Turbulence Closure Research Articles

An Analysis and Comparison of the Hydrodynamic Behavior of Ships Using Mesh-Based and Meshless Computational Fluid Dynamics Simulations

This paper presents a comparison of two turbulence models implemented in two different frameworks (Eulerian and Lagrangian) in order to simulate the motion in calm water of a displacement hull. The hydrodynamic resistance is calculated using two open-source Computational Fluid Dynamics (CFD) software packages: OpenFOAM and DualSPHysics. These two packages are employed with two different numerical treatments to introduce turbulence closure effects. The methodology includes rigorous validation using a Wigley hull with experimental data taken from the literature. Then, the validated frameworks are applied to model a ship hull with a 30 m length overall (LOA), and their results discussed, outlining the advantages and disadvantages of the two turbulence treatments. In conclusion, the resistance calculated with OpenFOAM offers the best compactness of results and a shorter simulation time, whereas DualSPHysics can better capture the free-surface deformations, preserving similar accuracy.

Spatially averaged, vegetated, oscillatory boundary and shear layers

Oscillatory boundary layers over flat and rippled seabeds are well described in the literature. However, the presence of protruding vegetation stems has received no theoretical or experimental attention. The present work establishes an analytical constant viscosity model akin to the Stokes oscillatory boundary layer solution and a nonlinear varying-viscosity numerical model with a turbulence closure. The two models are used to describe the importance of vegetation and free stream velocity characteristics on spatially averaged oscillatory boundary layers: their friction factors, thickness and phase leads over the free-stream velocity. The models are periodic in time and resolve boundary and shear layers over the vertical, contrary to past efforts applying two-layer models. The models are extended to investigate the importance of finite wavelengths with steady streaming stresses and their associated mean velocity profile. Steady streaming is quantified both for the near-bottom streaming within the canopy and for the streaming in the shear layer above the canopy. Finally, akin to theoretical and experimental works on mean flows over unvegetated and flat seabeds due to oscillatory and nonlinear free-stream velocities, the numerical model investigates varying degree of nonlinearity for velocity- and acceleration-skewed velocity signals, and it is identified that the presence of vegetation stems gives rise to an additional contribution to the horizontal momentum balance which is not present for unvegetated conditions. Finally, it is discussed how the presence of a free surface, contrary to purely oscillatory conditions, alters the horizontal momentum balance within and above the canopy.

Generalization Limits of Data-Driven Turbulence Models

AbstractMany industrial applications require turbulent closure models that yield accurate predictions across a wide spectrum of flow regimes. In this study, we investigate how data-driven augmentations of popular eddy viscosity models affect their generalization properties. We perform a systematic generalization study with a particular closure model that was trained for a single flow regime. We systematically increase the complexity of the test cases up to an industrial application governed by a multitude of flow patterns and thereby demonstrate that tailoring a model to a specific flow phenomenon decreases its generalization capability. In fact, the accuracy gain in regions that the model was explicitly calibrated for is smaller than the loss elsewhere. We furthermore show that extrapolation or, generally, a lack of training samples with a similar feature vector is not the main reason for generalization errors. There is actually only a weak correlation. Accordingly, generalization errors are probably due to a data-mismatch, i.e., a systematic difference in the mappings from the model inputs to the required responses. More diverse training sets unlikely provide a remedy due to the strict stability requirements emerging from the ill-conditioned RANS equations. The universality of data-driven eddy viscosity models with variable coefficients is, therefore, inherently limited.

Effects of rotor squealer tip with non-uniform heights on heat transfer characteristic and flow structure of turbine stage

Squealer tip has a significant influence on both aerodynamic and heat transfer characteristics of the high-pressure turbine. Among the geometric parameters of the squealer, squealer height is one of the essential parameters in the tip design. However, due to the complexity of parameterization and meshing of the squealer, the related research is usually carried out on the squealer with a constant height. In this paper, a parameterization strategy generates squealer of assigned heights at four key positions of the blade, the leading edge-pressure side, the leading edge-suction side, the trailing edge-pressure side, and the trailing edge-suction side. An in-house mesh generation platform (NuFlux) is adopted to automatically generate the structured meshes. The aerothermal performance of a transonic turbine stage is assessed using steady Reynolds-averaged Navier–Stokes simulations with the k−ω shear stress transport model for the turbulence closure. The main purpose is to obtain the squealer tip configuration with the lowest heat transfer coefficient. The results show that non-uniform squealer further reduces the cavity floor heat transfer on the basis of uniform squealer by changing the interaction process between the asymmetric vortex pair (the pressure-side corner vortex and the casing-driven scraping vortex), which provides a valuable reference for the design of the squealer tip of advanced high-pressure turbines.

