Without fluid turbulence, life might have rather different look. The atmosphere and oceans could nearly maintain a much larger temperature differences resulting in ultimate heating or cooling to the earth surface. The water and air flow could rather run much faster at rates of the speed of sound. Turbulence is a highly active nature of chaotic, random and three-dimensionality of swirling fluid. Its nonlinear convective property transports the momentum and energy in a helical mechanism leading eventually to an enriched fluid mixing and generating of small scale motions. These scales chiefly rule the hairpin vorticity dynamics, the strain production and the cascade of kinetic energy mechanisms. Hence, the key feature in turbulence is around disclosing the small scale motions. Studying the fine-scale dynamics gives us fundamental perspectives of flow topology and thus, improves our knowledge of turbulence physics. The turbulence dynamo becomes more complex when the active thermal gradient constitutes into the pure generator of turbulence. This particularly happens in the so-called buoyancy-driven Rayleigh-Bénard convection (RBC), when an infinite/bounded lying fluid is heated from below and cooled from above in the field of gravity. The main goal of this thesis is investigating the flow topology and small-scale dynamics in turbulent RBC, in order to better understanding its thermal turbulence mechanism and improve/validate the turbulence modeling for the foreseeable Computational-Fluid-Dynamics future. To do so, a complete direct numerical simulation (DNS) of turbulent RBC in a rectangular air-filled cavity of aspect ratio unity and pi spanwise open-ended distance, has been presented at Rayleigh numbers Ra={1e8, 1e10}, in chapter 1. A global kinetic energy conservation is inherited using a fourth-order symmetry-preserving scheme for the spatial discretization, and the flow dynamics is explored by analysis of kinetic and thermal energy power spectra, probability density function (PDF) of viscous and thermal dissipation rates, and identification of the wind in RBC. In chapter 2, the DNS dataset is used to investigate several universal small-scale features observed in various turbulent flows and recaptured here in turbulent RBC through the bulk. For instance, the inclined "teardrop" shape of joint PDF velocity gradient tensor invariants (Q,R), the preferential alignment of vorticity with the intermediate eigenstrain vector, and the spiraling degenerated behavior of the average rates invariants (,). It is found that a self-amplification of viscous straining -Qs results at Ra=1e10, helps in contracting the vorticity worms and enhances slightly the linear contributions of the vortex stretching mechanism. On the other hand, the evolution of relevant small-scale thermals has been addressed by investigating the average rate of invariants pertained to the traceless part of velocity-times-temperature gradient tensor i.e., (,). The new invariants are shown to follow correctly the evolution and lifetime of thermal plumes in RBC and hence disclose interactions of buoyant production and viscous dissipation. In chapter 3, the DNS dataset is employed to understand the underlying physics of the subgrid-scale (SGS) motions in turbulent RBC in the spirit of Large-eddy simulation (LES) turbulence modeling. To do so, the key ingredients of eddy-viscosity, eddy-diffusivity and turbulent Prandtl number, are calculated a priori and investigated in a topological point-of-view. As a result, it has been suggested the restricted application of the hypothesis of a constant turbulent Prandtl number only in the large-scale strain-dominated areas. More arguments have been attained through a priori investigation of the alignment trends imposed by existing parameterizations for the SGS heat flux. Finally, a new tensorial approach of modeling the SGS of thermal turbulence is sought, that opens new research trends in the future. Sin turbulencia, la vida tendría un aspecto bastante diferente. La atmósfera y los océanos podrían mantener una diferencia de temperatura mucho mayor que causaría un gran calentamiento o enfriamiento de la superficie de la tierra. Las corrientes de agua y aire podrían llegar a la velocidad del sonido. La turbulencia es un fenómeno caótico, aleatorio y tridimensional del flujo vortical. Su propiedad convectiva no lineal transporta moméntum y energía con un mecanismo helicoidal que conduce finalmente a una mezcla efectiva del fluido y una generación de escalas pequeñas de movimiento. Estas escalas dominan la dinámica de pequeña vorticidad, la disipación y la cascada de energía cinética. Por lo tanto, la clave de la turbulencia está en entender las escalas pequeñas. El estudio de la dinámica de estas escalas nos aportará una perspectiva de la topología del flujo y así mejorará nuestro conocimiento de la física de la turbulencia. El mecanismo turbulento se hace más complejo cuando el gradiente térmico constituye el productor principal de turbulencia. Esto sucede particularmente en la convección natural de Rayleigh-Bénard (RBC), donde una capa de fluido se calienta desde abajo y se enfría desde arriba. El objetivo principal de la tesis es investigar la topología del flujo y la dinámica de las escalas pequeñas en flujos turbulentos RBC con el fin de comprender mejor su mecanismo de turbulencia térmica y mejorar/validar su modelización en el futuro. En el capítulo 1 se presenta una completa Simulación Numérica Directa (DNS) de un flujo de aire turbulento RBC en una cavidad rectangular con sección cuadrada y longitud igual a pi, para números de Ra={1e8, 1e10}. Se utiliza un esquema de cuarto orden para la discretización espacial que garantiza la conservación la energía cinética global. La dinámica del flujo se explora con un análisis de: el espectro de energía térmica y cinética, la función densidad de probabilidad (PDF) de la disipación cinética viscosa y térmica, y la identificación del viento, en RBC. En el capítulo 2, los datos del DNS se utilizan para investigar las características universales de escalas pequeñas observadas en otros flujos turbulentos. Por ejemplo, el aspecto inclinado de "gota" del PDF conjunto de los invariantes del tensor gradiente de velocidad (Q,R), la alineación preferente de la vorticidad con el vector propio intermedio de la deformación y el comportamiento espiral deteriorado del ratio promediado de los invariantes (,). Se observa una amplificación de la deformación viscosa en el caso de Ra=1e10 que ayuda a contraer los tubos de vorticidad y mejora ligeramente la contribución lineal del mecanismo de estiramiento-vórtice. Por otro lado, se aborda la evolución de las escalas pequeñas térmicas con el estudio del ratio promediado de los invariantes del tensor gradiente de velocidad-por-temperatura (,). Los nuevos invariantes demuestran seguir correctamente la evolución de las plumas térmicas en RBC, revelando las interacciones de la producción flotante y la disipación viscosa. En el capítulo 3, los datos del DNS se emplean para comprender la física subyacente de los movimientos de la escala subrejilla (SGS) en turbulencia RBC con el espíritu de la modelización tipo simulación de grandes remolinos (LES). Para ello, se calculan a priori los componentes clave de viscosidad y difusividad de remolino y número de Prandtl turbulento, y se investigan desde un punto de vista topológico. Como resultado, se propone la aplicación de la hipótesis del número de Prandtl turbulento constante sólo en las áreas dominadas por la deformación a gran escala. Además, se alcanzan más argumentos con la investigación a priori de las tendencias de alineación geométrica impuestas por las parametrizaciones existentes del flujo de calor turbulento SGS. Finalmente, se estudia un nuevo enfoque tensorial para modelar la turbulencia térmica SGS, que abrirá nuevas líneas de investigación para el futuro.

