UNIVERSITÀ DI PISA S

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UNIVERSITÀ DI PISA S

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INGEGNERIA EDILE ARCHITETTURA

DIGITAL BIOMIMETIC MORPHOGENESIS OF A HIGH-RISE BUILDING WITH RESPECT

TO WIND ENERGY PRODUCTION

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Abstract

The design process of a skyscraper, or rather one of the most fascinating duty in which an architect or an engineer can be involved, has always been subordinated to the prog- ress in the technic; where technic is intended as the ensemble of scientific knowledge, materials exploitations, technologic solutions, etc., required in the building up of a tower. In the recent times, the remarkable support offered by modern computers has improved the analytical power, causing a significant spreading of possibilities. This thesis has been built on the investigation and the consequential optimization of some of these new possibilities, through the specific study of energy-producing systems building implementation and evolutionary solvers-based structural design.

The glue of this modern manifesto has been entrusted to the biomimetic approach, in order to reaffirm the central role of the nature into a context, the skyscraper, which in- trinsically represents the affirmation of the human supremacy over the natural forces.

The entire work has been developed through an extended series of iterative processes characterized by an equivalent hierarchic level, with the consequential request of a direct and automatic connection between all the phases of the project. Grasshopper, through its parametric modelling, has excellently epitomized this connection, producing a chain of entangled algorithms able to define and successively manage each building component after the introduction of certain boundary conditions.

In detail, this work has been focused on three specific aspects of the design. As first, the morphogenesis stage has been investigated, with the effective application of biomimetic principles in regard to the architectural and structural conception, and performance-based considerations, in the form of CFD analyses, for what has concerned the implementation of a wind-turbines system. Then, the structural field has been ex- amined through the design and the resultant verification of vertical resisting system, composed of concrete core, a steel diagrid and seven horizontal stiffening rings. As last, a statistic estimation of the wind-turbines energetic production has been elapsed.

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Riassunto

La progettazione di un grattacielo, ovvero uno dei più affascinanti compiti a cui un architetto o un ingegnere possono prendere parte, è sempre stato un processo subordi- nato al progresso della tecnica; dove la tecnica è intesa come l’insieme di conoscenze scientifiche, utilizzo dei materiali, soluzioni tecnologiche, ecc., richiesto per erigere una torre. Recentemente, l’importante supporto offerto dai moderni computer ha com- portato un sostanziale aumento della capacità analitica, causando essa, a sua volta, una crescita degna di nota delle possibilità di ricerca. Questa tesi è stata basata sullo studio e la conseguente ottimizzazione di alcune di queste nuove possibilità; nello specifico, attraverso lo sviluppo di un sistema di produzione energetica da integrare nell’edificio e la progettazione di un design strutturale mediate un evolutionary solver.

Il collante che ha permesso di trovare un filo comune a questi ambiti progettuali, ap- parentemente molto diversi tra loro, è stato impersonato dall’approccio biomimetico.

Esso ha permesso di riaffermare il ruolo centrale della natura in un contesto, quello del grattacielo, che intrinsecamente rappresenta l’affermazione della supremazia umana sulle forze naturali.

L’intero lavoro presentato in questa tesi è consistito in una considerevole serie di pro- cessi iterativi caratterizzati da uguale importanza gerarchica, con la conseguente ne- cessità di una certa connessione diretta ed automatica tra le varie fasi del progetto. La modellazione parametrica offerta da Grasshopper ha rappresentato eccellentemente questa connessione, producendo una catena di algoritmi, collegati tra loro, capaci di definire e successivamente gestire ogni componente dell’edificio, previo inserimento di determinate condizioni al contorno.

Nello specifico, in questa tesi sono stati affrontati tre particolari aspetti del processo di progettazione di un grattacielo. Inizialmente è stata curata la fase di morfogenesi, attraverso l’effettiva applicazione dei principi biomimetici nella realizzazione del concept architettonico e strutturale, e tramite lo studio sull’implementazione di un sistema di turbine eoliche, grazie ad analisi CFD. Successivamente è stato affrontato il cam- po strutturale, progettando e poi verificando un sistema resistente verticale composto da un core in calcestruzzo armato, un diagrid in acciaio e sette corone di irrigidimento orizzontali. Come conclusione, è stata elaborata una stima statistica della produzione energetica del sistema di turbine implementato nell’edificio.

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Acknowledgement

This thesis has been developed as completion of my studying period at University of Pisa. I would like to express my sincere appreciation to my Supervisors, Prof. M. Froli and Dr.-Ing. F. Laccone, for their support and constructive suggestions during the re- alization of this research work. The First has accepted this collaboration when I was nothing more than an unknown student and, through his unquestionable knowledge and special way of analyzing the problems, has contributed to change and certainly evolve my approach to the structural, and non-structural, design. The Second, who has guided me from the first to the last day of work, has constantly offered me his precious help in the development of each part of this project, with the result of a final duplication of my awareness level of the subjects involved in this study.

Then, I would like to thank my colleague Marco Sodano, who has shared this project with me from the beginning. His collaboration, always excellent in the positive as well as in the negative periods, has improved my skills significantly.

A special thank goes to my whole family, which represents, undoubtedly, the most important thing I have.

I also would like to thank each one of my friends. Dealing with me is probably not an easy duty, but this work has seen an end specially because of your support during all these years.

As last, I want to say thanks to you. My girl.

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List of Figures

Fig. 1: Resume of the design strategy. . . . 7

Fig. 2: Resume of the reasearch questions. . . . .11

Fig. 3: The temperature gradient and the circulation over the north hemisphere. 15 Fig. 4: Theorical power spectrum of the wind . . . 16

Fig. 5: Vectoral rappresentation of the point velocity. . . . 18

Fig. 6: Logarithmic velocity and turbulent intensity profiles. . . . 19

Fig. 7: Probability density functions of generic wind velocity and peak velocity. 20 Fig. 8: Example of annual wind hours histogram. . . . 22

Fig. 9: Example of annual wind hours - frequency of occurrence histogram. . . . . 22

Fig. 10: Demonstrative Weibull’s function. . . . 23

Fig. 11: Demonstrative construction of an average velocities wind rose. . . 23

Fig. 12: Demonstrative construction of average velocities wind rose, implemented of frequencies of occurrence. . . . 24

Fig. 13: Rapresentation of the lift and drag forces originated due to the approaching of a fluid flow against a generic body. . . . 26

