Consequences of Symmetries on the Analysis and Construction of Turbulence Models

Since they represent fundamental physical properties in turbulence (conservation laws, wall laws, Kolmogorov energy spectrum, ...), symmetries are used to analyse common turbulence models. A class of symmetry preserving turbulence models is proposed. This class is refined such that the models respect the second law of thermodynamics. Finally, an example of model belonging to the class is numerically tested.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Estudo de Modelos de Turbulência Aplicados à Ventilação de Espaços Interiores

Computational Fluid Dynamics has been implemented for indoor environments ventila‐ tion studies. Despite of its maturity and usefulness, its use for engineering applications such as heating, ventilation, and air conditioning (HVAC) projects is still scarce in Por‐ tugal. With this aim, this dissertation presents some introductory studies to create a computational fluid dynamics (CFD) workflow for the use by HVAC engineers with min‐ imal knowledge of CFD practices. Thus, some aspects were investigated, such as mesh design, discretization schemes, solvers, boundary conditions and turbulence models. For the latter, from a large set of turbulence models, six Reynolds‐averaged Navier‐Stokes (RaNS) turbulence models were tested and validated for indoor ventilation, the standard k − ε, the renormalization group (RNG) k − ε, the realizable k − ε, the v ′2 − f, the k − ω and the k−ω shear stress transport (SST). The standard k−ε model continues to present the most satisfactory results of all the studied turbulence models. The RNG k − ε model also showed good agreement with the experimental data, however it required more time to achieve convergence. It was not possible to achieve convergence with the realizable k −ε model. The k −ω and k −ω SST models yield results significantly different from the experimental measurements, especially in the far wall region. These studies were com‐ pared with the benchmarks from the International Energy Agency Annex 20. This work also presents 2D and 3D cases, mesh convergence studies, effects of flow buoyancy (incompressible, isothermal and non‐isothermal cases), and steady‐state and tran‐sient flow simulations.Mecânica dos Fluídos Computacional tem sido implementada em estudos de ventilação de espaços interiores. Apesar da sua maturidade e utilidade, a sua utilização para apli‐ cações de engenharia como projetos de aquecimento, ventilação e ar condicionado (AVAC) ainda é escassa em Portugal. Com este objetivo, esta dissertação apresenta alguns estudos introdutórios para a criação de um workflow de mecânica de fluídos computacional (CFD) para uso por engenheiros de AVAC com pouco conhecimento acerca de práticas de CFD. Assim, alguns aspetos foram investigados, tais como, geração de malhas, esquemas de discretização, solvers, condições de fronteira e modelos de turbulência. A partir de uma panóplia de modelos de turbulência, seis modelos de Reynolds‐averaged Navier‐Stokes (RaNS) de turbulência foram testados e validados para espaços interiores, standard k − ε, renormalization group (RNG) k − ε, realizable k − ε, v ′2 − f, k − ω e k−ω shear stress transport. O modelo standard k−ε apresenta os resultados mais satis‐ fatórios entre os estudados. O modelo RNG k−ε também demonstrou boa concordância com os resultados experimentais disponíveis na literatura, no entanto necessita de mais tempo de simulação para convergir do que o modelo standard k − ε. Com o realizable k − ε não foi possível obter convergência e os modelos k − ω e k − ω SST produzem resultados significativamente desfasados da realidade, especialmente na zona afastada das paredes. Estes estudos foram comparados com benchmarks do International Energy Agency Annex 20. Esta dissertação também apresenta estudos de convergência de malhas, efeitos de im‐ pulsão sobre o escoamento (casos incompressíveis, isotérmicos e não isotérmicos) e sim‐ ulações de escoamento em regime permanente e transiente

The Navier-Stokes equation and a fully developed turbulence

In fairly general conditions we give explicit (smooth) solutions for the potential flow. We show that, rigorously speaking, the equations of the fluid mechanics have not rotational solutions. However, within the usual approximations of an incompressible fluid and an isentropic flow, the remaining Navier-Stokes equation has approximate vorticial (rotational) solutions, generated by viscosity. In general, the vortices are unstable, and a discrete distribution of vorticial solutions is not in mechanical equilibrium; it forms an unstable vorticial liquid. On the other hand, these solutions may exhibit turbulent, fluctuating instabilities for large variations of the velocity over short distances. We represent a fully developed turbulence as a homogeneous, isotropic and highly-fluctuating distribution of singular centres of turbulence. A regular mean flow can be included. In these circumstances the Navier-Stokes equation exhibits three time scales. The equations of the mean flow can be disentangled from the equations of the fluctuating part, which is reduced to a vanishing inertial term. This latter equation is not satisfied after averaging out the temporal fluctuations. However, for a homogeneous and isotropic distribution of non-singular turbulence centres the equation for the inertial term is satisfied trivially, i.e. both the average fluctuating velocity and the average fluctuating inertial term are zero. If the velocity is singular at the turbulence centres, we are left with a quasi-ideal classical gas of singularities, or a solution of singularities in quasi thermal equilibrium in the background fluid. This is an example of an emergent dynamics. We give three examples of vorticial liquids.Comment: 33 page