Optical turbulence simulations over the Tibetan Plateau based on a single-column model with high-order closure

Optical turbulence limits the maximum resolution of ground-based telescopes and leads to image degradation. The use of atmospheric numerical techniques to forecast optical turbulence is crucial for observation scheduling and optimization of adaptive optic systems. Current research methods for forecasting optical turbulence are primarily based on mesoscale models with turbulence closure techniques to parameterize the key terms required for C n 2 calculations under the assumption of atmospheric quasi-steady-state balance, and then the integrated astroclimatic parameters related to C n 2 profile can be obtained. In this study, we propose what we believe to be a novel approach to forecast C n 2 using a boundary layer parameterization based on higher-order turbulence closure in the single-column framework of the CLUBB model. Compared to mesoscale models, the CLUBB model serves as a single-column model, which simplifies modifications and reduces compilation time, and is more conducive to testing the performance of C n 2 parameterization scheme. In the design of C n 2 parameterization scheme, we consider a more complete physical process rather than omitting certain terms to obtain a steady-state solution. The performance of the model is evaluated using measurements obtained during a field campaign conducted at Da Qaidam site above the Tibetan Plateau. The results show that the model is able to capture typical features of the C n 2 profile evolution under convective conditions. Comparison of the model with contemporaneous sounding measurements and quantification of the model’s performance using statistical operators demonstrate the statistical agreement between simulations and measurements. In terms of atmospheric seeing, we can observe a bias of 0.01 and a root-mean-square error (RMSE) of 0.31 without any model calibration, which outperforms the results of previous mesoscale modeling studies. In addition, the new parameterization scheme is also compared with two representative C n 2 algorithms previously used in the mesoscale models, with some improvements observed. The potential demonstrated by this approach is expected to bring greater value and advancement to the research of three-dimensional forecasting of optical turbulence in the future by coupling with the mesoscale model.

Numerical and geometric investigation of pool boiling heat transfer in cavities with isothermal rectangular corrugations

This numerical work presents a geometrical investigation of a corrugated isothermal surface placed in a two-dimensional cavity subjected to unsteady, turbulent pool boiling flows. The main purposes are maximizing the heat transfer rate between the isothermal surface and the surrounding water flow, and the volume of vapor generated into the cavity. The geometric investigation followed the constructal design method, being the ratio Hi/Li (i = 1, 2 or 3) of the corrugations varied for three different numbers of corrugations: N = 1, 2, and 3, keeping constant the corrugations area. The volume of fluid (VOF) and Lee's evaporation-condensation models are used to estimate the volume fractions of water vapor/liquid and interfacial mass transfer. The unsteady Reynolds Averaged Navier Stokes (URANS) continuity, momentum and conservation of energy equations, and volume fraction transport equation, are solved using the finite volume method (FVM) available in software Ansys FLUENT. For closure of turbulence, the k - ɛ model is adopted. For validation of the model, the heat flux and convection heat transfer coefficient obtained for a pool boiling bared surface case are compared with Rohsenow's correlations, and differences lower than 7.0 % are reached. Results indicated a strong influence of the ratio Hi/Li and number of corrugations (N) in the heat transfer rate per unit depth (qs) and dimensionless volume of vapor (Vdim) generated into the cavity. The highest intrusion of the corrugations led to the generation of few large and many small scales, benefiting the thermal performance, regardless of the performance indicator employed. The optimal configuration, N = 3 and H3/L3 = 2.0 improved 49 % and 188 % the Vdim and qs compared with the worst corrugated case, showing the importance of the geometry of the corrugation in this problem.

Numerical simulation on the influence of artificial island on reef hydrodynamics

The construction of artificial island can greatly change the reef hydrodynamics, leading to increased water level and wave height as well as changes in flow field distribution. These alterations can affect sediment transport on the reef, and increase the risk of overtopping and structure instability. A numerical model based on the Reynolds Averaged Navier-Stokes (RANS) equations and k-ε turbulence closure model was developed to investigate the influence of artificial island on reef hydrodynamics. The numerical model was validated against the experimental results of wave height, mean water level, and wave breaking morphology. Detailed flow field, wave height, and wave set-up in front of artificial island were further analyzed based on the validated model. After building the reef-top structure, the wave breaking and offshore currents at reef edge were amplified. The flow stratification and increase of the wave set-up were also found on the reef flat. Furthermore, we found the relationship between maximum flow velocities on the reef flat and incoming wave conditions could be characterized by two non-dimensional parameters: |u¯|max/g(η¯+hr), (η¯+hr)/Hi.

