Documents published in Scipedia

• On the conservation of primary and secondary properties in the simulation of multiphase flows

  N. Valle, F. Trias, R. Verstappen

  eccomas2022.

  
  

  Abstract

  The formulation of multiphase flows emanates from basic conservation laws: mass, momentum and energy. While these are embedded in the celebrated Navier-Stokes equations, none of these properties do necessarily hold when constructing a computational model, unless special care is taken in discretizing the different terms of the governing equations. The conservation of both primary (mass, momentum) and secondary (energy) quantities is not only relevant to mimic the dynamics of the system, but also computationally beneficial. Conservation of such quantities produce an enhanced physical reliability, removing most of the need for stabilization artifacts. In addition, discrete conservation implies numerical stability as well, producing inherently stable problems. Focusing on the capillary force, which is one of the most distinguishable features of multiphase flows, we present here our most recent developments in the quest for conservation. Departing from an inherently mass conservative method, in this work we sketch our previous developments to obtain an energy conservation and next we present our attempt at momentum. By carefully assessing the continuum formulation, we delve into the mathematical properties responsible for the conservation of linear momentum, which we then mimic in the regularized and discrete formulations.

  Abstract
  The formulation of multiphase flows emanates from basic conservation laws: mass, momentum and energy. While these are embedded in the celebrated Navier-Stokes equations, none [...]

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• An assessment of various discretizations of the energy equation in compressible flows

  C. De Michele, G. Coppola

  eccomas2022.

  
  

  Abstract

  Nonlinear instabilities are one of the major problems in turbulence simulations. One reason behind this problem is the accumulation of aliasing errors produced by the discrete evaluation of the convective term. This can be improved by preserving the quadratic invariants in a discrete sense. However, another source of instabilities is the error due to an incorrect evolution of thermodynamic variables, such as entropy. An appropriate discretization of the energy equation is needed to address this issue. An analysis of the preservation properties of various discretizations of the compressible Euler equations is reported, which includes some of the most common approaches used in the literature, together with some new formulations. Two main factors have been identified and studied: one is the choice of the energy equation to be directly discretized; the other is the particular splitting of the convective terms, chosen among the Kinetic Energy Preserving (KEP) forms. The energy equations analyzed in this paper are total and internal energy, entropy, and speed of sound. All the cases examined are locally conservative and KEP, since this is considered an essential condition for a robust simulation. The differences among the formulations have been theoretically investigated through the study of the discrete evolution equations induced by the chosen energy variable, showing which quantities may be preserved. Both one-dimensional and two-dimensional tests have been performed to assess the advantages and disadvantages of the various options in different cases.

  Abstract
  Nonlinear instabilities are one of the major problems in turbulence simulations. One reason behind this problem is the accumulation of aliasing errors produced by the discrete [...]

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• Development of a discontinuous Galerkin solver for the simulation of turbine stages

  A. Colombo, A. Ghidoni, E. Mantecca, G. Noventa, S. Rebay, D. Pasquale

  eccomas2022.

  
  

  Abstract

  A high-order Discontinuous Galerkin (DG) solver is assessed in the computation of the flow through an Organic Rankine Cycle turbine nozzle and stage. The flow features are predicted with a RANS (Reynolds averaged Navier­Stoke) approach and the k-log() turbulence model in a multi reference frame, where interfaces between fixed and rotating zones are treated with a mixing plane approach, and non reflecting boundary conditions are used. Primitive variables based on pressure and temperature logarithms are adopted to ensure non-negative thermodynamic variables at a discrete level. The fluid can be modeled with the polytropic ideal gas law and the Peng-Robinson equation of state.

  Abstract
  A high-order Discontinuous Galerkin (DG) solver is assessed in the computation of the flow through an Organic Rankine Cycle turbine nozzle and stage. The flow features are [...]

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• Modal analysis of a 3D gravitational liquid sheet

  A. Colanera, A. Della Pia, M. Acquaviva, M. Chiatto, L. de Luca

  eccomas2022.

