Paola Cinnella

Numerical solver for dense gas flows

Introduction D ENSE gas dynamics studies the dynamic behavior of gases in the dense regime, i.e., at temperatures and pressures close to the thermodynamic critical point. In such conditions, complex gasdynamic phenomena can appear in the transonic and supersonic regimes.1 In spite of the additional complexity of the fluid response in the dense regime, the use of dense gases is not only necessary but, in some applications, advantageous. For instance, dense gas effects play a critical role in the performance of turbomachinery and heat-transfer equipment of organic Rankine cycles (ORCs).2 This motivates the interest in developing numerical tools for the analysis and design of advanced ORC turbomachinery components. In the past, several methods for so-called “real gas flows” have been derived. Such methods were in general tailored to deal with hypersonic reacting flows, for which the use of robust upwind numerical solvers was mandatory. Unfortunately, upwind schemes require characteristic decompositions, making their realization for complex multidimensional systems quite involved. On the other hand, for nonreacting flows of gases close to saturation conditions, governed by complex equations of state, and characterized by “exotic” but quite weak waves, the use of sophisticated characteristic decompositions is not essential. For these flows, it could be more convenient to use central schemes, which, in spite of higher numerical diffusivity, have the advantage of conceptional simplicity and low computational cost. In the present work, a centered numerical solver for the computation of inviscid and viscous dense gas flows is developed. A thirdorder-accurate centered method for perfect gas flows3 is extended to the computation of dense gases. The proposed scheme is systematically compared to a well-known second-order flux-difference splitting scheme4 implemented within the same code. The computations are performed using either the van der Waals or the realistic Martin–Hou5 equation of state. The scheme is then extended to the computation of viscous dense gas flows. The fluid viscosity and thermal conductivity are evaluated using thermophysical models appropriate for gases close to saturation conditions. The proposed method is validated for several inviscid and viscous flow problems involving dense gas phenomena.

Aerodynamic Performance of Transonic Bethe-Zel'dovich-Thompson Flows past an Airfoil

Dense gasdynamics studies the flow of gases in the thermodynamic region above the upper saturation curve, close to the liquid-vapor critical point. In recent years, great attention has been paid to certain substances, known as the Bethe‐Zel’dovich‐Thompson (BZT) fluids, which exhibit negative values of the fundamental derivative of gasdynamics for a whole range of temperatures and pressures in the vapor phase. This can lead to nonclassical gasdynamic behaviors, such as rarefaction shock waves, mixed shock/fan waves, and shock splitting. The uncommon properties of BZT fluids can find practical applications, for example, in the reduction of losses as a result of wave drag and shock/boundary-layer interaction in organic Rankine cycle turbines. The present work provides a detailed numerical study of transonic BZT fluid flows past a simplified configuration, represented by an isolated NACA0012 airfoil. The objective is to investigate the influence of BZT effects on the airfoil performance (specifically on the lift-to-drag ratio).

Multiblock residual-based compact schemes for the computation of complex turbomachinery flows

A flexible multiblock implementation of second and third-order accurate residual-based compact (RBC) schemes is proposed and validated for turbomachinery flows of increasing complexity. Applications to complex transonic unsteady flows in turbomachinery show the advantages of using such schemes in terms of increased accuracy and better insight into the flow physics.

The high-order dynamic computational laboratory for CFD research and applications

A novel CFD code, named DynHoLab (Dynamic High-order Laboratory), is developed combining Python and Fortran languages. This enables fast development in a flexible, general and modular Python environment along with high CPU performance characteristic of Fortran language. At the present stage of development, the code is oriented towards the numerical simulation of compressible flows using high-order finite volume schemes (up to 7 order of accuracy) on block-structured meshes.

Development of Numerical Schemes for Hybrid Turbulence Modelling in an Industrial CFD Solver

Many turbulent flows are dominated by large turbulent structures caused by massive boundary layer separation, i.e : bluff body flows past launchers and missiles, cars, turbomachines. These flows represent a challenge for numerical simulation methods since models based on Reynolds averaged equations (URANS) are not able to give an accurate representation of unsteady turbulent structures. On the other hand, Large Eddy Simulation (LES) is generally too expensive for an industrial use. In the attempt to find a compromise between computation cost and accuracy, it becomes useful to consider hybrid approaches between RANS and LES modelling. The aim of such simulations is to resolve only that portion of the turbulent spectrum responsible for the aerodynamics forces acting on an immersed body, and to model the rest. A lot of simulation strategies hybrid exist (for example SAS, PANS, PITM, ZDES..) but exploring them is beyond the scope of this paper. Here we focuse instead on the impact of the numerical properties of the resolution scheme on hybrid RANS/LES simulations and investigate a simple but effective strategy to improve numerical accuracy of the solver for a given mesh resolution.

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.

Transonic Flows of BZT Fluids Through Turbine Cascades

In the above, ρ is the fluid density, a the sound speed, and s the entropy. The thermodynamic region characterized by negative values of Γ is referred to as the inversion zone, and is included between the upper saturation curve and the Γ = 0 contour (called the transition line). The Fundamental Derivative Γ represents a measure of the rate of change of the sound speed with density in isentropic perturbations. If Γ 1 for thermodynamic stability reasons; therefore, Γ > 1 as well. Examples of BZT fluids are given by heavy hydrocarbons (decane or higher), commercially available heat transfer fluids such as FC-71 (C18F39N), FC-72 (C6F14), PP9 (C11F20), PP10 (C13F22), and some methylsiloxanes. The dynamics of BetheZel’dovich-Thompson fluids has been studied extensively in recent years (e.g. [2] and references cited therein). The most impressive phenomenon is the disintegration of compression shocks in flows with Γ < 0. The entropy change through a weak shock can be written [3]:

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

Multi-Zone Quasi-Dimensional Combustion Models for Spark-Ignition Engines

The present work aims at improving the predictive capabilities of quasi-dimensional combustion models for fast and accurate automated design of spark engines. The models are based on mass and energy conservation principles supplemented by sub models based on experimental correlations. Here, we improve the accuracy of the classical two-zone model by means of two successive modifications. First, we generate a three-zone model by introducing a reacting zone near the walls. In the third zone, the gases burn at a lower temperature than in the main reacting zone, due to heat losses to the walls. Secondly, a multi-zone model is built by dynamically adding new reacting zones at given crank-angle intervals. The use of multiple zones allows to take into account temperature and concentrations gradients in the flame. To validate our models, the energy release rates and pressures time histories predicted by the three-zone and by the multi-zone models are compared to experimental data and to the standard two-zone approach for several operating conditions.

Shape optimization for dense gas flows in turbine cascades

In recent years, great attention has been paid to a class of fluids of the retrograde type (i.e. fluids that superheat when expanded), known as the Bethe–Zel’dovich–Thompson (BZT) fluids, which exhibit in the vapor phase, above the upper saturation curve, a region of negative values of the Fundamental Derivative of Gasdynamics \(\Gamma : = 1 + \frac{\rho }{a}{\left( {\frac{{{\partial _a}}}{{{\partial _\rho }}}} \right)_s}\) with ρ the fluid density, a the sound speed, and s the entropy. In the transonic and supersonic regimes, this leads to nonclassical gasdynamic behaviors, such as expansion shocks and mixed waves. Moreover, flow discontinuities with jump conditions in the vicinity of the Γ = 0 contour have necessarily limited strength, producing losses (entropy rise) one order of magnitude lower than usual [2].