Multiscale block spectral solution for unsteady flows

He, L.

doi:10.1002/fld.4472

Cited by 23 publications

(30 citation statements)

References 28 publications

(56 reference statements)

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“…An inflow velocity is taken as 55 m/s, and the Reynolds number is 174 based on the free stream velocity and the diameter of cylinder. For this case the experimental data are available from the early work of Thom [26], which is also recently used for validation purposes [27]. The mesh refined in the near wall region for capturing the laminar boundary layer is shown in Fig.…”

Section: Flow Around a Cylindermentioning

confidence: 99%

Implicit Discontinuous Galerkin Solution on Unstructured Mesh for Turbine Blade Secondary Flow

Yao

2019

Journal of Turbomachinery

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To enhance solution accuracy with high-order methods, an implicit solver using the discontinuous Galerkin (DG) discretization on unstructured mesh has been developed. The DG scheme is favored chiefly due to its distinctive feature of achieving a higher-order accuracy by simple internal sub-divisions of a given mesh cell. It can thus relieve the burden of mesh generation for local refinement. The developed method has been assessed in several test cases. First, an examination on the mesh-dependency with different DG orders for discretization has demonstrated the expected mesh convergence order of accuracy correlation. The flow around a cylinder solved with up to the fifth-order accuracy demonstrates the need for a high-order geometrical representation corresponding to the high-order flow field discretization. A calculated turbulent flat plate boundary layer demonstrates the capability of the high-order DG in capturing the laminar sub-layer for a given coarse mesh (y + >20) without a wall function, in a clear contrast to a conventional second-order scheme. The focal test case of the present work is a high-pressure (HP) turbine cascade with the flow losses being strongly influenced by both the laminar separation induced transition on the blade suction surface and the secondary flow development in the endwall region. Fully turbulent RANS solutions consistently overpredict the losses, which can be significantly reduced by an empirically specified transition at a mid-chord point. Of particular interest is a contrasting behavior of pure laminar flow solutions. A steady laminar flow solution is difficult to converge, and even when converging, tends to give an unrealistically large separation. On the other hand when the laminar solution is run in a time-accurate unsteady mode, a qualitatively different flow pattern emerges. The separated shear layer is then shown to lead to coherently shed unsteady vortices with a net entrainment from the main stream to the near-wall region. The resultant time-averaged near-wall flow then effectively becomes a reattached boundary layer. Both overall and distributed losses computed from unsteady laminar solutions are shown to be consistently much better than the fully turbulent RANS solutions. It is remarkable and quite unexpected that for such a seemingly complex 3D flow problem, the straightforward unsteady laminar solutions with no empirical input seem to be comparable with (or slightly better than) the tripped RANS with empirical input.

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Section: Flow Around a Cylindermentioning

confidence: 99%

Implicit Discontinuous Galerkin Solution on Unstructured Mesh for Turbine Blade Secondary Flow

Yao

2019

Journal of Turbomachinery

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“…3 Method for Implementation 3.1 Unsteady Navier-Stokes Solver. The baseline flow solution method adopted is an in-house multi-block code which the author has developed and updated over many years [30][31][32]. Flow is governed by the three-dimensional unsteady compressible Navier-Stokes equations.…”

Section: Space-timementioning

confidence: 99%

“…This is carried out in a moving-average (e.g., Refs. [31,32]). At time-step N, the corresponding space-time averaged for a coarse-mesh cell with local fine-mesh cells embedded is…”

Section: Source Term Generation Frommentioning

confidence: 99%

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Averaging for High Fidelity Modelling: Towards Large Eddy Simulations in Multi-Passage Multi-Row Configurations

2020

Volume 2C: Turbomachinery

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A major challenge in high-fidelity turbomachinery flow computations is the need for high resolution in a very large domain of multiple blade-passages and multiple blade-rows. Scale-resolving turbulent solutions are prohibitively costly. The question is, what will it take to get high-fidelity solutions if we are only after time-mean flows for aerothermal performance? A novel two-scale approach is adopted to address the issue by coupling between a local fine-mesh domain in a singlepassage and a global coarse-mesh multi-passage domain. This is achieved by harnessing the extra product terms generated when averaging a nonlinear process in time, as well as in space. As such a space-time averaging is purposely utilized in either a direct mode or an inverse one in the two domains respectively. The source terms in a compact form (one scalar for one equation) can be conveniently obtained and used to enable the interaction between the single-passage fine-mesh and the multipassage coarse-mesh solutions. The converged solution for this two-scale coupled system should meet two seemingly conflicting requirements: an otherwise poorly conditioned local fine-mesh domain is now subject to a right environment/flow conditions, and an otherwise poorly resolved global coarse-mesh domain is now effectively subject to high resolution. In this paper, the concepts, the formulations of the framework methodology and the implementation methods will be described. The validity and feasibility of the approach for efficient scale-resolving high-fidelity turbomachinery flow simulations will be illustrated by several computational examples of practical interest.

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“…He applied the same idea to film cooling configurations (He, 2011a), dimples (He, 2013a) and lined acoustic intakes (He, 2013b). Recently (He, 2018), also extended the methodology to unsteady flows of short temporal and spatial scales (e.g. those due to selfexcited unsteady vortices and turbulence disturbances), where a source term-based approach was adopted to facilitate a two-way coupling in terms of time-averaged flow solutions.…”

Section: Introductionmentioning

confidence: 99%

Impact of Downstream Potential Perturbations on the Nonlinear Stability of a Generic Fan

Romera

Corral²

2020

J. Glob. Power Propuls. Soc.

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The dependence of the aerodynamic stability of fan blades with amplitude and nodal diameter of potential perturbations associated with the presence of pylons is studied. The analysis is conducted using a novel block-wise spatial Fourier decomposition of the reduced-passages to reconstruct the full-annulus solution. The method represents very efficiently unsteady flows generated by outlet static pressure non-uniformities. The explicit spatial Fourier approximation is exploited to characterize the relevance of each nodal diameter of outlet perturbations in the fan stall process, and its nonlinear stability is studied in a harmonic by harmonic basis filtering the nonlinear contribution of the rest. The methodology has been assessed for the NASA rotor 67. The maximum amplitude of the downstream perturbation at which the compressor becomes unstable and triggers a stall process has been mapped. It is concluded that the fan stability dependence with the amplitude of the perturbation is weaker than in the case of intake distortion. For perturbations with an odd number of nodal diameters, the nonlinear stability analysis leads to the same conclusions as to the small amplitude linear stability analysis. However, if the perturbations have an even number nodal diameters, the flow exhibits a supercritical bifurcation and have a stabilizing effect.

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Multiscale block spectral solution for unsteady flows

Cited by 23 publications

References 28 publications

Implicit Discontinuous Galerkin Solution on Unstructured Mesh for Turbine Blade Secondary Flow

Implicit Discontinuous Galerkin Solution on Unstructured Mesh for Turbine Blade Secondary Flow

Averaging for High Fidelity Modelling: Towards Large Eddy Simulations in Multi-Passage Multi-Row Configurations

Impact of Downstream Potential Perturbations on the Nonlinear Stability of a Generic Fan

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