Large Eddy Simulations of gaseous flames in gas turbine combustion chambers

Recent developments in numerical schemes, turbulent combustion models and the regular increase of computing power allow Large Eddy Simulation (LES) to be applied to real industrial burners. In this paper, two types of LES in complex geometry combustors and of specific interest for aeronautical gas turbine burners are reviewed: (1) laboratory-scale combustors, without compressor or turbine, in which advanced measurements are possible and (2) combustion chambers of existing engines operated in realistic operating conditions. Laboratory-scale burners are designed to assess modeling and funda- mental flow aspects in controlled configurations. They are necessary to gauge LES strategies and identify potential limitations. In specific circumstances, they even offer near model-free or DNS-like LES computations. LES in real engines illustrate the potential of the approach in the context of industrial burners but are more difficult to validate due to the limited set of available measurements. Usual approaches for turbulence and combustion sub-grid models including chemistry modeling are first recalled. Limiting cases and range of validity of the models are specifically recalled before a discussion on the numerical breakthrough which have allowed LES to be applied to these complex cases. Specific issues linked to real gas turbine chambers are discussed: multi-perforation, complex acoustic impedances at inlet and outlet, annular chambers.. Examples are provided for mean flow predictions (velocity, temperature and species) as well as unsteady mechanisms (quenching, ignition, combustion instabil- ities). Finally, potential perspectives are proposed to further improve the use of LES for real gas turbine combustor designs

Cooling by Free Convection at High Rayleigh Number of Cylinders Positioned Above a Plane

Free convection cooling of isothermal circular cylinders positioned above a horizontal plane is investigated numerically, using a commercial Computational Fluid Dynamics (CFD) software package. Computation is performed for high Rayleigh number, in the range 109 − 1011. Chien’s turbulence model of low-Reynolds-number K-ε is used, with Prandtl number of 0.707, corresponding to air near standard conditions. Influence of the underlying plane on heat transfer from the cylinders' surface is examined. As the gap between the plane and cylinders is narrowed, a pattern can be seen whereby heat transfer reaches a minimum that moves closer to the cylinder surface with higher Rayleigh number. The plane’s thermal condition, adiabatic versus isothermal, produces no significant difference in the heat transfer for the present range of gap ratio, in contrast to laminar case

Turbulent heat transfer in spacer-filled channels: Experimental and computational study and selection of turbulence models

Heat transfer in spacer-filled channels of the kind used in Membrane Distillation was studied in the Reynolds number range 100–2000, encompassing both steady laminar and early-turbulent flow conditions. Experimental data, including distributions of the local heat transfer coefficient h, were obtained by Liquid Crystal Thermography and Digital Image Processing. Alternative turbulence models, both of first order (k-ε, RNG k-ε, k-ω, BSL k-ω, SST k-ω) and of second order (LRR RS, SSG RS, ω RS, BSL RS), were tested for their ability to predict measured distributions and mean values of h. The best agreement with the experimental results was provided by first-order ω-based models able to resolve the viscous/conductive sublayer, while all other models, and particularly ε-based models using wall functions, yielded disappointing predictions

Symmetry breaking phenomena in thermovibrationally driven particle accumulation structures

Following the recent discovery of new three-dimensional particle attractors driven by joint (fluid) thermovibrational and (particle) inertial effects in closed cavities with various shapes and symmetries [M. Lappa, Phys. Fluids 26(9), 093301 (2014); ibid. 31(7), 073303 (2019)], the present analysis continues this line of inquiry by probing influential factors hitherto not considered; among them, the role of the steady component of thermovibrational convection, i.e., the time-averaged velocity field that is developed by the fluid due to the non-linear nature of the overarching balance equations. It is shown how this apparently innocuous problem opens up a vast parameter space, which includes several variables, comprising (but not limited to) the frequency of vibrations, the so-called "Gershuni number,"the size of particles (Stokes number), and their relative density with respect to the surrounding fluid (density ratio). A variety of new particle structures (2D and 3D) are uncovered and a complete analysis of their morphology is presented. The results reveal an increase in the multiplicity of solutions brought in by the counter-intuitive triadic relationship among particle inertial effects and the instantaneous and time-averaged convective thermovibrational phenomena. Finally, a universal formula is provided that is able to predict correctly the time required for the formation of all the observed structures

Computational fluid mixing

Computational fluid dynamics (CFD) is an extremely powerful tool for solving problems associated with flow, mixing, heat and mass transfer and chemical reaction. Although the equations of motion for fluid flow were established in the first half of the nineteenth century (e.g. Navier, 1822; Stokes, 1845), it was not until the arrival of digital computers in the 1960s and 1970s that it became feasible to perform numerical simulations of complex engineering flows. In these early days, CFD was a very much a research tool and most of the early work was aimed at developing numerical methods, solution algorithms and Reynolds-averaged turbulence models. However, in the 1980s, the first commercial codes emerged — e.g. PHOENICS, FLUENT, FIDAP, Star-CD, FLOW3D (which later became CFX) — providing general purpose software packages for both academic and industry users. The aerospace and automotive industries were amongst the first to embrace the use of CFD in engineering design, but from the 1990s onwards commercial codes have found widespread applications, for example in: biomedical engineering, environmental and atmospheric modelling, meteorology, chemical reaction engineering and more recently in the food and beverage industries. This chapter will focus on mixing vessel applications for the last two of these industry sectors, where CFD is increasingly used to provide process understanding and semi-quantitative analysis. In their review, Norton and Sun (2006) presented a graph showing the very significant increase in the number of peer-reviewed papers related to CFD applications to food process engineering. Figure 0.1 is an updated version of this graph, containing more recent data and showing that the number of papers that specifically analyse food mixing operations using CFD is still relatively small. In contrast, there are a vast numbers of papers on CFD simulation of (i) other food process operations, (e.g. drying, sterilisation, thermal treatment and extrusion, many of which are described by Sun (2007)) and (ii) more conventional mixing operations in the chemicals and specialty product industries (see for example, Marshall and Bakker (2004)). This chapter will outline the background knowledge required for CFD studies, present some examples of CFD modelling of mixing vessel flows and finally will discuss the current difficulties in applying this approach to food mixing processes