Modeling and distributed computing of snow transport and delivery on meso-scale in a complex orography Modelitzaci´oi computaci´odistribu¨ıda de fen`omens de transport i dip`osit de neu a meso-escala en una orografia complexa Thesis dissertation submitted in fulfillment of the requirements for the degree of Doctor of Philosophy Programa de Doctorat en Societat de la Informaci´oi el Coneixement Alan Ward Koeck Advisor: Dr. Josep Jorba Esteve Distributed, Parallel and Collaborative Systems Research Group (DPCS) Universitat Oberta de Catalunya (UOC) Rambla del Poblenou 156, 08018 Barcelona – Barcelona, 2015 – c Alan Ward Koeck, 2015 Unless otherwise stated, all artwork including digital images, sketches and line drawings are original creations by the author. Permission is granted to copy, distribute and/or modify this document under the terms of the Creative Commons BY-SA License, version 4.0 or ulterior at the choice of the reader/user. At the time of writing, the license code was available at: https://creativecommons.org/licenses/by-sa/4.0/legalcode Es permet la lliure c`opia, distribuci´oi/o modificaci´od’aquest document segons els termes de la Lic`encia Creative Commons BY-SA, versi´o4.0 o posterior, a l’escollida del lector o usuari. En el moment de la redacci´o d’aquest text, es podia accedir al text de la llic`encia a l’adre¸ca: https://creativecommons.org/licenses/by-sa/4.0/legalcode 2 In memoriam Alan Ward, MA Oxon, PhD Dublin 1937-2014 3 4 Acknowledgements A long-term commitment such as this thesis could not prosper on my own merits alone. I am deeply indebted to many people from several institutions. At the Universitat Oberta de Catalunya (UOC), in the first place I would like to thank my advisor, Dr. Josep Jorba, for his constant help and guidance over these years. As they say, any merits of this work are probably his - and any errors most surely my own. Dr. Joan Manuel Marqu`es, co-leader of the Distributed, Parallel and Collaborative Systems (DPCS) research group at UOC has also been very enthusiastic in his reception of the initial idea, and supportive of the project as it evolved. In Andorra, friendly and constructive discussions have taken place with investigators from the Observatori de Sostenibilitat d’Andorra (OBSA) and Institut d’Estudis Andorrans (IEA). Many colleagues and fellow-teachers at Universitat d’Andorra (UdA) and Escola Andorrana have been helpful in maintaining steam as the years passed by, as has my former boss at the Department of Higher Education, Dr. Joan-Marc Miralles. I am also indebted to two anonymous reviewers who, by their comments, pointed out several weaknesses that have since been removed and in general helped give the thesis a better cohesion. On a more personal note, my late father Dr. Alan Ward (Alan Mac an Bh´aird) has always been a role model for me, both as an academic of high standards and as a warm and caring human being. Unfortunately, he left us in February 2014 as the process of thesis redaction was getting underway. Last, but not least, my partner Merc`eRey has been very supportive and patient both with my quirks and with the amount of time spent in research and investigation. i CHAPTER 0. ACKNOWLEDGEMENTS ii Abstract Human activities in mountain terrain are increasing in scope, as are their impact on the natural environment, such as the effects of artificial snow generation. This study describes the working principles, development and validation of a Computational Fluid Dynamics (CFD) computer model of snowfall over a complex orography, with the aim of optimizing ski slope or other installations according to local weather patterns, thus helping the decision-making process. In the first step, the spatial domain is discretized, with the main focus on challenging topography that tends to produce deformed mesh volumes. A novel measure of mesh deformation is then defined and applied to discuss different strategies of mesh optimization with the goal of facilitating parallel computer solutions of the Navier-Stokes fluid transport equations. These strategies are evaluated with regards to their implementation as a parallel computer algorithm. In the second step, a computer model is designed to solve the Navier- Stokes incompressible turbulent fluid equations. Slip- and no-slip boundary layers are considered, modeling surface roughness with the ks method. The efficiency of the CFD computational toolkit are discussed, as applied within the limits of a small or medium-sized commodity computation cluster using commercially available equipment. Finally, the degree of coupling required between the snow- and air-phases of the fluid during the computer modeling of snowfall is discussed. A two- fluid (Euler-Lagrangian) methodology is implemented. The effects of tangent surface wind speed on primary and secondary snow transport are integrated into the model. An assessment is made of the application of parallel com- puting to the solution of Lagrangian movement of individual snow parcels. Experimental data is used to verify the suitability of computational tech- niques. Additionally, real-world applications of such snowfall models are discussed in relation to ski-slope planning and high-altitude road snow clearing. An application of the model to wind energy production planning is presented. iii CHAPTER 0. ABSTRACT iv CONTENTS Contents Acknowledgements i Abstract iii List of Figures ix Symbols and Abbreviations xiii 1 Introduction and goals 1 1.1 Background ............................ 