over curved surfaces, an extra wall-normal pressure gradient is imposed to the flow through excessive surface pressure, such that the flow turns in alignment with the surface. In turn, turbulent fluctuations are suppressed over the convex surface; whereas, they are enhanced over the concave. Recently, the direct numerical simulation (DNS) of turbulent channel flow experiencing a 60 degree circular bend shows highly complex flow phenomena. Particularly, the mean flow properties are directly related to the channel geometry; in the impulse response of the mean flow to the step change of streamline curvature, sudden changes in mean strain rate and extra rates of strain emerge. This mean flow process is prior to the response of the turbulence structures. Due to the large streamline curvature, the underlying turbulence lagging mechanism and the stress strain misalignment are difficult to model. For this, the new DNS data for the wall bounded flow with high streamline curvature and large integral length scales is used to explore RANS performance. For eddy-viscosity models, this leads to the Boussinesq approximation being questionable. Also, for a Reynolds-stress model (RSM) with closure approximations applicable to homogeneous turbulent flows that are nearly in equilibrium, the current case can result in substantial predictive error. This is because of, for example, the linear approximation for the rapid pressure-strain correlation. To help move towards better turbulence modelling, Reynolds-averaged Navier-Stokes (RANS) predictions are compared for the same flow configuration as the DNS, using some popular turbulent models. These models include the second-order closure with the stress-ω formulation, the standard k−ω and the Menter’s shear-stress transport (SST) models, the standard Spalart-Allmaras (S-A) model with and without the corresponding strainvorticity correction. As expected, overall, the RSM provides closer predictions to the DNS data than the selected eddy-viscosity models, even though the predictive accuracy needs to be further improved. Potentially, a non-linear constitutive relation or second-order closure, incorporating a relaxation approximation for the lagging mechanism, may lead to a remedy for the current non-equilibrium flow. Moreover, all models would also benefit from sensitisation to the impact of the large integral length scales.At the end of the first of the two consecutive papers, the authors would like to acknowledge the EPSRC and Rolls Royce for their financial support, as well as the U.K. Turbulence Consortium.This is the final version of the article. It was first available from Elsevier via http://dx.doi.org/10.1016/j.compfluid.2015.11.01

Large eddy simulation of turbine internal cooling ducts

Large-Eddy Simulation (LES) and hybrid Reynolds-averaged Navier-Stokes-LES (RANSLES) methods are applied to a turbine blade ribbed internal duct with a 180 degree bend containing 24 pairs of ribs. Flow and heat transfer predictions are compared with experimental data and found to be in agreement. The choice of LES model is found to be of minor importance as the flow is dominated by large geometric scale structures. This is in contrast to several linear and nonlinear RANS models, which display turbulence model sensitivity. For LES, the influence of inlet turbulence is also tested and has a minor impact due to the strong turbulence generated by the ribs. Large scale turbulent motions destroy any classical boundary layer reducing near wall grid requirements. The wake-type flow structure makes this and similar flows nearly Reynolds number independent, allowing a range of flows to be studied at similar cost. Hence LES is a relatively cheap method for obtaining accurate heat transfer predictions in these types of flows.This is the accepted manuscript. The final version is available at http://www.sciencedirect.com/science/article/pii/S0045793015000663

Assessment of turbulence model performance: Severe acceleration with large integral length scales

Turbulence is substantially laminarised, when the mean flow experiences streamwise acceleration above a certain critical acceleration parameter. Recently, to essentially reveal aero engine intake acceleration scenarios, Direct Numerical Simulations (DNS) have been performed for turbulent flow through a rapidly contracting channel. On average, the streamwise acceleration parameter K_s is of the magnitude of 1×10^−5. Converged statistics show that it is the streamwise acceleration that causes the first term of the production rate for u′u′ to be negative. This initiates the degeneration towards laminar flow and also closes the usual wall turbulence self-sustaining mechanism. Further downstream, the progressive turbulence recovery is largely streamwise dominant. Importantly, the laminarisation effects are lagging to the rate of contraction. To assess the corresponding turbulence model performance and for better modelling, for the same flow configurations, Reynolds-averaged Navier-Stokes (RANS) predictions are compared, using some available Reynolds-stress (RSM) and eddy-viscosity models. These are the second-order closure with the strain-ω formulation, the standard k − ω and the Menter’s shear-stress transport (SST) models, the standard Spalart-Allmaras (S-A) model, and that with the strain-vorticity correction. As will be shown, through the contraction, all the benchmarked models are able to predict the essential characteristics of the laminarisation; whereas, further downstream, the eddy-viscosity models tend to return the flow immediately back to the fully developed turbulence. In contrast, the RSM predicts the gradually recovery process, in spite of the lower growth rate, relative to that of the DNS. The S-A model has been modified for the lagging mechanism caused by severe acceleration. The corresponding modified predictions better match the mean flow characteristics. Moreover, all models would also benefit from sensitisation to the impact of the large integral length scales.This is the final version of the article. It was first available from Elsevier via http://dx.doi.org/10.1016/j.compfluid.2015.12.00

