A "poor man's" approach to topology optimization of natural convection problems

Topology optimization of natural convection problems is computationally expensive, due to the large number of degrees of freedom (DOFs) in the model and its two-way coupled nature. Herein, a method is presented to reduce the computational effort by use of a reduced-order model governed by simplified physics. The proposed method models the fluid flow using a potential flow model, which introduces an additional fluid property. This material property currently requires tuning of the model by comparison to numerical Navier-Stokes based solutions. Topology optimization based on the reduced-order model is shown to provide qualitatively similar designs, as those obtained using a full Navier-Stokes based model. The number of DOFs is reduced by 50% in two dimensions and the computational complexity is evaluated to be approximately 12.5% of the full model. We further compare to optimized designs obtained utilizing Newton's convection law.Comment: Preprint version. Please refer to final version in Structural Multidisciplinary Optimization https://doi.org/10.1007/s00158-019-02215-

A co-operating solver approach to building simulation

This paper describes the co-operating solver approach to building simulation as encapsulated within the ESP-r system. Possible adaptations are then considered to accommodate new functional requirements

Stabilized finite element methods for natural and forced convection-radiation heat transfer

Thermal radiation in forced and natural convection can be an important mode of heat transfer in high temperature chambers, such as industrial furnaces and boilers, even under non-soot conditions. Growing concern with high temperature processes has emphasized the need for an evaluation of the eect of radiative heat transfer. Nevertheless, the modelling of radiation is often neglected in combustion analysis, mainly because it involves tedious mathematics, which increase the computation time, and also because of the lack of detailed information on the optical properties of the participating media and surfaces. Ignoring radiative transfer may introduce signicant errors in the overall predictions. The most accurate procedures available for computing radiation transfer in furnaces are the Zonal and Monte Carlo methods. However, these methods are not widely applied in comprehensive combustion calculations due to their large computational time and storage requirements. Also, the equations of the radiation transfer are in non-dierential form, a signicant inconvenience when solved in conjunction with the dierential equations of ow and combustion. For this reason, numerous investigations are currently being carried out worldwide to assess computationally ecient methods. In addition ecient modelling of forced and natural convection-radiation would help to simulate and understand heat transfer appearing in various engineering applications, especially in the case of the heat treatment of high-alloy steel or glass by a continuously heating process inside industrial furnaces, ovens or even smaller applications like microwaves. This thesis deals with the design of such methods and shows that a class of simplied approximations provides advantages that should be utilized in treating radiative transfer problems with or without ow convection. Much of the current work on modelling energy transport in high-temperature gas furnaces or chemically reacting ows, uses computational uid dynamics (CFD) codes. Therefore, the models for solving the radiative transfer equations must be compatible with the numerical methods employed to solve the transport equations. The Zonal and Monte Carlo methods for solving the radiative transfer problem are incompatible with the mathematical formulations used in CFD codes, and require prohibitive computational times for spatial resolution desired. The main objectives of this thesis is then to understand and better model the heat treatment at the same time in the furnace/oven chamber and within the workpieces under specied furnace geometry, thermal schedule, parts loading design, initial operation conditions, and performance requirements. Nowadays, there is a strong need either for appropriate fast and accurate algorithms for the mixed and natural convection-radiation or for reduced models which still incorporate its main radiative transfer physics. During the last decade, a lot of research was focused on the derivation of approximate models allowing for an accurate description of the important physical phenomena at reasonable numerical costs. Hence, a whole hierarchy of approximative equations is available, ranging from half-space moment approximations over full-space moment systems to the diusion-type simplied PN approximations. The latter were developed and extensively tested for various radiative transfer problems, where they proved to be suciently accurate. Although they were derived in the asymptotic regime for a large optical thickness of the material, these approximations yield encouraging even results in the optically thin regime. The main advantage of considering simplied PN approximations is the fact that the integro-dierential radiative transfer equation is transformed into a set of elliptic equations independent of the angular direction which are easy to solve. The simplied PN models are proposed in this thesis for modelling radiative heat transfer for both forced and natural convection-radiation applications. There exists a variety of computational methods available in the literature for solving coupled convection-radiation problems. For instance, applied to convection-dominated ows, Eulerian methods incorporate some upstream weighting in their formulations to stabilize the numerical procedure. The most popular Eulerian methods, in nite element framework, are the streamline upwind Petrov-Galerkin, Galerkin/least-squares and Taylor-Galerkin methods. All these Eulerian methods are easy to formulate and implement. However, time truncation errors dominate their solutions and are subjected to Courant-Friedrichs-Lewy (CFL) stability conditions, which put a restriction on the size of time steps taken in numerical simulations. Galerkin-characteristic methods (also known by semi-Lagrangian methods in meteorological community) on the other hand, make use of the transport nature of the governing equations. The idea in these methods is to rewrite the governing equations in term of Lagrangian co-ordinates as dened by the particle trajectories (or characteristics) associated with the problem. Then, the Lagrangian total derivative is approximated, thanks to a divided dierence operator. The Lagrangian treatment in these methods greatly reduces the time truncation errors in the Eulerian methods. In addition, these methods are known to be unconditionally stable, independent of the diusion coecient, and optimally accurate at least when the inner products in the Galerkin procedure are calculated exactly. In Galerkin-characteristic methods, the time derivative and the advection term are combined as a directional derivative along the characteristics, leading to a characteristic time-stepping procedure. Consequently, the Galerkin-characteristic methods symmetrize and stabilize the governing equations, allow for large time steps in a simulation without loss of accuracy, and eliminate the excessive numerical dispersion and grid orientation eects present in many upwind methods. This class of numerical methods have been implemented in this thesis to solve the developed models for mixed and natural convection-radiation applications. Extensive validations for the numerical simulations have been carried out and full comparisons with other published numerical results (obtained using commercial softwares) and experimental results are illustrated for natural and forced radiative heat transfer. The obtained convectionradiation results have been studied under the eect of dierent heat transfer characteristics to improve the existing applications and to help in the furnace designs

