Xavier Merle

Bayesian quantification of thermodynamic uncertainties in dense gas flows

Abstract A Bayesian inference methodology is developed for calibrating complex equations of state used in numerical fluid flow solvers. Precisely, the input parameters of three equations of state commonly used for modeling the thermodynamic behavior of the so-called dense gas flows, – i.e. flows of gases characterized by high molecular weights and complex molecules, working in thermodynamic conditions close to the liquid–vapor saturation curve – are calibrated by means of Bayesian inference from reference aerodynamic data for a dense gas flow over a wing section. Flow thermodynamic conditions are such that the gas thermodynamic behavior strongly deviates from that of a perfect gas. In the aim of assessing the proposed methodology, synthetic calibration data – specifically, wall pressure data – are generated by running the numerical solver with a more complex and accurate thermodynamic model. The statistical model used to build the likelihood function includes a model-form inadequacy term, accounting for the gap between the model output associated to the best-fit parameters and the true phenomenon. Results show that, for all of the relatively simple models under investigation, calibrations lead to informative posterior probability density distributions of the input parameters and improve the predictive distribution significantly. Nevertheless, calibrated parameters strongly differ from their expected physical values. The relationship between this behavior and model-form inadequacy is discussed.

Sensitivity of Supersonic ORC Turbine Injector Designs to Fluctuating Operating Conditions

The design of an efficient organic rankine cycle (ORC) expander needs to take properly into account strong real gas effects that may occur in given ranges of operating conditions, which can also be highly variable. In this work, we first design ORC turbine geometries by means of a fast 2-D design procedure based on the method of characteristics (MOC) for supersonic nozzles characterized by strong real gas effects. Thanks to a geometric post-processing procedure, the resulting nozzle shape is then adapted to generate an axial ORC blade vane geometry. Subsequently, the impact of uncertain operating conditions on turbine design is investigated by coupling the MOC algorithm with a Probabilistic Collocation Method (PCM) algorithm. Besides, the injector geometry generated at nominal operating conditions is simulated by means of an in-house CFD solver. The code is coupled to the PCM algorithm and a performance sensitivity analysis, in terms of adiabatic efficiency and power output, to variations of the operating conditions is carried out.Copyright

Staggered Finite Difference Scheme for Global Stability Analysis of Incompressible Flows

Stability of flows, and especially global stability, has become a crucial point in fluid mechanics over the past few decades. Not only asymptotic dynamics is of interest in this case, which is a natural issue of stability analyses, but also short time behaviour with flow control objectives. However, with certain configurations, namely with finitedifference schemes and collocated grids, problems with pressure boundary conditions can occur for incompressible flows. These difficulties are mainly due to decoupling between the velocity and the pressure in the linearized Navier-Stokes equations as well as the continuity equation. In this paper, we show that a staggered approach allows to overcome these defects. Three academic test cases a backward facing step, a flow over an open cavity and a flow around a cylinder the stability of which is analyzed with both the staggered and the collocated approaches, and the results are compared.