Numerical Investigations of Film Cooling

Linn, Jens; Kloker, Markus J.

doi:10.1007/978-3-540-77819-6_9

Cited by 22 publications

(3 citation statements)

References 4 publications

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“…All computations are performed with the compressible high-order in-house DNS code ; fundamentals are described in Babucke (2009), Linn & Kloker (2008, 2011), Keller & Kloker (2014, 2016) and Wenzel et al. (2018 a ).…”

Section: Methodology and Numerical Set-upmentioning

confidence: 99%

“…All computations are performed with the compressible high-order in-house DNS code NS3D; fundamentals are described in Babucke (2009), Linn & Kloker (2008, Keller & Kloker (2014, 2016 and Wenzel et al (2018a). With the velocity vector u = [u, v, w] T with components in the streamwise, wall-normal and spanwise directions x, y and z, the dimensionless solution vector is Q = [ρ, ρu, ρv, ρw, E] T , where ρ and E are the density and the total energy, respectively.…”

Section: Methodsmentioning

confidence: 99%

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Self-similar compressible turbulent boundary layers with pressure gradients. Part 1. Direct numerical simulation and assessment of Morkovin’s hypothesis

et al. 2019

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A direct numerical simulation study of self-similar compressible flat-plate turbulent boundary layers (TBLs) with pressure gradients (PGs) has been performed for inflow Mach numbers of 0.5 and 2.0. All cases are computed with smooth PGs for both favourable and adverse PG distributions (FPG, APG) and thus are akin to experiments using a reflected-wave set-up. The equilibrium character allows for a systematic comparison between sub- and supersonic cases, enabling the isolation of pure PG effects from Mach-number effects and thus an investigation of the validity of common compressibility transformations for compressible PG TBLs. It turned out that the kinematic Rotta–Clauser parameter $\unicode[STIX]{x1D6FD}_{K}$ calculated using the incompressible form of the boundary-layer displacement thickness as length scale is the appropriate similarity parameter to compare both sub- and supersonic cases. Whereas the subsonic APG cases show trends known from incompressible flow, the interpretation of the supersonic PG cases is intricate. Both sub- and supersonic regions exist in the boundary layer, which counteract in their spatial evolution. The boundary-layer thickness $\unicode[STIX]{x1D6FF}_{99}$ and the skin-friction coefficient $c_{f}$, for instance, are therefore in a comparable range for all compressible APG cases. The evaluation of local non-dimensionalized total and turbulent shear stresses shows an almost identical behaviour for both sub- and supersonic cases characterized by similar $\unicode[STIX]{x1D6FD}_{K}$, which indicates the (approximate) validity of Morkovin’s scaling/hypothesis also for compressible PG TBLs. Likewise, the local non-dimensionalized distributions of the mean-flow pressure and the pressure fluctuations are virtually invariant to the local Mach number for same $\unicode[STIX]{x1D6FD}_{K}$-cases. In the inner layer, the van Driest transformation collapses compressible mean-flow data of the streamwise velocity component well into their nearly incompressible counterparts with the same $\unicode[STIX]{x1D6FD}_{K}$. However, noticeable differences can be observed in the wake region of the velocity profiles, depending on the strength of the PG. For both sub- and supersonic cases the recovery factor was found to be significantly decreased by APGs and increased by FPGs, but also to remain virtually constant in regions of approximated equilibrium.

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Section: Methodology and Numerical Set-upmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Self-similar compressible turbulent boundary layers with pressure gradients. Part 1. Direct numerical simulation and assessment of Morkovin’s hypothesis

et al. 2019

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“…Other strategies for the film cooling technique consist in wall-parallel and inclined blowing. In both cases a wall-parallel velocity component is provided to the injected coolant, which helps coolant staying closer to the wall, as observed in Linn and Kloker (2008). The recent work of Peter and Kloker (2022) investigated via DNS the effect of film cooling in a supersonic turbulent boundary layer with wall-parallel blowing through a backward facing step, for the thermal protection of the nozzle extension of rocket engines.…”

Section: Introductionmentioning

confidence: 99%

Turbulence Effect on Transpiration Cooling Effectiveness Over a Flat Plate in Hypersonic Flow and Sensitivity to Injection Parameters

Cerminara

2023

Flow Turbulence Combust

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This work presents a numerical study of coolant porous injection in hypersonic turbulent boundary layer, with an analysis of blowing ratio and pore diameter effects on the cooling performance. Direct numerical simulations (DNS) are carried out for a Mach 5 flow over a flat plate with induced transition, and with a porous injection model to mimic injection from a bed of equally-spaced circular pores. The cooling performance in turbulent flow is compared to laminar 2D flow cases. Results show downstream development of a turbulent wedge-shaped structure, where a dramatic decay of the near-wall coolant concentration is observed. Blowing ratio and pore size are seen to affect the calmed and transitional regions, however they have a marginal or negligible effect within the turbulent region. A cooling effectiveness deficit/reduction of 15% to 30% for the turbulent cases, with respect to the laminar 2D cases, is observed above the injection region due to the 3D flow effects associated with the porous injection, whereas it reaches values as high as 80% in the developed turbulent region due to the turbulent convective effects. The present results shed light on the effects of turbulence on porous wall cooling and clearly indicate that alternative (ad-hoc) injection strategies and parameter calibration are needed to guarantee appropriate wall cooling in a turbulent flow.

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