This work explores the turbulence anisotropy behavior of a fluidized gas-particle suspension obtained from highly resolved kinetic-theory-based two-fluid model simulations. Therein, the phase-filtered anisotropy Reynolds stress tensor is considered to classify the possible states of turbulence in the barycentric anisotropy invariants map. The temporal turbulence trajectories have revealed a nonlinear converging demarcation line that evolved differently on the gas and solid phases. It isolates the prolate-like cluster's turbulence from the oblate-like background strain on the solid phase, while on the gas phase, the trajectories turn from nearly three-dimensional (3-D) turbulence inside the clusters to 1-D turbulence in the transition regions (from dense to dilute), which then develops into 2-D turbulence in the dilute areas. The converged trajectories at the demarcation lines are found to move always toward isotropy, revealing the return-to-isotropy problem and the tendency to extinguish the bulk anisotropy. The prevalent turbulence type on the solid phase has indicated a 1-D turbulence preference, which is consistent with the reported cluster-induced turbulence in the literature. Moreover, the granular temperature as a quantitative measure of uncorrelated particle agitation is found to accumulate predominantly in 1-D turbulence (dominant solid divergence and strain) and moderately in 2-D turbulence (dominant solid convergence) at the upstream parts of clusters. Similar disclosure of turbulence types is adopted as well, for the variance of solid concentration, drag production, and the magnitudes of the gas-phase Reynolds stress and rate-of-strain tensors. They have demonstrated a similar preferential turbulence anisotropy, which in turn promotes the applicability of the eddy-viscosity approach for modeling the gas-phase Reynolds stress contributions.

