Journal of Building Engineering 6 (2016) 225–235
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Journal of Building Engineering journal homepage: www.elsevier.com/locate/jobe
Aerodynamic Mitigation and Shape Optimization of Buildings: Review Maryam Asghari Mooneghi a, Ramtin Kargarmoakhar b,I a b
PhD, Advanced Technology and Research, Arup, San Francisco, CA, USA PhD, T.Y. Lin International, San Francisco, CA, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 3 October 2015 Received in revised form 28 January 2016 Accepted 29 January 2016 Available online 4 February 2016
Usually the design of the external shape and orientation of buildings is driven by architectural considerations, functional requirements and site limitations, rather than by aerodynamic considerations. This, most of the times, results in structures becoming bluff bodies characterized by high wind-structure interaction induced loads. These effects can be significantly reduced through novel aerodynamic mitigation techniques and optimal aerodynamic shape design procedures. This paper reviews the past/recent work on various aerodynamic mitigation techniques developed for reducing wind loads on buildings by modifying their shapes and/or adding simple architectural elements. Aerodynamic mitigation techniques applicable to low-rise and high-rise buildings have been reviewed. In addition, aerodynamic shape optimization techniques for reducing wind loads on tall buildings are presented and the suitability and challenges of using Computational Fluids Dynamics (CFD) for this application are discussed. An overview of the optimization techniques namely gradient based methods and non-gradient based methods are presented. It is expected that this research can ignite an interest in using aerodynamic shapes and consideration of the structures’ shape, in terms of wind performance, early in the design process. This paper also serves as a source for various techniques that can be used for reducing wind loads on buildings. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Buildings Wind Aerodynamic Mitigation Shape Optimization CFD
Contents 1. 2.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Aerodynamic mitigation techniques for buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 2.1. High-rise buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 2.1.1. Minor modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 2.1.2. Major modifications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 2.2. Low-rise buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 2.2.1. Parapets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 2.2.2. Passive aerodynamic devices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 3. Aerodynamic shape optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 3.1. An overview of optimization algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 3.2. Aerodynamic shape optimization of tall buildings using CFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 Acknowledgement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 Appendix Optimization algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
E-mail address:
[email protected] (M. Asghari Mooneghi). http://dx.doi.org/10.1016/j.jobe.2016.01.009 2352-7102/& 2016 Elsevier Ltd. All rights reserved.
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1. Introduction Wind loads are one of the most critical parameters for design of buildings. Buildings typically have sharp corners which can cause wind flow separation resulting in strong wind-structure interaction induced loads (e.g. high roof suctions in case of low-rise buildings and acrosswind loads and wind-induced vibrations produced by unfavorable aerodynamic corners in case of high-rise buildings). One approach for reducing the wind loads on buildings is to use “Aerodynamic Mitigation” techniques. These methods effectively use simple and innovative architectural features to modify the aerodynamic shape of the buildings in order to reduce the wind loads. Aerodynamic modifications assist either by disrupting the formation of strong corner vortices; or by breaking the coherent formation of vortices; or by diverting flows in the separation zone over the roof edge or away from the weak members. A second strategy to achieve reductions in wind-induced loads on buildings is to use “Aerodynamic Shape Optimization” techniques. In optimal shape design problems, the optimization of a performance criterion depends on the shape of a boundary. The creativity and insight of an experienced designer is required to reduce the design problem to a well-posed optimization problem. This involves the definition of objective functions that specify the goals of the optimization, design variables that determine the aerodynamic shape, as well as constraints that define a feasible region of the design space. The optimization algorithm finds the values of the geometric parameters that optimize the objective function while satisfying the constraints. For optimizing the shape of civil structures like long-span bridges and tall slender towers different objective functions can be taken into account e.g. reducing the drag force and/or vortex-induced forces. Aerodynamic shape optimization allows the designer to explore more alternatives for the design of new aerodynamic shapes compared to the traditional methods which are limited to a certain number of preselected geometries by the designer. Shape optimization has progressed significantly over the years and has been used in many areas of engineering. Examples include but are not limited to the design of external surfaces of aircrafts, especially wings, design of cars and civil structures, such as tall buildings and long-span bridges [1]. Several algorithms have been developed that can efficiently perform aerodynamic shape optimization. Dulikravich [2] presented a comprehensive review on the aerodynamic shape optimization methods with applications in aircraft airfoil design. The intention of the current paper is to review the past/recent work on aerodynamic mitigation and aerodynamic shape optimization methods developed for reducing wind loads on buildings. In the first part of this paper different aerodynamic mitigation techniques which aim at reducing wind loads on high-rise and low-rise buildings are reviewed. In the second part, an overview of
aerodynamic shape optimization approach is presented and the suitability and challenges of using computational fluid dynamics (CFD) for aerodynamic shape optimization of tall buildings are discussed. Different optimization algorithms which can be used for aerodynamic shape optimization problems are briefly presented. It is shown that the use of aerodynamic shapes and consideration of the structures’ shape, in terms of wind performance, early in the design can result in significant improvements in the response of buildings under wind loads.