Fig. 14: Differences between the streamlined and bluff bodies. . . 27

Fig. 15: Reynold’s number-flow dependency on smooth, infinitely tall cylinder. . . 27

Fig. 16: Relations between Strouhal’s number and Reynold’s number and variation of the Strouhal’s number among the base on depth ratio increasing. . . . 28

Fig. 17: Beranek and Van Koten’s illustration of the air flow against a generic tall building. . . . .. . . 30

Fig. 18: Pressure coefficients distribution on a prismatic element characterized by a 2:1 aspect ratio. . . . 31

Fig. 19: Drag cofficient - corner radius relation. . . . 32

Fig. 20: Effects of cross-section tapering and twisting on the flow. . . . 33

Fig. 21: Comparison of several cross-sectional shapes with respect to their relative peak deflection.. . . 34

Fig. 22: Variation of the pressure coefficient due the effect of an interference building. . . .35

Fig. 23: Example of CFD case set-up. . . . 36

Fig. 24: Relation between the cells number and the results accuracy. . . . 37

Fig. 25: Forces acting on a drag-driven wind turbine. . . 44

Fig. 26: Representation of an actuator model adopted to simulate the behavior of a lift-driven wind turbine. . . . 45

Fig. 27: Examples of horizontal-axis and vertical-axis wind turbines. . . . 47

Fig. 28: Comparison of several power coefficients in relation with the tip speed ratio, with respect to different turbine typologies. . . . 48

Fig. 29: Relation between sound power level and wind speed with respect to different turbine models. . . . 49

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Fig. 30: Comparison of a generic wind power curve and its related Betz’s power

curve and actually-available power curve. . . . 51

Fig. 31: Possible implementations of a wind turbine on a generic building. . . . 53

Fig. 32: Conceptual views of Project ZED. . . 55

Fig. 33: ZED’s Project plan. . . . 56

Fig. 34: Conceptual and functioning views of Project Web . . . 56

Fig. 35: Pictures of the WEB’s prototypes with and without the channelling system. . . . .57

Fig. 36: Power curves and power coefficients obtained by the prototypes testing. . 57

Fig. 37: Conceptual views of the COR Tower and Burj Al-Taqa Energy Tower. . . . 58

Fig. 38: Rendering and facades of Strata Tower. . . 59

Fig. 39: Planimetric sections of Bahrain WTC’s 17th, 27th and 37th floors. . . . 60

Fig. 40: Views of Bahrain WTC and Pearl River Tower.. . . 61

Fig. 41: Resuming charts of the wind site characterization. . . . 78

Fig. 42: Wind vertical profile of the analyzed directions. . . . 79

Fig. 43: Turbulence intensity vertical profile. . . . 80

Fig. 44: Vertical section of the lower part of a bamboo’s plant. . . . 81

Fig. 45: Internode number - internode lenght relation. . . . 83

Fig. 46: Internode number - internode diameter relation. . . 83

Fig. 47: Internode number - internode thickness relation. . . . 83

Fig. 48: Synthesis of bamboo’s static-based principles. . . . 84

Fig. 49: Project guide-lines diagrams. . . 85

Fig. 50: Rescaled internode number - internode lenght relation. . . 86

Fig. 51: Rescaled internode number - internode diameter relation.. . . 87

Fig. 52: Grasshopper’s first definition based on the bamboo’s proportion. . . . 88

Fig. 53: Examples of possible building configurations. . . . 89

Fig. 54: Geometrical construction of the towers.. . . 89

Fig. 55: Displacement comparison between the bamboo-based and the equivalent building with respect to the tapered and no tapered case. . . . 90

Fig. 56: Lateral drifts in relation to the height of each building configurations, with respect to the 55% and 60% cases. . . . 91

Fig. 57: Comparison of the maximum displacement with respect to the 55% and 60% cases. . . . 92

Fig. 58: Description of the 2d-CFD analyses case set-up. . . . 93

Fig. 59: Streamlines characterizing the flow of the various cases among the negative X direction. . . . 94

Fig. 60: Streamlines characterizing the flow of the various cases among the positive X direction. . . . 95

Fig. 61: Streamlines characterizing the flow of the various cases among the positive Y direction. . . . 96

Fig. 62: Resuming average velocity increase of each 2d-CFD cases. . . . 98

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Fig. 63: Conceptual view of the building functions. . . . 101

Fig. 64: Conceptual view of the vertical circulation. . . . 102

Fig. 65: Realistic view of the building. . . . 103

Fig. 66: Generic spectral density of the seismic and wind actions. . . . 105

Fig. 67: Vertical profile of gravitational loading, design pressure and aerodynamical force per unirt lenght. . . . 106

Fig. 68: Moon-based pre-dimensioning model. . . . 109

Fig. 69: Components of the first structural model. . . .110

Fig. 70: Diagrid optimization criteria conceptual view. . . .111

Fig. 71: Conceptual comparison of the natural selection and optimization processes. . . . .113

Fig. 72: Example of 2d fitness landscape through several generations. . . . .114

Fig. 73: Drifts comparison between the complete and the single tower models. . .115 Fig. 74: Comparison of the fitness and the displacement functions during the whole optimization process. . . .117

Fig. 75: Perspectical views of a stiffening ring. . . . .118

Fig. 76: Lateral displacement comparison between the infinitely rigid diaphragms model and the effective stiffening rings-based model. . . .119

Fig. 77: Detailed lateral displacement comparison between the infinitely rigid diaphragms model and the effective stiffening rings-based model. . . . 120

Fig. 78: Inter-stories drift comparison between the infinitely rigid diaphragms model and the effective stiffening rings-based model. . . 121

Fig. 79: Perspective views of the final structure components. . . . 124

Fig. 80: Turbine model of study characteristics. . . . 125

Fig. 81: Planimetric and perspective views of the turbine-stiffening ring connection. . . . . .126

Fig. 82: Detailed view of the turbine-building connection. . . 127

Fig. 83: Conceptual representation of the generic environmet discretization. . . 128

Fig. 84: Conceptual representation of the twelve analyzed case. . . 129

Fig. 85: Perspective view of the +X case mesh. . . . 130

Fig. 86: Streamline-style representation of the flow with respect to one -X case (90º). . . . . .132