Spatially Local Surrogate Modeling of Subgrid-Scale Effects in Idealized Atmospheric Flows: A Deep Learned Approach Using High-Resolution Simulation Data

Abstract We introduce a machine learned surrogate model from high-resolution simulation data to capture the subgrid-scale effects in dry, stratified atmospheric flows. We use deep neural networks (NNs) to model the spatially local state differences between a coarse-resolution simulation and a high-resolution simulation. The setup enables the capture of both dissipative and antidissipative effects in the state differences. The NN model is able to accurately capture the state differences in offline tests outside the training regime. In online tests intended for production use, the NN-coupled coarse simulation has higher accuracy over a significant period of time compared to the coarse-resolution simulation without any correction. We provide evidence of the capability of the NN model to accurately capture high-gradient regions in the flow field. With the accumulation of the errors, the NN-coupled simulation becomes computationally unstable after approximately 90 coarse simulation time steps. Insights gained from these surrogate models further pave the way for formulating stable, complex, physics-based spatially local NN models which are driven by traditional subgrid-scale turbulence closure models. Significance Statement Flows in the atmosphere are highly chaotic and turbulent, comprising flow structures of broad scales. For effective computational modeling of atmospheric flows, the effects of the small- and large-scale structures need to be captured by the simulations. Capturing the small-scale structures requires fine-resolution simulations. Even with the current state-of-the-art supercomputers, it can be prohibitively expensive to simulate these flows when computed for the entire earth over climate time scales. Thus, it is necessary to focus on the larger-scale structures using a coarse-resolution simulation while capturing the effects of the smaller-scale structures using some parameterization (approximation) scheme and incorporating it into the coarse-resolution simulation. We use machine learning to model the effects of the small-scale structures (subgrid-scale effects) in atmospheric flows. Data from a fine-resolution simulation is used to compute the missing subgrid-scale effects in coarse-resolution simulations. We then use machine learning models to approximate these differences between the coarse- and fine-resolution simulations. We see improved accuracy for the coarse-resolution simulations when corrected using these machine learned models.

Generalized field inversion strategies for data-driven turbulence closure modeling

Most data-driven turbulence closures are based on the general structure of nonlinear eddy viscosity models. Although this structure can be embedded into the machine learning algorithm and the Reynolds stress tensor itself can be fit as a function of scalar- and tensor-valued inputs, there exists an alternative two-step approach. First, the spatial distributions of the optimal closure coefficients are computed by solving an inverse problem. Subsequently, these are expressed as functions of solely scalar-valued invariants of the flow field by virtue of an arbitrary regression algorithm. In this paper, we present two general inversion strategies that overcome the limitation of being applicable only when all closure tensors are linearly independent. We propose to either cast the inversion into a constrained and regularized optimization problem or project the anisotropy tensor onto a set of previously orthogonalized closure tensors. Using the two-step approach together with either of these strategies then enables us to quantify the model-form error associated with the closure structure independent of a particular regression algorithm. Eventually, this allows for the selection of the a priori optimal set of closure tensors for a given, arbitrary complex test case.

Hydrodynamic force coefficients for spherical triangle shell fragments: Dependence on the aspect ratio and flatness

Euler–Lagrange simulations of particle-laden flow require hydrodynamic models of drag and lift forces for individual particles. Our goal is to develop models that can prescribe these forces for arbitrarily orientated shell objects. Here, we use computational fluid dynamics simulations of steady bottom-boundary layer flow over a series of spherical triangle shell fragments to calculate the hydrodynamic forces. The simulations explicitly resolve the wall boundary layers using grid resolution on the order of y+=1 at the shell fragment surface and use the SST k-omega turbulence closure model. These fragments cover a range of aspect ratio and flatness characteristics. The shell fragments are generated as triangular selections of a spherical shell with azimuthal and longitudinal angles proscribed based on elongation and flatness parameters (varying between 1 to 5, and 0.02 to 0.2 respectively), while characteristic length of the fragment is held constant to define the overall fragment size. Fragment orientations are considered with independently varying pitch, roll, and yaw each ranging from 0 to 180 degrees. The numerical estimates for the forces from all simulations were used to develop robust parameterizations of the drag and lift as a function of aspect ratio and flatness characteristics, as well as orientation of the shell fragments.