2. Aerodynamic mitigation techniques for buildings 2.1. High-rise buildings The world is currently undergoing the biggest wave of tall building construction in history. The use of higher-strength materials, lightweight floors, and curtain wall system in the construction of tall buildings has reduced building weight, stiffness, and damping values. Therefore, tall buildings are more susceptible to wind loads and wind-induced excitations which have the potential to reduce their structural safety and cause discomfort to the occupants. Also, these excessive motions can create high base loads which increase the cost of the structure. For typical tall buildings, aerodynamic forces are drag force (alongwind), lift force (acrosswind) and torsional moment (Fig. 1a). The wind-induced response of tall buildings is usually dominated by dynamic acrosswind loading resulting from wind vortex shedding [3] as shown in Fig. 1b. When wind blows over a bluff structure, flow separates and causes periodic shedding of vortices. This periodic vortex shedding exerts acrosswind forces on the body by creating fluctuating pressures. Strouhal number is a nondimensional parameter that defines the dominant frequency of the fluctuations in the acrosswind forces and is expressed as (Eq. (1)):
S = fB/U
(1)
where, f is the frequency of vortex shedding, S is the Strouhal number, U is the wind speed and B is the building width. Strouhal number is a function of the shape of the building with values between 0.1 to 0.3, e.g. about 0.14 for a square cross section and 0.2 for a roughly circular cylinder [4]. Vortex-induced vibrations (VIV) occurs when the frequency of vortex shedding, f , approaches one of the natural frequencies of the building. This leads to amplified acrosswind response. Vortex-induced vibrations are the prime problem in self-excited vibration of tall flexible buildings. Aerodynamic mitigation techniques which utilize modifications to the external shape of a building (e.g. corner modifications, variation of the cross section shape and size along the height of the building, etc.) can significantly reduce building response under
Fig. 1. (a) Aerodynamic forces on a tall building; (b) Vortex shedding (plan view).
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wind loads by altering the wind flow pattern around the building and can lead to a more economic and comfortable design [4–6]. Shape effects from a wind engineering perspective have been investigated by Davenport [7] through aerodynamic model tests. Many researches were performed to study the relationship between the aerodynamic characteristics of a structure and the resulting wind-induced excitation level [8–17]. Aerodynamic modification techniques aim particularly at suppression of vortex shedding and can generally be classified into two groups [18]: 2.1.1. Minor modifications These modifications have negligible effects on the overall structural and architectural design of the building. Common building shapes are square or rectangle which cause the building to experience relatively strong vortex-induced forces. These excitation forces can be reduced through minor modifications to the aerodynamic shape of the tower. For instance, modifications in the corners of the cross sectional shape of the building such as slotted corners, chamfered corners, corner recession, roundness of corners and changing the orientation of the building relative to the most frequent strong wind direction are among the minor modification
Fig. 2. Minor aerodynamic modifications.
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methods that can be utilized to improve the wind performance of tall buildings (Fig. 2). These methods can result in reductions in both alongwind and acrosswind responses compared to plain rectangular shape buildings. The modification of windward corners can change the characteristics of the separated shear layers leading to narrower downstream wake and thus can be very effective in reducing the drag and fluctuating lift forces. Fig. 3 shows a graphical representation of the flow field around six different cross section alternatives obtained using CFD simulations. The analysis was performed using ANSYS Fluent Software. All the models were run transiently with 20 m/s uniform inlet velocity using k-ω SST turbulence model. The k-ω SST model was selected because of its proved ability for modeling detached flows with periodic vortex shedding [19]. The outlet was considered to be a pressure outlet. Top, bottom, and the two sides of the computational domain were assigned as symmetric plane. All the building faces were assigned to be “No-slip” walls. It can be seen form Fig. 3 that corner modifications (in this case modifications were made to a building with square plan shape) can change the flow pattern around the building. The effectiveness of each of these strategies does depend on the type and size of the corner modifications relative to the size of the plan. For example, it can be seen that the plan shapes with “Recessed Corners” or “Double Chamfered” caused smaller separation zones and narrower wakes as compared to a simple square shape. These techniques can be effective in reducing the alongwind (drag) as well as acrosswind (lift) forces as compared to a sharped edged square cross section. Many researchers studied the effect of corner modifications and their impact on the aerodynamic forces on tall buildings including chamfered, recessed and slotted corners [3,4,13,20–22]. While many of these studies demonstrated the benefits of corner geometry modifications, there are some cases showing that modifications to building corners can be ineffective and even sometimes result in adverse effects [14,23]. As a matter of fact, these methods should be utilized with care to avoid any unfavorable effects. It should also be noted that the effectiveness of corner modifications depends on the oncoming wind direction [20] and the size of the modifications relative to the size of the plan [3,11]. Irwin et al [24] suggested that the corner modifications
Fig. 3. Flow field around different cross sections.
