Uncertainty Quantification of an ORC turbine blade under a low quantile constrain

Typical energy sources for ORC power systems, such as waste heat recovery or biomass, geothermal, and solar energy, typically feature variable heat load and turbine-inlet thermodynamic conditions. In this context, advanced uncertainty quantification and robust optimization methodologies are nowadays available and could be used during the ORC turbine design process in order to account for multiple uncertainties. This study presents a preliminary ANOVA and Uncertainty Quantification analysis, prior to apply robust shape optimization approach to ORC turbine blades, to overcome the limitation of a deterministic optimization that neglects the effect of uncertainties of operating conditions or design variables. The analysis is performed by applying a two-dimensional inviscid computational fluid dynamic model to a typical supersonic turbine cascade for ORC applications. The working fluid is siloxane MDM, which in the conditions of interest exhibits relevant non-ideal effects, here modeled by using of a Peng-Robinson-Stryjek-Vera equation of state

corrigendum to the article entitled uncertainty quantification of inviscid flows through a supersonic orc turbine cascade in energy procedia volume 129 september 2017 pages 1149 1155

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Simulation d'écoulements de gaz denses en turbines

Des gaz denses particuliers (gaz BZT) présentent en régime transsonique des propriétés atypiques qui peuvent être exploitées pour obtenir des rendements élevés dans des turbines les utilisant comme fluides moteurs. La difficulté d'étudier expérimentalement ces écoulements motive le développement d'outils de simulation efficaces. Un code turbulent (RANS) non-structuré sera appliqué à la simulation d'une turbine en considérant différents points de fonctionnement pour le gaz BZT

Accelerating hypersonic reentry simulations using deep learning-based hybridization (with guarantees)

In this paper, we are interested in the acceleration of numerical simulations. We focus on a hypersonic planetary reentry problem whose simulation involves coupling fluid dynamics and chemical reactions. Simulating chemical reactions takes most of the computational time but, on the other hand, cannot be avoided to obtain accurate predictions. We face a trade-off between cost-efficiency and accuracy: the simulation code has to be sufficiently efficient to be used in an operational context but accurate enough to predict the phenomenon faithfully. To tackle this trade-off, we design a hybrid simulation code coupling a traditional fluid dynamic solver with a neural network approximating the chemical reactions. We rely on their power in terms of accuracy and dimension reduction when applied in a big data context and on their efficiency stemming from their matrix-vector structure to achieve important acceleration factors ($\times 10$ to $\times 18.6$). This paper aims to explain how we design such cost-effective hybrid simulation codes in practice. Above all, we describe methodologies to ensure accuracy guarantees, allowing us to go beyond traditional surrogate modeling and to use these codes as references.Comment: Under revie

Optimal Design of ORC Turbine Blades Under Geometric and Operational Uncertainties

International audienceTypical energy sources for Organic Rankine Cycle (ORC) power systems feature variable heat load, hence turbine inlet/outlet thermodynamic conditions. The use of organic compounds with heavy molecular weight introduces uncertainties in the fluid thermodynamic modeling and complexity in the turbomachinery aerodynamics, with supersonic flows and strong shocks, which grow in relevance in the aforementioned off-design conditions. These features also depend strongly on the local blade shape, which can be influenced by the geometric tolerances of the blade manufacturing. This study presents a Robust Optimization (RO) analysis on a typical supersonic nozzle cascade for ORC applications under the combined effect of uncertainties associated to operating conditions and geometric tolerances: a classical formulation consisting in minimizing the mean of a well-suited performance function, constraining the average mass flow rate to be within a prescribed range is addressed, by means of a bi-level Gaussian Process (GP) surrogate-based approach. Influence of the operating conditions range and geometric variability are investigated considering several scenarios, in which the different effects act in combination or separated; results indicate that the combination of different classes of uncertainites has an impact on the robust-optimal blade shape and, in turn, in their response in the frame of uncertain scenarios

Influence of the heat transfer model on the estimation of mass transfer

The efficient design and performance of turbopumps in rocket propulsion systems demands a robust numerical tool predicting the phenomenon of cavitation in cryogenic fluids. Building robust models for this complex physics, according to a not-large set of experimental data, is very challenging. In fact, cryogenic fluids are thermo-sensitive, and therefore, thermal effects and strong variations in fluid properties can alter the cavitation properties. This work illustrates how thermal effects can be estimated considering both convective and conductive heat transfer. The Rayleigh-Plesset (RP) equation is coupled with a bubbly flow model to assess the prediction of thermal effects, and used in order to simulate some reference experimental test-cases in literature. Moreover, some tuning parameters, not measured experimentally, such as initial volume vapor phase α0 and initial radius bubbles R0 and the specific coefficient of the heat transfer models are treated like epistemic uncertainties in a probabilistic framework, permitting to obtain numerical error bars for some quantities of interest, and then to perform a robust analysis of the thermal effect