Fig. 87: Velocity increase curves with respect to each direction. . . . 133

Fig. 88: Mean velocity increase curves with respect to each main case. . . . 134

Fig. 89: Resuming chart of wind energy, before (WIND) and after (CFD) the building effect, at the eight of each turbine, with respect to the twelve analyzed directions. . . . . .136

Fig. 90: Comparison between the power output of each turbine (Pt) and the wind power (Pw) at the height of each turbine. . . . 138

Fig. 91: Comparison between the annual energetic production of each turbine (Et) and the annual wind energy (Ew) at the height of each turbine. . . . 138

Fig. 92: Percentage of energy producted by each turbine. . . . 139

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List of Tables

Tab. 1: Comparison of scale and shape Weibull’s parameters with respect to Euro-

pean Wind Atlas and MLE-obtained values. . . . 77

Tab. 2: Friction velocities of the analyzed directions. . . . 79

Tab. 3: Results of the 2d-CFD shaping. . . . 97

Tab. 4: Wind loading resume. . . 105

Tab. 5: Vertical loading resume. . . . 106

Tab. 6: Resume of requested core walls thickness. . . . 108

Tab. 7: Resuming of the diagrid elements pre-dimensioning. . . 109

Tab. 8: Resuming of the diagrid elements designed cross-sections. . . .117

Tab. 9: Steel elements verifications resuming. . . . 124

Tab. 10: Forces and pre-stress load on the highest turbine. . . . 126

Tab. 11: Cable dimensioning of the seve connection systems. . . . 126

Tab. 12: Resume of the inlet boundary conditions of each case. . . . 131

Tab. 13: Average velocity at the eight of each turbine, and relative percentage of increasing or decreasing. . . 131

Tab. 14: Resume of the tubines energetic productions. . . . 137

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I. INTRODUCTION

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1. PERFORMANCE-BASED DESIGN AND BIOMIMETIC APPROACH

The problem statement for this thesis has been to analyze and investigate a skyscraper design guided by biomimetic principles, in the specific form of the bamboo’s laws, and performance-based considerations, through the turbines-implementation orient- ed shape modelling.

The advent of digital technologies is transforming the architecture practice in several ways, surely unpredictable until few years back. The continuous advances in computer aided design and computer aided manufacturing are encouraging the production and construction of extremely complex forms, either impossible or too expensive to design using traditional technologies. This shifting from digital software as representation tools to digital software as generative tools is modifying the design paradigm from “making of form” to “finding of form”.

Contemporary, the global awareness of our planet health situation, mixed with the social and economic importance of a conscientious use of the natural resources, has led to the emergence of a new architectural approach in which building performances are the guiding line design principle. The so-called performance-based design finds a good definition of itself in the words of Michael Hensel, who articulates that the “[..]

form is redefined not as the shape of a material-object alone, but as the multitude of effects, a milieu of effects of conditions, modulations and microclimates that emanate from an object’s exchange with its specific environment; a dynamic relationship that is perceived and interacted with by a subject.” The employment of digital technologies operates in a quantitative and qualitative simulation in order to project an inclusive approach to design of the build environment.

From a wider point of view, Architecture has been always based on some kind of performance. The primary aim of an architectonic project has never been the pure esthetic appearance, never since the origin of history. What is changed in the new millennium is the range of these performance, which now are able to approach detailed environ- mental aspects. Moreover, Algorithm-aided Design tools, such as Grasshopper, allow a direct interconnection between the form definition process and the analysis result, making possible a continuous manipulation of the shape in order to fit a predeter- mined performance threshold.

In parallel, the last decade has seen a strong exploration in a field proper of the human being since its ancient period: the biomimetic. The idea of imitating the nature for some specific purpose is surely not something new, especially in architecture where the nature is always being a primary source of design ideas. What is new is the will of investigate and consequentially apply not just the natural shapes, but also the effective behavior of the natural organisms. A correct example to explain this concept can

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be represented by the comparison of a modern airplane and the famous Leonardo da Vinci’s ornithopter. At a first view, the second could appear more appropriate to be classified as a biomimetic machine, since Leonardo studied accurately the bird wings figure and mechanism and tried to replicate them in larger scale. Going deeper, anyway, it’s possible to observe that a modern airplane still takes treasure of the natural lesson, the wing profiles are clearly a mechanical reinterpretation of an animal wing, but also it understands the basic concepts behind a bird fly, say the production of a lift force intense enough to juxtapose the gravity, and it reapply these concepts to a different context. Under this point of view, the correct approach for Architecture is definitely represented by the first machine.

Benyus, the biggest contributor of the biomimetic cause of the last century, defines the biomimetic as “the conscious emulation of nature’s genius.” In this thesis, the meaning of

“emulation” will be defined as “investigation and reinterpretation” instead of “repli- cation”.

2. MOTIVATION

Imagine a country of more than sixty million people, with a surface of 300’000 square kilometers, and half of its territory occupied by cultural heritage or natural protected areas. Consider then a land use index ranked as fifth in the European Union list and an average ground occupation of 340 square meters per person, which means the double of fifty years ago and the half of the next twenty years projection. Merge together all this information and ask yourself: “Why we should continue to smother one of the most historically/naturally rich territory of this world instead of turn our eyes to the sky?”. “Why the vertical direction seems to be forbidden in Italy?”. Shortly: “Why Not?”.

Even the Tradition, an aspect impossible to not consider in our architectural culture, confirms this idea: many major Italian ancient cities has already experimented a high- rise buildings period in the past, around the rise of the past millennium. Clearly, different reasons brought the medieval people to “go tall”, but the point is that, anyhow, they did it.

Based on the spirit of the previous words, the aim of this thesis is to investigate and furthermore elaborate a design strategy for a high-rise building able to manage and handle the modern times requests. Specifically, if the vertical direction clearly appears as a direct solution to land consumption problem, an integrate energy-production system surely represents an interesting tactic regarding the ecological aspect. Keep- ing our self in the field of the realizable and actually-implementable technologies, the wind-energy production identifies the most suitable way of taking advantages of the nature of a tall structure. Two points makes this option particularly appropriate:

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• The production method is totally clean, with a zero-production of wastes and a zero-request of energy to initiate the process. The only negative aspect is denoted by the acoustic noise, but a clever internal function dispositions matched with an accurate acoustic isolation easily minimize the problem.

• The shape of the building can be modelled so to increase the wind velocity and consequentially maximize the energy obtained. This means that a turbine placed on a two hundred meters height basement tower will produce less energy than the same turbine positioned between two tall buildings designed to augment the wind flow through each other.

