Session T01: Convection and Buoyancy-Driven Flows: General (8:00am - 8:45am CST)

Conjugate heat transfer modeling and optimization of in plane cooling channels

With the current advancements in electrical engineering the heat dissipation from electronic components is increasing at a rapid pace. Efficient thermal management of these components is imperative for the systems survivability and efficiency. High fidelity CFD simulations are computationally expensive and therefore not apt for optimization schemes. Here, we formulate a rapid kernel-based model for the conjugate heat transfer of a plate heated by different heat components and cooled by forced convection. The conjugate heat transfer kernel-based model is validated with high-fidelity CFD code, and a significant reduction in computation time is observed. The model is extended to account for spatially dependent thermal conduction coefficients to account for embedded high conductivity paths as a thermal management technique. The complete model is used to optimize the design of in-plane cooling channels. The heat transfer coefficient (Nusselt number) is reported and compared for different heat source configurations.   

Artificial Neural Network for the prediction of heat transfer of mixed convection in lid-driven cavity with double vertical or horizontal blocks.

The capability of using Artificial Neural Network (ANN) to predict Nusselt number for laminar mixed convection, is established. Numerical simulations are carried out in lid-driven square cavity with two internal rectangular blocks, positioned in vertical or horizontal direction. The objective is to predict the optimum distance between the two rectangular blocks W/L that provides the maximum heat transfer coefficient. CFD results are used for training and testing the ANN to predict new cases; thus, saving effort and computation time and validate the obtained numerical results. A wide range of flow and heat transfer parameters are considered. The maximum Nu number obtained for the vertical blocks was at W/L $=$ 0.4 (Re $=$ 500 and Gr $=$ 5 \texttimes 10$^{\mathrm{4}})$ and for the horizontal blocks case was at W/L $=$ 0.3 (Re $=$ 500 and Gr $=$ 5 \texttimes 10$^{\mathrm{4}})$. These numerical results agree well with the ANN predictions; thus, the ANN may help reduce analysis-time and effort.   

Airflow optimization to prevent transmission of COVID-19

Motivated by attempts to reduce the spread of disease during the pandemic, we investigate modifications to HVAC systems. Our aim is to minimise airborne droplet transport through optimization of ventilation and design of airflow patterns within the buildings. Thus, we consider the optimization of turbulent flows within enclosed environments using the so-called one-shot method for adjoint-based optimization. We use the incompressible Reynolds-averaged Navier-Stokes (RANS) equations, derive the corresponding adjoint equations and solve the resulting sensitivity equations with respect to inlet conditions. For validation, we solve a series of inverse-design problems, for which we recover known globally optimal solutions. We then solve the maximal mixing problem for a passive scalar in a region of interest, as representative of potentially infected droplet transfer between occupants, with minimum energy budget. The role of an approximate Hessian as a preconditioner as well as tuned step-size for the one-shot method iterations are highlighted. It is shown, by employing an efficient optimization algorithm, that the one-shot method can solve the PDE-constrained optimization problem with a cost comparable, (about fourfold) to that of a single iteration of the simulation problem alone.   

The convective Stefan problem: Transitional shapes under natural convection

Fluids sculpt many of the shapes we see in the world around us, from melting ice cubes to "stone forests" of limestone rock spires. We present a new mathematical model describing the shape evolution of a body that dissolves or melts under gravitationally stable buoyancy-driven convection, driven by thermal or solutal transfer at the solid-fluid interface. For high Schmidt number, the system is reduced to a single integro-differential equation for the shape evolution. Focusing on the case of an initially conic or wedge-shaped body, we derive complete predictions for the underlying self-similar shapes, intrinsic scales and descent rates that apply to bodies that melt or dissolve in a quiescent ambient fluid. The theoretical predictions show excellent agreement with the results of a new series of laboratory experiments.   