LES-RANS of installed ultra-high-bypass-ratio coaxial jet aeroacoustics with flight stream

EPSRC EP/L000261/1; EU-funded project “JERONIMO” (ACP2-GA-2012-314692-JERONIMO

Direct numerical simulation of a wall jet: flow physics

A direct numerical simulation (DNS) of a plane wall jet is performed at a Reynolds number of $Re_{j}=7500$. The streamwise length of the domain is long enough to achieve self-similarity for the mean flow and the Reynolds shear stress. This is the highest Reynolds number wall jet DNS for a large domain achieved to date. The high resolution simulation reveals the unsteady flow field in great detail and shows the transition process in the outer shear layer and inner boundary layer. Mean flow parameters of maximum velocity decay, wall shear stress, friction coefficient and jet spreading rate are consistent with several other studies reported in the literature. Mean flow, Reynolds normal and shear stress profiles are presented with various scalings, revealing the self-similar behaviour of the wall jet. The Reynolds normal stresses do not show complete similarity for the given Reynolds number and domain length. Previously published inner layer budgets based on LES are inaccurate and those that have been measured are only available in the outer layer. The current DNS provides fully balanced, explicitly calculated budgets for the turbulence kinetic energy, Reynolds normal stresses and Reynolds shear stress in both the inner and outer layers. The budgets are scaled with inner and outer variables. The inner-scaled budgets in the near wall region show great similarity with turbulent boundary layers. The only remarkable difference is for the turbulent diffusion in the wall-normal Reynolds stress and Reynolds shear stress budgets. The outer layer interacts with the inner layer through turbulent diffusion and the excess energy from the wall-normal direction is transferred to the spanwise direction.</jats:p

High-Order Flux Reconstruction on Stretched and Warped Meshes

High-order computational fluid dynamics is gathering a broadening interest as a future industrial tool, with one such approach being flux reconstruction (FR). However, due to the need to mesh complex geometries if FR is to displace current lower?order methods, FR will likely have to be applied to stretched and warped meshes. Therefore, it is proposed that the analytical and numerical behaviors of FR on deformed meshes for both the one-dimensional linear advection and the two-dimensional Euler equations are investigated. The analytical foundation of this work is based on a modified von Neumann analysis for linearly deformed grids, which is presented. The temporal stability limits for linear advection on such grids are also explored analytically and numerically, with Courant?Friedrichs?Lewy (CFL) limits set out for several Runge?Kutta schemes, with the primary trend being that contracting mesh regions give rise to higher CFL limits, whereas expansion leads to lower CFL limits. Lastly, the benchmarks of FR are compared to finite difference and finite volumes schemes, as are common in industry, with the comparison showing the increased wave propagating ability on warped and stretched meshes, and hence FR?s increased resilience to mesh deformation

Numerical investigation of secondary flows in a high-lift low pressure turbine

In turbomachines, secondary flows (or endwall flows) typically originate at the junction between endwalls and the blade surface. Within the blade passage, the strength of the secondary flows is amplified by the crossflow from the pressure to the suction surface of the blade. The enhanced mixing due to secondary flows induce additional losses into the system. This decreases the overall work output and also changes the flow incidence onto the downstream blade rows. Using a series of high-fidelity eddy resolving simulations, the current study attempts to provide an improved understanding for the complex flow physics over the endwalls of a high-lift Low Pressure Turbine (LPT) blade. The effect of three different inflow conditions has been studied. These include a laminar boundary layer (LBL), a turbulent boundary layer (TBL) and wakes with secondary flow (W&S) from an upstream blade row. For the simulations with TBL and W&S, precursor eddy resolving simulations were used to prescribe realistic inflows. The loss generation mechanisms were subsequently studied both at the endwall and the midspan, which includes evaluating the mass-averaged total pressure loss coefficient (Y$_p$) and the loss generation rate. When compared to LBL, additional disturbances from an incoming TBL and wakes with secondary flows enhanced the mixing within the blade passage resulting in a substantial increase in the total pressure loss. Prior to flow transition, incoming wakes with secondary flows increased the local loss generation rate at both the endwall and the midspan in the front portion of the blade passage ($\textit{x}$/C$_x$ 0.8), the incoming wakes effectively suppressed the separation bubble at the midspan thereby decreasing the local loss generation rate. It is also demonstrated that the wakes shed from the trailing edge at the mid-span mix out rapidly when compared to the passage vortex at the endwall.Cambridge Overseas TrustThis is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.ijheatfluidflow.2016.05.01

