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http://hdl.handle.net/10985/18556
Dense-gas effects on compressible boundary-layer stability
GLOERFELT, Xavier; ROBINET, Jean-Christophe; SCIACOVELLI, Luca; CINNELLA, Paola; GRASSO, Francesco
A study of dense-gas effects on the stability of compressible boundary-layer flows is conducted. From the laminar similarity solution, the temperature variations are small due to the high specific heat of dense gases, leading to velocity profiles close to the incompressible ones. Concurrently, the complex thermodynamic properties of dense gases can lead to unconventional compressibility effects. In the subsonic regime, the Tollmien–Schlichting viscous mode is attenuated by compressibility effects and becomes preferentially skewed in line with the results based on the ideal-gas assumption. However, the absence of a generalized inflection point precludes the sustainability of the first mode by inviscid mechanisms. On the contrary, the viscous mode can be completely stable at supersonic speeds. At very high speeds, we have found instances of radiating supersonic instabilities with substantial amplification rates, i.e. waves that travel supersonically relative to the free-stream velocity. This acoustic mode has qualitatively similar features for various thermodynamic conditions and for different working fluids. This shows that the leading parameters governing the boundary-layer behaviour for the dense gas are the constant-pressure specific heat and, to a minor extent, the density-dependent viscosity. A satisfactory scaling of the mode characteristics is found to be proportional to the height of the layer near the wall that acts as a waveguide where acoustic waves may become trapped. This means that the supersonic mode has the same nature as Mack’s modes, even if its frequency for maximal amplification is greater. Direct numerical simulation accurately reproduces the development of the supersonic mode and emphasizes the radiation of the instability waves.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/185562020-01-01T00:00:00ZGLOERFELT, XavierROBINET, Jean-ChristopheSCIACOVELLI, LucaCINNELLA, PaolaGRASSO, FrancescoA study of dense-gas effects on the stability of compressible boundary-layer flows is conducted. From the laminar similarity solution, the temperature variations are small due to the high specific heat of dense gases, leading to velocity profiles close to the incompressible ones. Concurrently, the complex thermodynamic properties of dense gases can lead to unconventional compressibility effects. In the subsonic regime, the Tollmien–Schlichting viscous mode is attenuated by compressibility effects and becomes preferentially skewed in line with the results based on the ideal-gas assumption. However, the absence of a generalized inflection point precludes the sustainability of the first mode by inviscid mechanisms. On the contrary, the viscous mode can be completely stable at supersonic speeds. At very high speeds, we have found instances of radiating supersonic instabilities with substantial amplification rates, i.e. waves that travel supersonically relative to the free-stream velocity. This acoustic mode has qualitatively similar features for various thermodynamic conditions and for different working fluids. This shows that the leading parameters governing the boundary-layer behaviour for the dense gas are the constant-pressure specific heat and, to a minor extent, the density-dependent viscosity. A satisfactory scaling of the mode characteristics is found to be proportional to the height of the layer near the wall that acts as a waveguide where acoustic waves may become trapped. This means that the supersonic mode has the same nature as Mack’s modes, even if its frequency for maximal amplification is greater. Direct numerical simulation accurately reproduces the development of the supersonic mode and emphasizes the radiation of the instability waves.Numerical Study of Multistage Transcritical Organic Rankine Cycle Axial Turbines
http://hdl.handle.net/10985/10145
Numerical Study of Multistage Transcritical Organic Rankine Cycle Axial Turbines
SCIACOVELLI, Luca; CINNELLA, Paola
Transonic flows through axial, multi-stage, transcritical ORC turbines, are investigated by using a numerical solver including advanced multiparameter equations of state and a high-order discretization scheme. The working fluids in use are the refrigerants R134a and R245fa, classified as dense gases due to their complex molecules and relatively high molecular weight. Both inviscid and viscous numerical simulations are carried out to quantify the impact of dense gas effects and viscous effects on turbine performance. Both supercritical and subcritical inlet conditions are studied for the considered working fluids. In the former case, flow across the turbine is transcritical, since turbine output pressure is subcritical. Numerical results show that, due to dense gas effects characterizing the flow at supercritical inlet conditions, supercritical ORC turbines enable, for a given pressure ratio, a higher isentropic efficiency than subcritical turbines using the same working fluid. Moreover, for the selected operating conditions, R134a provides a better performance than R245fa.