The interest towards supersonic ejectors as replacement for compressors in various industrial applications has grown over the last decade. In contrast with the simplicity of their working principle, the turbulent phenomena responsible for the entrainment and mixing are still not fully understood nor well captured by numerical simulations. Indeed, mostly Reynolds-Averaged Navier-Stokes (RANS) simulations have been performed up now, where the unsteady phenomena responsible for the entrainment are solely modeled using an effective turbulent viscosity, and that also needs calibration. This work aims at providing the tools to improve the understanding and design of those devices by analyzing the instantaneous and averaged fields from a Large Eddy Simulation (LES) of a supersonic air ejector. First, the structure of the mixing layers is analyzed, showing a very early transition to turbulence in the shear layers and the necessity to properly capture the associated fluctuations. The impact of turbulence injection in the primary flow is also discussed. Then, the post-processing tools, using total exergy fluxes, are presented. The exergy fluxes between the streams in the mixing duct are computed, and are compared to their incomplete counterpart obtained using RANS simulation results. The observed discrepancies are shown to be due to the large differences in the turbulent shear stress and turbulent heat flux through the shear layer between the RANS and LES results. A new criterion to measure the completion of the mixing between the flows is introduced thanks to a novel decomposition of the total exergy flux. Finally, the complete mixing of both streams, as newly defined, is shown not to be a sufficient condition to find the optimum performance of the ejector, e.g. a maximum compression at the maximum flow rate of the secondary stream. This optimum is found to be much more dependent on the balance between shear stress between streams and wall-friction.

The transonic aerodynamics of a low pressure turbine (LPT) cascade, mimicking geared turbofan conditions during cruise, is currently under study using direct numerical simulation. In the first step of this endeavour, transition, separation and loss generation were examined at Mach 0.7, 0.9, and 0.95, with a constant Reynolds number of 70× 10^3 based on the true chord, in clean inlet conditions. The aim is to identify the impact of sonic conditions and choking on self-induced transition, generated purely by flow features around the blade. The pressure distribution was slightly overestimated with respect to experimental conditions. Separation occurs over the suction side (SS) at 58% and 69% of blade length for the first two Mach numbers. Skin friction is low in the Mach 0.95 case, but unexpectedly separation does not take place for this case. The choking of the passage was considered as influencing factor. A supersonic region followed by a shock appears at Mach 0.9 or higher, and a fully choked passage is found at 0.95. Separation bubbles with turbulent reattachment are formed on the pressure side (PS) between 0% and 50% of the blade length. Separation on the SS was identified as laminar separation long bubble, while reversed transition develops on the PS after reattachment. Wake losses increase with higher Mach numbers, and turbulence is more prominent at lower Mach numbers. This investigation provides insights into the aerodynamic characteristics of the linear low pressure turbine cascade, addressing separation, transition, losses, and wake behavior in sonic conditions at low Reynolds numbers.

In the context of fundamental flow studies, experimental databases are expected to provide uncertainty margins on the measured quantities. With the rapid increase in available computational power and the development of high-resolution fluid simulation techniques, Direct Numerical Simulation and Large Eddy Simulation are increasingly used in synergy with experiments to provide a complementary view. Moreover, they can access statistical moments of the flow variables for the development, calibration, and validation of turbulence models. In this context, the quantification of statistical errors is also essential for numerical studies. Reliable estimation of these errors poses two challenges. The first challenge is the very large amount of data: the simulation can provide a large number of quantities of interest (typically about 180 quantities) over the entire domain (typically 100 million to 10 billion of degrees of freedom per equation). Ideally, one would like to quantify the error for each quantity at any point in the flow field. However, storing a long-term sequence of signals from many quantities over the entire domain for a posteriori evaluation is prohibitively expensive. The second challenge is the short time step required to resolve turbulent flows with DNS and LES. As a direct consequence, consecutive samples within the time series are highly correlated. To overcome both challenges, a novel economical co-processing approach to estimate statistical errors is proposed, based on a recursive formula and the rolling storage of short-time signals.

Wall modelling in large-eddy simulation (LES) is of high importance to allow scale resolving simulations of industrial applications. Numerous models were developed and validated for incompressible flows, including a simple quasi-analytical model based on Reichardt's formula that approximates the law of the wall. In this paper, a scaling is proposed to generalize this wall model to highly compressible flows. First, the results of wall-resolved LES (wrLES) of adiabatic compressible turbulent channel flows at $Re_\tau = 1000$ and at centreline Mach numbers of $M_c= 0.76$ and $1.5$ are presented. Then, three potential scalings of the incompressible wall model are proposed, and their a priori performance is evaluated : (i) the Howarth–Stewartson scaling, (ii) an improved Van Driest scaling and (iii) a new scaling obtained from a blending of those two. The results of wall-modelled LES (wmLES) of compressible channel flows using these three models are compared with the reference wrLES data, showing the superior accuracy of the hybrid scaling. The consistency of the new wall model at low Mach numbers is also verified by comparing the results of a wmLES at $M_c= 0.25$ with those of reference incompressible DNS data at $Re_\tau = 1000$ and $5200$ . Finally, the proposed wall model is also applied to a turbulent channel flow at $M_c=1.5$ and $Re_\tau =5200$ .