Numerical Modeling of Hydrogen Flame Acceleration and DDT Using Generalized Turbulent Flame Closure Approach

ABSTRACT In this work, a numerical methodology based on the paradigm of Turbulent Flame Closure (TFC) has been tested to simulate flame acceleration and Deflagration-to-Detonation Transition (DDT) in hydrogen air mixtures. Flame tracking is based on the transport equation for the progress variable. To minimize the need for tuning/calibration of model parameters, a generalized transport equation for the flame-wrinkling factor is adopted rather than algebraic closure models. The progress variable equation has been augmented with a sub-model based on the autoignition delay time parameter, which is crucial for capturing local explosions. Turbulence modeling is based on RANS. For sharp resolution of shocks, the conservative form of governing equations has been adopted. Relatively under-resolved numerical grid has been employed with the objective of establishing its scalability potential for large-scale computations. The TFC approach is strictly valid for fully turbulent flames. In the present work, its applicability for flame acceleration and DDT in obstructed channels has been investigated. Initial testing has been carried out for a closed and circular shock tube fitted with a single concentric obstacle. Further, a detailed study has been carried out for the GraVent explosion channel. Based on the validation of (1) flame speed variation during flame acceleration, (2) final detonation speed and (3) incident and reflected shock pressures, the capabilities and limitations of the approach have been presented. For the range considered in the present study, reasonably good predictions have been obtained with no tuning/calibration of model parameters. The model is able to capture flame acceleration and predict the conditions under which DDT can take place. However, it is further observed that actual DDT mechanism could not be reproduced.

Response of Upper Ocean to Parameterized Schemes of Wave Breaking under Typhoon Condition

The study of upper ocean mixing processes, including their dynamics and thermodynamics, has been a primary focus for oceanographers and meteorologists. Wave breaking in deep water is believed to play a significant role in these processes, affecting air–sea interactions and contributing to the energy dissipation of surface waves. This, in turn, enhances the transfer of gas, heat, and mass at the ocean surface. In this paper, we use the FVCOM-SWAVE coupled wave and current model, which is based on the MY-2.5 turbulent closure model, to examine the response of upper ocean turbulent kinetic energy (TKE) and temperature to various wave breaking parametric schemes. We propose a new parametric scheme for wave breaking energy at the sea surface, which is based on the correlation between breaking wave parameter RB and whitecap coverage. The impact of this new wave breaking parametric scheme on the upper ocean under typhoon conditions is analyzed by comparing it with the original parametric scheme that is primarily influenced by wave age. The wave field simulated by SWAVE was verified using Jason-3 satellite altimeter data, confirming the effectiveness of the simulation. The simulation results for upper ocean temperature were also validated using OISST data and Argo float observational data. Our findings indicate that, under the influence of Typhoon Nanmadol, both parametric schemes can transfer the energy of sea surface wave breaking into the seawater. The new wave breaking parameter RB scheme effectively enhances turbulent mixing at the ocean surface, leading to a decrease in sea surface temperature (SST) and an increase in mixed layer depth (MLD). This further improves upon the issue of uneven mixing of seawater at the air–sea interface in the MY-2.5 turbulent closure model. However, it is important to note that wave breaking under typhoon conditions is only one aspect of wave impact on ocean disturbances. Therefore, further research is needed to fully understand the impact of waves on upper ocean mixing, including the consideration of other wave mechanisms.

Numerical investigation of premixed syngas/air flame evolution in a closed duct with tulip flame formation

In this study, the dynamic behavior of the premixed syngas/air flames in enclosed ducts with obstacles at the blockage ratio of 0.5, as well as without obstacles, was studied via large eddy simulation and the turbulent flame speed closure model. The hydrogen volume fraction (hydrogen content in fuel) was set to 50 %. Results indicate that the simulation reproduced the flame shapes, flame speed and explosion overpressure observed in the experiments. In cases without obstacles, a “tulip” flame with a tulip cusp can be seen, and secondary cusps emerge on tulip lips due to the high-pressure zone ahead of “tulip” flame lips, leading to in a distorted “tulip” flame. In cases with obstacles, the flame develops hemispherical and finger shapes upstream of the obstacles and evolves into a “tulip” flame downstream of the obstacles due to vortices and adverse pressure gradients. The alteration of the flow direction within the unburned and burned zones results in intricate flame shapes. Flame speed and overpressure show a close relationship and exhibit oscillations following the generation of the “tulip” flame. Typically, the velocity, pressure and flow fields adjacent to the flame front can affect dynamic behaviors of premixed syngas/air flames.