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/101452014-01-01T00:00:00ZSCIACOVELLI, LucaCINNELLA, PaolaTransonic flows through axial, multi-stage, transcritical ORC turbines, are investigated by using a numerical solver including advanced multiparameter equations of state and a high-order discretization scheme. The working fluids in use are the refrigerants R134a and R245fa, classified as dense gases due to their complex molecules and relatively high molecular weight. Both inviscid and viscous numerical simulations are carried out to quantify the impact of dense gas effects and viscous effects on turbine performance. Both supercritical and subcritical inlet conditions are studied for the considered working fluids. In the former case, flow across the turbine is transcritical, since turbine output pressure is subcritical. Numerical results show that, due to dense gas effects characterizing the flow at supercritical inlet conditions, supercritical ORC turbines enable, for a given pressure ratio, a higher isentropic efficiency than subcritical turbines using the same working fluid. Moreover, for the selected operating conditions, R134a provides a better performance than R245fa.Bayesian quantification of thermodynamic uncertainties in dense gas flows
http://hdl.handle.net/10985/10073
Bayesian quantification of thermodynamic uncertainties in dense gas flows
MERLE, Xavier; CINNELLA, Paola
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 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 func-tion 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 infor-mative 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.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/100732015-01-01T00:00:00ZMERLE, XavierCINNELLA, PaolaA 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 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 func-tion 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 infor-mative 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.Convergence of Fourier-based time methods for turbomachinery wake passing problems
http://hdl.handle.net/10985/10074
Convergence of Fourier-based time methods for turbomachinery wake passing problems
GOMAR, Adrien; BOUVY, Quentin; SICOT, Frédéric; DUFOUR, Guillaume; CINNELLA, Paola; FRANCOIS, Benjamin
The convergence of Fourier-based time methods applied to turbomachinery flows is assessed. The focus is on the harmonic balance method, which is a timedomain Fourier-based approach standing as an efficient alternative to classical time marching schemes for periodic flows. In the literature, no consensus exists concerning the number of harmonics needed to achieve convergence for turbomachinery stage configurations. In this paper it is shown that the convergence of Fourier-based methods is closely related to the impulsive nature of the flow solution, which in turbomachines is essentially governed by the characteristics of the passing wakes between adjacent rows. As a result of the proposed analysis, a priori estimates are provided for the minimum number of harmonics required to accurately compute a given turbomachinery configuration. Their application to several contra-rotating open-rotor configurations is assessed, demonstrating the practical interest of the proposed methodology.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/100742014-01-01T00:00:00ZGOMAR, AdrienBOUVY, QuentinSICOT, FrédéricDUFOUR, GuillaumeCINNELLA, PaolaFRANCOIS, BenjaminThe convergence of Fourier-based time methods applied to turbomachinery flows is assessed. The focus is on the harmonic balance method, which is a timedomain Fourier-based approach standing as an efficient alternative to classical time marching schemes for periodic flows. In the literature, no consensus exists concerning the number of harmonics needed to achieve convergence for turbomachinery stage configurations. In this paper it is shown that the convergence of Fourier-based methods is closely related to the impulsive nature of the flow solution, which in turbomachines is essentially governed by the characteristics of the passing wakes between adjacent rows. As a result of the proposed analysis, a priori estimates are provided for the minimum number of harmonics required to accurately compute a given turbomachinery configuration. Their application to several contra-rotating open-rotor configurations is assessed, demonstrating the practical interest of the proposed methodology.Bayesian estimates of parameter variability in the k − ε turbulence model
http://hdl.handle.net/10985/10077
Bayesian estimates of parameter variability in the k − ε turbulence model
EDELING, Wouter Nico; CINNELLA, Paola; DWIGHT, Richard P.; BIJL, H.
