Wind load performance of high-rise building cross-sections

Wind Load

Rapid urbanization coupled with exponential population growth has seen an exponential increase in high-rise buildings, surpassing even the dramatic wave of construction that followed the Industrial Revolution. Furthermore, where once high-rise buildings were limited to a few major cities, over the last few decades they have begun to appear all over the globe, from Shanghai to Dubai and elsewhere. The rapid increase in the construction of high-rise buildings coupled with the ever-present desire for new and exciting designs has meant that buildings are increasingly susceptible to natural forces such as seismic events and strong winds, a fact that demands more intricate analyses of these designs in order to determine their structural performance capabilities well before construction is complete. Wind flow in particular is a pressing issue, because it has received somewhat less attention than seismic events until very recently, when computer science developed enough such that the accurate modeling of air flow became a real possibility.

Because different building cross-sections effect wind load differently, predicting, measuring, and accounting for these differences is crucial for the construction of safe high-rises. Wind-tunnel testing has shown that square buildings with modified corners and helical buildings both perform better than buildings with a square cross section or helical buildings with modified corners (Tanaka et. al. 2012, p. 190). Other experiments have shown that a tapered building model reduces wind excitations, although a discrepancy appears between suburban and urban flow settings (Kim & You 2002, p. 1781). Finally, wind-tunnel research into triangular cross-sections has shown that they also reduce wind excitations (Yoshida et. al. 2012). However, while these wind-tunnel tests have produced useful results, not enough has been done to compare the wide variety of cross sections across the board in order to determine the most effective design, because most previous work focuses on a rather limited selection of cross-sections.

Obviously, much work has been done towards determining not only the most wind-resistant designs, but also the most effective means of testing those designs. There are multiple ways of testing a structure's potential performance in high-wind situations, and wind tunnels in particular have proved crucial in testing the structural performance of high-rise designs. However, wind tunnels and full-scale testing have certain drawbacks that do not allow them to be used in every situation, including cost or the need for more detailed data. In these situations, computational fluid dynamics (CFD) becomes essential, because numerical simulation simultaneously cuts down on the cost of testing and allows for greater control over the data produced and analyzed, allowing researchers to simulate "real-world" conditions and events that might be impossible to test with a wind-tunnel.

Obviously, in order to effectively test the potential performance of any given design one must have a robust and verifiably accurate means of testing, and so determining which of the available options works best is one of the most pressing issues in the field of engineering. When taking into account the aforementioned benefits and drawbacks of wind tunnels, full-scale testing, and numerical simulation, as well as previous literature concerning each method's utility, it becomes clear that numerical simulation is ultimately a better choice when attempting to determine the effect of wind on any given design. The speed, accuracy, and repeatability of numerical simulation cannot be challenged by other testing methods. This is not to suggest that there is no place for wind tunnels and full-scale testing, but rather that numerical simulation should be considered the preeminent means of testing, rather than a novel or secondary method.

CFD may be performed via different simulations and models depending on the proposed design, and by using the Reynolds Averaged Navier-Stokes Equation (RANS) model one can easily simulate the effects of wind on high-rises with different cross-sections using widely available software such as CFX. The benefits of this approach are many, but the most obvious is the fact that the RANS model can produce results quickly and has been shown to "yield encouraging results in most cases" when compared to both wind-tunnel tests and Large Eddy Simulations (LES) (Huang, Li, & Xu 2007, p. 612). This means that one can compare the results from multiple different cross sections (relatively) easily, allowing one to determine, with much greater accuracy than has heretofore been possible, the best cross-sectional designs for minimizing wind-induced excitations of high-rise buildings.

Atmospheric Boundary Layer

Arguably the most important concept when discussing wind effects on high-rise buildings is the atmospheric boundary layer or ABL. The ABL is the layer of atmosphere immediately above the surface of the planet, and it is here that all terrestrial human activity, including the construction and habitation of high-rises, occurs. Understanding the nature of the ABL and the unique airflow characteristics at each level of the ABL is crucial when testing designs for their potential wind load, because the variability of the ABL is precisely the kind of "real-world" effect that is difficult to model in wind-tunnel tests but can be effectively analyzed using the tools of computational fluid dynamics. As such, an introduction to the ABL by means of a brief review of extant literature on the subject will be extremely helpful.

The ABL can vary in height depending on certain environmental conditions, and it is effected by a number of variables including surface temperature variability, topographical features, and surface friction. In fact, the height of the ABL can vary from under one hundred meters to as high as multiple kilometers, depending on the aforementioned variables (Stull 1988). The sheer range of the ABL's height should give some indication as to the importance of including the ABL in one's calculations, particularly because every high-rise design will be effected differently due to topographical and environmental differences depending on the proposed location.

There are multiple layers within the ABL, and although there is some ongoing discussion regarding the precise number and makeup of these layers, there is general agreement on the two major regions of the ABL, referred to as the Ekman layer, after Vagn Walfrid Ekman, the Swedish oceanographer who first theorized its existence, and the inner layer (Garratt 1992). It should be noted that the Ekman layer of the ABL is merely a particular instance of a general concept; Ekman first developed his theory to describe the flow of ice, but ending up discovering what appears to be a form of fluid motion common to any fluids given the right forces. Thus, in general an Ekman layer is the potential layer in a fluid wherein a balance exists between the Coriolis and pressure-gradient forces, and as such the Ekman layer of the ABL is that (theorized) top-most layer wherein this balance gives rise to geostrophic winds, which in turn influence the air at lower levels.

