Fully turbulent discrete adjoint solver for non-ideal compressible flow applications

Vitale, Salvatore; Albring, Tim; Pini, Matteo; Gauger, Nicolas R.; Colonna, Piero

doi:10.22261/jgpps.z1fvoi

Cited by 25 publications

(35 citation statements)

References 41 publications

(52 reference statements)

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“…The original cascade, referred to as baseline in the following and shown in Figure 1, was the subject of several optimization trials in recent years [13,14,15]. In the present work, the baseline as well as the following optimized blades are studied from a UQ perspective.…”

Section: Problem Definition 21 Blade Configurationsmentioning

confidence: 99%

“…Novel semi-analytical design guidelines have been recently proposed [10,11] to define the blade channel shapes of such nozzles in a cost-e↵ective way. However, the design of these machines can greatly benefit from the application of automated shape-optimization methods [12,13,14,15]. These design methods lead to converging-diverging cascades which resemble an adapted nozzle in design conditions.…”

Section: Introductionmentioning

confidence: 99%

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Assessment of Deterministic Shape Optimizations Within a Stochastic Framework for Supersonic Organic Rankine Cycle Nozzle Cascades

Romei

Congedo

Persico

2019

Journal of Engineering for Gas Turbines and Power

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The design of converging–diverging blades for organic Rankine cycle (ORC) applications widely relies on automated shape-optimization processes. As a result, the optimization produces an adapted-nozzle cascade at the design conditions. However, only few works account for the uncertainties in those conditions and their consequences on cascade performance. The proposed solution, i.e., including uncertainties within the optimization routine, demands an overall huge computational cost to estimate the target output statistic at each iteration of the optimization algorithm. With the aim of understanding if this computational cost is avoidable, we study the impact of uncertainties in the design conditions on the robustness of deterministically optimized profiles. Several optimized blades, obtained with different objective functions, constraints, and design variables, are considered in the present numerical analysis, which features a turbulent compressible flow solver and a state-of-the-art uncertainty-quantification (UQ) method. By including measured field variations in the formulation of the UQ problem, we show that a deterministic shape optimization already improves the robustness of the profile with respect to the baseline configuration. Guidelines about objective functions and blade parametrizations for deterministic optimizations are also provided. Finally, a novel methodology to estimate the mass-flow-rate probability density function (PDF) for choked supersonic turbines is proposed, along with a robust reformulation of the constraint problem without increasing the computational cost.

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Section: Problem Definition 21 Blade Configurationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Assessment of Deterministic Shape Optimizations Within a Stochastic Framework for Supersonic Organic Rankine Cycle Nozzle Cascades

Romei

Congedo

Persico

2019

Journal of Engineering for Gas Turbines and Power

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“…Those methodologies play an even more critical role in the case of technologies entailing NICFD flows, where design experience and experimental information is very limited [3]. In the context of deterministic optimization, concerted research efforts have been recently devoted to develop FSO techniques for NICFD applications, such as for nozzles and turbomachinery blades, using either gradient-based [4] [5] [6] [7] or gradient-free algorithms. The latters are often coupled with surrogate models to reduce the computational cost [8] [9] [10] [11] [12].…”

Section: Introductionmentioning

confidence: 99%

“…The blade of interest here is a typical 2D ORC turbine cascade [13], previously studied in the context of gradientbased [4] [5] [6] or gradient-free [9] deterministic optimization.…”

Section: Introductionmentioning

confidence: 99%

Optimization of an ORC Turbine Stator Under Turbulence Uncertainty

Razaaly¹,

Gori²,

Iaccarinoc³

et al. 2019

GPPS Zurich19

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Organic Rankine Cycle (ORC) turbines usually operate in thermodynamic regions characterized by high-pressure ratios and strong non-ideal gas effects in the flow expansion, complicating their aerodynamic design significantly. This study presents the shape optimization of a typical 2D ORC turbine cascade (Biere), under epistemic uncertainties due to turbulence models (RANS). A design vector of size eleven controls the blade geometry parametrized with Bsplines. The EQUiPS module integrated into the SU2 CFD suite, incorporating perturbations to the eigenvalues and the eigenvectors of the modeled Reynolds stress tensor, is used to evaluate the interval estimates on the predictions of integrated Quantity of Interest (QoI), performing only five specific RANS simulations. For a given blade profile, the QoIs total loss pressure and mass flow rate, are assumed to be independent uniform random variables, defined by those estimates. A global surrogate-based method allowing to propose different designs at each optimization step is used to solve the constrained mono-objective optimization problem. To illustrate the suitability of the method, several statistics of the total pressure are considered for the minimization, under the constraint that the mean of the mass flow rate to be within a range.