In this paper we are concerned with obtaining estimates for the error in Reynolds-Averaged Navier-Stokes (RANS) simulations based on the Launder-Sharma k−ε turbulence closure model, for a limited class of flows. In particular we search for estimates grounded in uncertainties in the space of model closure coeffi-cients, for wall-bounded flows at a variety of favourable and adverse pressure gradients. In order to estimate the spread of closure coefficients which repro-duces these flows accurately, we perform 13 separate Bayesian calibrations – each at a different pressure gradient – using measured boundary-layer velocity profiles, and a statistical model containing a multiplicative model inadequacy term in the solution space. The results are 13 joint posterior distributions over coefficients and hyper-parameters. To summarize this information we compute Highest Posterior-Density (HPD) intervals, and subsequently represent the to-tal solution uncertainty with a probability-box (p-box). This p-box represents both parameter variability across flows, and epistemic uncertainty within each calibration. A prediction of a new boundary-layer flow is made with uncer-tainty bars generated from this uncertainty information, and the resulting error estimate is shown to be consistent with measurement data.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/100772014-01-01T00:00:00ZEDELING, Wouter NicoCINNELLA, PaolaDWIGHT, Richard P.BIJL, H.In this paper we are concerned with obtaining estimates for the error in Reynolds-Averaged Navier-Stokes (RANS) simulations based on the Launder-Sharma k−ε turbulence closure model, for a limited class of flows. In particular we search for estimates grounded in uncertainties in the space of model closure coeffi-cients, for wall-bounded flows at a variety of favourable and adverse pressure gradients. In order to estimate the spread of closure coefficients which repro-duces these flows accurately, we perform 13 separate Bayesian calibrations – each at a different pressure gradient – using measured boundary-layer velocity profiles, and a statistical model containing a multiplicative model inadequacy term in the solution space. The results are 13 joint posterior distributions over coefficients and hyper-parameters. To summarize this information we compute Highest Posterior-Density (HPD) intervals, and subsequently represent the to-tal solution uncertainty with a probability-box (p-box). This p-box represents both parameter variability across flows, and epistemic uncertainty within each calibration. A prediction of a new boundary-layer flow is made with uncer-tainty bars generated from this uncertainty information, and the resulting error estimate is shown to be consistent with measurement data.Multi-fidelity optimization strategy for the industrial aerodynamic design of helicopter rotor blades
http://hdl.handle.net/10985/10072
Multi-fidelity optimization strategy for the industrial aerodynamic design of helicopter rotor blades
LEUSINK, Debbie; ALFANO, David; CINNELLA, Paola
The industrial aerodynamic design of helicopter rotor blades needs to consider the two typical flight conditions of hover and forward flight simultaneously. Here, this multi-objective design problem is tackled by using a genetic algorithm, coupled to rotor performance simulation tools. The turn-around time of an optimization loop is acceptable in an industrial design loop when using low-cost, low-fidelity tools such as the comprehensive rotorcraft code HOST, but becomes excessively high when employing high-fidelity models like CFD methods. To incorporate high-fidelity models into the optimization loop while maintaining a moderate computational cost, a Multi-Fidelity Optimization (MFO) strategy is proposed: as a preliminary step, a HOST-based genetic algorithm optimization is used to reduce the parameter space and select a set of blade geometries used for initializing the high-fidelity stage. Secondly, the selected blades are re-evaluated by CFD and used to construct a high-fidelity surrogate model. Finally, a Surrogate Based Optimization (SBO) is carried out and the Pareto optimal individuals according to the SBO are recomputed by CFD for final performance evaluation. The proposed strategy is validated step by step. It is shown that an industrially acceptable number of CFD-simulations is sufficient to obtain blade designs with a significantly higher performance than the baseline and then SBO results issued from a standard Latin-Hypercube-Sampling initialization. The proposed MFO strategy represents an efficient method for the simultaneous optimization of rotor blade geometries in hover and forward flight.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/100722015-01-01T00:00:00ZLEUSINK, DebbieALFANO, DavidCINNELLA, PaolaThe industrial aerodynamic design of helicopter rotor blades needs to consider the two typical flight conditions of hover and forward flight simultaneously. Here, this multi-objective design problem is tackled by using a genetic algorithm, coupled to rotor performance simulation tools. The turn-around time of an optimization loop is acceptable in an industrial design loop when using low-cost, low-fidelity tools such as the comprehensive rotorcraft code HOST, but becomes excessively high when employing high-fidelity models like CFD methods. To incorporate high-fidelity models into the optimization loop while maintaining a moderate computational cost, a Multi-Fidelity Optimization (MFO) strategy is proposed: as a preliminary step, a HOST-based genetic algorithm optimization is used to reduce the parameter space and select a set of blade geometries used for initializing the high-fidelity stage. Secondly, the selected blades are re-evaluated by CFD and used to construct a high-fidelity surrogate model. Finally, a Surrogate Based Optimization (SBO) is carried out and the Pareto optimal individuals according to the SBO are recomputed by CFD for final performance evaluation. The proposed strategy is validated step by step. It is shown that an industrially acceptable number of CFD-simulations is sufficient to obtain blade designs with a significantly higher performance than the baseline and then SBO results issued from a standard Latin-Hypercube-Sampling initialization. The proposed MFO strategy represents an efficient method for the simultaneous optimization of rotor blade geometries in hover and forward flight.Predictive RANS simulations via Bayesian Model-Scenario Averaging