Quantifying uncertainties in a Venturi multiphase configuration

Modeling the complex physical structures of cavitating flows makes numerical simulation far to be predictive, and still a challenging issue. Understanding the role of physical and parametric uncertainties in cavitating flows is of primary importance in order to obtain reliable numerical solutions. In this paper, the impact of various sources of uncertainty on the prediction of cavitating flows is analyzed by coupling a non-intrusive stochastic method with a cavitating CFD solver. The proposed analysis is applied to a Venturi tube, where experimental data concerning vapor formation are available in literature. Numerical solutions with their associated error bars are compared to the experimental curves displaying a large sensitivity to the uncertainties of inlet boundary conditions. Furthermore, this is confirmed by computing the hierarchy of most predominant uncertainties by means of an ANOVA analysis. Finally, a simple algorithm is proposed in order to provide an optimized set of parameters for the cavitation model, thus permitting to obtain a deterministic solution equal to the most probable one when considering physical inlet uncertainties

Experimental assessment of the open-source SU2 CFD suite for ORC applications

Abstract The first-ever experimental assessment of a Computational Fluid Dynamics (CFD) software for Non-Ideal Compressible-Fluid Dynamics (NICFD) flows of interest for ORC applications is presented here. Numerical results using SU2, the open-source suite for multi-physics simulation and design recently extended to deal with complex thermodynamic models of organic fluids, are compared here to experimental results from the Test-Rig for Organic VApours (TROVA) of the Laboratory of Compressible-fluid dynamics for Renewable Energy Applications (CREA), Politecnico di Milano. Experimental results regard supersonic expanding flows of siloxane fluid MDM (Octamethyltrisiloxane, C 8 H 24 O 2 Si 3 ) in non-ideal conditions representative of ORC applications. Three different geometries are considered for the assessment of the CFD solver. The first is a converging-diverging nozzle, representative of ORC supersonic stators, in which the fluid is accelerated to supersonic speed from highly non-ideal conditions, with inlet compressibility factor Z = Pv/(RT), computed using reference Equations Of State (EOS) for MDM fluid, as low as Z ~ 0.81. The second geometry is a diamond-shaped airfoil at a neutral angle of attack. The airfoil is plunged into a supersonic flow at Mach 1.5 and Z ~ 0.9, in mildly non-ideal conditions. Oblique shock waves are observed at the airfoil leading edge and interact with the wind-tunnel walls and the rarefaction fan from the airfoil. This test case is useful to understand the physics of oblique shock-wall and shock-shock interactions in turbine cascades operating in off-design conditions. The third geometry is a supersonic backward facing step, in which the formation of an oblique shock is observed experimentally at the reattachment point past the step. The Mach number is around 1.1 and the compressibility factor Z ~ 0.89. This geometry is representative of the trailing edge of turbine blades and it is useful to study the formation of fish-tail shock waves. These NICFD flows are fairly well captured by the CFD solver, thus confirming the validity of both the thermodynamic models and of the CFD implementation, using both the Euler equations for inviscid flows with negligible thermal conductivity and the full Reynolds-averaged compressible Navier-Stokes equations, for non-ideal compressible turbulent flows. In the considered shocked flows, grid adaptation is found to be key to capture the relevant flow features using a reasonable amount of grid points

A One-Time Truncate and Encode Multiresolution Stochastic Framework

In this work a novel adaptive strategy for stochastic problems, inspired to the classical Harten's framework, is presented. The proposed algorithm allows building, in a very general manner, stochastic numerical schemes starting from a whatever type of deterministic schemes and handling a large class of problems, from unsteady to discontinuous solutions. Its formulations permits to recover the same results concerning the interpolation theory of the classical multiresolution approach, but with an extension to uncertainty quantification problems. The interest of the present strategy is demonstrated by performing several numerical problems where different forms of uncertainty distributions are taken into account, such as discontinuous and unsteady custom-defined probability density functions. In addition to algebraic and ordinary differential equations, numerical results for the challenging 1D Kraichnan-Orszag are reported in terms of accuracy and convergence. Finally, a two degree-of-freedom aeroelastic model for a subsonic case is presented. Though quite simple, the model allows recovering some physical key aspect, on the fluid/structure interaction, thanks to the quasi-steady aerodynamic approximation employed. The injection of an uncertainty is chosen in order to obtain a complete parameterization of the mass matrix. All the numerical results are compared with respect to classical Monte Carlo solution and with a non-intrusive Polynomial Chaos method