Effect of Uncertainty in Blowing Ratio on Film Cooling Effectiveness

Babaee, Hessam; Wan, Xiaoliang; Acharya, Sumanta

doi:10.1115/1.4025562

Cited by 21 publications

(3 citation statements)

References 22 publications

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“…In particular, we solved the velocity field in the entire domain using the spectral/hp element method on an unstructured mesh with 4008 quadrilateral elements and polynomial order 5. For more details on the spectral element method see for example [56,57]. At the inlet, a parabolic velocity is prescribed, with an average velocity of u¯.…”

Section: Demonstrationsmentioning

confidence: 99%

Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with time-dependent bases

Donello,

Palkar,

Naderi

et al. 2023

Proc. R. Soc. A.

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Time-dependent basis reduced-order models (TDB ROMs) have successfully been used for approximating the solution to nonlinear stochastic partial differential equations (PDEs). For many practical problems of interest, discretizing these PDEs results in massive matrix differential equations (MDEs) that are too expensive to solve using conventional methods. While TDB ROMs have the potential to significantly reduce this computational burden, they still suffer from the following challenges: (i) inefficient for general nonlinearities, (ii) intrusive implementation, (iii) ill-conditioned in the presence of small singular values and (iv) error accumulation due to fixed rank. To this end, we present a scalable method for solving TDB ROMs that is computationally efficient, minimally intrusive, robust in the presence of small singular values, rank-adaptive and highly parallelizable. These favourable properties are achieved via oblique projections that require evaluating the MDE at a small number of rows and columns. The columns and rows are selected using the discrete empirical interpolation method (DEIM), which yields near-optimal matrix low-rank approximations. We show that the proposed algorithm is equivalent to a CUR matrix decomposition. Numerical results demonstrate the accuracy, efficiency and robustness of the new method for a diverse set of problems.

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Section: Demonstrationsmentioning

confidence: 99%

Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with time-dependent bases

Donello,

Palkar,

Naderi

et al. 2023

Proc. R. Soc. A.

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show abstract

“…For the spatial discretization, spectral/hp element method is used with N e = 4008 quadrilateral elements and polynomial order of 5. For more details of the spectral/hp element method see [58][59][60]. The fourth-order Runge-Kutta scheme is used for the time integration with ∆t = 5 × 10 −4 and the system is solved till t f = 5 units of time.…”

Section: Incompressible Reactive Flowmentioning

confidence: 99%

On-the-fly Reduced Order Modeling of Passive and Reactive Species via Time-Dependent Manifolds

Ramezanian,

Nouri,

Babaee

2021

Preprint

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One of the principal barriers in developing accurate and tractable predictive models in turbulent flows with a large number of species is to track every species by solving a separate transport equation, which can be computationally impracticable. In this paper, we present an on-the-fly reduced order modeling of reactive as well as passive transport equations to reduce the computational cost. The presented approach seeks a low-rank decomposition of the species to three time-dependent components: (i) a set of orthonormal spatial modes, (ii) a low-rank factorization of the instantaneous species correlation matrix, and (iii) a set of orthonormal species modes, which represent a low-dimensional time-dependent manifold. Our approach bypasses the need to solve the full-dimensional species to generate high-fidelity data -as it is commonly performed in data-driven dimension reduction techniques such as the principle component analysis. Instead, the low-rank components are directly extracted from the species transport equation. The evolution equations for the three components are obtained from optimality conditions of a variational principle. The time-dependence of the three components enables an on-the-fly adaptation of the low-rank decomposition to transient changes in the species. Several demonstration cases of reduced order modeling of passive and reactive transport equations are presented.

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“…This can be attributed to the small mass flow rate of the coolant. Furthermore, low blowing ratios cause the detrimental ingestion of the hot mainstream gas into the hole [9,21]. Bogard [22] reported that the overall film cooling effectiveness increases with the blowing ratio up to the blowing ratio of 0.6.…”

Section: Introductionmentioning

confidence: 99%

Effects of Bulk Flow Pulsations on Film Cooling with Two Sister Holes

Baek

Ahn

2021

Applied Sciences

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In a triple-hole system comprising a primary hole and two sister holes, when the sister holes are positioned slightly downstream of the main hole under steady flow conditions, their jets generate an anti-counter-rotating vortex pair. Vortex interactions between the jets increase the effectiveness of adiabatic film cooling. In this study, a series of large-eddy simulations were conducted to understand how pulsations in the main flow affect film cooling in a triple hole. To understand the effects of pulsations on film cooling performance is important for better cooling design of the gas turbine engines. The numerical simulations were carried out on a flat plate geometry with a triple cylindrical hole system at 35° injection angle. The pulsations were approximately sinusoidal, and their effect on film cooling was investigated at several frequencies (2, 16, and 32 Hz) and Strouhal numbers (Sr = 0.1005, 0.8043, and 1.6085) at an average blowing ratio of 0.5. The results for the triple-hole system were compared with those for a single hole for the same amount of cooling air and the same cross-sectional area of the holes. Increasing the Strouhal number of the main flow decreased η in both systems. However, at each Strouhal number, η was higher in the triple hole. Furthermore, the triple-hole system was found to be better for film cooling than a single-hole system for higher values of the pulsation Strouhal number. Contours of time-averaged film cooling effectiveness and dimensionless temperature, instantaneous film cooling effectiveness contours on a test plate, mean velocity magnitude contours in the hole, and Q-contours for the triple holes under the application of pulsations to the flow were investigated.

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Effect of Uncertainty in Blowing Ratio on Film Cooling Effectiveness

Cited by 21 publications

References 22 publications

Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with time-dependent bases

Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with time-dependent bases

On-the-fly Reduced Order Modeling of Passive and Reactive Species via Time-Dependent Manifolds

Effects of Bulk Flow Pulsations on Film Cooling with Two Sister Holes

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