1 1.2 Goals and Contributions of this thesis . 4 1.2.1 Addressing the challenges posed by modeling the air volumeabovemountainterrain . 4 1.2.2 Bridging the gap between large- and small-scale modeling 5 1.2.3 Handling the complex physical nature of snow particles 6 1.3 Outlineofthesis.......................... 7 2 Snow transport and deposition theory 9 2.1 TheNavier-Stokesequations . 10 2.1.1 Conservationofmass . 10 2.1.2 Conservationofmomentum . 12 2.1.3 Conservationofenergy . 15 2.1.4 Application to air flow and simplifications . 15 2.2 Primaryandsecondarysnowtransport . 18 2.2.1 Primarysnowtransport . 19 2.2.2 Secondarysnowtransport . 20 2.3 Chapterconclusions. .. .. 22 3 Optimizing domain discretization 23 3.1 Meshtypesandformation . 24 3.2 Theneedforameasureofmeshquality. 26 3.3 Optimizing mesh quality . 31 v CONTENTS 3.3.1 Creating an initial mesh . 32 3.3.2 Refiningthemesh..................... 36 3.4 Experimentalresults . .. .. 38 3.5 Chapterconclusions. .. .. 43 4 Solving the Navier-Stokes equations 45 4.1 Computational methods used in Fluid Mechanics . 46 4.1.1 Thechoiceofcomputationalmethod . 46 4.1.2 Open-andclosed-sourcesoftware . 47 4.1.3 Classification of software packages . 49 4.2 StructureoftheOpenFOAMsolvers . 51 4.2.1 ThechoiceofanOpenFOAMsolver. 52 4.2.2 Executing a CFD case with OpenFOAM . 54 4.2.3 Specificities of the PISO solver . 57 4.3 Parallel strategies for solving the equations . 59 4.3.1 Executing an OpenFOAM case in a parallel computing environment........................ 60 4.3.2 Elements contributing to parallel scalability . 63 4.4 Application to complex mountain orography. Experimental results ............................... 64 4.4.1 Mesh deformation and computational workload . 65 4.4.2 Mesh decomposition strategies . 67 4.4.3 Efficiency of OpenFOAM parallel execution . 70 4.5 Chapterconclusions. .. .. 74 5 Coupling snowfall with transport fluid motion 77 5.1 Mixedandmultiphaseflows . 77 5.2 Degree of coupling of a mixed fluid . 79 5.3 Determining the degree of coupling required in a mixed fluid . 80 5.4 Determining the degree of coupling in the specific case of snowfall 86 5.5 Computing parcel trajectories in a parallel environment . 88 5.6 Experimentalresults . .. .. 90 5.7 Chapterconclusions. .. .. 93 6 Case Studies 95 6.1 Skislopeplanning......................... 96 6.1.1 Constructing the computer model . 98 6.1.2 Computermodelexecution. 99 6.1.3 Experimentalresults . .103 6.2 Highaltituderoadsnowdrift management . 105 6.2.1 Snowdriftformationmodel. 106 vi CONTENTS 6.2.2 The effect of an immobilized vehicle . 109 6.2.3 Model validation . 111 6.2.4 Conclusions ........................111 6.3 Wind turbine implantation . 112 6.3.1 Materialandmethods . .114 6.3.2 Circulation model output . 117 6.3.3 HAWTmodeloutput. .119 6.3.4 Model validation . 121 6.4 Chapterconclusions. .123 7 Concluding notes 127 7.1 Analysis of contributions . 127 7.2 Applications of findings . 130 7.2.1 Preparingforafutureconstruction . 130 7.2.2 Understanding an existing installation . 131 7.2.3 Optimizing planning and taking into account collateral consequences .......................132 7.3 Openquestionsforfutureinvestigation . 133 7.3.1 Dynamic load balancing during model execution . 133 7.3.2 Modelparameterinfluence . 134 7.3.3 Snow transformation during and after transport . 134 7.3.4 Dynamic variations during snowfall . 135 A Publications associated with this thesis 137 A.1 An iterative method for the creation of structured hexahedral meshesovercomplexorography . 137 A.2 Harmonic buffeting in a high-altitude ridge-mounted triblade HorizontalAxisWindTurbine . 138 A.3 Planning passive snowdrift reduction on high-altitude roads withlateralobstaclestowindflow. 138 A.4 Otheractivities ..........................139 Bibliography 141 vii CONTENTS viii LIST OF FIGURES List of Figures 1.1 Colonization by Pinus nigra of the Alpine prairie stratum pre- viously occupied by grasses and lichens. La Rabassa, Princi- palityofAndorra.......................... 2 1.2 Digital Elevation Model of the Pyrenees Mountains, centered on the Principality of Andorra. Based on data from (T.G. Farr et al.,2007).......................... 3 1.3 Various simple forms of snowflake. Adapted from (C. Magono andC.W.Lee,1966)....................... 6 2.1 Flowthroughacontrolvolume. 11 2.2 Undisturbed primary snow deposition on containers and street- lights.Ordino,Andorra.. 18 2.3 Snowdrifts formed by wind on a ridge. Pic de Sal`oria, Alt Urgell,Catalonia.......................... 19 2.4 Various secondary snow transport mechanisms. 21 3.1 Structured and unstructured 2D meshes formed by triangular cells................................. 24 3.2 Streamlines and vortices in a model of a weir supplying a wa- terwheel.