The time-efficient method of recurrence CFD (rCFD) uses the pseudo-periodic nature of a flow, extrapolating the passive transport quickly to infinity. In that scope, the recurrence/distance matrix for bubbling and turbulent fluidization regimes are investigated to find the recurrence properties. The results indicate the need for posterior spatial filtering in the turbulent regime which, in turn, reveals recurrent uniform superstructures with a clear fingerprint on the distance/recurrence matrix.

We present a novel approach for the fast modeling of exothermic chemical reactions in industrial-scale fluidized bed reactors. It implicates a fast olefin polymerization process, accounting for the catalyst activity, the solubility of the reaction gases in polymer, the particles crystallinity, and the reaction masses and heat transfer. We principally apply the transport-based recurrence computational fluid dynamics (rCFD) model upon the base of a short-term non-reactive simulation performed by a coarse-grained two-fluid model (cgTFM). Following the captured recurrent flows, the methodology propagates rapidly passive scalars far beyond the recorded simulation. The reaction kinetics of production/consumption rates due to polymerization are locally embedded into the individual solid/gas species concentrations. These in turn are considered in transporting the enthalpy and the generated heat by reaction. By doing so, the significant computational effort required to couple the thermodynamic effects of polymerization with the cgTFM (hybrid model), is drastically reduced using rCFD with very reliable agreement.

AIChE JournalVolume 67, Issue 5 e17271 ISSUE INFORMATION – TABLE OF CONTENTSFree Access Issue Information – Table of Contents First published: 09 April 2021 https://doi.org/10.1002/aic.17271AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume67, Issue5May 2021e17271 RelatedInformation

The small-scale flow topologies in a moderately dense (gas-particle) turbulent fluidization have been investigated using highly-resolved Eulerian two-fluid model simulations. Enhanced contraction of focal (enstrophy) and nodal (strain) gas phase structures are found as a result of the solid particles presence. The gas structures, thereby, revealed a tendency towards boundary-layer-like turbulence. In the solid phase, the focal topologies are arranged in elongated vortical tubes corresponding to dense clusters, which in turn induce a pseudo-turbulence on the gas phase.

In this work, we aim to shed light to the following research question: can we find a nonlinear tensorial subgrid-scale (SGS) heat flux model with good physical and numerical properties, such that we can obtain satisfactory predictions for buoyancy-driven turbulent flows? This is motivated by our findings showing that the classical (linear) eddy-diffusivity assumption fails to provide a reasonable approximation for the actual SGS heat flux: namely, a priori analysis for air-filled Rayleigh-Bénard convection (RBC) clearly shows a strong misalignment. In the quest for more accurate models, we firstly study and confirm the suitability of the eddy-viscosity assumption for RBC carrying out a posteriori tests for different models at very low Prandtl numbers (liquid sodium, Pr=0.005) where no heat flux SGS activity is expected. Then, a new tensorial SGS heat flux model is proposed and studied a priori using DNS data of an air-filled (Pr=0.7) RBC at Rayleigh numbers up to 10. Apart from having good alignment trends with the actual SGS heat flux, it is numerically stable per se and has the proper cubic nearwall behavior. Our near future research plans include testing a posteriori this new tensorial SGS heat flux model. Prior to that, we also aim to properly discretize these models in space and time.