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“…NICFD stands for Non Ideal Compressible Fluid Dynamics. NICFD is a new branch of fluid mechanics [120] with the flows of dense vapours, supercritical fluids, and two-phase fluids, in cases in which the ideal gas law does not apply [121]. In these flows, the variation of the speed of sound with density is different if compared to the flow of an ideal gas [122].…”

Section: Solution For Non Ideal Compressible Fluid Dynamicsmentioning

confidence: 99%

Development and application of simulation tools for supercritical carbon dioxide radial inflow turbine

Qi¹

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Supercritical CO 2 (sCO 2) cycles are considered a promising technology for next generation concentrated solar thermal, waste heat recovery and nuclear applications. Particularly at small to medium scale, where radial inflow turbines can be employed, using sCO 2 results in both system advantages and simplifications of the turbine design, leading to improved performance and cost reductions. Using CO 2 as operating fluid for a radial inflow turbine creates new design, new operating and new modelling challenges. These include mean-line design with enhancing loss models suitable for large dense gas, non-ideal gas behaviour within the blade channel and blade geometry optimisations. Since the supercritical CO 2 has a larger density than the steam or air at the same condition, it might not be adequate to use the well developed loss model to conduct the mean-line design of the whole stage. Since the flow phenomena within the blade channels are complex, involving fluid flow, shock wave position, boundary layer separation, use of the ideal gas model to predict the performance of the turbine might not be adequate. To address these issues, the enhanced one-dimensional loss models, a non-ideal compressible fluid dynamics Riemann solver, and a stator geometry optimiser are developed to create insight on the flow dynamics of supercritical CO 2 radial inflow turbines. The mean-line design results, nonideal compressible fluid dynamics Riemann solver development and stator geometry optimisation are described in details next. The first part aims to provide new insight towards the design of radial turbines for operation with sCO 2 in the 100 kW to 200 kW range. The quasi one-dimensional (1D) mean-line design code TOP-GEN is enhanced to explore and map the radial turbine design space. This mapping process over a state space defined by Head and Flow coefficients allows the selection of an optimum turbine design, while balancing performance and geometrical constraints. By considering three operating points with varying power levels and rotor speeds the effect of these on feasible design space and performance is explored. This provides new insight towards the key geometric features and operational constraints that limit the design space as well as scaling effects. Finally review of the loss breakdown of the designs elucidates the importance of the respective loss mechanisms. Similarly it allows the identification of a design directions that lead to improved performance. Overall this work shows that turbine design with efficiencies in the range 78 % to 82 % are possible in this power range and provides insight into the design space that allows the selection of optimum designs. Next, a new solver for OpenFOAM for non-ideal compressible fluid dynamics is developed. The new solver uses a real-gas Riemann solver, which is based on look-up tables to capture real gas properties. This is achieved by the addition of a new thermodynamic library tightly coupled with the OpenFOAM library. For the solver, the HLLC ALE flux calculator has been modifi...

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Fully turbulent discrete adjoint solver for non-ideal compressible flow applications

Cited by 25 publications

References 41 publications

Assessment of Deterministic Shape Optimizations Within a Stochastic Framework for Supersonic Organic Rankine Cycle Nozzle Cascades

Assessment of Deterministic Shape Optimizations Within a Stochastic Framework for Supersonic Organic Rankine Cycle Nozzle Cascades

Optimization of an ORC Turbine Stator Under Turbulence Uncertainty

Development and application of simulation tools for supercritical carbon dioxide radial inflow turbine

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