Rapid multi-component phase-split calculations using volume functions and reduction methods

We present a new family of fast and robust methods for the calculation of the vapor–liquid equilibrium at isobaric-isothermal (PT-flash), isochoric-isothermal (VT-flash), isenthalpic-isobaric (HP-flash), and isoenergetic-isochoric (UV-flash) conditions. The framework is provided by formulating phase-equilibrium conditions for multi-component mixtures in an effectively reduced space based on the molar specific value of the recently introduced volume function derived from the Helmholtz free energy. The proposed algorithmic implementation can fully exploit the optimum quadratic convergence of a Newton method with the analytical Jacobian matrix. This article provides all required exact analytic expressions for the general cubic equation of state. Computational results demonstrate the effectivity and efficiency of the new methods. Compared to conventional methods, the proposed reduced-space iteration leads to a considerable speed-up as well as to improved robustness and better convergence behavior near the spinodal and coexistence curves of multi-component mixtures, where the preconditioning by the reduction method is most effective.Aerodynamic

Analysis of improved digital filter inflow generation methods for compressible turbulent boundary layers

We propose several enhancements to improve the accuracy and performance of the digital filter turbulent inflow generation technique and assess their efficacy in the context of wall-resolved large-eddy simulations of a compressible turbulent boundary layer. Improvements of accuracy include a more realistic correlation function for the transversal directions, target length scales that vary with wall-distance, and a counter-intuitive approach that involves the suppression of streamwise velocity fluctuations at the inflow. For improving the computational performance, we propose to generate the inflow data in parallel in single precision and at a prescribed time interval based on the turbulence time scale, and not at every time-step of the simulation. Based on the results of 7 wall-resolved large-eddy simulations, we find that the new correlation functions and the considered performance improvements are beneficial and therefore desired. Suppressing streamwise velocity fluctuations at the inflow leads to the fastest relaxation of the pressure fluctuations; however, this approach increases the adaptation length defined in terms of compliance with the von Kármán integral equation. The adaptation length can be shortened by artificially increasing the wall-normal Reynolds stresses, thereby preserving the desired turbulence kinetic energy level. A detailed inspection of the Reynolds stress transport budgets reveals that the observed spurious spatial transients are largely driven by pressure-related terms. For instance, increased values of u′p′¯ are found throughout the computational domain when a physical Reynolds stress distribution is prescribed at the inflow. Therefore, efforts to enhance digital filter techniques should aim at modeling pressure fluctuations as well as their correlation with the velocity components.Aerodynamic

Multi-component vapor-liquid equilibrium model for LES of high-pressure fuel injection and application to ECN Spray A

We present and evaluate a two-phase model for Eulerian large-eddy simulations (LES) of liquid-fuel injection and mixing at high pressure. The model is based on cubic equations of state and vapor-liquid equilibrium calculations and can represent the coexistence of supercritical states and multi-component subcritical two-phase states via a homogeneous mixture approach. Well-resolved LES results for the Spray A benchmark case of the Engine Combustion Network (ECN) and three additional operating conditions are found to agree very well with available experimental data. We also address well-known numerical challenges of trans- and supercritical fluid mixing and compare a fully conservative formulation to a quasi-conservative formulation of the governing equations. Our results prove physical and numerical consistency of both methods on fine grids and demonstrate the effects of energy conservation errors associated with the quasi-conservative formulation on typical LES grids.Aerodynamic

Multi-component vapor-liquid equilibrium model for LES and application to ECN Spray A

We present and evaluate a detailed multi-species two-phase thermodynamic equilibrium model for large-eddy simulations (LES) of liquid-fuel injection and mixing at high pressure. The model can represent the coexistence of supercritical states and multicomponent subcritical two-phase states. LES results for the transcritical Spray A of the Engine Combustion Network (ECN) are found to agree very well to available experimental data. We also address well-known numerical challenges of trans- and supercritical fluid mixing and compare a fully conservative formulation to a quasi conservative formulation of the governing equations. Our results prove physical and numerical consistency of both methods on fine grids and demonstrate the effects of energy conservation errors associated with the quasi conservative formulation on typical LES grids.Aerodynamic

ALMD: A modeling environment for ILES

Further development of Large Eddy Simulation faces as major obstacle the strong coupling between subgrid-scale model and the truncation error of the numerical discretization. Recent analyzes indicate that for certain discretizations and certain flow configurations the truncation error itself can act as implicit SGS model. Relevant discretizations are e.g. finite-volume schemes with a nonlinear regularization to maintain nonlinear stability. Whereas previous approaches in implicit subgrid-scale (SGS) modeling employed available discretization schemes without analyzing the effective SGS model, and not incorporating physical modeling approaches into the implicit model, we have developed an approach where a full coupling of SGS model and discretization scheme is accomplished. The ALDM (Adaptive Local Deconvolution Method) approach is introduced as an implicit subgrid-scale modeling environment and discussed with respect to its numerical and turbulence-theoretical background. We summarize recent accomplishments in terms of complex flows computed successfully with ALDM and provide a brief outlook on future work