http://hdl.handle.net/10985/10035
Predictive RANS simulations via Bayesian Model-Scenario Averaging
CINNELLA, Paola
The turbulence closure model is the dominant source of error in most Reynolds-Averaged Navier–Stokes simulations, yet no reliable estimators for this error component currently exist. Here we develop a stochastic, a posteriori error estimate, calibrated to specific classes of flow. It is based on variability in model closure coefficients across multiple flow scenarios, for multiple closure models. The variability is estimated using Bayesian calibration against experimental data for each scenario, and Bayesian Model-Scenario Averaging (BMSA) is used to collate the resulting posteriors, to obtain a stochastic estimate of a Quantity of Interest (QoI) in an unmeasured (prediction) scenario. The scenario probabilities in BMSA are chosen using a sensor which automatically weights those scenarios in the calibration set which are similar to the prediction scenario. The methodology is applied to the class of turbulent boundary-layers subject to various pressure gradients. For all considered prediction scenarios the standard-deviation of the stochastic estimate is consistent with the measurement ground truth. Furthermore, the mean of the estimate is more consistently accurate than the individual model predictions.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/100352014-01-01T00:00:00ZCINNELLA, PaolaThe turbulence closure model is the dominant source of error in most Reynolds-Averaged Navier–Stokes simulations, yet no reliable estimators for this error component currently exist. Here we develop a stochastic, a posteriori error estimate, calibrated to specific classes of flow. It is based on variability in model closure coefficients across multiple flow scenarios, for multiple closure models. The variability is estimated using Bayesian calibration against experimental data for each scenario, and Bayesian Model-Scenario Averaging (BMSA) is used to collate the resulting posteriors, to obtain a stochastic estimate of a Quantity of Interest (QoI) in an unmeasured (prediction) scenario. The scenario probabilities in BMSA are chosen using a sensor which automatically weights those scenarios in the calibration set which are similar to the prediction scenario. The methodology is applied to the class of turbulent boundary-layers subject to various pressure gradients. For all considered prediction scenarios the standard-deviation of the stochastic estimate is consistent with the measurement ground truth. Furthermore, the mean of the estimate is more consistently accurate than the individual model predictions.Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence
http://hdl.handle.net/10985/15598
Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence
SCIACOVELLI, Luca; CINNELLA, Paola; GRASSO, Francesco
The present paper investigates the influence of dense gases governed by complex equations of state on the dynamics of homogeneous isotropic turbulence. In particular, we investigate how differences due to the complex thermodynamic behaviour and transport properties affect the small-scale structures, viscous dissipation and enstrophy generation. To this end, we carry out direct numerical simulations of the compressible Navier–Stokes equations supplemented by advanced dense gas constitutive models. The dense gas considered in the study is a heavy fluorocarbon (PP11) that is shown to exhibit an inversion zone (i.e. a region where the fundamental derivative of gas dynamics Γ is negative) in its vapour phase, for pressures and temperatures of the order of magnitude of the critical ones. Simulations are carried out at various initial turbulent Mach numbers and for two different initial thermodynamic states, one immediately outside and the other inside the inversion zone. After investigating the influence of dense gas effects on the time evolution of mean turbulence properties, we focus on the statistical properties of turbulent structures. For that purpose we carry out an analysis in the plane of the second and third invariant of the deviatoric strain-rate tensor. The analysis shows a weakening of compressive structures and an enhancement of expanding ones. Strong expansion regions are found to be mostly populated by non-focal convergence structures typical of strong compression regions, in contrast with the perfect gas that is dominated by eddy-like structures. Additionally, the contribution of non-focal expanding structures to the dilatational dissipation is comparable to that of compressed structures. This is due to the occurrence of steep expansion fronts and possibly of expansion shocklets which contribute to enstrophy generation in strong expansion regions and that counterbalance enstrophy destruction by means of the eddy-like structures.