The design of skyscraper treats an incredibly high number of subjects, which includes not only the common urbanistic, architectural, structural and energetic aspects. Plus, each one of these parts acquires a remarkable complexity due to notable dimensions of the project. By saying so, it appears clear that a thesis should be focused on one particular field to be considered an appropriate scientific work. In the case of this thesis, three specific aspects have been explored:

• The morphogenesis process, under a biomimetic and a performance-based point of view. It has been investigated the possibility of taking inspiration from some natural scheme for an optimal design of the structure and the habitable spaces; and at the same time, fluid-dynamical considerations have been improved to assure a building able to produce wind-energy since its early stages of conception. This process can be considered as the fundamental process in a design work, since every single choice taken at this level of the project will influence in a crucial way all the consecutive calculations and planning operations. Moreover, since in a such big scale project many executive design arrangements are usually relegated to some standards in order to facilitate the construction phase, the morphogenesis stage appears surely a more interesting field to investigative.

• The structural static design of a composite system based on a concrete core and a steel diagrid, connected through several stiffening rings. As before, the complete analysis of a structure with these dimensions requires the investigation of many other fields, such as the dynamic behavior of the building or the aeroelastic interaction with the wind. Anyhow, an accurate and deep study on the static design certainly represents a stimulating subject, especially if new techniques, say for example the evolutionary solvers, has been introduced.

• The energy-production estimation of the wind turbines. After the performance-based considerations applied to the morphogenesis phase, an accurate estimation of the effective energy produced by the wind turbines has been elaborated, with the introduction of statistical calculations.

Among all the mentioned and not investigated aspects, the urbanistic topic necessi-

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tates a special remark. A skyscraper deeply influences the urban landscape in both the horizontal and vertical direction: this means that the common urban considerations on the viability, the public spaces serviceability etc. should be integrated with shadow- ing considerations, pedestrian comfort among the wind flow augmentation and many other aspects directly consequence of the height. For this reason, the project has been decided to not be located in an exact site. Anyhow, structural analyses and energetic considerations oblige data from a real context, data that are chosen to belong to city of Pisa (Italy).

3. THESIS ORGANIZATION

This work has been developed with the collaboration of the student Marco Sodano. A strong interaction between us has been kept during all the phases of the work, making it hard to precisely distinguish the parts elaborated by the one from the parts elaborated by the other. Anyway, since a final thesis must be an individual work, the organization can be represented as it follows:

• The morphogenesis process has been developed entirely in parallel. Here, my performance-based considerations have been mixed with his biomimetic approach so to obtain a building concept able to fit both the guide-lines. Clearly, to achieve an elegant result, we both have studied each other field, with the result of a com- pletely equal level of competence.

• The structural part can be classified as Sodano’s work. My contribution has regarded the evolutionary solvers part and the design of the turbine-building connection; where, talking about the first of the two parts, a robust collaboration of two brains has been requested due to the complexity of the problem.

• The energetic study on the turbines is a work of mine.

Resuming, after a complete cooperation in the morphogenesis process, it’s possible to assign the structural side of this work to Sodano and the energetic part to me. For the sake of completeness, both the thesis will report the entire project, since a mutilated presentation would not be able to reflect this work in the correct way. Anyhow, the parts which belong properly to different authors will be threaten more accurately.

The structure of this thesis follows the standard scientific dissertation style with six major sections denoted by an introduction and followed by a part for the research questions, the literature review, the methods adopted to achieve the required results, the case study and the relative conclusions.

The Introduction section contains an overview of the biomimetic and the performance-based design subjects. Then, a motivation for this work is redacted before an

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explanation of the thesis organization with a resume of each parts.

Afterward, the objectives of this study are defined in the Research Questions section.

The Literature Review, for readability reasons, includes only the subjects relative to the performance-based design approach, leaving the biomimetic and the structural parts to the thesis of my colleague. Specifically, the first chapter describes the wind theory fundaments, from the origin of the phenomena to the mathematical model which describes it in the structural and energetic calculations. Then, the second chapter intro- duces the aerodynamical interaction between the high-rise buildings and the air flow, with a particular focus on the shape-flow relationship. After this, the third chapter treats about the principles behind the modern Computer Wind Engineering, with a consequential focus on the Computer Fluid Dynamics topic. The last two chapters of this section analyze respectively the wind turbines theory and the state-of-the-art of the turbine-building implementation.

The Methods section defines all the operations employed to achieve the previously declared objectives. In detail, after the explanation of the statistical operations used to characterize the wind in the context, the evolution of the numerical models is exposed.

The Case Study section includes the effective exposition of all the effective operations executed and it will be composed of five principal chapters. After the wind-characterization of the site, the morphogenesis chapter is introduced with the description of the parametric model based on the bamboo law, the consequentially choice of the most advantageous aspect ratio and the two-dimensional fluid-dynamic planimetric shaping. A third chapter defines the building from the functionality point of view, by the designation of the different internal spaces, the internal viability and the fire safety. Afterward, a brief of the whole structural analysis is presented, with particular attention to three specific phases: the diagrid cross-sections optimization among the evolutionary solvers implementation, the design of the turbine-building connection and the application of the effective CFD-obtained pressure distribution to the structure. A last chapter then reports the energetic calculation results acquired by the final 3D CFD analyses.

As last, the Conclusions section includes a complete resume of the project and an overview of the complete grasshopper’s algorithm involved in the case study, with some final considerations on the adaptability of this work to many different locations.

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Fig. 1: Resume of the design strategy.

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II. RESEARCH QUESTIONS

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1. RESEARCH QUESTIONS

Three general field of interest are investigated in this work: the morphogenesis process of a skyscraper, its structural verification for what concerning the static part and an energetic study on the implemented wind turbine.

Regard the morphogenesis part, the study verges on the possibility of applying a re- visited bamboo growth concept as a fundamental guide-line for the design of a tall building. What happens if the bamboo’s proportions become the basis for a cage, instead of an effective building? In the end, such a lateral restraining system is supposed to do its work independently by the vertical structure connected. So, what if we design several different towers, each one with its proper structural system, and we enclose them inside this imaginary macro-structure? The answers to these questions represent the main concept behind this project.

Moreover, the implementation of performance-based considerations, through CFD analyses, completes the process, with the purpose of obtaining a shape able to maximize the energy production of the wind turbines.