A Conservative Cut-Cell Immersed Boundary Method for Accurate Simulation of Hypersonic Flows with Gas-Surface Interactions

A conservative cut-cell immersed boundary (IB) method including gas-surface interactions (GSI) for the simulation of atmospheric entry flows under thermochemical nonequilibrium (TCNE) conditions is presented. The performanceof the method is demonstrated for three test cases: a compression ramp, a cylinder, and a plasma wind tunnel ablator sample. The computational predictions are in excellent agreement with reference simulations and experimental data for translational and vibrational temperature variations in the flow field, pressure and heat flux distributions over the geometries, and the mass blowing rates over a surface undergoing ablation.Aerodynamic

Mixing and phase separation at supercritical and transcritical pressures

We have developed a thermodynamically consistent and tuning-parameter-free two-phase model for Eulerian large-eddy simulations (LES) of liquid-fuel injection and mixing at high pressure. The model is based on cubic equations of state and vaporliquid equilibrium calculations. It can represent the coexistence of supercritical states and multi-component subcritical two-phase states via a homogeneous mixture approach without any semiempirical break-up and evaporation models. Computational results for liquid-fuel injection at transcritical operating conditions are found to agree very well with available experimental data for the ECN Spray A.Aerodynamic

A one equation explicit algebraic subgrid-scale stress model

Nonlinear Explicit Algebraic Subgrid-scale Stress Models (EASSMs) have shown high potential for Large Eddy Simulation (LES) of challenging turbulent flows on coarse meshes. A simplifying assumption made to enable the purely algebraic nature of the model is that the Subgrid-Scale (SGS) kinetic energy production and dissipation are in balance, i.e., P/ε = 1. In this work, we propose an improved EASSM design that does not involve this precalibration and retains the ratio P/ε as a space and time dependent variable. Our model is based on the partial differential evolution equation for the SGS kinetic energy ksgs and the assumption that the ratio P/ε evolves slower in time than ksgs. Computational results for simple cases of forced isotropic turbulence show that the new model is able to track the evolution of the SGS kinetic energy significantly better than the dynamic and non-dynamic EASSMs of Marstorp et al. (2009). Also the predicted kinetic energy spectra and resolved dissipation evolution are in excellent agreement with reference data from Direct Numerical Simulations (DNS).Aerodynamic

Permeability and Turbulence Over Perforated Plates

We perform direct numerical simulations of turbulent flow at friction Reynolds number Reτ≈ 500 - 2000 grazing over perforates plates with moderate viscous-scaled orifice diameter d+≈ 40 - 160 and analyse the relation between permeability and added drag. Unlike previous studies of turbulent flows over permeable surfaces, we find that the flow inside the orifices is dominated by inertial effects, and that the relevant permeability is the Forchheimer and not the Darcy one. We find evidence of a fully rough regime where the relevant length scale is the inverse of the Forchheimer coefficient, which can be regarded as the resistance experienced by the wall-normal flow. Moreover, we show that, for low porosities, the Forchheimer coefficient can be estimated with good accuracy using a simple analytical relation.In this article the author name Stefan Hickel was incorrectly written as Hickel Stefan. The original article has been corrected.Aerodynamic

Large eddy simulations of reacting and non-reacting transcritical fuel sprays using multiphase thermodynamics

We present a novel framework for high-fidelity simulations of inert and reacting sprays at transcritical conditions with highly accurate and computationally efficient models for complex real-gas effects in high-pressure environments, especially for the hybrid subcritical/supercritical mode of evaporation during the mixing of fuel and oxidizer. The high-pressure jet disintegration is modeled using a diffuse interface method with multiphase thermodynamics, which combines multi-component real-fluid volumetric and caloric state equations with vapor-liquid equilibrium calculations for the computation of thermodynamic properties of mixtures at transcritical pressures. Combustion source terms are evaluated using a finite-rate chemistry model, including real-gas effects based on the fugacity of the species in the mixture. The adaptive local deconvolution method is used as a physically consistent turbulence model for large eddy simulation (LES). The proposed method represents multiphase turbulent fluid flows at transcritical pressures without relying on any semi-empirical breakup and evaporation models. All multiphase thermodynamic model equations are presented for general cubic state equations coupled with a rapid phase-equilibrium calculation method that is formulated in a reduced space based on the molar specific volume function. LES results show a very good agreement with available experimental data for the reacting and non-reacting engine combustion network benchmark spray A at transcritical operating conditions. AerodynamicsFluid Mechanic