The Implications of Tolerance Optimization on Compressor Blade Design

Dow, Eric; Wang, Qiqi

doi:10.1115/1.4030791

Cited by 46 publications

(13 citation statements)

References 13 publications

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“…The first step is to describe the design space uncertainties in a probabilistic framework. For example, model parameters are replaced with random variables (Loeven, Witteven and Bijl [4], Ahlfeld and Montomoli [12]), or a domain region is defined as a random field (Dow and Wang [13], Doostan, Geraci and Iaccarino [14]). In the second step, the model is run repeatedly for random samples drawn from the input probability distributions.…”

Section: Introductionmentioning

confidence: 99%

A hybrid approach combining DNS and RANS simulations to quantify uncertainties in turbulence modelling

Voet

Ahlfeld

Gaymann

et al. 2021

Applied Mathematical Modelling

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Uncertainty quantification (UQ) has recently become an important part of the design process of countless engineering applications. However, up to now in computational fluid dynamics (CFD) the errors introduced by the turbulent viscosity models in Reynolds-Averaged Navier Stokes (RANS) models have often been neglected in UQ studies. Although Direct Numerical Simulations (DNS) are physically correct, obtaining a large enough set of DNS data for UQ studies is currently computationally intractable.UQ based only on RANS simulations or on DNS often leads to physical and statistical inaccuracies in the output probability distribution functions (PDF). Therefore, three hybrid methods combining both RANS simulations and DNS to perform non-intrusive UQ are suggested in this work. Low-fidelity RANS simulations and high-fidelity DNS are combined to give an approximation of an output PDF using the advantages of both data sets: the physical accuracy via the DNS and the statistical accuracy via the RANS simulations. The hybrid methods are applied to the flow over 2D periodically arranged hills. It is shown that the Gaussian CoKriging (GCK) method is the best hybrid method and that a non-intrusive hybrid UQ approach combining both DNS and RANS simulations is possible, with both physically more accurate and statistically better PDF.

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Section: Introductionmentioning

confidence: 99%

A hybrid approach combining DNS and RANS simulations to quantify uncertainties in turbulence modelling

Voet

Ahlfeld

Gaymann

et al. 2021

Applied Mathematical Modelling

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“…(20) obtained for the MLMF is the same as the one obtained for the multifidelity MC in eq. (6). Moreover substutiting eq.…”

Section: Insights On Model Correlation and Optimal Samplingmentioning

confidence: 94%

“…Determining performance deterioration of turbomachines due to manufacturing variations is important to engine manufacturers when determining trade-offs between manufacturing cost and performance. Many studies have been conducted in the literature with focus on change in performance due to manufacturing variations on blade shapes 4,5,6,7,8,9,10 . The main challenge of modelling the effect of geometric variations on the blade performance is the large number of uncertain parameters that have to be considered.…”

Section: Introductionmentioning

confidence: 99%

“…UQ using the Monte Carlo method (MC) has been widely adopted 9,10,5,6 due to the following key reasons; (i) convergence of statistical moments is independent of the number of input uncertainties 12,13 , (ii) computational cost versus statistical errors can be established clearly hence the statistical estimates can be improved on the fly with additional samples 14 and (iii) the method can be applied to highly non-linear and non-smooth systems 15 . The computational cost of MC becomes prohibitively expensive for problems where the computational cost per sample is high due to the slow convergence with the number of samples.…”

Section: Introductionmentioning

confidence: 99%

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An adjoint‐assisted multilevel multifidelity method for uncertainty quantification and its application to turbomachinery manufacturing variability

Mohanamuraly

Müller

2021

Numerical Meth Engineering

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In this work we propose, analyse, and demonstrate a new adjoint-based multilevel multifidelity Monte Carlo framework called FastUQ. The framework unifies the multifidelity analysis of Ng 1 , multilevel multifidelity analysis of Geraci 2 and an adjoint error correction surrogate model due to Ghate 3. The optimal mean squared error estimator shows that introducing multilevel in a multifidelity framework guarantees reduction in computational cost. Moreover, unlike the surrogate model of Ghate 3 , the method does not suffer from the curse of dimensionality. FastUQ is demonstrated here to quantify uncertainties in aerodynamic parameters due to surface variations caused by the manufacturing processes for a highly loaded turbine cascade. A stochastic model for surface variations on the cascade is proposed and optimal dimensionality reduction of model parameters is realised using goal-based principal component analysis considering the adjoint sensitivities of multiple quantities of interest (QoI). The proposed method achieves a reduction of 70% in computational cost in predicting the mean quantities like total-pressure loss and mass flow rate compared to state-of-art MLMC method. The robustness of the method is shown in application to the highly non-linear case of a heavily loaded turbine cascade operating at off-design conditions.

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“…Based on measurement data, Principal Component Analysis (PCA) can be used to build a probabilistic model of variability from the empirical mean and covariance of surface deviations at different locations on the blade [22,23,24]. Following [25,26], we assume that the geometric variability in manufactured turbine blades can be accurately described as a non-stationary Gaussian Random Field e(s, ω), ω being a coordinate in the sample space Ω, and (Ω, F , P) a complete probability space. The arclength s ∈ [0, 1] parametrizes the location on the blade surface, starting at the trailing edge (s = 0), going around the leading edge (s = 1 2 ), and continuing back to the trailing edge on the opposite side of the blade (s = 1).…”

Section: Modeling Geometric Variabilitymentioning

confidence: 99%

Impact of geometric, operational, and model uncertainties on the non-ideal flow through a supersonic ORC turbine cascade

Razaaly

Persico

Congedo

2019

Energy

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Typical energy sources for Organic Rankine Cycle (ORC) power systems feature variable heat load and turbine inlet/outlet thermodynamic conditions. The use of organic compounds with heavy molecular weight introduces uncertainties in the fluid thermodynamic modeling. In addition, the peculiarities of organic fluids typically leads to supersonic turbine configurations featuring supersonic flows and shocks, which grow in relevance in the aforementioned off-design conditions; these features also depends strongly on the local blade shape, which can be influenced by the geometric tolerances of the blade manufacturing. This study presents an Uncertainty Quantification (UQ) analysis on a typical supersonic nozzle cascade for ORC applications, by considering a two-dimensional high-fidelity turbulent Computational Fluid Dynamic (CFD) model. Kriging-based techniques are used in order to take into account at a low computational cost, the combined effect of uncertainties associated to operating conditions, fluid parameters, and geometric tolerances. The geometric variability is described by a finite Karhunen-Loeve expansion representing a non-stationary Gaussian random field, entirely defined by a null mean and its autocorrelation function. Several results are illustrated about the ANOVA decomposition of several quantities of interest for different operating conditions, showing the importance of geometric uncertainties on the turbine performances.

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The Implications of Tolerance Optimization on Compressor Blade Design

Cited by 46 publications

References 13 publications

A hybrid approach combining DNS and RANS simulations to quantify uncertainties in turbulence modelling

A hybrid approach combining DNS and RANS simulations to quantify uncertainties in turbulence modelling

An adjoint‐assisted multilevel multifidelity method for uncertainty quantification and its application to turbomachinery manufacturing variability

Impact of geometric, operational, and model uncertainties on the non-ideal flow through a supersonic ORC turbine cascade

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