The structural part, by its side, is focused on the complete design and the resulting verification of the vertical and lateral load resisting systems. Through the necessary static calculations, the feasibility of a rigid concrete core surrounded by a steel diagonal grid is investigated, such as the possibility of exploiting evolutionary solvers for the cross-sections optimization. Then, a study on the rigid diaphragm systems is reported, with the purpose of confirming the correctness of the whole structural choice. As last, a study on a highly light suspended turbine-building attachment system is reported.

Lastly, the wind turbines energy production is investigated with a complete check on how each design decision has influenced the energetic behavior.

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• MORPHOGENESIS

• STRUCTURE

• ENERGY

Fig. 2: Resume of the reasearch questions.

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III. LITERATURE REVIEW

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1. WIND THEORY

1.1. The Physical Behavior

What we call wind is, scientifically, the motion of the air inside the atmosphere. The origin of this phenomenon can be referred to the pressure gradients which affect our planet gaseous parts. Sun’s radiation, in fact, reaches the Earth with various angles and consequentially different zones have different temperature. As it is well known, a low temperature corresponds to a high pressure and vice versa; thus, perturbations of the atmosphere equilibrium appear, followed by circulations from the poles (the high-pressure zones) to the equator (the low-pressure zone). Due to the inhomoge- neous distribution of oceans, two more bands find place between the zero and the ninety latitude: the low-pressure sup-polar cell and the high-pressure sub-tropical cell.

Moreover, the heat flux does not only have a horizontal direction: Earth’s surface, in effect, absorbs more energy than the upper stratus and this gives rise to a vertical temperature gradient, which, of course, implies a motion of the air from the down to the up.

Merging together the previously explained behaviors, it’s possible to describe what is called the primary atmospheric circulation, composed by the seasonal winds, which spire at a mean speed of 4-5 m/s with a season length duration.

Focusing the attention on a scale that varies from hundreds to thousands of kilometers, the secondary atmospheric circulation acquires a dominant role. It’s composed by the cyclones, the anti-cyclones and the monsoons, all caused by a temperature gradient lo- calized in the lower stratus of the atmosphere. In opposition to the trade winds, which determine the climate of a certain geographic region, these phenomena influence the local weather, since their relatively short duration of one to two weeks.

Local winds complete the picture, taking origin because of specific characteristics of a single area with no effects on the secondary circulation.

Despite at the moment there is no meteorological model able to describe the whole system from a unique point of view, the engineering/architectural field requires to take in account analysis and statistics related only to the local weather winds. Con- sidering the most usual length scale used to classify the atmospheric events that is composed by a Synoptic scale (L > 2000 km) where the cyclones prevail, a Mesoscale (2 km < L < 2000 km) in which the local winds take place and a Microscale (L < 2÷10 km) where the environment interference must be considered; then the focus of wind based engineering studies must be pointed on the last of these magnitudes.

Clarified the global behavior of the phenomenon, a more detailed analysis of the physical quantities involved into the motion of the air will follow. Thus, it’s required to

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define a fundamental differentiation between the heights where our attention is focused: the free atmosphere, which varies from eight to eighteen kilometers, and the atmospheric boundary layer, which set itself up from a few hundred meters to at least three thousand. This classification is based on the dynamic equilibrium of a generic mass of air, so that the force originated by a pressure gradient is contrasted only by the force of Coriolis in the free atmosphere and, in opposition, only by the surface friction in the atomospheric boundary layer..

Our area of interest is clearly represented by the lowest of the two atmospheric parts;

anyway, for the sake of completeness, an explanation of the geostrophic equilibrium and the respective velocity will be given.

Starting with the definition of a pressure gradient force per unit mass, it’s only necessary to apply the well-known Newton’s second law and compare the fluid dynamic force with the apparent force of Coriolis, caused by the Earth’s rotation.

Pressure gradient force per unit mass:

P 1 px

a 2

2

= -bt l Coriolis acceleration:

( ) sin

a =U$2X m =f U$ Geostrophic wind speed:

U f1 px

$ a 2 2

= -b t l

Where ρ_a is the density of the air, Ω is the angular velocity of the Earth, λ is the latitude and f is the Coriolis parameter.

1.2. The Atmospheric Boundary Layer

Approaching the ground, the Coriolis force becomes neglectable and it leaves its duty to surface friction. At this point, before to extrapolate a mathematical correlation between the wind velocity and the retarding force, it’s necessary to define what we mean

Fig. 3: The temperature gradient and the circulation over the north hemisphere.

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exactly when we talk about wind velocity.

The velocity of a fluid, in general, is a three-dimensional quantity composed by a vector, function of space and time, in each direction. Such a complex variable would lead to unaffordable calculations without any simplification; so, in wind’s engineering, the Reynold’s approach is a fundamental concept.

( , , , )x y z t V=V

Decomposing the V vector in a mean and fluctuating part, we obtain a first term representing the average value of the velocity in a given period, and a second one which denotes the turbulence affecting the hypothetic virtual steady flow.

( ) '( , , , ) U z x y z t V = r i v+

This approach, exploited also in other contexts such as the resolution of Navier-Stokes equations in fluid dynamic problems, has a solid experimental base. If we analyze the power spectrum of the wind velocity, nSv(n), it’s possible to recognize two different harmonic contents. The first one, called macro-meteorological peak, takes place in a period included from some months to one hour and it obviously can be interpreted as the contribution of an average speed. The second one, which appears from ten minutes to few seconds, is named micro-meteorological peak and it has to be intended as a con- tribute offered by a speed of a very short durance, in other words a gust.

In the next section will be presented a more detailed explanation of the just stated model, but now let’s focus on the average element, or rather the largest magnitude’s one.

The mathematical base which describes the relation between the wind speed and the retarding force offered by the surface friction is called Logarithmic Law and it can be obtained by an integration. It can be postulated that the rate of change of the wind speed with the height is a function of the following variables:

• The height above the ground, z;

Tab. 1: Theorical power spectrum of the wind

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• The surface shear stress, τ₀;

• The density of the air, ρ_a.

