Thermal Performance of Transonic Cooled Tips in a Turbine Cascade

Zhou, Chao

doi:10.2514/1.b35392

Cited by 15 publications

(8 citation statements)

References 33 publications

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“…The interactions with the shocks and their angle are affected by the trailing edge of the next blade. All described flow features are coherent with the previously observed tornado vortex phenomenon, which according to Hagen and Kurosaka [29], Carnevale et al [15] and recently Zhou et al [30], is responsible for the local reduction of the cooling effectiveness. Fig.…”

Section: Grid and Test Case Modellingsupporting

confidence: 89%

Autonomous Uncertainty Quantification for Discontinuous Models Using Multivariate Padé Approximations

Ahlfeld

Montomoli

Carnevale

et al. 2018

Journal of Turbomachinery

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Problems in turbomachinery computational fluid dynamics (CFD) are often characterized by nonlinear and discontinuous responses. Ensuring the reliability of uncertainty quantification (UQ) codes in such conditions, in an autonomous way, is challenging. In this work, we suggest a new approach that combines three state-of-the-art methods: multivariate Padé approximations, optimal quadrature subsampling (OQS), and statistical learning. Its main component is the generalized least-squares multivariate Padé–Legendre (PL) approximation. PL approximations are globally fitted rational functions that can accurately describe discontinuous nonlinear behavior. They need fewer model evaluations than local or adaptive methods and do not cause the Gibbs phenomenon like continuous polynomial chaos methods. A series of modifications of the Padé algorithm allows us to apply it to arbitrary input points instead of optimal quadrature locations. This property is particularly useful for industrial applications, where a database of CFD runs is already available, but not in optimal parameter locations. One drawback of the PL approximation is that it is nontrivial to ensure reliability. To improve stability, we suggest to couple it with OQS. Our reasoning is that least-squares errors, caused by an ill-conditioned design matrix, are the main source of error. Finally, we use statistical learning methods to check smoothness and convergence. The resulting method is shown to efficiently and correctly fit thousands of partly discontinuous response surfaces for an industrial film cooling and shock interaction problem using only nine CFD simulations.

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Section: Grid and Test Case Modellingsupporting

confidence: 89%

Autonomous Uncertainty Quantification for Discontinuous Models Using Multivariate Padé Approximations

Ahlfeld

Montomoli

Carnevale

et al. 2018

Journal of Turbomachinery

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“…OTL flow Mach number is reduced greatly due to the blockage effect by cooling injection, which is in concert with the findings of Ref. [45]. OTL flow becomes subsonic near PS edge, which is upstream of cooling ejection, as well as in coolant wakes.…”

Section: Tip Leakagesupporting

confidence: 87%

Impact of Cooling Injection on Shock Wave Over a Flat Tip in High Pressure Turbine

Zeng

Jiang

et al. 2021

Journal of Turbomachinery

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Cooling design of highly-loaded turbine blade tips is challenged by the scarcity of experimental data and the lack of physical understanding in cooling and over-tip leakage (OTL) interaction under transonic conditions. To address these issues, this paper carried out transient thermal measurements through infrared thermography on a transonic flat tip with and without cooling injection. Experimental data of Nusselt number and cooling effectiveness were obtained and compared with computational fluid dynamics results for numerical validation. Both experimental data and simulation results show that cooling injection drastically augments tip Nusselt number near pressure side which is upstream of ejection, and in areas around coolant holes. Moreover, a strikingly low Nusselt number stripe is observed downstream of cooling injection from one of the holes in aft portion of blade. The strip is directed transverse to local OTL streamline flowing from pressure to suction side and sprawls to adjacent coolant wakes. Further numerical analyses concluded that cooling injection changes tip aerodynamics and overtip shock wave structure fundamentally. Oblique shock waves across uncooled flat tip are replaced by a confined shock train downstream of cooling injection and between cooling holes, which is constituted by two shocks normal to local OTL flow coming from pressure side. Across the first shock, density and pressure increases abruptly, contributing to thickening of tip boundary layer and the plummet of skin friction on tip surface, which is responsible for the sharp decline of tip Nusselt number and therefore, formation of low heat transfer stripe downstream cooling injection.

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“…Within the figure, color variations denote tip surface heat flux variations, and greyscale variations denote flow density gradient distributions which were employed in these studies utilized squealer configurations [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72], partial squealer configurations [61,64,69], and winglet configurations [73,74]. Smooth blade tips were employed by Thorpe et al [75], Green et al [59], Key and Arts [62], O'Dowd et al [76,77], Wheeler et al [78], Zhang et al [55,56], Shyam et al [79], Atkins et al [80], Wheeler and Saleh [70], Anto et al [81], Virdi et al [68], Wheeler and Sandberg [82], Li et al [65], Zhang et al [83], Zhang and He [84], Wang et al [69], Zhou [71], Jung et al [61], Gao et al [85], and Kim et al [64]. Most of these investigations (which involved experimental measurements) employed annular or linear cascades with stationary blades.…”

Section: Interactions Which Included Thermal Transport and Convectivementioning

confidence: 99%

Recent investigations of shock wave effects and interactions

et al. 2020

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Despite over fifty years of research on shock wave boundary layer effects and interactions, many related technical issues continue to be controversial and debated. The present survey provides an overview of the present state of knowledge on such effects and interactions, including discussions of: (i) general features of shock wave interactions, (ii) test section configurations for investigation of shock wave boundary layer interactions, (iii) origins and sources of unsteadiness associated with the interaction region, (iv) interactions which included thermal transport and convective heat transfer, and (v) shock wave interaction control investigations. Of particular interest are origins and sources of low-frequency, large-scale shock wave unsteadiness, flow physics of shock wave boundary layer interactions, and overall structure of different types of interactions. Information is also provided in regard to shock wave investigations, where heat transfer and thermal transport were important. Also considered are investigations of shock wave interaction control strategies, which overall, indicate that no single shock wave control strategy is available, which may be successfully applied to different shock wave arrangements, over a wide range of Mach numbers. Overall, the survey highlights the need for additional understanding of fundamental transport mechanisms, as related to shock waves, which are applicable to turbomachinery, aerospace, and aeronautical academic disciplines.

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Thermal Performance of Transonic Cooled Tips in a Turbine Cascade

Cited by 15 publications

References 33 publications

Autonomous Uncertainty Quantification for Discontinuous Models Using Multivariate Padé Approximations

Autonomous Uncertainty Quantification for Discontinuous Models Using Multivariate Padé Approximations

Impact of Cooling Injection on Shock Wave Over a Flat Tip in High Pressure Turbine

Recent investigations of shock wave effects and interactions

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