The dependence of plumes on Reynolds number

Buoyant plumes in stratified environments are a common fluid-dynamical phenomenon present across a wide range of Reynolds numbers (Re), from volcanic eruptions to the convection generated above a human head. However, classical theories of turbulent plumes, such as the Morton, Taylor {\&} Turner (1956) model, do not incorporate the dependence of plumes on viscosity (nor thermal diffusivity). They are therefore unable to address the dynamics of plumes at intermediate scales, and the transition to Re-independent dynamics. In order to address these open questions, we conduct the first complete theoretical investigation of plume dynamics in stratified ambients across the full range of Re using direct numerical simulations of the Navier-Stokes equations. By constructing a universal regime diagram, we reveal the asymptotic transition from a new theory of the rise height of a laminar plume in a stratified environment to a Re-independent turbulent regime at sufficiently large Re. The results establish the general dependence of plumes on viscosity, and clarify for the first time the conditions necessary for simulations to reproduce high-Re natural phenomena such as volcanic eruptions.   

Physical mechanism of erythrocytes sedimentation rate

Red blood cells (or erythrocytes) sedimentation rate (ESR) is a physical parameter of blood which is often checked in medical diagnosis. It is indeed well known that in case of inflammation, the increase in fibrinogen and other proteins induces a higher ESR. Until now, researchers thought that the increase of fibrinogen accelerates the ESR by creating bigger aggregates of red blood cells (RBC). Fibrinogen is indeed an aggregation agent of RBCs, and bigger aggregates tend to sediment faster in Stokes regime. However, modeling the ESR measurements with this hypothesis is challenging and often requires physical assumptions specific to this system. Besides, modern colloidal science has shown that attractive particles form percolating aggregates, as wide as the container. The sedimentation of those colloids then follows a so-called "colloidal gel collapse" regime. Here, we show that RBCs actually follow the same behavior. We present details measurements of experimental ESR curves, and original micro- and meso-scopic pictures supporting this claim. Besides, those experimental observations are supported by 2D and 3D numerical simulations. We also demonstrate that such assumption naturally leads to efficient analytical modeling for the sedimentation curve of RBC.   

Dust Free Zones in Natural Convection Boundary Layers Over Horizontal Plate

We present a study on the dust free region above hot horizontal surfaces of uniform temperature in natural convection and propose relations to predict its height in the limit of small particle inertia. Trajectory analysis of the particles inside the flow field revealed the existence of two special trajectories, called separatrices, originating from a saddle point and forming the boundary of the dust free region. These separatrices follow a curve of constant $\eta$, denoted as $\eta_{df}$, where $\eta$ is the boundary layer similarity variable. An equation developed for the separatrices showed that $\eta_{df}$ is a function of Prandtl number, $Pr$, and the thermophoretic number, $Th$. Scaling laws are developed for $\eta_{df}$ using the boundary layer equations of Rotem and Classen corresponding to the asymptotic cases of $Pr$, i.e, $Pr>>1$ case and $Pr<<1$ case. Interestingly these scaling laws obtained for the asymptotic cases of $Pr$ are found to be valid even for the intermediate $Pr$ regime except for intermediate $Pr>1$ in the large $\eta$ limit. Brownian effects on the particles are neglected for the entire analysis. Gravitational effects are also ignored for the major portion of the work except for the initial discussions on the effect of inclusion of gravitational term.   

Modulation of Rayleigh-Benard Convection by Lagrangian Thermal Forcing

The Rayleigh-Benard (R-B) convection, consisting of a layer of fluid heated from the top and cooled from the bottom, has been widely investigated as an archetype of turbulent convection. \footnote {G. Ahlers, S. Grossmann, D. Lohse, Rev. Mod. Phys. 81 (2009) 503-537} The enhancement (diminution) of turbulence is known to strongly increase (decrease) the heat transfer in convection. \footnote{J. J. Niemela, K. R. Sreenivasan, Phys. Rev. Lett. 100 (2008) 184502}\\ The use of a ``nudging term" \footnote{P. Clark Di Leoni, A. Mazzino, L. Biferale, Phys. Rev. X 10 (2020) 011023} is a technique to force a dynamic system towards a given state. In this study, we use a nudging term added to the thermal component of the R-B equations to simulate tracer particles suspended in a R-B system releasing heat in a Lagrangian manner. \\ Our first investigations indicate it is possible to vary the degree of turbulence and thus modulate the bulk heat transfer using such a Lagrangian thermal forcing approach.   

