This article shows the first parametric study on turbulent multi-jet impingement cooling flows using large-eddy simulations (LES). We focus on assessing the influence of the inter-jet distance and the cross-flow conditions on the heat transfer at the impingement wall. The LES setup is thoroughly validated with both experimental and direct numerical simulation data, showing an excellent agreement. The inter-jet distance effect on the heat transfer is studied comparing three different distances, where the full Nusselt number profile decreases in amplitude when the jet distance is increased. To evaluate the cross-flow effects, we prescribe both laminar and turbulent inflow conditions at different cross-flow magnitudes ranging between 20% and 40% of the impinging jet speed. Large cross-flow intensities cause a jet deflection which reduces the maxima in the Nusselt number distribution, and it increases the heat transfer in the areas of the wall less affected by the jet impingement. Adding realistic turbulent fluctuations to the inflow enhances the cross-flow effects on the heat transfer at the impingement wall.

The focus of the present study is to understand the effect of Rayleigh number on a high Rossby number flow in a high pressure compressor (HPC) inter-disk cavity. These cavities form between the compressor disks of a gas turbine engine, and they are an integral part of the internal air cooling system. We perform highly resolved large eddy simulations for two Rayleigh numbers of 0.76 × 10 8 and 1.54 × 10 8 at a fixed Rossby number of 4.5 by solving the compressible Navier–Stokes equations. The results show a flow structure dominated by a toroidal vortex in the inner region of the cavity. In the outer region, the flow is observed to move radially outwards by Ekman layers formed on the side disks and to move radially inwards through the central core region of the cavity. An enhancement in the intensity of the radial flares is observed in the outer region of the cavity for the high Rayleigh number case with no perceivable effect in the inner region. The near shroud region is mostly dominated by the centrifugal buoyancy-induced flow and the wall Nusselt number calculated at the shroud is in close agreement with centrifugal buoyancy-induced flow without an axial bore flow.

We report on a series of highly resolved large-eddy simulations of the LS89 high-pressure turbine (HPT) vane, varying the exit Mach number between Ma = 0.7 and 1.1. In order to accurately resolve the blade boundary layers and enforce pitchwise periodicity, we for the first time use an overset mesh method, which consists of an O-type grid around the blade overlapping with a background H-type grid. The simulations were conducted either with a synthetic inlet turbulence condition or including upstream bars. A quantitative comparison shows that the computationally more efficient synthetic method is able to reproduce the turbulence characterictics of the upstream bars. We further perform a detailed analysis of the flow fields, showing that the varying exit Mach number significantly changes the turbine efficiency by affecting the suction-side transition, blade boundary layer profiles, and wake mixing. In particular, the Ma = 1.1 case includes a strong shock that interacts with the trailing edge, causing an increased complexity of the flow field. We use our recently developed entropy loss analysis (Zhao and Sandberg, GT2019-90126) to decompose the overall loss into different source terms and identify the regions that dominate the loss generation. Comparing the different Ma cases, we conclude that the main mechanism for the extra loss generation in the Ma = 1.1 case is the shock-related strong pressure gradient interacting with the turbulent boundary layer and the wake, resulting in significant turbulence production and extensive viscous dissipation.

This work shows the application of Gene Expression Programming to augment RANS turbulence closure modelling for flows through complex geometry, designed for additive manufacturing. Specifically, for the design of optimised internal cooling channels in turbine blades. One of the challenges in internal cooling design is the heat transfer accuracy of the RANS formulation in comparison to higher fidelity methods, which are still not used in design on account of their computational cost. However, high fidelity data can be extremely valuable for improving current lower fidelity models and this work shows the application of data driven approaches to develop turbulence closures for an internally ribbed duct. Different approaches are compared and the results of the improved model are illustrated; first on the same geometry, and then for an unseen predictive case. The work shows the potential of using data driven models for accurate heat transfer predictions even in non-conventional configurations.

The trailing edge slot is a canonical representation of the pressure-side bleed flow encountered in high pressure turbines. Predicting the flow and temperature downstream of the slot exit remains challenging for RANS and URANS, with both significantly overpredicting the adiabatic wall-effectiveness. This over-prediction is attributable to the incorrect mixing prediction in cases where the vortex shedding is present. In case of RANS the modelling error is rooted in not properly accounting for the shedding scales while in URANS the closures account for the shedding scales twice, once by resolving the shedding and twice with the model for all the scales. Here, we present an approach which models only the stochastic scales that contribute to turbulence while resolving the scales that do not, i.e. scales considered as contributing to deterministic unsteadiness. The model for the stochastic scales is obtained through a data-driven machine learning algorithm, which produces a bespoke turbulence closure model from a high-fidelity dataset. We use the best closure (blowing ratio of 1.26) for the anisotropy obtained in the a priori study of Lav, Philip & Sandberg [A New Data-Driven Turbulence Model Framework for Unsteady Flows Applied to Wall-Jet and Wall-Wake Flows, 2019] and conduct compressible URANS calculations. In the first stage, the energy equation is solved utilising the standard gradient diffusion hypothesis for the heat-flux closure. In the second stage, we develop a bespoke heat-flux closure using the machine-learning approach for the stochastic heat-flux components only. Subsequently, calculations are performed using the machine-learnt closures for the heat-flux and the anisotropy together. Finally, the generalisability of the developed closures is evaluated by testing them on additional blowing ratios of 0.86 and 1.07. The machine-learnt closures developed specifically for URANS calculations show significantly improved predictions for the adiabatic wall-effectiveness across the different cases.