Wall models reduce the computational cost of large eddy simulations (LES) by modeling the near-wall energetic scales and enable the application of LES to complex flow configurations of engineering interest. However, most wall models assume that the boundary layer is fully turbulent, at equilibrium, and attached. Such models have also been successfully applied to turbulent boundary layers under moderated adverse pressure gradients. When the adverse pressure gradient becomes too strong, and the boundary layer separates, equilibrium wall models are no longer applicable. In this work, the relations between the instantaneous wall shear stress, velocity field, and pressure gradients are evaluated using space-time correlations for the purpose of analyzing the near-wall physics in different flow configurations. These correlations are extracted from two wall-resolved LES: a channel flow at a friction Reynolds number Re_τ of 950 and the two-dimensional periodic hill at a bulk Reynolds number Re _b of 10595. This analysis highlights that no instantaneous and local correlation is observed in the vicinity of the separation. The domain of high correlation appears to be shifted downstream. This study of the near-wall physics is a step for developing a data-driven wall model applied to separated flows and, in particular, selecting suitable input parameters for the training of neural networks.

Preliminary high-fidelity simulations of the MTU T161 low pressure turbine cascade with diverging end walls have been performed on massively parallel computational resources with four different high-order methods at outlet isentropic Mach number $$M_{2s}=0.601$$ and two outlet isentropic Reynolds numbers, namely $$Re_{2s}=90\,\text {K}$$ and $$Re_{2s}=200\,\text {K}$$ . First the flow regime and the boundary conditions are thoroughly described. The implementation of each method is then briefly introduced before the main results are presented. The main flow features of this test case have been qualitatively highlighted by these simulations. However, discrepancies have been observed quantitatively in terms of separation point on the suction side of the blade, especially at the lowest Reynolds. These simulations relied mainly on a laminar boundary layer at the inlet of the domain, which is likely the root cause of the observed discrepancies. Additional simulations with turbulent boundary layer imposed at the inlet are required to characterize the flow separation based on the turbulence intensity at the inlet.

Aeronautic flows are characterized by turbulence, which consists of chaotic perturbations around a time-averaged flow field. Turbulence appears in a large variety of length scales, ranging from unsteady flow features of the size of the aircraft, wing, blade down to tiny whirls, which are many orders of magnitude smaller. Turbulence has a profound impact on aerodynamic performance, but unfortunately, explicit computation of all turbulent features remains intractable for the design and analysis of real-life geometries [1]. The smallest structures, requiring the largest computational effort, are found in the so-called boundary layer near the wall. This cost can be avoided by modeling their time-averaged impact on the forces exchanged between fluid and the wall. This saving, in turn, allows for the direct computation of the largest turbulent flow features away from the wall, which govern important large-scale effects. The present work proposes the use of Deep Neural Networks (DNN) to link the wall shear stress components to volume data extracted at multiple wall-normal distances hwm and wall-parallel locations. The model focuses on separation since this phenomenon is currently not well-represented, whereas it has a huge impact on aerodynamic performance and operating range. The model is trained using a high-fidelity database of the well-known two-dimensional periodic hill flow. The conditions of this separated flow are such that it is still affordable to compute all turbulent flow features directly, using Tier-1 modern supercomputers.

While the exascale computing era is approaching, the growing gap between computing resources and IO bandwidth for massively parallel simulations has already become a major bottleneck for the scientific discovery process. In this context, various strategies to enable and accelerate the analysis of data produced by massively parallel high-order methods are presented, with an emphasis on in-situ visualization and co-processing techniques. First, a library of parallel procedures is presented for an efficient collection of turbulence statistics within the framework of a modal discontinuous Galerkin method. Afterwards, an acoustic co-processing strategy is presented whereby sound radiation calculations are performed concurrently with CFD calculations in order to avoid the need to store prohibitive amount of data. Finally, an open-source and scalable post-hoc visualization and processing tool dedicated to the analysis of large data sets produced by high order methods is first presented. This post-hoc processing tool has then been extended to a co-processing interface which enables live in-situ visualization and analysis of high-order solutions produced by massively parallel simulations.

The term "in situ processing" has evolved over the last decade to mean both a specific strategy for visualizing and analyzing data and an umbrella term for a processing paradigm. The resulting confusion makes it difficult for visualization and analysis scientists to communicate with each other and with their stakeholders. To address this problem, a group of over 50 experts convened with the goal of standardizing terminology. This paper summarizes their findings and proposes a new terminology for describing in situ systems. An important finding from this group was that in situ systems are best described via multiple, distinct axes: integration type, proximity, access, division of execution, operation controls, and output type. This paper discusses these axes, evaluates existing systems within the axes, and explores how currently used terms relate to the axes.