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should extend about 10% of the building width to be effective. Taipei 101 skyscraper in Taiwan and Mitsubishi Heavy Industries Yokohama Building in Japan are examples of tall buildings that successfully utilized the corner modification techniques to reduce the alongwind and acrosswind responses. Corner modifications in Taipei 101 skyscraper resulted in 25% reductions in the base moment [24]. Creating rounded corners is another effective approach for improving the aerodynamic behavior of tall buildings against the wind excitations [5,16,25]. 2.1.2. Major modifications These modifications have significant effects on the structural and architectural design of the building. For instance, varying the shape of building and setbacks along the height, tapering, inclusion of openings at top and twisting the building are among the major modification methods that can be utilized to come up with an aerodynamically favorable building shape (Fig. 4). Some of these approaches are discussed in the following. ○ Tapering and setbacks: Through tapering or setbacks, the width of a building can be varied along its height causing the vortices to become incoherent and shed at different frequencies at different heights. This is mainly due to the fact that the frequency of vortex shedding depends on the width of the building (Eq. 1). This results in dramatic reduction of the associated fluctuating forces. Kim et al [26], Kim and You [17], and You et al [27] investigated the effects of tapering for reducing the windinduced response of tall buildings. Tapering has a more significant effect in acrosswind direction than that in the alongwind direction [17,26]. This method has been in part used in order to optimize the shape of Burj Khalifa, Dubai. The building shape is extremely efficient from a wind loading point of view so that the tower does not need any supplementary damping system [28]. The Millennium Tower in Tokyo, Japan and Transamerica pyramid in San Francisco also exploit the use of tapering effects along their heights for mitigating the wind forces. ○ Varying cross-section shape: Varying the cross-section shape with height, e.g. going from square to round has a similar effect. In this case, Strouhal number varies with height (Eq. 1) which causes the vortices to shed over a broad range of frequencies. This method can be especially effective in reducing the acrosswind forces [24]. ○ Porosity or openings: The addition of openings to a building is another method to improve the aerodynamic behavior of a structure. By allowing air to bleed through the building via openings or porous sections, the formation of the vortices
becomes weakened and disrupted by the flow of air through the structure. This aerodynamic modification method was investigated by several researchers [12,14,29,30]. These studies showed that openings in the upper half of the buildings (especially openings in the alongwind direction) can be very effective for reducing the acrosswind response of tall buildings. However, the efficacy of this approach does depend on the location and size of the openings. Dutton and Isyumov [12] also showed that the effectiveness of these gaps might be influenced by the level of turbulence in the approaching flow. ○ Twisting or rotating the buildings: Rotating the building can be very effective because the designer can assign the orientation of the building such that its least favorable aspect does not coincide with the strongest wind direction. Also, twisted building forms are effective in reducing vortex-induced vibrations by avoiding simultaneous vortex shedding along the building height. The availability of studies investigating the effects of twisting the building on the wind loads is limited [31]. The twisted form can be found in today’s tall building designs such as Turning Torso, in Malmo, Sweden and Shanghai Centre, in Shanghai, China. 2.2. Low-rise buildings Wind-related disasters are among the most costly natural hazards to occur in the US each year in addition to loss of many lives [32]. Low-rise buildings such as residential houses, commercial and industrial structures, constitute more than 70 percent of the building stuck in the United States and account for the majority of losses due to wind storms [33]. Roof systems are exposed to higher loading than any other building element. The worst wind suctions on roofs normally occur for cornering or oblique wind directions. These extreme suctions are the result of conical vortices which form along the roof edges (Fig. 5) and are the main reason for most of the wind-induced damages. Shingles, tiles, or pavers placed on roofs are most vulnerable to being dislodged and becoming wind-borne debris [34]. Loose roofing components could lead to rain water intrusion and losses to interior appliances and building contents [35]. The need to reduce roof damages due to wind effects has recently become one of the most important challenges for designers, manufacturers, and building code officials [34,36–39]. Simple modifications to the shape of the roof edge and/or utilizing roof accessory structures can change the flow pattern on the roof and can lead to reductions in the wind loads and consequently damage to low-rise buildings. These methods are appropriately entitled “vortex suppression” techniques since they mainly aim at disrupting and deflecting the conical vortices from the roof which are the main causes of extreme roof suctions. These methods are mainly in form of using parapets with various shapes and configurations or passive aerodynamic edges that suppress vortex generation on the roof. Vortex suppression techniques can be classified in the following four categories based on their aerodynamic mechanism [40]: 1. Methods aiming at eliminating straight sharp edges which create the vortices 2. Methods aiming at disrupting the vortex formation (like partial or porous parapets) 3. Methods aiming at disturbing the vortices (like porous fence or screen, rooftop cylinders and splitters) 4. Methods aiming at displacing the formed vortices (like high parapets)
Fig. 4. Major aerodynamic modifications.