  
  

  Abstract

  Modal analysis of three-dimensional gravitational thin liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, is performed in the present work. Numerical data of this relevant two-phase flow configuration are obtained through the single-phase formulation and the Volume-of-Fluid (VOF) technique implemented in the flow solver Basilisk. This class of flows exhibits a variety of spatial and temporal relevant structures, both in free and forced configurations, that are investigated through the Spectral Proper Orthogonal Decomposition (SPOD). By means of such methodology, we explore the effect of two main governing parameters on the flow dynamics, namely the liquid sheet aspect ratio, AR = W/H, where H and W are the sheet inlet thickness and width, and the Weber number, We = lU2H/(2), in which U is the inlet liquid velocity, lthe liquid density, and the surface tension coefficient. Finally, for the highest aspect ratio value considered (AR = 40), we investigate the forced dynamics of the system excited by a harmonic perturbation in transverse velocity component applied at the inlet section, comparing results with ones arising from a purely two-dimensional analysis of the flow. The obtained results highlight the low rank behavior exhibited by the flow, suggesting that reduced order modeling could be particularly appealing to reduce complexity and computational effort in numerical simulation of this class of flows.

  Abstract
  Modal analysis of three-dimensional gravitational thin liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, is performed [...]

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• A fully-discrete entropy conserving/stable discretization for inviscid unsteady flows

  A. Colombo, A. Crivellini, A. Nigro

  eccomas2022.

  
  

  Abstract

  The aim of this work is to contribute to the development of a high-order accurate discretization that is entropy conserving and entropy stable both in space and in time. To do this, the general framework is based on a high-order accurate discontinuous Galerkin (dG) method in space with entropy working variables, several entropy conservative and stable numerical fluxes and an entropy conserving modified Crank-Nicolson method. We present the first results, obtained with the discretizations here proposed, for two bi-dimensional unsteady viscous test-case: the Taylor-Green vortex and the double shear layer.

  Abstract
  The aim of this work is to contribute to the development of a high-order accurate discretization that is entropy conserving and entropy stable both in space and in time. To [...]

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• Influence of the turbulent wake downstream offshore wind turbines on larval dispersal: development of a new Lagrangian-Eulerian model

  S. Ajmi, M. Boutet, A. Bennis, J. Dauvin

  eccomas2022.

  
  

  Abstract

  In the context of future offshore wind farms along the French coasts of the English Channel, the impacts of foundations on larval dispersal from bentho-pelagic species colonizing the hard substratum of artificial structures are studied in order to assess how the species connectivity could be modified by the farms. In particular, the effects of turbulent wake and horseshoe vortices are investigated. To this end, a new numerical approach is developed that combines the Eulerian model, OpenFoam, solving the 3D Navier-Stokes equations to compute the hydrodynamics, and the Lagrangian model, Ichthyop, based on an advection-diffusion equation to compute the larval trajectories. Firstly, some simple test cases are performed to validate the numerical coupling between OpenFoam and Ichthyop, such as the dispersion of larvae downstream a 2D cylinder in water. Secondly, the ability of OpenFoam turbulence models to simulate turbulent structures around monopile and gravity type foundations is evaluated. The RANS (Reynolds Averaged Navier-Stokes) k-omega SST turbulence model is chosen for the realistic application because it can reproduce the horseshoe vortices and turbulent wake with less computing time than the Smagorinsky LES (Large Eddy Simulation) model. Lastly, larval dispersal simulations for four benthic species and for a set of monopile and gravity foundations are performed.

  Abstract
  In the context of future offshore wind farms along the French coasts of the English Channel, the impacts of foundations on larval dispersal from bentho-pelagic species colonizing [...]

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• Surrogate modeling of unsteady aerodynamic loads acting on a plunging airfoil

  R. Sundar, V. KUMAR, D. Majumdar, C. Shah, S. Sarkar

  eccomas2022.