Combining all the terms, we can form a non-dimensional wind shear and we can as- sume it constant. The constant value is known as Von Karman’s constant and it has been found experimentally to be around 0.4. u* is named friction velocity and, despite it has the actual dimension of a speed, it cannot be considered a physical velocity.

dU /

dz z dUdz

uz constant 1 k

* a

x0

t = = =

r r

Integrating, we obtain:

( ) log U z uk

zz

*

= 0

r _{a k}

The roughness length z₀ appears as a constant of integration and it clearly has a primary importance in the determination of the mean wind speed profile. It can be interpreted as the tallness of the posed on the ground elements which represents an obstacle for the flow. Usually, the various building codes divide the different terrains in four to five categories, so to have standard values of the parameter. It must be noted, anyway, that particular orographic conditions require appropriate studies.

It is possible to obtain the friction velocity value from the measurement of a real veloc- ity at a given height (H_ref), which takes the name of reference velocity. The international standard for the reference velocity U_ref defines it as the ten-minute mean wind speed at ten meters above terrain with a roughness length of 0.05 m and a return period of 50 years.

u* logU kHz

ref ref

0

= b l

It can be observed, experimentally, that the accuracy of the logarithmic law decreases with the increasing of the height. For example, the Eurocode 1 sets a limit of validity of 200 m. This is caused by the influence of the previous mentioned Coriolis force, which is neglectable near the ground level, but it gains importance for elevated altitudes.

Among the various empirical formulations, a high precise one is the expression based on the Harris and Deaves mathematical model.

( ) log( . . . . )

U z uk

zz 5 75a 1 88a 1 33a 0 25a

*

0

2 3 4

= + - - +

r Where:

a z Z Z uf

f Coriolis parameter 6^*

g

=

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1.3. The Velocity Definition

The complete definition of point velocity is given by:

( , , , )x y z t U z( ) '( , , , )x y z t U z( ) u z t'( , ) v z t'( , ) w z t'( , )

V = r i v+ = r i+ i+ j+ k

Where:

• Ū(z) represents the average component, and it’s a variable which varies only with the height as previously exposed.

• v’(x,y,z,t) denotes the turbulent part and it’s composed by a fluctuating com- ponent in each direction (u’ for the main axis, v’ for the transversal and w’ for the vertical), all function of height and time.

Since the longitudinal gustiness has in general significantly larger magnitude respect to the other two, we usually refer to the wind velocity by considering only this con- tribute.

( , ) ( ) '( , ) U z t =U zr +u z t

The level of turbulence in the wind speed can be expressed by its standard deviation.

The general method used to measure it is the RMS, which consists in a depuration of the steady part from the velocity function, first squared and then rooted in a way to deal with both positive and negative values. Evaluation time is mostly taken as one

Fig. 4: Vectoral rappresentation of the point velocity.

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hour, so the wind record is not affected by the segment of time considered and it can be assumed as a stationary random function.

( , ) ( ) T1 U z t U z dt

u

T 0

2 0

v =

#

0₆ - r _@

From the standard deviation it’s possible to introduce a new parameter with the purpose of expressing how much a flow is affected by the gustiness: the turbulence intensity. Defined as the ratio between the fluctuating component of the speed and its mean value, it varies as the inverse of the average velocity, increasing with the decreasing of the height.

I^u U vu

= r

Often, it becomes useful to consider Armitt’s statement regarding the relation between the standard deviation of the speed and the friction velocity. The following equations can be assumed to be true for a homogenous terrain:

. . .

u 2 5 0 75 0 5

* u

u v

w

u

. . . v

v v

The first one lead to a remarkable simplification for the calculus of the turbulent inten- sities, which help us to relate it only with the height and the roughness length.

. .

log log

I u

zz u

zz 0 4

2 5 1

*

* u

0 0

= =

` j a k a k

Fig. 5: Logarithmic velocity and turbulent intensity profiles.

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1.4. The Gust Factor Method

The variations of the wind velocity in the atmospheric boundary layer are random in nature. They’re caused by eddies within the air flow, moving along at the mean wind speed. These eddies are never identical, so it’s necessary to use statistical methods to describe the gustiness.

Measurements show that the function U(z,t) closely fits the Gaussian probably density function, which can be fully described once we know the mean value and the standard deviation.

( ) exp

f U 1 U U

2 21

u u

2

v r v

= _:- _b - r _l_D

For many purposes, a mean value is usually not a suitable one. For example, structural analyses require maximum values, such as energetic previsions must deal with a minimum threshold of advantageous data. In wind engineering, the probabilistic approach finalized to determine extreme values from the mean and the standard deviation of a given distribution is called gust factor method.

The gust factor, G, is defined as the ratio between the expected maximum gust speed within a specified period and the mean wind speed.

G U

= rUt

In a Normal distribution, the usual way to obtain a max value is the following:

Ut =U gr+ vu

Where g represents the peak factor and, in wind’s theory, it’s a function of the averag- ing time of the gust, τ, as well as the sample time T. Merging together the previously

Fig. 6: Probability density functions of generic wind velocity and peak velocity.

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exposed equations, it’s possible to relate the gust factor to turbulent intensity:

G U U

g ^u 1 gIu

= + v r = + r

Multiplying it by the mean value, it’s possible to obtain the expected maximum veloc- ity for a given return period. Without specific analyses, a secure estimation of g can be 3.5.

Ut =GUr

1.5. The Wind Characterization of a Site

The aim of a site wind characterization is the identification of three fundamental trends:

• The annual mean wind speed;

• The wind distribution profile;

• The prevailing wind directions.

Years of measurements have clarified that wind data fit approximately well the Weibull’s distribution, especially in a range of speed which varies from 4 to 16 m/s, or rather the interest field of this thesis. A so-called arrangement follows a probability density function, f(U), identified by two parameters: the shape factor, k, and the scale factor, c, with U, the velocity, representing the variable of the function.

( ) exp

f U ck Uc

Uc

k 1 k

= a k^- 9-a kC

When k assumes the specific values of 1 and 2, the Weibull’s distribution degenerates in two special distributions: respectively the exponential and the Rayleigh. This last is common in the northern Europe. Anyhow, the classical two-parameters Weibull function will be treated in the following paragraphs.

The probability density function describes the frequency of occurrence of a certain wind velocity, and by doing so, it appears clear that such a powerful tool can com- pletely solve the problem of a site characterization. The wind speed records required for this purpose must contain the hourly average velocity and the flow direction, expressed in degrees. A consequential reduction of the possible directions is then necessary, in a way to align the wind with the cardinal points. The choice between 8, 16, or 32 wind directions is strictly related to the variability of the case study.