Ice melting in stratified shear turbulence

Ice shelves are floating tongues of ice that extend from grounded glaciers on land, and are important for ocean stratification and bottom water formation. We perform direct numerical simulations (DNS) of the flow below a melting ice shelf. The flow is driven by a far-field current (via an imposed pressure gradient) and by the competing action of two scalar fields: temperature, which is an unstably-stratified, rapidly-diffusing scalar, and salinity, which is a stably-stratified, slowly-diffusing scalar. The ice melting rate depends on the local ice-seawater interface gradients of temperature and salinity. The entire problem is controlled by six dimensionless parameters, namely: shear Reynolds number $Re_\tau$, Grashof number $Gr$, density stability ratio $\Lambda$, Prandtl number $Pr$, Schmidt number $Sc$ and Stefan number $St$. The value of these dimensionless parameters are chosen so to mimick the case of a melting oceanic ice shelf. Our preliminary results show that the ice melting mechanism influences the underneath flow stratification, thereby modulating the turbulence structure. At the same time -- feedback effect -- such turbulence modification influences the ice shelf melting rate.   

Not Participating

Solidification experiments and numerical studies were conducted to assess the influence of solidification structures on flow patterns during natural convection. Two transparent organic systems of succinonitrile and salol were chosen for the study. Succinonitrile is known to develop smooth tree-like ``dendritic'' structures while salol develops sharp hill-like ``faceted'' solid structures. The first part of the study involved performing experiments to observe the morphology of the solid-liquid interface and estimate its permeability. The second part involved performing numerical simulations using the experimental data to investigate the effect of these structures on the evolution of convection patterns observed during natural convection. Solidification experiments were conducted in a custom in-situ directional solidification cell which allows for imaging the interface real-time through the process of solidification. The images were segmented and a mesh for the solid structure was generated. OpenFOAM was used to perform natural convection simulations on the time-evolving mesh obtained from the experiments to simulate the initiation and development of convection patterns in the bulk liquid. The dendritic system displayed vertical plumes rising amidst the bulk liquid, while the faceted system displayed a random convection pattern. The effect of the characteristic features of the solid structures such as solid fraction and surface area per unit volume on the convection patterns are discussed.   

The gain in temperature during freezing of mixtures: an effect of permeability on natural convection

Permeability of mushy zone plays a significant role during natural convection dominated solidification of mixtures. Permeability is strongly influenced by the solid fraction, morphology of the solid, and the length scale between growing solid structures. In this study, in situ \quad water-salts \quad bottom-cooled solidification observations are reported. During freezing, salt is the primary solidifying component and grows as either a dendrite or a facet, while the less dense water is rejected into the bulk. Dendritic growth has higher permeability than faceted. During the dendritic growth, the rejection of less dense solute forms plumes as convective patterns, and temperature continuously decreases at a nominal rate. Faceted solids are more packed in nature and have a higher solid fraction, which led to random convective patterns. This results in homogeneous mixing in the bulk and the temperature is reduced at a considerably faster rate. The convection becomes weak eventually, and a gain in temperature at the onset of eutectic growth was observed. A similar gain in temperature was also observed during solidification of the ternary systems, where faceted was the primary solid. Additionally, we have described a scaling analysis to correlate the role of permeability with flow behaviour.   