This paper presents development of accurate turbulence closures for wake mixing prediction by integrating a machine-learning approach with Reynolds Averaged Navier-Stokes (RANS)-based computational fluid dynamics (CFD). The data-driven modeling framework is based on the gene expression programming (GEP) approach previously shown to generate non-linear RANS models with good accuracy. To further improve the performance and robustness of the data-driven closures, here we exploit that GEP produces tangible models to integrate RANS in the closure development process. Specifically, rather than using as cost function a comparison of the GEP-based closure terms with a frozen high-fidelity dataset, each GEP model is instead automatically implemented into a RANS solver and the subsequent calculation results compared with reference data. By first using a canonical turbine wake with inlet conditions prescribed based on high-fidelity data, we demonstrate that the CFD-driven machine-learning approach produces non-linear turbulence closures that are physically correct, i.e. predict the right downstream wake development and maintain an accurate peak wake loss throughout the domain. We then extend our analysis to full turbine-blade cases and show that the model development is sensitive to the training region due to the presence of deterministic unsteadiness in the near wake region. Models developed including this region have artificially large diffusion coefficients to over-compensate for the vortex shedding steady RANS cannot capture. In contrast, excluding the near wake region in the model development produces the correct physical model behavior, but predictive accuracy in the near-wake remains unsatisfactory. We show that this can be remedied by using the physically consistent models in unsteady RANS, implying that the non-linear closure producing the best predictive accuracy depends on whether it will be deployed in RANS or unsteady RANS calculations. Overall, the models developed with the CFD-assisted machine learning approach were found to be robust and capture the correct physical behavior across different operating conditions.

The unsteady flow prediction for turbomachinery applications relies heavily on unsteady RANS (URANS). For flows that exhibit vortex shedding, such as the wall-jet/wake flows considered in this study, URANS is unable to predict the correct momentum mixing with sufficient accuracy. We suggest a novel framework to improve that prediction, whereby the deterministic scales associated with vortex shedding are resolved while the stochastic scales of pure turbulence are modelled. The framework first separates the stochastic from the deterministic length scales and then develops a bespoke turbulence closure for the stochastic scales using a data-driven machine-learning algorithm. The novelty of the method lies in the use of machine-learning to develop closures tailored to URANS calculations. For the walljet/wake flow, three different mass flow ratios (0.86, 1.07 and 1.26) have been considered and a high-fidelity dataset of the idealised geometry is utilised for the sake of model development. This study serves as an a priori analysis, where the closures obtained from the machine-learning algorithm are evaluated before their implementation in URANS. The analysis looks at the impact of using all length scales versus the stochastic scales for closure development, and the impact of the extent of the spatial domain for developing the closure. It is found that a two-layer approach, using bespoke trained models for the near wall and the jet/wake regions, produce the best results. Finally, the generalisability of the developed closures is also evaluated by applying a given closure developed using a particular mass flow ratio to the other cases.

Entropy loss is widely used to quantify the efficiency of components in turbomachines, and empirical relations have been developed to estimate the contribution of different mechanisms. However, further analysis is still needed to not only get a deeper insight of the physics, but also to more accurately quantify the loss generation caused by different terms. In the present study, the entropy transport equations based on averaged flow quantities are first derived, and the entropy generation process is fully decomposed into several terms representing different physical mechanisms, such as mean viscous dissipation, turbulence production, mean and turbulent heat flux, etc. This decomposition framework is then applied to high-resolution LES and RANS results of a VKI LS-89 HPT vane, and a detailed quantification of different entropy generation terms is obtained. The results show that the entropy generation caused by mean flow features like mean viscous dissipation and mean heat flux are in close agreement between LES and RANS, indicating that RANS provides an overall good prediction for the mean flow. Furthermore, we find that turbulence production plays an important role in entropy generation as it represents the energy extracted from the mean flow to turbulent fluctuations. However, the difference between RANS and LES results for the turbulence production term is not negligible, particularly in the wake region. This implies that the failure of RANS to predict the correct total loss might be largely caused by errors in capturing the correct turbulence production in the near wake region.