The Ekman layer is not usually influenced by surface temperature or friction, because the effect of these variables diminish rapidly with height, but the inner or surface layer is effected to a substantial degree (Garratt 1992). During the day, when the surface is warmer, the increased temperature results in decreased air density, allowing for the formation of convectional currents and thermals, while the cooler night generally tends to diminish this convection and replace it with a smoother boundary layer with relatively little turbulence (Stull 1988). In addition to the effect that temperature variability has on the inner layer, the simple movement of air across a plane (in this case the surface of the earth) also determines the make-up of wind in the ABL, because this movement creates different regions of turbulence, viscosity, and laminar flow that must be taken into account when modeling.

This inner layer, with its greater range of variability than the Ekman layer, is arguably the most important element of the ABL when considering high-rise buildings, because the lower-most section of the inner layer is roughly ten percent of the total height, which comes out to about one hundred meters depending on the actual height of the ABL at any given time and location (Garratt 1992). The aforementioned layer of convection and thermals which occurs during the day can extend as high as one thousand meters, and the nocturnal layer of calmer air only extends to about half that (Garratt 1992). Currently the tallest completed building in the world is the Burj Khalifa in Dubai, and it stands roughly eight-hundred thirty meters tall, meaning that it feels the effects of the entire surface layer as well as the upper layer. Using the Burj Khalifa as an example, one can immediately see the importance of determining wind effects on high-rises, because the design of the Burj Khalifa, and indeed any modern high-rise, means that it must be able to withstand not only the turbulence and fluctuations which occur at lower levels, but also the dramatically higher-speed winds seen further up into the ABL.

However, simple matters of height are not the only variable of the ABL that concerns engineers, because differences in terrain can substantially effect both wind speed and turbulence. For example, air speed is effected differently depending on surface roughness, such that the transition from smooth to rough or rough to smooth can dramatically alter wind speed (Azad 1993). This effect is particularly important for structures on the boundary of different topographical features, such as those in Chicago, which sits next to Lake Michigan and thus feels the brunt of wind sweeping in from across the surface of the water while at the same time feeling the effects of the polar jet stream, or Los Angeles, which is positioned between the ocean and a range of tall mountains and so experiences the turbulence of ocean winds hitting the land. Furthermore, because the acceleration or deceleration of the velocity profile diffuses itself through turbulence, the higher up a structure, the more turbulence it will experience (Azad 1993).

Turbulence modeling

Arguably the most complex area of computational fluid dynamics is the modeling of turbulence, and not only because the concept itself is not even fully defined. At its simplest, turbulence, or at least the movement of turbulence, might be described as "the whole cascade of energy down through smaller and smaller scales until finally a limit is reached when the eddies become so tiny that viscosity takes over," and this description reveals some of the difficulties related to modeling turbulence. For one, it is extremely difficult to model each scale of the entire process even as the movement between these scales is the core of what is being examined. Furthermore, when using RANS to simulate turbulent flows one must draw on additional models, because the formulation of the RANS equations leaves the set not closed; this is one of the major distinctions between direct numerical simulation, which deals with the directly solvable Navier-Stokes equations, and the RANS equations, which require additional equations in order to effectively solve the remaining unknown terms, dubbed Reynolds stresses (Stangroom 2004, p. 79-80).

Though a number of additional models have been developed to help model turbulence, the first "industry standard" is the k-? (k-epsilon) model, which uses two equations in order to model the energy dissipation per unit mass and the kinematic viscosity (Stangroom 2004, p. 83). In the model k is the kinetic energy per unit mass and ? is the dissipation rate of kinetic energy as heat by the action of viscosity, which allows one to define both the velocity and length scales at any given time and space. With this information in hand, one can then define eddy viscosity which allows one to then make k and ? The subject of transport equations.

The k-? model has become the standard for modeling turbulence largely because "it has relatively low computational costs and is numerically more stable than the more advanced and complex stress models," and "has been verified and validated for a wide variety of flows" (Stangroom 2004, p. 85). However, while the standard k-? model has proved extremely useful, it does have its limits, particularly when it comes to modeling "wake flows, buoyancy, Coriolis, curved flows and other effects" (Stangroom 2004, p. 85). As a result, researchers have developed alternatives that can more accurately model the kind of effects that will be most important for a study of high-rise cross sections. The first of these modified models is the k-? RNG model, so named because "it is based on renormalization group analysis of the Navier-Stokes equations," resulting in a slightly more complex, but ultimately more accurate computation (Stangroom 2004, p. 86). The k-? RNG model differs from the standard k-? model due to its inclusion of different constants and the combination of one constant with a function, resulting in a more accurate separation of flow and recirculation in the model.

The main benefit of the k-? RNG model over the standard model is the way that the former can more accurately model complex flows. For example, the k-? RNG can produce accurate turbulence models for flows over complex terrain with a variety of recirculation patterns, something that the standard model is simply ill-equipped to deal with (Stangroom 2004, p. 87). Furthermore, the increase in computational cost is minimal when compared to the increase in accuracy, making the trade-off well worth it in most situations. However, because the k-? RNG is "still based on the isotropic eddy viscosity concept," it will not necessarily produce better results in all situations, and in some cases, it can actually reduce accuracy (Stangroom 2004, pp. 86-87).

The main issue effecting k-? models tends to be "the overestimation of turbulent kinetic energy," meaning an overestimation of the value for k in any given instance, leading to inaccurate results (Stangroom 2004, p. 90). Situation-specific alterations to the k-? model have proved effective while simultaneously demonstrating the fragility of the model, or at least the sensitivity of the model to inaccurate or variable values. For example, while one modification accurately modeled "the flow over urban canopies," it simultaneously demonstrated that flow is extremely susceptible to obstructions such as buildings, meaning that this model would possibly need adjusting for every application, due to the extreme variability in any given building's surroundings (Stangroom 2004, p. 90).