Investigation of volume diffusion hydrodynamics : application to tight porous media

Various engineering problems imply rarefied gas flows that rely in the transition and free molecular regimes, e.g., micro and nano devices. The recent expansion of shale gas production where rarefied conditions are found in reservoirs exposed another area of application with a major importance. Continuum based methods like standard Navier- Stokes equations break down in the transition regime and free molecular regime. In order to model such flows discrete methods are usually adopted. Boltzmann equation can theoretically be used to simulate rarefied gas flows. However, complexity of its collision integral limits its applications mostly to simple cases (i.e., one dimension problems). The direct simulation Monte Carlo method which mimics the Boltzmann equation is the dominant method for simulating rarefied gas flows. It has been tested in several engineering problems, ranging from nano scale flow to re-entry vehicles with very consistent results in comparison with experimental data and analytical solutions. Its computational cost is, however, enormous for complex cases. Observations from Crookes radiometer inspired extending the continuum methods so that they could capture non-equilibrium phenomena in small scales. In the present thesis two different hydrodynamic model are presented. The first one is based on the Korteweg expression and the second one is called “Bi-velocity”. Firstly, the two models are presented in their mathematical forms. The proposed models are then developed in open-source computational fluid dynamics solvers. The models are tested and benchmarked in different rarefied gas flows problems in the whole range of Knudsen number. We used problems that are found in micro and nano systems and tight porous media. Results from the hydrodynamic models are compared against experimental data where available and the direct simulation Monte Carlo method. The two extended hydrodynamic models show improved results in comparison with standard Navier-Stokes

3-D Multiscale Adaptive Eulerian-Lagrangian Method for Multiphase Flows with Phase Change

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83641/1/AIAA-2010-1295-103.pd

Finite element techniques for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation

Finite element procedures for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation have been implemented. For both formulations, streamline-upwind/Petrov-Galerkin techniques are used for the discretization of the transport equations. The main problem associated with the vorticity stream-function formulation is the lack of boundary conditions for vorticity at solid surfaces. Here an implicit treatment of the vorticity at no-slip boundaries is incorporated in a predictor-multicorrector time integration scheme. For the primitive variable formulation, mixed finite-element approximations are used. A nine-node element and a four-node + bubble element have been implemented. The latter is shown to exhibit a checkerboard pressure mode and a numerical treatment for this spurious pressure mode is proposed. The two methods are compared from the points of view of simulating internal and external flows and the possibilities of extensions to three dimensions