Non-linear turbulence closures were developed that improve the prediction accuracy of wake mixing in low-pressure turbine (LPT) flows. First, Reynolds-averaged Navier–Stokes (RANS) calculations using five linear turbulence closures were performed for the T106A LPT profile at exit Mach number 0.4 and isentropic exit Reynolds numbers 60,000 and 100,000. None of these RANS models were able to accurately reproduce wake loss profiles, a crucial parameter in LPT design, from direct numerical simulation (DNS) reference data. However, the recently proposed k v 2 ¯ ω transition model was found to produce the best agreement with DNS data in terms of blade loading and boundary layer behavior and thus was selected as baseline model for turbulence closure development. Analysis of the DNS data revealed that the linear stress-strain coupling constitutes one of the main model form errors. Hence, a gene-expression programming (GEP) based machine-learning technique was applied to the high-fidelity DNS data to train non-linear explicit algebraic Reynolds stress models (EARSM). In particular, the GEP algorithm was tasked to minimize the weighted difference between the DNS and RANS anisotropy tensors, using different training regions. The trained models were first assessed in an a priori sense (without running any CFD) and showed much improved alignment of the trained models in the region of training. Additional RANS calculations were then performed using the trained models. Importantly, to assess their robustness, the trained models were tested both on the cases they were trained for and on testing, i.e. previously not seen, cases with different flow features. The developed models improved prediction of the Reynolds stress, TKE production, wake-loss profiles and wake maturity, across all cases, in particular those trained on just the wake region.

Large eddy simulations of a linear low-pressure turbine cascade with the T106A profile and different surface roughness patches were carried out. The aim was to investigate the effects on the laminar and turbulent boundary layer on the blade suction surface. Two different approaches were used to represent the roughness patches. Firstly, a forcing model, reducing the computational costs compared to fully resolved roughness surfaces, was incorporated. Secondly, an immersed boundary method representing an as-cast roughness surface was used, for a more detailed analysis of flow mechanisms over roughness. It was found that the roughness model was able to induce boundary layer transition and alter the turbulent boundary layer, with the results in line with findings in the literature. The instantaneous flow data at different time instants of the as-cast roughness case showed the development of streaks due to distinct roughness peaks, resulting in highly uneven transition positions across the spanwise direction.

The validity of the Boussinesq approximation in the wake behind a high-pressure turbine blade is explored. We probe the mathematical assumptions of such a relationship by employing a least-squares technique. Next, we use an evolutionary algorithm to modify the anisotropy tensor a priori using highly resolved LES data. In the latter case we build a non-linear stress-strain relationship. Results show that the standard eddy-viscosity assumption underpredicts turbulent diffusion and is theoretically invalid. By increasing the coefficient of the linear term, the farwake prediction shows minor improvement. By using additional non-linear terms in the stress-strain coupling relationship, created by the evolutionary algorithm, the near-wake can also be improved upon. Terms created by the algorithm are scrutinized and the discussion is closed by suggesting a tentative non-linear expression for the Reynolds stress, suitable for the wake behind a high-pressure turbine blade.

The effect of inflow turbulence intensity and turbulence length scales have been studied for a linear high-pressure turbine vane cascade at Re is = 590,000 and M is = 0.93, using highly resolved compressible large-eddy simulations employing the WALE turbulence model. The turbulence intensity was varied between 6% and 20% while values of the turbulence length scales were prescribed between 5% and 20% of axial chord. The analysis focused on characterizing the inlet turbulence and quantifying the effect of the inlet turbulence variations on the vane boundary layers, in particular on the heat flux to the blade. The transition location on the suction side of the vane was found to be highly sensitive to both turbulence intensity and length scale, with the case with turbulence intensity 20% and 20% length scale showing by far the earliest onset of transition and much higher levels of heat flux over the entire vane. It was also found that the transition process was highly intermittent and local, with spanwise parts of the suction side surface of the vane remaining laminar all the way to the trailing edge even for high turbulence intensity cases.

Classical RANS turbulence models have known deficiencies when applied to jets in crossflow. Identifying the linear Boussinesq stress-strain hypothesis as a major contribution to erroneous prediction, we consider and contrast two machine learning frameworks for turbulence model development. Gene Expression Programming, an evolutionary algorithm that employs a survival of the fittest analogy, and a Deep Neural Network, based on neurological processing, add non-linear terms to the stress-strain relationship. The results are Explicit Algebraic Stress Model-like closures. High fidelity data from an inline jet in crossflow study is used to regress new closures. These models are then tested on a skewed jet to ascertain their predictive efficacy. For both methodologies, a vast improvement over the linear relationship is observed.

In this paper we establish a benchmark data set of a generic high-pressure turbine vane generated by direct numerical simulation (DNS) to resolve fully the flow. The test conditions for this case are a Reynolds number of 0.57 million and an exit Mach number of 0.9, which is representative of a modern transonic high-pressure turbine vane. In this study we first compare the simulation results with previously published experimental data. We then investigate how turbulence affects the surface flow physics and heat transfer. An analysis of the development of loss through the vane passage is also performed. The results indicate that free-stream turbulence tends to induce streaks within the near wall flow, which augment the surface heat transfer. Turbulent breakdown is observed over the late suction surface, and this occurs via the growth of two-dimensional Kelvin-Helmholtz spanwise roll-ups, which then develop into lambda vortices creating large local peaks in the surface heat transfer. Turbulent dissipation is found to significantly increase losses within the trailing-edge region of the vane.