A comparison study of four numerical modeling strategies has been conducted for separation control based on synthetic jets and applied to a vertical tail/rudder assembly. These modeling strategies include the combination of two turbulence modeling techniques with two synthetic jet modeling approaches. The two turbulence modeling strategies include the Spalart-Allmaras Reynolds Averaged Navier-Stokes (RANS-SA) and Delayed Detached Eddy Simulation (DDES-SA), whereas the two synthetic jet modeling approaches include zero-net-mass-flux periodic unsteady blowing and suction (characteristic of a synthetic jet), and steady blowing. The integrated side force, wall pressure and shear stress distributions, as well as velocity and vorticity field isosurfaces are compared to understand and contrast the predictions of all four modeling pairs. The case combining zero-net mass flux with the delayed detached eddy simulation turbulence model was previously validated through comparison with coordinated experiments and shows the best agreement in the current study, but carries a significant computational cost. The lowest cost case combining steady blowing and Reynolds Averaged Navier-Stokes turbulence model is able to match roughly the same change in side force, but requires elevated levels of blowing to do so. All four modeling cases generate an oblique vortex outboard of the jet orifice, which is primarily responsible for changes in integrated side force, but with different patterns and strengths which are analyzed in this work.

This paper presents two recent numerical tools developed respectively to perform traditional post-processing and more advanced in situ processing of high-order polynomial data generated by massively parallel finite element codes. For post-processing and visualisation of high-order solutions, we present a new ParaView plugin that integrates Gmsh used as an external library. This plugin therefore combines respectively ParaView's scalability in parallel and Gmsh's ability to apply h-refinement of the initial mesh followed by solution interpolation on the resulting visualisation grid, thus enabling parallel visualisation of any arbitrary high-order polynomial solutions in client-server mode. In a second stage, this capacity has been extended to an in situ interface based on the Catalyst library which enables in situ analysis and visualisation of high-order solutions. These new capacities are demonstrated with the visualisation of high-order solution of the unsteady flow generated by a discontinuous Galerkin method for an unsteady turbomachinery application.

This paper concerns implicit large eddy simulation (ILES) of turbulent flows of industrial interest using high order discontinuous Galerkin method (DGM). DGM has a high potential for industrial applications using ILES. As dissipation is only active on very small scale features, the method mimics a subgrid scale model, while its high accuracy ensures that large scale dynamics are not contaminated by dispersive/dissipative errors. Previously DGM/ILES has been assessed on many low Mach number canonical test cases (e.g. Carton et al. Numer Methods Fluids, 78:335–354, (2015), [3]). This paper recapitulates recent validation on transonic benchmarks (Hillewaert et al. Proceedings of CTR summer program, pp. 363–372, Stanford University, (2016), [6]) and proceeds to the application on the LS89 cascade, a well-known turbomachinery benchmark.

Abstract Absorbing heat from the fuel rod surface, water as coolant can undergo subcooled boiling within a pressurized water reactor (PWR) fuel rod bundle. Because of the buoyancy effect, the vapor bubbles generated will then rise along and interact with the subchannel geometries. Reliable prediction of bubble behavior is of immense importance to ensure safe and stable reactor operation. However, given a complex engineering system like a nuclear reactor, it is very challenging (if not impossible) to conduct high-resolution measurements to study bubbly flows under reactor operation conditions. The lack of a fundamental two-phase-flow database is hindering the development of accurate two-phase-flow models required in more advanced reactor designs. In response to this challenge, first-principles–based numerical simulations are emerging as an attractive alternative to produce a complementary data source along with experiments. Leveraged by the unprecedented computing power offered by state-of-the-art supercomputers, direct numerical simulation (DNS), coupled with interface tracking methods, is becoming a practical tool to investigate some of the most challenging engineering flow problems. In the presented research, turbulent bubbly flow is simulated via DNS in single PWR subchannel geometries with auxiliary structures (e.g., supporting spacer grid and mixing vanes). The geometric effects these structures exert on the bubbly flow are studied with both a conventional time-averaging approach and a novel dynamic bubble tracking method. The new insights obtained will help inform better two-phase models that can contribute to safer and more efficient nuclear reactor systems.

Some possible future High Fidelity CFD codes for LES simulation of turbomachinery are compared on several test cases increasing in complexity, starting from a very simple inviscid Vortex Convection to a multistage axial experimental compressor. Simulations were performed between 2013 and 2016 by major Safran partners (Cenaero, Cerfacs, CORIA and Onera) and various numerical methods compared: Finite Volume, Discontinuous Galerkin, Spectral Differences. Comparison to analytical results, to experimental data or to RANS simulations are performed to check and measure accuracy. CPU efficiency versus accuracy are also presented. It clearly appears that the level of maturity could be different between codes and numerical approaches. In the end, advantages and disadvantages of every codes obtained during this project are presented.