On dissipation timescales of the basic second-order moments: the effect on the energy and flux budget (EFB) turbulence closure for stably stratified turbulence

Abstract. The dissipation rates of the basic second-order moments are the key parameters playing a vital role in turbulence modelling and controlling turbulence energetics and spectra and turbulent fluxes of momentum and heat. In this paper, we use the results of direct numerical simulations (DNSs) to evaluate dissipation rates of the basic second-order moments and revise the energy and flux budget (EFB) turbulence closure theory for stably stratified turbulence. We delve into the theoretical implications of this approach and substantiate our closure hypotheses through DNS data. We also show why the concept of down-gradient turbulent transport becomes incomplete when applied to the vertical turbulent flux of potential temperature under stable stratification. We reveal essential feedback between the turbulent kinetic energy (TKE), the vertical turbulent flux of buoyancy, and the turbulent potential energy (TPE), which is responsible for maintaining shear-produced stably stratified turbulence for any Richardson number.

Simulating Mixed‐Phase Open Cellular Clouds Observed During COMBLE: Evaluation of Parameterized Turbulence Closure

AbstractMarine cold‐air outbreaks, or CAOs, are airmass transformations whereby relatively cold boundary layer (BL) air is transported over relatively warm water. To more deeply understand BL and mixed‐phase cloud properties during CAO conditions, the Cold‐Air Outbreaks in the Marine Boundary Layer Experiment (COMBLE) took place from late 2019 into early 2020. During COMBLE, the U.S. Department of Energy's first Atmospheric Radiation Measurement Mobile Facility (AMF1) was deployed to Andenes, Norway, far downstream (∼1,000 km) from the Arctic pack ice. This study examines the two most intense CAOs sampled at the AMF1 site. The observed BL structures are open cellular with high (∼3–5 km) and cold (−30 to −50 C) cloud tops, and they often have pockets of high liquid water paths (LWPs; up to ∼1,000 g ) associated with strong updrafts and enhanced turbulence. We use a high‐resolution mesoscale model to explore how well four turbulence closure methods represent open cellular clouds. After applying a radar simulator to model outputs for direct evaluation, cloud top properties agree well with AMF1 observations (within ∼10%), but radar reflectivity and LWP agreement is more variable. Results suggest that the turbulent Prandtl number may play an important role for the simulated BL and cloud properties. All simulations produce enhanced precipitation rates that are well‐correlated with a cloud transition. Finally, the eddy‐diffusivity/mass‐flux approach produces the deepest cloud layer and therefore the largest and most coherent cellular structures. We recommend the use of a non‐local turbulence closure approach to better capture turbulent processes in intense CAOs.

Experimental and CFD studies on collection efficiency of separator with arc settlers of fluidized bed catalytic reactor

Separation of catalyst dust from gas in a fluidized bed reactor is an important process. A new solid-gas separator with arc settlers was developed, in which a stable wave flow pattern of the dusty gas flow is formed. The model was based on the RANS approach using the Reynolds Stress Model for the turbulence closure and the Discrete Phase Model. Validating the simulation results with the test data showed good convergence, no more than 6% in the pressure drop and less than 15.5% in collection efficiency at different inlet gas velocities. The CFD study revealed that with a dusty gas inlet velocity of no more than 1 m/s and a catalyst particle larger than 20 μm, efficiency close to 100% is achieved with a pressure drop of less than 60 Pa. Maximum efficiency is achieved when the number of rows of the arc settlers with 40 mm diameter is 8.

Strategies for Enhancing One-Equation Turbulence Model Predictions Using Gene-Expression Programming

This paper introduces innovative approaches to enhance and develop one-equation RANS models using gene-expression programming. Two distinct strategies are explored: overcoming the limitations of the Boussinesq hypothesis and formulating a novel one-equation turbulence model that can accurately predict a wide range of turbulent wall-bounded flows. A comparative analysis of these strategies highlights their potential for advancing RANS modeling capabilities. The study employs a single-case CFD-driven machine learning framework, demonstrating that machine-informed models significantly improve predictive accuracy, especially when baseline RANS predictions diverge from established benchmarks. Using existing training data, symbolic regression provides valuable insights into the underlying physics by eliminating ineffective strategies. This highlights the broader significance of machine learning beyond developing turbulence closures for specific cases.