Numerical study of surface tension driven convection in thermal magnetic fluids

Microgravity conditions pose unique challenges for fluid handling and heat transfer applications. By controlling (curtailing or augmenting) the buoyant and thermocapillary convection, the latter being the dominant convective flow in a microgravity environment, significant advantages can be achieved in space based processing. The control of this surface tension gradient driven flow is sought using a magnetic field, and the effects of these are studied computationally. A two-fluid layer system, with the lower fluid being a non-conducting ferrofluid, is considered under the influence of a horizontal temperature gradient. To capture the deformable interface, a numerical method to solve the Navier???Stokes equations, heat equations, and Maxwell???s equations was developed using a hybrid level set/ volume-of-fluid technique. The convective velocities and heat fluxes were studied under various regimes of the thermal Marangoni number Ma, the external field represented by the magnetic Bond number Bom, and various gravity levels, Fr. Regimes where the convection were either curtailed or augmented were identified. It was found that the surface force due to the step change in the magnetic permeability at the interface could be suitably utilized to control the instability at the interface.published or submitted for publicationis peer reviewe

Thermal Lattice Boltzmann Methods for the Simulation of Turbulent Flows with Conjugate Heat Transfer – Application to Refrigerated Vehicles

In dieser Arbeit wird eine thermische Lattice-Boltzmann-Methode (TLBM) für die instationäre Simulation turbulenter Strömungen mit natürlicher Konvektion und konjugierter Wärmeübertragung vorgestellt. Turbulente Strömungen mit ihren chaotischen Druck- und Geschwindigkeitsschwankungen stellen eine besondere Herausforderung für numerische Simulationen dar, wobei turbulente Strömungen, angetrieben durch thermische Auftriebskräfte, eine besonders schwierige Aufgabe darstellen. Wie in dieser Arbeit gezeigt wird, ermöglicht TLBM Large Eddy Simulationen (LES) solcher Probleme im industriellen und technischen Maßstab unter Verwendung eines Smagorinsky-Feinstruktur-Modells und unter Ausnutzung seiner intrinsischen Parallelisierbarkeit sowie der Möglichkeit, mehrere tausend Prozessorkerne zu verwenden. Die Eignung der vorliegenden Methode wird in dieser Arbeit anhand von Anwendungen zur Simulation der Innenluftströmung und der Isolationseffizienz eines Kühlwagens, des Wärmetransports im Luftspalt zwischen Rotor und Stator bei Elektromotoren, der Weiterentwicklung hocheffizienter Isolation auf der Basis von Vakuumisolationspaneelen (VIP) und Latentwärmespeichern sowie deren Anwendung in Kühlwagen gezeigt. Eine umfassende Validierung der Methode und ihrer Implementierung im Open-Source-Framework OpenLB wird durchgeführt. Gitterkonvergenz zweiter Ordnung wird gegen das analytische Porous Plate Problem demonstriert, während stabile Simulationen auch bei grober Diskretisierung mit hohen Reynolds- und Rayleigh-Zahlen erreicht werden. Eine sehr gute Übereinstimmung wird für natürliche Konvektion in einem quadratischen Hohlraum, ein bekannter Benchmark-Fall, vom laminaren zum turbulenten Regime mit 10^3 <= Ra <= 10^10 und bei Auflösungen von y+ ~ 2 gezeigt. Im ersten Teil der Ergebnisse werden Simulationen eines leeren Kühlaufbaus für einen Kühllastwagen vorgestellt. Das Strömungsfeld und der Wärmeübergang innerhalb eines gegebenen Kühllastwagens zeigt eine sehr gute Übereinstimmung mit den Messergebnissen, insbesondere den experimentellen Daten für ein Kühlfahrzeug bei Re ~ 53000 an vier charakteristischen Geschwindigkeits- und 13 Temperaturpositionen im Lastwagen. Die Wärmeübertragung durch die Wände wird in den Simulationen durch konjugierte Wärmeübertragung aufgelöst. Dies ermöglicht nun die präzise Vorhersage von Wärmeströmen nahe von Nusselt-Korrelationen für den gegebenen Aufbau, aber - im Gegensatz zu gewöhnlichen Nusselt-Korrelationen - wird der Wärmestrom in der Simulation räumlich aufgelöst. Im zweiten Teil der Ergebnisse wird die Strömung und der Wärmeübergang in einem Ringspalt mit innen rotierendem Zylinder untersucht. Die besondere Herausforderung bei der Simulation dieser Taylor-Couette-Strömung ist die Bildung von Taylor-Wirbeln, die durch ihre Rotation senkrecht zur Hauptströmungsrichtung den entsprechenden Wärmeübergang deutlich erhöhen. Detaillierte instationäre Simulationen werden über einen weiten Drehzahlbereich von fast schleichender Strömungen bis hin zum Auftreten von Taylor-Wirbeln durchgeführt. Es wird eine gute Übereinstimmung mit bisherigen Ergebnissen für die Strömungsstrukturen und die Verbesserung des Wärmeübergangs durch Taylor-Wirbel festgestellt. Insbesondere wird die vorliegende Methode mit Messungen, einer Korrelation und Simulationen unter Verwendung des Scherspannungstransport-Turbulenzmodells (SST) verglichen. Besonderes Augenmerk wird auf die Vorhersage der kritischen Taylor-Zahl gelegt. Während direkte numerische Simulationen (DNS) mit LBM die kritische Taylor-Zahl aus den Experimenten nahezu identisch vorhersagen, wird sie von LBM-LES leicht und vom SST-Modell weiter überschätzt, was auf die übermäßig dissipative Natur der Turbulenzmodelle für die Transition zurückzuführen ist. Im dritten Teil der Ergebnisse werden innovative Konzepte für verbesserte, nachhaltigere Kühlfahrzeuge numerisch untersucht. Um den Kraftstoffverbrauch und die damit verbundenen Emissionen zu reduzieren, werden zwei Ansätze als vielversprechend angesehen: (a) der Einbau von Vakuum-Isolationspaneelen (VIP) in die Wände des Kühlkoffers und (b) die Einführung eines Latentwärmespeichers (LHS) zum Austausch der kraftstoffbetriebenen Klimaanlage (AC). Die Verwendung des vorliegenden TLBM erlaubt in den Simulationen die Auflösung der durch die AC und die natürliche Konvektion induzierten turbulenten Luftströmung, des Wärmeflusses innerhalb der Isolierwände und der tiefgefrorenen Ladung. Dies liefert neue Erkenntnisse über den Einfluss der Konzepte auf die Wärmeübertragung in verschiedenen Kühlaufbauten. Die Simulationen zeigen einen stark reduzierten und homogenisierten einströmenden Wärmestrom für das kombinierte PUR- und VIP-Isoliermaterial im Vergleich zu einer reinen PUR-Isolierung. Die Dämmung des Kühlaufbaus mit VIPs halbiert daher die erforderliche Kühlenergie. Dies ermöglicht den Ersatz der AC durch einen LHS in Dachnähe und ein zusätzliches Lüftungssystem mit deutlich geringerer Gesamtleistung. Unter Berücksichtigung der Temperaturhomogenität von Tiefkühlprodukten wird eine leichte Umströmung des Kühlgutes als notwendig erachtet. Die maximal zulässige Ausfallzeit der AC wird in den Simulationen mit jeweils ca. 3,3 min (PUR), 8 min (PUR+VIP) und 11 min (PUR+VIP+LHS) ermittelt. Im vierten Teil der Ergebnisse wird eine LBM zur Simulation des Schmelzens und des konjugierten Wärmeübergangs auf der Basis des Transports der Gesamtenthalpie vorgestellt, welche bei Validierung gegen die analytische Lösung des zeitabhängigen Stefan-Problems präzise Ergebnisse liefert. Die in dieser Arbeit entwickelte Methode zeigt geringe Grenzflächendiffusion für einen weiten Bereich von Relaxationszeiten und Stefan-Zahlen. Weiterhin wird eine enge Übereinstimmung für das Schmelzen von Gallium einschließlich der natürlichen Konvektion in 2D und 3D mit Messungen und Simulationen mit unterschiedlichen Ansätzen gezeigt. Das Modell wird ferner auf das Schmelzen von Paraffin in zwei komplexen Metallschaumgeometrien angewendet. Es wird eine Voxel-basierte parallele Vernetzung vorgestellt, die eine schnelle und automatisierte Verarbeitung der komplexen Geometrie in wenigen Minuten ermöglicht. Die Simulationen erfassen erfolgreich den materialübergreifenden Wärmetransfer in 3D, wobei die Wärmeleitfähigkeit des Schaums mehr als 1000-mal größer als die des Paraffins ist. Die Form der Schmelzfront und der Einfluss der spezifischen Oberfläche der verschiedenen Metallschäume stehen in enger Übereinstimmung mit früheren Simulationen