Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session D33: Convection and Buoyancy Driven Flows: Convection and Heat TransferConvection
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Chair: Saleh Nabi, Mitsubishi Electric Research Laboratories Room: 106 |
Sunday, November 19, 2017 2:15PM - 2:28PM |
D33.00001: Nonlinear optimal control policies for buoyancy-driven flows in the built environment Saleh Nabi, Piyush Grover, Colm Caulfield We consider optimal control of turbulent buoyancy-driven flows in the built environment, focusing on a model test case of displacement ventilation with a time-varying heat source. The flow is modeled using the unsteady Reynolds-averaged equations (URANS). To understand the stratification dynamics better, we derive a low-order partial-mixing ODE model extending the buoyancy-driven emptying filling box problem to the case of where both the heat source and the (controlled) inlet flow are time-varying. In the limit of a single step-change in the heat source strength, our model is consistent with that of Bower et. al (JFM 2008). Our model considers the dynamics of both `filling' and `intruding' added layers due to a time-varying source and inlet flow. A nonlinear direct-adjoint-looping optimal control formulation yields time-varying values of temperature and velocity of the inlet flow that lead to `optimal’ time-averaged temperature relative to appropriate objective functionals in a region of interest. [Preview Abstract] |
Sunday, November 19, 2017 2:28PM - 2:41PM |
D33.00002: Synchronization of natural convection in thermostatically-controlled adjacent cavities Rafael Chavez-Martinez, Mario Sanchez-Lopez, Francisco Javier Solorio-Ordaz, Mihir Sen Synchronization is a phenomenon observed in complex dynamical systems. It was first noticed by Huygens in the 17th century, and since then has been observed in systems of different types such as mechanical, biological and social. In thermal systems, numerical and analytical studies have found that two or more similar heat sources, with independent thermostatic temperature control and communicating with each other through a common interface, can have temperature oscillations. In the present study, laboratory experiments were carried out to study the thermal synchronization in two cuboid rooms separated by a common wall. Computer-based thermostats independently control the temperature of each cavity. The experiments show the effect of the ambient temperature and the initial condition in the cavities on the phase difference $\Delta\phi$. The results demonstrate in-phase and out-of-phase synchronization. An increase of the temperature difference between the cavity and the ambient, $\Delta T$, increases $\Delta\phi$. When $\Delta T < 2^\circ$C, $\Delta\phi$ oscillates around zero. $\Delta\phi$ is negative independently of the initial condition. The results of these experiments will be useful in the desing of heating in full-scale buildings. [Preview Abstract] |
Sunday, November 19, 2017 2:41PM - 2:54PM |
D33.00003: Lagrangian transport in a class of three-dimensional buoyancy-driven flows Sebastian Contreras, Michel Speetjens, Herman Clercx The study concerns the Lagrangian dynamics of three-dimensional (3D) buoyancy-driven cavity flows under steady and laminar conditions due to a global temperature gradient imposed via an opposite hot and cold sidewall. This serves as archetypal configuration for natural-convection flows in which gravity is perpendicular to the global temperature gradient. Limited insight into the Lagrangian properties of this class of flows motivates this study. The 3D Lagrangian dynamics are investigated in terms of the generic structure of the Lagrangian flow topology that is described in terms of the Grashof number (Gr) and the Prandtl number (Pr). Gr is the principal control parameter for the flow topology: vanishing Gr yields a state of closed streamlines (integrable state); increasing Gr causes the formation of toroidal coherent structures embedded in chaotic streamlines governed by Hamiltonian mechanisms. Fluid inertia prevails for ``smaller'' Gr. A buoyancy-induced bifurcation of the flow topology occurs for ``larger'' Gr and underlies the emergence of ``secondary rolls'' and secondary tori for ``larger'' Pr. Stagnation points and corresponding manifold interactions are key to the dynamics. [Preview Abstract] |
Sunday, November 19, 2017 2:54PM - 3:07PM |
D33.00004: A theoretical model of unbalanced exchange flows through openings Nicholas Wise, Gary Hunt Buoyancy-driven exchange flows through a single horizontal opening, for example through an opening at high level in a room containing warm air, are balanced, as there must be equal volume flux into and out of the opening. If a second, smaller, opening is introduced at low level in the room, air will enter through this opening. The volume flux out of the primary opening will therefore be larger than the volume flux in. This is an unbalanced exchange flow. A theoretical model to predict the volume flux of unbalanced buoyancy-driven exchange flows is developed. The model builds from a linear stability analysis for perturbations on a density interface, between buoyant and ambient fluid, advected out of the primary opening. Following this approach, we predict the criterion for the onset of bi-directional flow across circular openings as has been previously observed experimentally by others. The method developed is extended to non-circular geometries and comparisons are made between the volume fluxes predicted for circular and square openings. [Preview Abstract] |
Sunday, November 19, 2017 3:07PM - 3:20PM |
D33.00005: Experimental Analysis of Single Phase Buoyancy driven flow inside a Rectangular closed Loop for a Bottom Finite Heat Sink configuration Pandurang Rajiwade, Rajendra Vedula Natural circulation due to the presence of a heat source and heat sink in a closed loop is well reported phenomenon. There are very few studies where the heat sink capacity is finite while the source continues to be a constant wall flux/temperature one and there are no studies available where the heat sink is located below the heat source. The heat removal capacity of heat sink in such cases decreases with time and no steady state conditions can be expected. An experimental and numerical investigation for single phase natural circulation in a rectangular closed loop with water as working fluid is reported in this study. The heat sink is a fixed volume of water and is located at bottom of the loop such that the sink has a lower elevation with respect to heat source which is a constant power electric heater. Flow rate in the loop and also temperature of the heat sink as a function of time are presented. It is observed that a circulation is established soon after heater is powered on and the heat is removed effectively. A one dimensional numerical code for predicting the circulation flow rate and heat sink temperature based on standard formulations available in the literature was used to predicting experiment results and comparison was noted to be reasonably good. [Preview Abstract] |