Fig. 6 shows a schematic of some types of aerodynamic mitigation techniques that were proposed in the literature to alleviate
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the corner suction pressures on roofs of low-rise buildings. Please note that the drawings in Fig. 6 are not in their actual scale for better presentation of each approach. 2.2.1. Parapets Parapets have been used as a standard architectural feature for many years mainly for buildings with flat roofs. Many wind tunnel testing and field studies have been performed on the effectiveness of parapets for reducing wind loads on building roofs. Basically, the parapets lift the separated shear layers clear of the roof surface and thus dissipate the high local corner or edge suctions over a larger area. However, this can result in increased loads on interior regions, thus influencing the overall effectiveness of parapets [44]. One of the first studies that specifically considered the role of these building components in vortex suppression was carried out by Baskaran and Stathopoulos [41]. Their results showed that high parapets generally reduce the high suctions on roof corners while low parapets may increase the roof suctions at the edges and corners. A similar effect was observed by Asghari Mooneghi et al [49] by performing large-scale testing on a flat roof building with solid parapets of different heights in Wall of Wind open jet facility at Florida International University. Baskaran and Stathopoulos [41] also showed that generally the perimetric parapets have a more significant effect on reducing corner pressure coefficients than a parapet present on only one side of the roof. The effectiveness of parapets is also a function of the parapet configuration. Surry and Lin [40] investigated the effectiveness of various parapet configurations, including saw-tooth partial parapets, semi-cylindrical parapets, solid and porous roof corner splitters and isolated porous parapets on a scaled model of Texas Tech University (TTU) research building. The isolated porous parapets were shown to be the most effective alternative in reducing suctions near the roof corner. Kopp et al [43] studied the effects of various parapets in decreasing area-averaged loads under the corner vortices. The spoilers and porous continuous parapets performed best with 44% and 56% maximum reductions in peak pressure coefficients near roof corners. Wu [44] investigated a specific parapet called a Conical Vortex Disrupter through full-scale tests. Results showed significant reductions on both local and area-averaged wind loads near the roof corners on a flat roof building. Other studies on the effect of parapet configuration on mitigating peak suctions on the roof of low-rise buildings include those of Pindado and Meseguer [42] and Suaris and Irwin [50]. 2.2.2. Passive aerodynamic devices Beyond investigating the efficacy of parapets in reducing high wind suctions on the roofs, recent studies have focused on modifying the roof corners or edges and/or adding various aerodynamic edge elements to mitigate the extreme negative pressures caused by conical vortices. These elements can be used as
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permanent architectural elements or can be attached to the roof during preparations for high-wind events. The effectiveness of roof edge configuration on mitigating wind loadings was investigated by Blackmore [51] and Savory et al [52] using wind tunnel testing or field measurements performed on aerodynamic curved and chamfered roof eave edges. Although these methods were shown to be effective, they are not practical sometimes e.g. for buildings with eaves. A variety of roof edge devices have been developed that can be attached to roof eaves (e.g. semicircular gutters, cantilevered spoilers, etc.). These devices were shown to facilitate the reduction of extreme wind pressures on the roof with varying degrees of aerodynamic effectiveness and architectural practicality [53–56]. For instance, Huang et al [57] investigated the effectiveness of eight typical soffits that are commonly used in the residential houses in China for alleviating rooftop extreme wind pressures using wind tunnel testing. Results showed that the presence of these elements significantly reduced the negative peak wind pressures at edges and corners of the roof while not changing the wind loads on the other roof regions. Most of these studies have been based on small-scale model testing (scales between 1:50 and 1:200) in wind tunnels. However, large-scale and full-scale testing is more favorable for assessing the performance of aerodynamic devices [58] because they allow for accurate modeling of architectural details, avoiding adverse scale effect by testing at higher Reynolds numbers (which is more pronounced for curved surfaces that might be used in aerodynamic devices [59] and using greater spatial resolution of the pressure taps in critical regions on the roof (e.g. corners and edges) to capture the high localized suctions [49]. For this reason large- and full-scale tests have been performed recently for developing roof suction mitigation techniques. Blessing et al [60] exploited roof gravel scour testing and pressure testing to assess the effectiveness of several aerodynamic devices in reducing high uplift pressures at corners and edges of flat roofs through full-scale testing. Huang et al [47] carried out field measurements to examine the efficacy of three types of aerodynamic mitigation plates, including full-length roof-edge plate, roof-corner plate, and discrete roof-edge plates with different spaces on pitched roofs. Results showed that these plates could significantly reduce the mean and fluctuating pressure coefficients in the windward corner. Bitsuamlak et al [48] investigated the effectiveness of simple architectural elements including gable end and ridgeline extensions, trellis, and wall extensions for the reduction of roof and wall corner suctions using 6-fan Wall of Wind facility at Florida international University. The wind loading mechanism of aerodynamic mitigation devices were also investigated using CFD. Aly [61] used CFD simulations to study the efficacy of aerodynamic roof mitigation devices in reducing wind suctions on the roof of low-rise buildings. Mitigation devices including barriers, circular edges, inclined edges and airfoil edges were investigated. The objective was to propose an aerodynamic mitigation technique which could not only reduce the
Fig. 5. (a) Conical vortices on a flat roof at cornering winds; (b) Suction variation under conical vortices.