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/155982017-01-01T00:00:00ZSCIACOVELLI, LucaCINNELLA, PaolaGRASSO, FrancescoThe present paper investigates the influence of dense gases governed by complex equations of state on the dynamics of homogeneous isotropic turbulence. In particular, we investigate how differences due to the complex thermodynamic behaviour and transport properties affect the small-scale structures, viscous dissipation and enstrophy generation. To this end, we carry out direct numerical simulations of the compressible Navier–Stokes equations supplemented by advanced dense gas constitutive models. The dense gas considered in the study is a heavy fluorocarbon (PP11) that is shown to exhibit an inversion zone (i.e. a region where the fundamental derivative of gas dynamics Γ is negative) in its vapour phase, for pressures and temperatures of the order of magnitude of the critical ones. Simulations are carried out at various initial turbulent Mach numbers and for two different initial thermodynamic states, one immediately outside and the other inside the inversion zone. After investigating the influence of dense gas effects on the time evolution of mean turbulence properties, we focus on the statistical properties of turbulent structures. For that purpose we carry out an analysis in the plane of the second and third invariant of the deviatoric strain-rate tensor. The analysis shows a weakening of compressive structures and an enhancement of expanding ones. Strong expansion regions are found to be mostly populated by non-focal convergence structures typical of strong compression regions, in contrast with the perfect gas that is dominated by eddy-like structures. Additionally, the contribution of non-focal expanding structures to the dilatational dissipation is comparable to that of compressed structures. This is due to the occurrence of steep expansion fronts and possibly of expansion shocklets which contribute to enstrophy generation in strong expansion regions and that counterbalance enstrophy destruction by means of the eddy-like structures.Automatic Hybrid RANS/LES Strategy for Industrial CFD
http://hdl.handle.net/10985/15320
Automatic Hybrid RANS/LES Strategy for Industrial CFD
PONT, Grégoire; CINNELLA, Paola; ROBINET, Jean-Christophe; BRENNER, Pierre
An automatic HRL (Hybrid RANS/LES) strategy is investigated in FLUSEPA, a finite-volume solver developed by Airbus Defense and Space. A HRL turbulence model is coupled to a high-order hybrid numerical approximation method. Concerning the turbulence model, the well-known k − ε two equations RANS turbulence model is sensitized to the grid as suggested by Perot and Gadebusch (Phy Fluids 19:1–11, 2007). Concerning the numerical strategy, a third-order accurate upwind approximation method is locally re-centered in vortex dominated regions to achieve non-dissipative fourth-order accuracy. Results are presented for a 2D backward facing step and an an axisymmetry backward facing step, which represent good prototypes of after body flows.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/153202015-01-01T00:00:00ZPONT, GrégoireCINNELLA, PaolaROBINET, Jean-ChristopheBRENNER, PierreAn automatic HRL (Hybrid RANS/LES) strategy is investigated in FLUSEPA, a finite-volume solver developed by Airbus Defense and Space. A HRL turbulence model is coupled to a high-order hybrid numerical approximation method. Concerning the turbulence model, the well-known k − ε two equations RANS turbulence model is sensitized to the grid as suggested by Perot and Gadebusch (Phy Fluids 19:1–11, 2007). Concerning the numerical strategy, a third-order accurate upwind approximation method is locally re-centered in vortex dominated regions to achieve non-dissipative fourth-order accuracy. Results are presented for a 2D backward facing step and an an axisymmetry backward facing step, which represent good prototypes of after body flows.Simplex-stochastic collocation method with improved scalability
http://hdl.handle.net/10985/15517
Simplex-stochastic collocation method with improved scalability
EDELING, Wouter Nico; DWIGHT, Richard P.; CINNELLA, Paola
The Simplex-Stochastic Collocation (SSC) method is a robust tool used to propagate uncertain input distributions through a computer code. However, it becomes prohibitively expensive for problems with dimensions higher than 5. The main purpose of this paper is to identify bottlenecks, and to improve upon this bad scalability. In order to do so, we propose an alternative interpolation stencil technique based upon the Set-Covering problem, and we integrate the SSC method in the High-Dimensional Model-Reduction framework. In addition, we address the issue of ill-conditioned sample matrices, and we present an analytical map to facilitate uniformly-distributed simplex sampling.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/155172016-01-01T00:00:00ZEDELING, Wouter NicoDWIGHT, Richard P.CINNELLA, PaolaThe Simplex-Stochastic Collocation (SSC) method is a robust tool used to propagate uncertain input distributions through a computer code. However, it becomes prohibitively expensive for problems with dimensions higher than 5. The main purpose of this paper is to identify bottlenecks, and to improve upon this bad scalability. In order to do so, we propose an alternative interpolation stencil technique based upon the Set-Covering problem, and we integrate the SSC method in the High-Dimensional Model-Reduction framework. In addition, we address the issue of ill-conditioned sample matrices, and we present an analytical map to facilitate uniformly-distributed simplex sampling.