  
  

  Abstract

  Cost-effective parameteric surrogate models of unsteady aerodynamic loads acting on a flapping wing are highly desirable. They would enable real time aerodynamic load prediction, multiobjective optimisation and optimal control of intelligent flapping wing flight devices. In the present work, a parametric surrogate modeling framework for unsteady aerodynamic loads based on a non-intrusive reduced order modeling approach is presented. The unsteady flow past a plunging 2D flat plate is considered where the aerodynamic load time histories are obtained for different plunging frequencies and amplitudes using a potential flow solver. The parametric non-intrusive reduced order model (p-NIROM) for the obtained loads is constructed using a combination of snapshot proper orthogonal decomposition (POD) for dimensionality reduction and a fully connected feed forward neural network (FCNN) for modeling the input parametric dependency. Both, linear and non-linear FCNN based p-NIROM are explored and compared on the basis of load time history reconstruction accuracy. The non-linear FCNN regression for the p-NIROM is observed to generalise well for unseen parametric instances as compared to the linear approach when a systematic data sampling strategy is adopted.

  Abstract
  Cost-effective parameteric surrogate models of unsteady aerodynamic loads acting on a flapping wing are highly desirable. They would enable real time aerodynamic load prediction, [...]

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• Linear and quadratic invariants preserving discretization of Euler equations

  G. Coppola, A. Veldman

  eccomas2022.

  
  

  Abstract

  In the context of the numerical treatment of convective terms in compressible transport equations, general criteria for linear and quadratic invariants preservation, valid on uniform and non-uniform (Cartesian) meshes, have been recently derived by using a matrix-vector approach, for both finite-difference and finite-volume methods ([1, 2]). In this work, which constitutes a follow-up investigation of the analysis presented in [1, 2], this theory is applied to the spatial discretization of convective terms for the system of Euler equations. A classical formulation already presented in the literature is investigated and reformulated within the matrix-vector approach. The relations among the discrete versions of the various terms in the Euler equations are analyzed and the additional degrees of freedom identified by the proposed theory are investigated. Numerical simulations on a classical test case are used to validate the theory and to assess the effectiveness of the various formulations.

  Abstract
  In the context of the numerical treatment of convective terms in compressible transport equations, general criteria for linear and quadratic invariants preservation, valid [...]

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• Validation on a new anisotropic four-parameter turbulence model for low Prandtl number fluids

  L. Sirotti, G. Barbi, A. Chierici, V. Giovacchini, S. Manservisi

  eccomas2022.

  
  

  Abstract

  This work aims to validate a new anisotropic four-parameter turbulence model for low-Prandtl number fluids in forced and mixed convection. Traditional models based on the gradient-diffusion hypothesis and Reynolds analogy are inadequate to simulate the turbulent heat transfer in low-Prandtl number fluids. Additional transport equations for thermal variables are required to predict the characteristic thermal time scale. In a four-parameter turbulence model, two additional transport equations are solved for the temperature variance and its dissipation rate. Thus, it is possible to formulate appropriate characteristic time scales to predict the near-wall and bulk behaviour of mean and turbulent variables. The isotropic version of the four-parameter model has been widely studied and validated in forced and mixed convection. We aim to extend the model validity by proposing explicit algebraic models for the closure of Reynolds stress tensor and turbulent heat flux. For the validation of the anisotropic four-parameter turbulence model, low-Prandtl number fluids are simulated in several flow configurations considering buoyancy effects and numerical results are compared with DNS data.

  Abstract
  This work aims to validate a new anisotropic four-parameter turbulence model for low-Prandtl number fluids in forced and mixed convection. Traditional models based on the [...]

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• Numerical Testcases to Study Proudman Resonance Using Shallow Water Models

  N. Beisiegel, J. Behrens

  eccomas2022.

  
  

  Abstract

  Proudman resonance is the dominant mechanism behind meteotsunamis. We develop a comprehensive set of testcases to validate numerical methods focusing on the performance with respect to represent mentioned resonance. With the test cases we assess the wave amplification in dependence of characteristics of the pressure perturbation, model parameters, model resolution, and bathymetry characteristics. We use the compilation of tests to validate an adaptive discontinuous Galerkin (DG) model for the two-dimensional non-linear shallow water equations. As the tests are highly sensitive to model resolution, we use the adaptive mesh capabilities of the model to locally refine the disturbance and thus gain considerable efficiency.

  Abstract
  Proudman resonance is the dominant mechanism behind meteotsunamis. We develop a comprehensive set of testcases to validate numerical methods focusing on the performance with [...]

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