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Solid parapet [41]
Porous parapet [42]
Discontinuous parapet [43]
Partial parapet [25]
Perimetric spoiler [44]
Aerodynamic edge [45]
Discontinuous perforated parapets [46]
Full length roof-edge plate [47]
Trellis (pergola) [48]
Fig. 6. Various aerodynamic mitigation techniques for reducing wind loads on roof of low-rise buildings [25,41–48].
loads on the roofs but also had minimum drag and lift forces exerted on it. Aerodynamic mitigation devices with relatively high lift and drag forces can become wind born debris impacting other structures downwind or they may introduce excessive loads to the main structure. It was shown that slope-in aerodynamic mitigation devices which could be replaced by solar panels [62] were relatively effective in reducing roof induced suctions.
3. Aerodynamic shape optimization 3.1. An overview of optimization algorithms The search for an optimal state is one of the most fundamental principles in our world. Optimization is to find the best solution to a certain designated problem. Numerical methods for optimizing the performance of engineering problems have been studied for many years. For optimization of an objective, different categories of optimization techniques namely “Gradient based” methods and “Nongradient based” methods can be used. The basic idea behind the gradient based methods is that a given function reaches its extremes (minimum or maximum) in the direction of its gradient. Gradient based methods are in general computationally faster (they require fewer objective function evaluations in case of problems with low number of design variables) than non-gradient based methods. Their main drawback is that they might converge to local minima, and their convergence to global minima depends mainly on the chosen starting point (initial guess) by the user (Fig. 7a). On the other hand, non-gradient based methods, do not rely, most of the time, on strong mathematical basis and make use of neither the gradient or the second derivative of the objective function as a direction of descent. These methods work based on function evaluations alone.
In principle, they attempt to mimic nature in order to find the optimum of the objective function. One of the key features of these algorithms is that they search from multiple points in the design space, instead of moving from a single point like gradient based methods. Thus, although in general there is no proof that these methods converge to global optima, experience entails that they converge to global optima in most cases (Fig. 7b). The main drawback of non-gradient based methods is that these algorithms are generally computationally slower than the gradient based ones. Indeed, the non-gradient based algorithms can require thousands of function evaluations and, in some cases, become non-practical. In order to overcome these difficulties, the so-called Hybrid algorithms, which take advantage of the robustness of the non-gradient based methods and the fast convergence of the gradient based methods, have been proposed by different scholars. A set of analytically formulated rules and switching criteria can be coded into the program to automatically switch back and forth among the different algorithms as the iterative process advances. Each technique provides a unique approach with varying degrees of convergence, reliability and robustness at different stages during the iterative optimization process. It is also interesting to introduce to the reader the multi-objective optimization problems vs. single-objective optimization problems. In a large number of problems, there exists a need to find optimal solutions due to more than one objective. In this case, a multi-objective approach must be employed. Engineering problems demanding low cost, high performance and low losses are an example of applications where this approach is needed. For the single-objective optimization problems, a unique optimal solution exists. However, for multi-objective optimization problems, there exist a set of compromised solutions, known as the Pareto-optimal solutions or non-dominated solutions, which are based on the
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competing objectives. The goal of multi-objective optimization is to find such set of solutions. Once the solutions are obtained, the designer can choose a final design with further considerations. Non-gradient based methods are more suitable for multi-objective optimization problems since they are able to find the entire range of Pareto-optimal solutions. Gradient based methods typically use a weighting method to combine different objectives into one for handling multi-objective optimization problems. In this case, results would be dependent on the chosen weighting coefficients. An overview of different gradient based and non-gradient based optimization algorithms are provided in Appendix A. Clearly, knowledge about the nature of the problem is a requirement for choosing the most suitable optimization tool for an application. 3.2. Aerodynamic shape optimization of tall buildings using CFD The goal of aerodynamic shape optimization is to accurately and efficiently determine surface shapes that attain optimal aerodynamic performance [1]. While the effects of geometric modifications to the shape of tall buildings, such as utilizing recessed or chamfered corners, etc. (discussed in Section 2.1) can significantly improve the aerodynamic response of tall buildings, a systematic approach for taking full advantage of aerodynamic shape optimization for buildings is not fully explored yet. Experimental method using wind tunnel testing, provide the basis of the traditional “cut and try” approach for the design of new aerodynamic shapes. In this approach, several configurations are investigated in a wind tunnel and the one that yields the best aerodynamic performance is identified. The reason behind using wind tunnel testing for designing the new aerodynamic shapes is that the relation between the external shape of a building and the resulting intensity of the wind excitations is complicated and the improvements in wind effects that can be obtained by specific geometric modifications is difficult to predict without performing experiments [63]. Merrick and Bitsuamlak [64] examined the effects of building shape on wind loading patterns for high-rise buildings by analyzing various buildings with foot prints of square, circular, triangular, rectangular and elliptical shapes using wind tunnel database. Results of this research outlined the general wind loading characteristics of simple building shapes. The sensitivity of each building shape to vortex-shedding was determined. While it is possible to use wind tunnel testing for aerodynamic shape optimization, this approach is highly demanding due to the time and cost limitations for performing each test. As a matter of fact, only a limited number of possible configurations which are chosen based on engineering experience and judgement can be examined. The use of computational simulation to scan many alternative designs has proved extremely valuable in practice. With the advances in computational fluid dynamics and computing power of modern computers, CFD has contributed to cut aerodynamic design cost and time scales by reducing the number of required wind tunnel tests. Currently, CFD is mainly used for estimating aerodynamic performance of a given structure configuration and it still suffers the limitation that it does not guarantee the identification of the best possible design. To ensure the realization of the true best