Sunday, November 19, 2017 3:20PM - 3:33PM |
D33.00006: Optimal 2D convection cooling flows Silas Alben We generalize a recent method for computing optimal 2D convection cooling flows in a horizontal layer to a wide range of geometries, including those relevant for technological applications. We write the problem in a conformal pair of coordinates which are the pure conduction temperature and its harmonic conjugate. We find optimal flows for cooling a cylinder in an annular domain, a hot plate embedded in a cold surface, and a channel with hot interior and cold exterior. With a kinetic energy constraint, the optimal flows consist of vortices ranging in size from the length of the hot surface to a small cutoff length at the interface of the hot and cold surfaces. With a constraint on input power (fixed rate of viscous dissipation), the optimal flows are dominated by large-scale vortices, with the same size as the flow domain. [Preview Abstract] |
Sunday, November 19, 2017 3:33PM - 3:46PM |
D33.00007: The stability of variable Atwood number flows with preferential heating in the lower layer Bryan Kaiser, Jesse Canfield, Jon Reisner The conditions for instability in a flow consisting of two miscible, horizontal fluid strata when the lower fluid is preferentially heated by volumetric energy deposition (VED) is insufficiently understood. The flow is an approximation of the mechanical behavior of fuel capsule plasma during the compression phase of inertial confinement fusion (ICF). If the plasma becomes unstable then ignition ceases. The motivation for this study is not only to assist ICF research, but also to explore the stability of a variable Atwood number flow that develops features resembling both Rayleigh-Taylor instability and Rayleigh-B\'{e}nard instability (RBI). We use simulations to show that the instability observed in experiments can be reproduced by a stationary, spatially-variable thermal forcing and we show that the observed RBI in the bottom layer is a flow feature rather than a byproduct of imperfect experimental conditions. Paradoxically, a model by other researchers predicted the time of instability in an experiment with 2\% error using a model that assumes stationary forcing in the upper layer and linearly-growing-in-time forcing the lower layer. We discuss the paradox and present a new model for predicting the time of instability that accounts for spatially-variable VED. [Preview Abstract] |
Sunday, November 19, 2017 3:46PM - 3:59PM |
D33.00008: Three-dimensional numerical study of heat transfer enhancement in separated flows Saurav Kumar, S. Vengadesan The flow separation appears in a wide range of heat transfer applications and causes poor heat transfer performance. It motivates the study of heat transfer enhancement in laminar as well as turbulent flows over a backward facing step by means of an adiabatic fin mounted on the top wall. Recently, we have studied steady, 2-D numerical simulations in laminar flow and investigated the effect of fin length, location, and orientation. It revealed that the addition of fin causes enhancement of heat transfer and it is very effective to control the flow and thermal behavior. The fin is most effective and sensitive when it is placed exactly above the step. A slight displacement of the fin in upstream of the step causes the complete change of flow and thermal behavior. Based on the obtained 2-D results it is interesting to investigate the side wall effect in three-dimensional simulations. The comparison of two-dimensional and three-dimensional numerical simulations with the available experimental results will be presented. Special attention has to be given to capture unsteadiness in the flow and thermal field. [Preview Abstract] |
Sunday, November 19, 2017 3:59PM - 4:12PM |
D33.00009: Direct Numerical Simulation of turbulent heat transfer up to Re$_{\mathrm{\mathbf{\tau }}} \quad =$\textbf{2000} Sergio Hoyas, Jezabel Pérez-Quiles, Federico Lluesma-Rodríguez We present a new set of direct numerical simulations of turbulent heat transfer in a channel flow for a Prandtl number of 0.71 and a friction Reynolds number of 2000. Mixed boundary conditions, i.e., wall temperature is time independent and varies linearly along streamwise component, have been used as boundary conditions for the thermal field. The effect of the size of the box in the one point statistics of the thermal field, and the kinetic energy, dissipation and turbulent budgets has been studied, showing that a domain with streamwise and spanwise sizes of 4$\pi $h and 2$\pi $h, where h is the channel half-height, is large enough to reproduce the one point statistics of larger boxes. The scaling of the previous quantities with respect to the Reynolds number has been also studied using a new dataset of simulations at smaller Reynolds number, finding two different scales for the inner and outer layers of the flow. [Preview Abstract] |
Sunday, November 19, 2017 4:12PM - 4:25PM |
D33.00010: Using Covariant Lyapunov Vectors to Understand Spatiotemporal Chaos in Fluids Mark Paul, Mu Xu, Johnathon Barbish, Saikat Mukherjee The spatiotemporal chaos of fluids present many difficult and fascinating challenges. Recent progress in computing covariant Lyapunov vectors for a variety of model systems has made it possible to probe fundamental ideas from dynamical systems theory including the degree of hyperbolicity, the fractal dimension, the dimension of the inertial manifold, and the decomposition of the dynamics into a finite number of physical modes and spurious modes. We are interested in building upon insights such as these for fluid systems. We first demonstrate the power of covariant Lyapunov vectors using a system of maps on a lattice with a nonlinear coupling. We then compute the covariant Lyapunov vectors for chaotic Rayleigh-B\'enard convection for experimentally accessible conditions. We show that chaotic convection is non-hyperbolic and we quantify the spatiotemporal features of the spectrum of covariant Lyapunov vectors. [Preview Abstract] |
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