Due to variety of scale dynamics evolved in gas-solid flows, most of its numerical description is limited to expensive short durations. This has made the slow processes therein, such as the chemical species conversion, to be out of an appropriate reach. In this work, an application of the transport-based recurrence computational fluid dynamics (CFD) has been introduced for the fast modeling of passive scalar transport, which is considered as species conversion and heat transfer in fluidized beds. The methodology discloses the recurrent dynamics during a short-term full CFD simulation as Lagrangian shift operations upon which a passive scalar can infinitely be traced. Apart from convecting, a proper approach based on the turbulent kinetic energy of tracked dynamics is introduced for modeling the physical diffusion of the scalar transported. Our outcomes have revealed a subtle chasing to the full CFD species simulation with a speed-up up to 1,600.

We study the flow topology dynamics in terms of the paramount nonlinearities of enstrophy and strain production at hard turbulent regimes of Rayleigh-Benard convection (RBC). To do so, a data set of direct numerical simulations for air turbulent RBC at Rayleigh numbers Ra = {10(8), 10(10) , 10(11), j is analyzed. Considering the bulk dynamics therein, the classical two-dimensional mean Lagrangian evolution of Q(G) and R-G invariants of G del u is extended to three dimensions by decomposing R-G into two parts: the strain production R-S and the enstrophy production tr(Omega S-2). In this way, the three-dimensional phase space (Q(G) , R-S, tr(Omega S-2)) allows us to identify separately the nonlinear straining and rotational mechanisms in turbulence. The main resultant observations attest that, when the turbulent regime is notably hard, a rising local self-amplification of the velocity gradient takes place in strain-dominated areas. This process is strongly aided by vortex contraction. Concomitantly, a pronounced increase in the linear contributions of vortex stretching is also identified, particularly relevant to strain-dominated slots.

In this work, we plan to shed light on the following research question: can we find a nonlinear subgrid-scale (SGS) heat flux model with good physical and numerical properties, such that we can obtain satisfactory predictions for buoyancy-driven turbulent flows? This is motivated by our findings showing that the classical (linear) eddy-diffusivity assumption fails to provide a reasonable approximation for the SGS heat flux. This was shown in our work [1] where SGS features have been studied a priori for a Rayleigh–Bénard convection (RBC). We also concluded that nonlinear (or tensorial) models can give good approximations of the actual SGS heat flux. Briefly, the large-eddy simulation (LES) equations arise from applying a spatial commutative filter, with filter length δ , to the incompressible Navier–Stokes and thermal energy equations.