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design, the ultimate goal of computational simulation methods should not just be the analysis of prescribed shapes, but the automatic determination of the true optimum shape for the intended application. This is the underlying motivation for the combination of computational fluid dynamics with numerical optimization methods for aerodynamic shape optimization problems. Some of the earliest studies of such an approach were made by Hicks et al [65] and Hicks and Henne [66] for aircraft wing design. Aerodynamic shape optimization using CFD has been used for many years in aerospace [67,68] and automotive [69,70] industries and has recently become the subject of increasing interest in civil structures especially for aerodynamic design of the shape of tall buildings [71]. A general approach for aerodynamic shape optimization using CFD is shown in Fig. 8. The essential components of an aerodynamic shape optimization problem are objective functions, constraints, design variables that define the possible geometries, a flow solver, and a numerical optimization method. Examples of objective functions for aerodynamic shape optimization of tall buildings can be reducing the drag force and/or vortex-induced vibrations. The optimization algorithm finds the values of the geometric parameters that optimize the objective function while satisfying the constraints. These components should be selected carefully as they have a direct impact on the accuracy and efficiency of solution [1]. Samareh [72] provides summaries of shape parameterization techniques that can be used to define design variables. In general, it is important that the selected parameterization technique provides sufficient flexibility in order to realize truly optimal designs. It is also desirable that the number of parameters necessary to define the shape to be small so that a reasonable convergence rate of the optimization can be obtained. As discussed in Section 3.1, various numerical optimization methodologies can be used for aerodynamic shape optimization applications. Hicks et al [65] were the first to apply gradient based methods to aerodynamic shape optimization problems. They used the method of feasible directions, which is based on conjugate gradients, to optimize airfoil shapes in transonic flow governed by the small-disturbance equation. Since this pioneering work, the application of gradient based methods to aerodynamic shape optimization problems remained an active area of research. However, as the aerodynamic shape optimization problem is a complex one with possibly many local optima, non-gradient based methods (also called Evolutionary Algorithms (EA)) such as Genetic Algorithm (GA) are more suitable for this application to ensure reaching the global optimum. Evolutionary Algorithms have the advantages such as robustness, suitability to parallel computing and simplicity in coupling CFD codes. Owing to these advantages over the non-gradient based methods, EAs have become increasingly popular in a broad class of design problems [73]. However, the implementation of aerodynamic shape optimization using CFD is intrinsically difficult for bluff civil structures due mainly to the turbulent flow field in which the structures are immersed, the high Reynolds number values, and the multi-objective nature of the design problem [74]. So, while there are clear advantageous for using nongradient based optimization theories for aerodynamic shape optimization applications, the use of these algorithms for shape optimization
Fig. 7. Optimization methods: (a) Gradient based (b) Non-gradient based.
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of civil structures is often impractical since the objective functions and constraints are evaluated using CFD and an extremely high number of function calls which can easily reach the order of thousands, is required for obtaining the optimum solution. One way of tackling the efficiency issue of evolutionary search methods is to use a Surrogate-Based Optimization (SBO) methodology in CPU-intensive aerodynamic shape optimization applications. The main idea in SBO is to utilize data sampling and surface fitting strategies to parameterize the space of possible solutions via a simple, computationally inexpensive model to be used for the purpose of numerical optimization. So, the whole optimization process is managed by the surrogate model outputs. This is often referred to as optimizing the response surface of the system. The basic process for a surrogate-based optimization consists of the following steps [75]: 1. Defining a sampling plan for the design space: This contains both the samples required for constructing the surrogate model and some additional samples needed for verifying the surrogate model. 2. Performing numerical simulations at design points selected from the sampling plan. 3. Constructing the surrogate model: Different surrogate models can be used such as polynomial regression, Kriging, radial basis functions, neural networks, and support vector regression [76]. 4. Validating the model: This is to find out the predictive capabilities of the surrogate model. 5. Updating the model: Repeating the last four steps until the desired model validation accuracy is obtained. 6. Optimization: The search for the optimum is carried out on the surrogate model. The approximation efficiency and its accuracy are major issues in SBO. If the problem has a high number of design variables, the construction of surrogate model may cause extremely high computational cost, which makes the approximation inefficient. Design of Experiment (DoE) can be used to reduce the number of design points [77]. However, by using this approach the global
Fig. 8. Aerodynamic shape optimization utilizing CFD.