The first step of the analysis is denoted by the construction of a yearly hours-wind velocities histogram for each cardinal direction.

Then, a simple percentage operation can define the frequency of occurrence of each

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velocity in relation to one year (and one direction). The result can be plotted once again in a histogram, which will appear similar to the previously showed one. The hours of

“calm” are usually treated separately.

At this point, the mean value and the standard deviation can be obtained by the following formulas:

( )

Uf U dU p U

U i i

i n

0 1

n = ³ =

|

=

#

( )

n11 p U

U i i U

i n

2 1

v = - -n

|

=

Where:

• U_i is the i-th measured velocity;

• p_i is the frequency of occurrence of the i-th measured velocity;

• n is the total number of measurements.

Fig. 7: Example of annual wind hours histogram.

Fig. 8: Example of annual wind hours - frequency of occurrence histogram.

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Once the mean value and the standard deviation are evaluated, it’s possible to proceed with the calculation of the shape and the scale parameters with the following relations, which take advantages of the Gamma function, Γ:

c 1 k1 nU= Ca + k

c 1 k2

U 2

v = Ca + k

The determination of a Weibull’s probability density function for each cardinal direction gives us the researched quantities, but dealing an elevated number of histograms is surely not intuitive. Thus, in Wind’s engineering, it’s usual to recur to a wind rose- style visualization. The great advantage of a radial plotting is determined by the possibility of display a given variable with an independency from its direction.

Two kind of wind roses are usually adopted. The first one allows us to visualize the average wind velocity on each cardinal direction. It can be obtained by dividing a circumference in 8, 16 or 32 sectors, setting up, consequentially, a radial scale for the speed made by concentric sub-circumferences.

Changing the values displayed on the radial scale from velocities to hours, or either to probability density, we obtain the second typology of wind rose, which can be used to plot the frequency of occurrence of a wind velocity from each direction. In this case, a color gradient is required to differentiate the speed magnitudes.

Fig. 9: Demonstrative Weibull’s function.

Fig. 10: Demonstrative construction of an average velocities wind rose.

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Fig. 11: Demonstrative construction of average velocities wind rose, implemented of frequencies of occurrence.

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2. HIGH-RISE BUILDINGS AERODYNAMICS

2.1. The Aerodynamical Coefficients

Bernoulli’s equation relates the velocity of a fluid with its pressure. Denoting with p the pressure on the surface of a body affected by the flow and p0 the pressure of the undisturbed flow, we obtain:

( )

p 21 U p U p p U U

21

a a 2 a

2 0

0 0 " 02 2

t t t

+ = + - = -

Hence, it’s possible to introduce the pressure coefficient, which represents the stress on a body in a non-dimensional form.

( )

U C U

U

p p U

UU 21

21

21 1

p

a a

a 02

02

02 0

2

0 2

t t

= - t

= -

= -b l

U₀ is usually taken equal to the average speed at the top of element analyzed.

Clearly, this variable can present itself both as positive and negative, depending on the magnitude of the velocity that approaches the body. On the windward sides, for example, the velocity is always lower than the undisturbed one, because of the “impact”

between the flow and the obstacle. This lead to a positive value of the coefficient which reaches its maximum at the stagnation point, when U tends to zero. On the other hand, in the leeward sides, the stream leans to expand its velocity, letting the pressure coeffi- cient to acquire a negative form. A C_p greater than zero implies a pression, such as a C_p lower than zero implies a depression.

Different characteristics of the velocities inserted into the formula determine different coefficients. Thus, a distinction is made for the mean (C_p), the root-mean-square fluctu- ating (C’_p), the maximum (Ĉ_p) and the minimum (Č_p) values.

C

U U U UU C

C U

1 1 1 1

p

p p

u 0

2

0 2

0 2 0

2

v

= -

= - l

r r

t t

s s

b a c c

k l

m m

Pressure gradients lead to aerodynamic forces. Imagining a simple case, as a flat plate invested by the wind can be, the net force exerted by the flow on the windward side can be obtained by the difference between the front pressure and the back pressure, multiplicated by the area. This force gets the name of Drag force if it points against the element, or Lift force if it’s directed in an orthogonal direction. Now, dividing both the sides by the previously mentioned dynamic pressure (1/2ρ_aU₀²), which, in this case,

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must be considered multiplicated by the area of the element so deal with the force it can offer, we obtain the force coefficient. The sign of its value determines its name:

drag coefficient if it’s positive and lift coefficient if it’s negative.

/ ( )

C C U A

p p A

C C

21 ^, ^,

D L

a

p p

0

1 2

= -t

= -

a k

A generic two-dimensional body, invested by the wind, is affected by two forces orthogonal to each other and a momentum, normal to the flow and originated by the dealignment between the result of the dynamic pressure and the centroid. This model acquires a primary importance in the study of high-rise buildings, since their slender figure allows us to approximate them to a line-like two-dimensional element.

According to the definition of force coefficient and assuming L as a characteristic length of the body, we can deduce the force coefficient per unit length:

( / ) ( / ) ( / )

C F

C U l

F

C U l

U l

M 1 2 1 2

, 1 2

,

F x x

F

a

a y

y

M z z

a

02

02 2 02

t t t

=

When a body needs to be analyzed in its three-dimensional form, the force coefficients become six: three for the translating vectors and three the rotating ones.

2.2. The Flow Through a Generic Body

When the wind impacts an obstacle, a boundary layer originates on the surfaces of the object, with a smooth or turbulent nature depending on the Reynold’s number and the material friction. The following described behavior regards the case of bluff bodies, that are elements characterized by a separated flow where the fluid does not touch all the outline of the figure, in opposition to streamlined bodies where a conscious effort is made to align their shape with the anticipated streamlines in the flow. All the build-

Fig. 12: Rapresentation of the lift and drag forces originated due to the approaching of a fluid flow against a generic body.

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ings, independently from their aerodynamic propension, are considered elements of the first category.

A negative pressure gradient, connected by the Bernoulli’s principle with an acceleration of the stream, determines a reduction of the boundary layer width, with a displacement of the separation stratus in the direction of the body outlines. The vorticity is so relegated to a thin zone, comprised between the boundary layer and the body surface.

The opposite case of a positive pressure gradient leads to an inverse situation: the boundary layer width, in fact, grows under the push of the dynamic force, letting the vorticity to occupy a much larger space. These circumstances give rise to the phenomenon of the vortex wake, which represents a zone of high shear and high vorticity located at the back of the object.