At the crossroad between flow topology analysis and turbulence modeling, a priori studies are a reliable tool to understand the underlying physics of the subgrid-scale (SGS) motions in turbulent flows. In this paper, properties of the SGS features in the framework of a large-eddy simulation are studied for a turbulent Rayleigh-Bénard convection (RBC). To do so, data from direct numerical simulation (DNS) of a turbulent air-filled RBC in a rectangular cavity of aspect ratio unity and π spanwise open-ended distance are used at two Rayleigh numbers Ra∈{108,1010} [Dabbagh et al., “On the evolution of flow topology in turbulent Rayleigh-Bénard convection,” Phys. Fluids 28, 115105 (2016)]. First, DNS at Ra = 108 is used to assess the performance of eddy-viscosity models such as QR, Wall-Adapting Local Eddy-viscosity (WALE), and the recent S3PQR-models proposed by Trias et al. [“Building proper invariants for eddy-viscosity subgrid-scale models,” Phys. Fluids 27, 065103 (2015)]. The outcomes imply that the eddy-viscosity modeling smoothes the coarse-grained viscous straining and retrieves fairly well the effect of the kinetic unfiltered scales in order to reproduce the coherent large scales. However, these models fail to approach the exact evolution of the SGS heat flux and are incapable to reproduce well the further dominant rotational enstrophy pertaining to the buoyant production. Afterwards, the key ingredients of eddy-viscosity, νt, and eddy-diffusivity, κt, are calculated a priori and revealed positive prevalent values to maintain a turbulent wind essentially driven by the mean buoyant force at the sidewalls. The topological analysis suggests that the effective turbulent diffusion paradigm and the hypothesis of a constant turbulent Prandtl number are only applicable in the large-scale strain-dominated areas in the bulk. It is shown that the bulk-dominated rotational structures of vortex-stretching (and its synchronous viscous dissipative structures) hold the highest positive values of νt; however, the zones of backscatter energy and counter-gradient heat transport are related to the areas of compressed focal vorticity. More arguments have been attained through a priori investigation of the alignment trends imposed by existing parameterizations for the SGS heat flux, tested here inside RBC. It is shown that the parameterizations based linearly on the resolved thermal gradient are invalid in RBC. Alternatively, the tensor-diffusivity approach becomes a crucial choice of modeling the SGS heat flux, in particular, the tensorial diffusivity that includes the SGS stress tensor. This and other crucial scrutinies on a future modeling to the SGS heat flux in RBC are sought.

Small-scale dynamics is the spirit of turbulence physics. It implicates many attributes of flow topology evolution, coherent structures, hairpin vorticity dynamics, and mechanism of the kinetic energy cascade. In this work, several dynamical aspects of the small-scale motions have been numerically studied in a framework of Rayleigh-Bénard convection (RBC). To do so, direct numerical simulations have been carried out at two Rayleigh numbers Ra = 108 and 1010, inside an air-filled rectangular cell of aspect ratio unity and π span-wise open-ended distance. As a main feature, the average rate of the invariants of the velocity gradient tensor (QG, RG) has displayed the so-called “teardrop” spiraling shape through the bulk region. Therein, the mean trajectories are swirling inwards revealing a periodic spin around the converging origin of a constant period that is found to be proportional to the plumes lifetime. This suggests that the thermal plumes participate in the coherent large-scale circulation and the turbulent wind created in the bulk. Particularly, it happens when the plumes elongate substantially to contribute to the large-scale eddies at the lower turbulent state. Supplementary small-scale properties, which are widely common in many turbulent flows have been observed in RBC. For example, the strong preferential alignment of vorticity with the intermediate eigenstrain vector, and the asymmetric alignment between vorticity and the vortex-stretching vector. It has been deduced that in a hard turbulent flow regime, local self-amplifications of straining regions aid in contracting the vorticity worms, and enhance the local interactions vorticity/strain to support the linear vortex-stretching contributions. On the other hand, the evolution of invariants pertained to the traceless part of velocity-times-temperature gradient tensor has also been considered in order to determine the role of thermals in the fine-scale dynamics. These new invariants show an incorporation of kinetic and thermal gradient dynamics that indicate directly the evolution and lifetime of thermal plume structures. By applying an identical approach, the rates of the new invariants have shown a symmetric cycling behaviour decaying towards two skew-symmetric converging origins at the lower Ra number. The trajectories near origins address the hot and cold coherent plumes that travel as an average large-scale heat flux in the sidewall vicinities, and denote a periodic spin period close to the plumes lifetime. At the hard turbulent case, the spiraling trajectories travel in shorter tracks to reveal the reduced lifetime of plumes under the dissipative and mixing effects. The turbulent background kinetic derivatives get self-amplified and the trajectories converge to a zero-valued origin indicating that there is no contribution from the plumes to the average coherent large scales of heat flux. These and other peculiar scrutinies on the small-scale motions in RBC have been enlightened, and may have a fruitful consequence on modelling approaches of buoyancy-driven turbulence.