High-fidelity fluid-structure interaction applied to static aeroelasticity in transonic flows

Transonic flows at high Reynolds numbers can lead to high dynamic pressures and, consequently, to aerostructural deflections of aircraft structures. This study aims to develop and validate a high-fidelity static aeroelastic analysis environment that is efficient and that can be used in an industrial setting. The aerodynamics is represented by numerical solutions of the Reynolds-averaged Navier-Stokes equations with appropriate turbulence closures. The load transfer process uses finite element shape functions in order to distribute the aerodynamic loads into the structural discretization. The structural analysis employs a modal basis approach, and a wingtip deflection convergence study is performed to find an adequate modal basis size. Radial basis functions are used for the fluid mesh displacement, and the influence of the support radius is evaluated to determine the optimal values relative to the wing mean aerodynamic chord. The capability is tested using the static aeroelastic benchmarks of the High Reynolds Aerostructural Dynamics Project (HIRENASD) and NASA's Common Research Model (CRM). The static aeroelastic results demonstrate robustness and consistency for the aerodynamic coefficients, pressure distributions, and structural deflection predictions at different normalized dynamic pressure values and grid refinement levels.

Carbon dioxide separation from natural gas using a supersonic nozzle

Carbon Dioxide (CO2) is often released in the process of natural gases and is one of greenhouse gases that are being treated as the most troublesome environmental issues. One of the promising ways to economically remove CO2 in natural gas processes is to use the technology of supersonic separation that makes use of non-equilibrium condensation in supersonic swirling flows in convergent-divergent nozzle using wet outlet. In the present study, the mixture of Methane (CH4) and CO2 was considered as natural gas. Two-dimensional convergent–divergent nozzle was employed to produce supersonic swirling flow with non-equilibrium condensation. The Peng–Robinson real gas model was used for the mixture gas. A nucleation equation and a droplet growth equation were incorporated into the governing equations of the compressible Navier–Stokes with the k-ω turbulence closure. The predicted results were verified and validated with existing experimental data. The convergent–divergent nozzle was varied to investigate its effect on the non-equilibrium condensation of CO2 in the mixture flow. The Technique for Order of Preference by Similarity to Ideal Solution method was applied to achieve the optimum case with amounts of wetness (the mass fraction of liquid CO2 to the summation of the mass fraction of liquid and vapor CO2 at the outlet of the nozzle) and kinetic energy. Three locations of wet outlets for the optimum case were analyzed. The results show that an increase in the divergent angle of the nozzle, swirling intensity, and inlet supply pressure results in more nucleation of CO2. However, the enhancement of mole fractions of CO2 decreases the nucleation rate and wetness. The exit wetness from wet outlets was increased with increasing distance from the throat.

Implementation of a high-order spatial discretization into a finite volume solver: Applications to turbomachinery test cases using an eddy-viscosity turbulence closure

In this study, the implementation of a high-order spatial discretization method into a Finite Volume solver is presented. Specific emphasis is put on the analysis of the performance over selected turbomachinery test cases. High-order numerical discretization is achieved by adopting the cell-centered Least-Square reconstruction, which is implemented in the in-house solver HybFlow. The validation of the adopted methodology is performed by assessing the solution of a turbulent flat plate with zero pressure gradient, using a eddy-viscosity transitional model. The test case also evidences the effect of the discretization of gradient-based source terms when a high-order reconstruction methodology is used. In the second part of the paper, the solver is used for the solution of relevant two-dimensional turbomachinery test cases, assessing the impact of 2nd and 3rd order reconstruction on the prediction of the aerodynamics and the heat transfer for respectively a low-pressure blade and a high-pressure turbine vane. It is shown how a high-order reconstruction allows for obtaining a better prediction of turbomachinery aerodynamics, with lower number of elements. The benefits over heat transfer predictions in high Reynolds number conditions are instead limited to the reduction of heat transfer coefficient spikes in under-resolved regions of the blade. Eventually, the methodology is validated for a three-dimensional low-pressure turbine cascade with realistic boundary layer inflow conditions.