Assessment of Split Form Nodal Discontinuous Galerkin Schemes for the LES of a Low Pressure Turbine Profile

Bergmann, Michael; Morsbach, Christian; Ashcroft, Graham

doi:10.1007/978-3-030-42822-8_48

Cited by 8 publications

(7 citation statements)

References 10 publications

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“…The DGSEM employed in this work [17] requires conformal meshes consisting of hexahedra only. Furthermore, the elements need to have a geometry order greater than one to allow for the representation of smoothly curved boundaries.…”

Section: Meshing Strategymentioning

confidence: 99%

A Numerical Test Rig for Turbomachinery Flows Based on Large Eddy Simulations With a High-Order Discontinuous Galerkin Scheme—Part III: Secondary Flow Effects

Morsbach,

Bergmann,

Tosun

et al. 2023

Journal of Turbomachinery

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In this final paper of a three-part series, we apply the numerical test rig based on a high-order Discontinuous Galerkin scheme to the MTU T161 low pressure turbine with diverging end walls at off-design Reynolds number of 90,000, Mach number of 0.6 and inflow angle of 41'. The inflow end wall boundary layers are prescribed in accordance with the experiment. Validation of the setup is shown against recent numerical references and the corresponding experimental data. Additionally, we propose and conduct a purely numerical experiment with upstream bar wake generators at a Strouhal number of 1.25, which is well above what was possible in the experiment. We discuss the flow physics at midspan and in the end wall region and highlight the influence of the wakes from the upstream row on the complex secondary flow system using instantaneous flow visualization, phase averages and modal decomposition techniques.

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Section: Meshing Strategymentioning

confidence: 99%

A Numerical Test Rig for Turbomachinery Flows Based on Large Eddy Simulations With a High-Order Discontinuous Galerkin Scheme—Part III: Secondary Flow Effects

Morsbach,

Bergmann,

Tosun

et al. 2023

Journal of Turbomachinery

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“…Hence, it is relatively safe to assume that systematic issues in the reproduction of the experiment are the dominant factor, e.g., the assumption of spanwise periodicity is not justified and the growing endwall boundary layers affect the measurements at midspan due the relatively small aspect ratio of the cascade [7,18,33]. Despite the known deficiencies, the test case has been heavily used as a validation case in the High-Order CFD Methods workshops for different CFD solvers and the observed differences between numerical results are far smaller [10,18,34], indicating the relevance of thorough statistical error analysis to compare numerical approaches. The experimental results are, nevertheless, shown in this paper to put the numerical results into perspective.…”

Section: Les Of the T106c Low-pressure Turbine Cascadementioning

confidence: 99%

“…While scale-resolving simulations are still challenging in terms of computational requirements for multi-stage turbomachinery components, they are already commonly applied to simulate linear turbine or compressor cascades [7][8][9][10]. Due to the statistically stationary nature of the flow in linear cascades, main aspects of engineering interest in the analysis of SRS results are firstand second-order statistical moments.…”

Section: Introductionmentioning

confidence: 99%

Statistical Error Estimation Methods for Engineering-Relevant Quantities From Scale-Resolving Simulations

Bergmann

Morsbach

Ashcroft

et al. 2021

Journal of Turbomachinery

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Scale-resolving simulations, such as large eddy simulations, have become affordable tools to investigate the flow in turbomachinery components. The resulting time-resolved flow field is typically analyzed using first- and second-order statistical moments. However, two sources of uncertainty are present when recording statistical moments from scale-resolving simulations: the influence of initial transients and statistical errors due to the finite number of samples. In this paper, both are systematically analyzed for several quantities of engineering interest using time series from a long-time large eddy simulation of the low-pressure turbine cascade T106C. A set of statistical tools to either remove or quantify these sources of uncertainty is assessed. First, the Marginal Standard Error Rule is used to detect the end of the initial transient. The method is validated for integral and local quantities and guidelines on how to handle spatially varying initial transients are formulated. With the initial transient reliably removed, the statistical error is estimated based on standard error relations considering correlations in the time series. The resulting confidence intervals are carefully verified for quantities of engineering interest utilizing cumulative and simple moving averages. Furthermore, the influence of periodic content from large scale vortex shedding on the error estimation is studied. Based on the confidence intervals, the required averaging interval to reduce the statistical uncertainty to a specific level is indicated for each considered quantity.

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“…For the overintegration, we follow the procedure presented in, e.g., [22]. The interpolation and projection steps use sum factorization and efficient multiplication kernels using tools from LoopVectorization.jl 3 , which is on par with (and sometimes faster than) optimized BLAS libraries such as Intel MKL for matrix multiplications at these sizes [12]. The numerical solution is initialized on a Cartesian TreeMesh with a single element for the isentropic vortex initial condition described in Section 4.…”

Section: Comparison To Overintegrationmentioning

confidence: 99%

“…Flux differencing methods are not only useful for constructing entropy-conservative or -dissipative (EC/ED) methods but also to recover split forms used, for example, in finite difference methods [24]. While flux differencing methods are central-type schemes without explicit dissipation, they have been demonstrated to increase the robustness of numerical methods significantly [3,19,34,58,63,64,74]. Thus, these schemes can be used as baseline methods to which dissipation can be added in a controlled manner [16,17].…”

Section: Introductionmentioning

confidence: 99%

Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws

Ranocha¹,

Schlottke-Lakemper²,

Chan³

et al. 2021

Preprint

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Many modern discontinuous Galerkin (DG) methods for conservation laws make use of summation by parts operators and flux differencing to achieve kinetic energy preservation or entropy stability. While these techniques increase the robustness of DG methods significantly, they are also computationally more demanding than standard weak form nodal DG methods. We present several implementation techniques to improve the efficiency of flux differencing DG methods that use tensor product quadrilateral or hexahedral elements, in 2D or 3D respectively. Focus is mostly given to CPUs and DG methods for the compressible Euler equations, although these techniques are generally also useful for GPU computing and other physical systems including the compressible Navier-Stokes and magnetohydrodynamics equations. We present results using two open source codes, Trixi.jl written in Julia and FLUXO written in Fortran, to demonstrate that our proposed implementation techniques are applicable to different code bases and programming languages.

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Assessment of Split Form Nodal Discontinuous Galerkin Schemes for the LES of a Low Pressure Turbine Profile

Cited by 8 publications

References 10 publications

A Numerical Test Rig for Turbomachinery Flows Based on Large Eddy Simulations With a High-Order Discontinuous Galerkin Scheme—Part III: Secondary Flow Effects

A Numerical Test Rig for Turbomachinery Flows Based on Large Eddy Simulations With a High-Order Discontinuous Galerkin Scheme—Part III: Secondary Flow Effects

Statistical Error Estimation Methods for Engineering-Relevant Quantities From Scale-Resolving Simulations

Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws

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