Towards robust unstructured turbomachinery large eddy simulation

This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.compfluid.2015.06.017Industrial legacy codes usually have had long pedigrees within companies, and are deeply embedded into design processes. As the affordability and availability of computing power has increased, these codes have found themselves pushed into service as large eddy simulation solvers. The approximate Riemann solver of Roe, which is frequently used as the core method in such legacy codes, is shown to need much user care when adopted as the discretisation scheme for large eddy simulation. A kinetic energy preserving (KEP) scheme—which retains the same advantageous stencil and communications halo as the original Roe scheme—is instead implemented and tested. The adaptations of code required to switch between the two schemes were found to be extremely straightforward. As the KEP scheme intrinsically bounds the growth of the kinetic energy, it is significantly more stable than the classical non-dissipative schemes. This means that the expensive smoothing terms of the Roe scheme are not always necessary. Instead, an explicit subgrid scale turbulence model can be sensibly applied. As such, a range of mixed linear–non-linear turbulence models are tested. The performance of the KEP scheme is then tested against that of the Roe for canonical flows and engine-realistic turbine blade cutback trailing edge cases. The new KEP scheme is found to perform better than the original in all cases. A range of mesh topologies: hexahedral; prismatic; and tetrahedral; are also tested with both schemes, and the KEP scheme is again found to perform significantly better on all mesh types for these flows.This work was supported by an iCASE studentship from the Engineering and Physical Sciences Research Council, via Rolls-Royce plc. The funding from both organisations is gratefully acknowledged

A mixed-fidelity numerical study for Fan-Distortion interaction

Inlet distortion often occurs under off-design conditions when a flow separates within an intake and this unsteady phenomenon can seriously impact fan performance. Fan–distortion interaction is a highly unsteady aerodynamic process into which high-fidelity simulations can provide detailed insights. However, due to limitations on the computational resource, the use of an eddy resolving method for a fully resolved fan calculation is currently infeasible within industry. To solve this problem, a mixed-fidelity computational fluid dynamics method is proposed. This method uses the large Eddy simulation (LES) approach to resolve the turbulence associated with separation and the immersed boundary method (IBM) with smeared geometry (IBMSG) to model the fan. The method is validated by providing comparisons against the experiment on the Darmstadt Rotor, which shows a good agreement in terms of total pressure distributions. A detailed investigation is then conducted for a subsonic rotor with an annular beam-generating inlet distortion. A number of studies are performed in order to investigate the fan's influence on the distortions. A comparison to the case without a fan shows that the fan has a significant effect in reducing distortions. Three fan locations are examined which reveal that the fan nearer to the inlet tends to have a higher pressure recovery. Three beams with different heights are also tested to generate various degrees of distortion. The results indicate that the fan can suppress the distortions and that the recovery effect is proportional to the degree of inlet distortion.</jats:p

Toward Future Installations: Mutual Interactions of Short Intakes With Modern High Bypass Fans

In this paper, we investigate the coupled interaction between a new short intake design with a modern fan in a high-bypass ratio civil engine, specifically under the off-design condition of high incidence. The interaction is expected to be much more significant than that on a conventional intake. The performance of both the intake-alone and rotor-alone configurations are examined under isolation. Subsequently, a comprehensive understanding on the two-way interaction between intake and fan is presented. This includes the effect of fan on intake angles of attack (AoA) tolerance (FoI) and the effect of circumferential and radial flow distortion induced by the intake on the fan performance (IoF). In the FoI scenario, the rotor effectively redistributes the mass flow at the fan-face. The AoA tolerance of the short-intake design has increased by ≈4 deg when compared with the intake-alone configuration. Dynamic nature of distortion due to shock unsteadiness has been quantified. ST plots and power spectral density (PSD) of pressure fluctuations show the existence of a spectral gap between the shock unsteadiness and blade passing, with almost an order of magnitude difference in the corresponding frequencies. In the IoF scenario, both the “large” (O(360 deg)) and “small” scale distortion (O(10–60 deg)) induced by the intake results in a non-uniform inflow to the rotor. Sector analysis reveals a substantial variation in the local operating condition of the fan as opposed to its steady characteristic. Streamline curvature, upwash, and wake thickening are identified to be the three key factors affecting the fan performance. These underlying mechanisms are discussed in detail to provide further insights into the physical understanding of the fan-intake interaction. In addition to the shock-induced separation on the intake lip, the current study shows that shorter intakes are much more prone to the upwash effect at higher AoA. Insufficient flow straightening along the engine axis is reconfirmed to be one of the limiting factors for the short-intake design