In this last case, the behavior of the flow is highly influenced by the shape of the body.

A main distinction must be done between round and sharp corners bodies. The flow over the first category is influenced by the Reynold’s number and the friction exert- ed by the surface. Considering a smooth cylinder of an infinite height, with Re < 30, the boundary layer is smooth, and it follows the edges of the figure for almost all its length. With Re = 30 ÷ 10000, the boundary layer is still smooth, but vortexes start to shed one by one from the cylinder surface. This behavior gives rise a vortex wake, known as a Von Karman’s vortex street. Increasing the Reynold’s number more, we firstly obtain a phase characterized by a turbulent nature of the eddies, and as last a turbulent comportment of the flow itself.

Fig. 13: Differences between the streamlined and bluff bodies.

Fig. 14: Reynold’s number-flow dependency on smooth, infinitely tall cylinder.

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Bodies with sharp corners require a different approach. As previously mentioned, they cause the separation of the boundary layer since the velocity of the outer regions is generally very high, matched with a pressure consequentially low, and without a split of the flow, in the subsequent zones after the corners, the inversion of the pressure gradient would be too high to be supported. Thus, the correlation with the Reynold’s number and the surface friction is lost.

The previously mentioned vortex shedding phenomenon requires an in-depth treat- ment because of its possible dangerous consequences on high-rise buildings. At lower speeds, in fact, vortexes are shed simultaneously in pair, one from each side of the separated flow. This leads to a null resultant impulse, with beneficial significances for the structure. Otherwise, at higher speeds, the eddies are shed alternately with a frequency that can be calculated by the following formula:

f U BHS

= r Where:

• Ū_H is the mean wind speed at the top of the building;

• B is the width of the object normal to the wind;

• S is a non-dimensional parameter called Strouhal number.

The shed of an eddy gives rise to an impulse in the direction transversal to the wind.

Since we’re talking about a periodical behavior, which sees a constant shedding from the left to the right and vice versa, the building becomes affected by an across-wind vibration. Moreover, if its natural frequency is near to the impulse one, a dangerous aeroelastic phenomenon can occur: the lock in. It consists in a resonance condition that can be translated in an amplification of the vibrational effect.

Strouhal’s number, the main parameter dominating this behavior, can be related with Reynold’s number for round corners bodies and with the geometric ratio (B/D) for sharp corners ones.

Fig. 15: Relations between Strouhal’s number and Reynold’s number and variation of the Strouhal’s number among the base on depth ratio increasing.

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2.3. The Flow Through a Tall Building

Two parameters are usually used to characterize the flow around a building: the stagnation point at the upwind surface and the amplitude of the separation bubble at the top of the building.

The height of the stagnation point is an important aerodynamic quantity, since it defines the flow around a building and it gives the point on the upwind façade where the highest pressure appears. Measurements of Sharan, Baines and Jensen report a neglectable correlation between the elevation of this parameter and the aspect ratio and the roughness length. The values tend to the 80/90% of the building height, which make 0.85 a good approximation.

At a sharp upwind edge of the roof, the boundary layer separates from the building.

The separation results in a region with low velocities, a high turbulence level and recirculation of the flow at the roof and sides of a building.

Because of the separation at the upwind roof edge, the velocity vector outside the recirculation region is not parallel to the roof. The angle between roof and velocity vector outside the recirculation region is called the skew angle to distinguish it from the yaw angle in the horizontal plane. The skew angle varies with:

• position on the roof,

• roughness of the upwind area,

• sizes of the building,

• upwind edge rounding and

• yaw of the free stream wind to the building.

The dependence on the position on the roof is easy to understand. The velocities close to the building are high and decrease with increasing distance to the building. The pressures close to the building are consequently low and increase with increasing distance to the building. This pressure gradient forces the flow in a curved path. On the curved path, the radius of the curvature is defined by equilibrium between the force caused by the pressure gradient and the centrifugal force caused by the curvature. The effect of roughness and size of the building on the skew angle can be understood from the amount of lateral momentum caused by blockage of the building. Compared to a low roughness, a high roughness results in a smaller mass flow towards the building (reduced velocities in the boundary layer for high roughness). A high roughness thus results in less lateral momentum because a smaller mass-flow has to move around the building. The same argumentation is valid for small building sizes. Therefore, the flow stays closer to the building for high roughness or small building sizes compared to low

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roughness and large building sizes.

The common way to characterize the flow around a tall building is to start by considering an ideal prismatic object with a rectangular cross-section. Beranek and van Koten studies represent a good introduction. As the illustration shows, two new phenomena must be introduced: the downwash and the horseshow vortex. The first consists in an acceleration of wind speed in the up to the down direction, caused by difference in the pressure which occurs between the upper and the down level of the building. The second is clearly a consequence of the first, since the flow redirected to the ground must impact against it and gives rise to a vorticity zone. Both the cases are usually object of study for what regards the pedestrian comfort, due to their low structural influence.

Where:

1. Air flow over the building 2. Air flow in front of the building

3. Air flow separating vertical in front of the building 4. Air flow separating horizontal in front of the building 5. Downwash

6. Horseshoe vortex

7. Stagnation point at the ground in front of the building 8. Strongly increased wind speed at corners

Fig. 16: Beranek and Van Koten’s illustration of the air flow against a generic tall building.

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9. Board jet streams with increased wind speed 10. Reversed wind flow at the wake of the building 11. Stagnation point at the ground in the wake 12. Air stream behind the stagnation point

13. Horizontal standing vortex at the wake of the building 14. Stagnation point in front of the building

15. Upward-directed air stream behind the building (not in view) 16. Small high-speed vortices

17. Vertical standing vortices at the wake of the building

Wind tunnel tests on a prismatic body with a squared cross-section and an aspect ratio (H/B) of 8:1 show how the stagnation point usually appears at circa 80% of the total height.

Going further, studies of a prismatic element with a 2:1 aspect ratio describe how the fluctuating component of the velocity influences the just described model. Both the analyses confirm that the highly stressed side is the side wall, due to the vortices cre- ated by the separation of the flow which occurs in the windward face.

Fig. 17: Pressure coefficients distribution on a prismatic element characterized by a 2:1 aspect ratio.

UNIVERSITÀ DI PISA S