optimum might be missed due to the uncertainty at the predicted point which may mislead the optimization process in a wrong way. As a matter of fact, the selected DoE strategy is of paramount importance for achieving a satisfactory accuracy of the surrogate model. Generally, sampling plans that more evenly fill the design space can reduce the bias error of the surrogate. A plenty of surrogate methods, search algorithms and updating algorithms have been proposed in the literature for a variety of applications including CFD-based aerodynamic shape optimization [67,74,76,78]. It should also be noted that the repeated evaluation of the objective functions required during the optimization demands fast flow solutions [1]. As a matter of fact, the flow solver has a significant influence on the efficiency of the optimization. Buildings are immersed in very turbulent flows due to ground roughness effect which after interacting with buildings represent very wide temporal and spatial scales governed by highly non-linear Navier-Stokes differential equations which are computationally expensive to solve [79]. Detailed reviews of effective flow solvers for the Navier-Stokes equations are given by Pueyo [80]. Reynolds-Averaged Navier-Stokes (RANS) models can be used for obtaining fast and reasonably reliable simulations even for complex shapes and high Reynolds numbers, and can be used for obtaining both steady and unsteady aerodynamic measures (URANS). On the other hand, Large Eddie Simulation (LES) methods and/or hybrid RANS/LES methods are more accurate than RANS models for the prediction of the unsteady forces at the cost of higher computational burden. Note that the Navier-Stokes equations should be solved repeatedly for each updated geometry as the optimization progresses. This issue makes the problem further complicated. Therefore, an efficient approach can be to use URANS models for narrowing down the solution domain and then use the higher accuracy LES models when a greater level of detail is needed for example when comparing two final competing shapes [63]. One challenge in the application of numerical optimization to a building aerodynamic shape design problem is regeneration of the mesh for geometry variations from the initial base geometry. So, one very important feature of the CFD-based shape optimization technique should be to have the possibility of updating the CFD meshes automatically. Without this ability, the CFD model may need to be reprocessed before a suitable mesh with the required quality can be obtained. Also, the boundary conditions may need to be reapplied before the analysis can be launched. Mesh morphing techniques allow performing mesh modifications without changing the mesh topology and avoid a costly recalculation of the physics equations with every new CFD model. In these methods, the mesh is first imported into to the mesh morpher tool. The mesh is parameterized and then based on design constraints and realistic assumptions, deformation vectors are added to the model. After each optimization iteration the mesh morpher modifies the mesh with respect to the original topology, thus allowing a more robust and faster design optimization environment using CFD. Quality controls for meshing can be set to guarantee the quality of the CFD simulation results. This ensures that the algorithm is independent from external inputs during the optimization and makes mesh generation process faster. Mesh morphers have been used in many applications of shape optimization using CFD [81–83] mainly for aerospace and automotive structures. Wei et al [84] and Wei et al [85] developed a mesh morphing algorithm based on a Laplacian smoothing approach which was very robust even for marked geometric modifications which are expected in aerodynamic shape optimization of tall buildings. Civil engineering structures which often have square or rectangular shapes provide a wide variety of applications for bluff body aerodynamics. The optimization of a trapezoidal bluff body was conducted by Burman et al [86]. This study focused on the response surface optimization of Navier-Stokes flow over a bluff body. The optimization objectives were to minimize the mean drag coefficient and to maximize the measure of mixing defined as the time average
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maximum negative velocity. Response surface methodology was utilized in the optimization process. Mack et al [87] used multiple surrogates for the shape optimization of a 2D trapezoidal bluff body model. Polynomial response surface and radial basis neural networks were used as surrogates. Objective functions were minimizing the total pressure loss coefficient and maximizing the mixing capability of time dependent flows over a 2-D bluff body. Very recently, attempts have been made to use aerodynamic shape optimization in the field of tall building design. Bobby et al [71] proposed a framework for the aerodynamic shape optimization of tall buildings using CFD based on the concept of low-dimensional models for describing the global aerodynamic performance of tall buildings. A low-dimensional model was introduced which allows an efficient way for reducing the computational demand of the CFD simulations, thus expediting the optimization. A mesh morphing tool was used for automatically updating the mesh. The objective function was to minimize the drag force. Twodimensional CFD simulation was used for each optimization iteration using Reynolds-Averaged Navier-Stokes (RANS) model. The low-dimensional model allowed extension of the results to the overall aerodynamic performance of tall buildings. Elshaer et al [88] proposed an optimization framework for aerodynamic shape optimization of tall buildings. The method couples the optimization algorithm using genetic algorithm (GA), computational fluid dynamics (CFD) solver, and