Supercritical Water Flow Influence on Synthesizing Uniformly Sized Nanoparticles

The drastic thermodynamic changes of supercritical phase fluids near the critical point leads to a highly tunable environment for nanoparticle synthesis. Once synthesis conditions are defined, a high throughput method that results in uniformly sized nanoparticles is necessary for the successful transition of new materials into the real-world. Understanding the flow characteristics of such complex reactors aids in optimized operation, hence this work describes how these characteristics inside a built reactor affect the temperature field, which can lead to variation in particle size and distribution. High-fidelity 3D numerical simulations provide insight using the Helmholtz energy-based Span-Wagner equation of state for a reactor operated at 23-24 MPa and 650-700K (very close to water's critical point of 647K and 22.1MPa). From simulations and experimental validation, it is concluded that a quenching flow is not necessarily the optimal method to achieving a uniform, low-temperature field and furthermore, partial quenching can decrease uniformity while having a negligible effect on mean particle size. By comparing different operating conditions, the properties of supercritical fluids as a suitable reaction medium for uniformly sized nanoparticles is discussed.   

Variational Multiscale Large Eddy Simulations of Rayleigh-B\'{e}nard Convection at High $Ra$

Large eddy simulations (LES) of two- and three-dimensional Rayleigh-B\'{e}nard convection are performed up to $Ra=10^{14}$ for $Pr=1$ and $Pr=7$. These simulations are performed using novel LES models based on the variational multiscale (VMS) formulation. The new model is presented as a mixed model which combines the VMS formulation for Rayleigh-B\'{e}nard convection with an eddy viscosity model (EVM) to capture the effects of the Reynolds stresses in high $Ra$ convection. In the present work, the Wall-Adapting Local Eddy-viscosity (WALE) model is used as the EVM. The new models were implemented in the finite element code Drekar and simulations were performed using continuous, piecewise linear finite elements. The two dimensional simulations were performed in a domain with aspect ratio $2$ while the three-dimensional simulations were performed in a cylinder of aspect ratio $1/4$. Least squares fits to the $Nu$-$Ra$ data show $Nu_{_{2D}} = 0.127 Ra^{0.284}$ and $Nu_{_{3D}} = 0.104 Ra^{0.310}$.   

A 0D/3D nodal-CFD method of cylindrical pressurized tanks

The current study focused on developing a novel method for modeling a closed pressurized cylindrical tank driven by natural convection. The conventional techniques for capturing the physic and thermodynamic in such systems are the nodal model or computational fluid dynamics (CFD) model. A fully CFD model would be computationally expensive and restricted to short-duration response regimes, and the nodal model could be complicated and often not sufficient for certain but abundant flow conditions. We develop a unique 0D/3D approach by coupling the nodal-CFD models. Considering that the liquid domain is prone to greater complexity, the CFD method is used for the liquid and nodal models are employed for both tank structure and the gas domain. The CFD model considers the conservation of mass, momentum, and energy. A thermodynamic based nodal model is developed for the gas part. We explore different temporal and mass coupling of CFD and nodal models at their interfaces to capture the flow dynamics and temperature distribution of the pressurized cryogenic tanks. It is shown how the proposed method accounts for different flow dynamics and heat transfer in a self-consistent manner and can be employed to derive an adaptive low-dimensional performance model for different applications.   

Stability of buoyancy-driven flow in a vertical channel with one heated wall

\section*{Abstract} The linear stability of the temporally-evolving buoyant flow in a channel between an isothermal vertical wall and an adiabatic vertical wall is investigated by numerical integration of the derived two-dimensional stability equations for the 2D buoyant flow. Stability calculations are carried out for Prandtl number of 0.7 (air) inside four channels with length-to-width aspect ratios of 20, 13.33, 10, and 8 for a Grashof number of $Gr=6.1\times10^{10}$. The buoyant flow is numerically modeled by means of direct numerical simulation (DNS), and the solved temperature and velocity fields are used as the base flow properties in the linear stability equations. The stability of the developing buoyant flow in the channel for the four aspect ratios are compared in terms of the computed phase velocities, wave numbers, and stability envelopes. The predictions of the linear instability theory are compared and validated with the actual behavior of the simulated flow by means of the short-time Fourier transform of the velocity field computed from the DNS.