At the crossroad between flow topology analysis and the theory of turbulence, a new eddy-viscosity model for Large-eddy simulation has been recently proposed by Trias et al.[PoF, 27, 065103 (2015)]. The S3PQR-model has the proper cubic near-wall behaviour and no intrinsic limitations for statistically inhomogeneous flows. In this work, the new model has been tested for an air turbulent Rayleigh-Benard convection in a rectangular cell of aspect ratio unity and n span-wise open-ended distance. To do so, direct numerical simulation has been carried out at two Rayleigh numbers Ra = 108 and 1010, to assess the model performance and investigate a priori the effect of the turbulent Prandtl number. Using an approximate formula based on the Taylor series expansion, the turbulent Prandtl number has been calculated and revealed a constant and Ra-independent value across the bulk region equals to 0.55. It is found that the turbulent components of eddy-viscosity and eddy-diffusivity are positively prevalent to maintain a turbulent wind essentially driven by the mean buoyant force at the sidewalls. On the other hand, the new eddy-viscosity model is preliminary tested for the case of Ra = 108 and showed overestimation of heat flux within the boundary layer but fairly good prediction of turbulent kinetics at this moderate turbulent flow.

Small-scale universal features captured normally in many turbulent flows have been reviewed in Rayleigh-Benard convection. Namely, dynamical Lagrangian representations of the velocity gradient tensor invariants have displayed the so-called “tearing drop” spiraling feature within the bulk region. Furthermore, essential common aspects as the asymmetric alignment of vorticity with the vortex-stretching vector, and the preferential alignment between vorticity and the intermediate eigenvector of the rate-of-strain tensor have been observed in that scope. Further and in more appropriate implement, we have performed a similar dynamical study of flow topology pertained to the traceless part of the gradient velocity-times-temperature tensor. The new invariants are related basically with the small-scale dynamics associated with the evolution of thermal plumes and buoyant production. We find that a self-amplification of velocity derivatives developed at harder turbulent flow supports indirectly the local effects of vortex-stretching generation. Moreover, the averaged evolution of the new invariants have revealed a converging change towards two skew-symmetric origins at Rayleigh number equals to 1e8 but one zero-valued origin at 1e10.

where u denotes the velocity field, p represents the pressure, the non-linear convective term is defined by C(u,v) = (u · ∇)v, and the diffusive term reads Du = ν∆u, where ν is the kinematic viscosity. However, direct simulations at high Rayleigh numbers (Ra) are not feasible yet because the convective term produces far too many relevant scales of motion. Hence, in the foreseeable future numerical simulations of turbulent flows will have to resort to models of the small scales. The most popular example thereof is the LargeEddy Simulation (LES): the (unresolved) subgrid stress (SGS) tensor is approximated in terms of the resolved velocity (filtered velocity). Many SGS models have been proposed in the last decades (see [1], for instance). Alternatively, regularizations of the non-linear convective term basically reduce the transport towards the small scales: the convective term in the NS equations is replaced by a smoother approximation [2]. In our previous works (see [3, 4] and reference therein), we restricted ourselves to the C4 approximation [2]: the convective term in the NS equations (1) is then replaced by the following O( )accurate smooth approximation C4(u,v) given by C4(u,v) = C(u,v) + C(u,v′) + C(u′,v), (2)

The main aim of this work is understanding the phenomenon of B enard cells in laminar and turbulent regimes as an application of studying the air flow in the air gap and honey comb cells that installed in the flat plate solar collector. Furthermore analyzing the turbulent Rayleigh-B enard convection components by performing direct numerical simulation of turbulent air ow in too long inclined cavity like the air gap. The fi rst two chapters treat with known problems of laminar and turbulent flow as a necessary presentation of numerical methods used in solving the governing equation of flow motion and heat transfer, afterward the third chapter deals with the main object of investigating the turbulent and laminar Rayleigh-B enard convection flow.