the neural networks (NN) model. The objective was to reduce the drag force acting on a tall building by changing the shape of its corners. Large eddy simulation (LES) models were used for numerical simulation of the wind behavior. Bernardini et al [74] performed multi-objective aerodynamic shape optimization of tall buildings using a surrogate-based optimization method. The multiple objectives were minimizing the mean drag coefficient as well as the standard deviation of the lift coefficient. Ordinary Kriging surrogate model was used. A specifically developed strategy was adopted to update the Kriging models in order to perform additional CFD runs efficiently. Shell scripting, parallelized computations and mesh morphing algorithms were used to improve the efficiency and consistency of the framework. These researches showed that in spite of recent advancements, there are still many challenges for the CFD-based aerodynamic shape optimization of tall buildings. These limited studies mainly focused on optimizing the dimensions of some predefined local corner modifications in tall buildings. To the author’s knowledge, there is no reported work till date on global shape optimization of tall buildings against wind load effects. Although this field of research is fairly new and is constantly improving, it is believed that full utilization of aerodynamic shape optimization could enable design of tall buildings that withstand wind load effects more efficiently. With the rapidly increasing use of the distributed parallel computing and adequate computing hardware, aerodynamic shape optimization is becoming more affordable than before.
4. Conclusions The shape and orientation of most buildings are driven mainly by architectural considerations, functional requirements and site limitations, rather than by aerodynamic considerations. Consequently, these structures are characterized by high wind-structure interaction induced loads. Significant reduction in wind loads can be achieved by various types of aerodynamic modifications to the shape of the structure and/or aerodynamic shape optimization techniques. In this paper the past/recent work on various techniques developed by many researchers to reduce wind loads on buildings were reviewed which are summarized in the following:
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○ Various aerodynamic modifications to the shape of tall buildings for mitigating the wind induced loads were reviewed. The aerodynamic modifications of a building’s cross-sectional shape (e.g. corner cut, corner recession, slotted corner, etc.), variation of the cross section shape and/or its size along the height of building, twisting the building, porosity and openings, etc. can significantly reduce building response in alongwind (drag force) as well as acrosswind (acrosswind force due to vortex shedding) directions by altering the wind flow characteristics around the building. ○ Aerodynamic mitigation techniques for low-rise buildings were discussed. Various methods for the mitigation of wind high suctions on the roof of low-rise buildings were described. Parapets and aerodynamic edge devices are simple, economic, and non-intrusive elements and can be utilized for reducing wind loads and mitigating damage risk at the source. In addition, they can be used as a comparatively cost-effective solution to the roof edge damage problem which is widely experienced during high wind events. These elements can either be used for retrofitting of existing buildings or they can be incorporated into the design of new buildings for reducing peak suctions at critical locations of the building envelope. ○ An overview of optimization techniques including gradient based and non-gradient based was briefly presented. Advantages and disadvantageous of each category were discussed. Non-gradient based optimization methods can converge to global optimum at the expense of more computational cost compared to gradient based algorithms. Although these methods seem to be more attractive for aerodynamic shape optimization problems which have possibly a lot of local optimum points, they require hundreds or thousands of analysis code implementation. This is extremely costly, and often impossible, for CFD-based aerodynamic shape optimization of civil structures in which each evaluation of the objective/constrained functions requires a full CFD analysis to be carried out. Surrogate-based optimization can be used to tackle the efficiency issue of non-gradient based optimization methods. ○ The suitability and challenges of aerodynamic shape optimization using CFD for reducing wind loads on tall buildings were discussed and the recent researches on this topic were presented. Although published information on how to design structures for optimal aerodynamic performance is limited, full utilization of aerodynamic optimal design could enable properly designed buildings to withstand extreme wind loads cost-effectively. Therefore, the aerodynamics of a tower shape needs to be considered as a critical design parameter from the very outset. In this way, designers could optimally control building geometric parameters to favorably impact the wind loads and other adverse wind-induced responses.
Acknowledgement We would like to thank Florida International University (FIU) for funding this research. The helpful comments received from Professor Girma Bitsuamlak from Western University are greatly appreciated. Authors would like to acknowledge Dimple Rana and Alexej Goehring of Arup for their inputs in the flow simulation using CFD.
Appendix Optimization algorithms Fig. A1 shows an overview of different gradient based and nongradient based optimization algorithms.
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Fig. A1. Figure A: Summary of optimization methods.
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