# Sky type sail

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<p>Chapter 5. Performance analysis of the proposed wind harnessing solutions</p>
<p>For ship resistance prediction, CFD has become increasingly important and is now an indispensable part of the design process. Typically inviscid free-surface methods based on the boundary element approach are used to analyze the forebody, especially the interaction of bulbous bow and forward shoulder. Viscous flow codes often neglect wave making and focus on the aft body or appendages. Flow codes modelling both viscosity and the wavemaking are at the threshold of practical applicability. Instead, it is used to gain insight into local flow details and derive recommendation on how to improve a given design or select a most promising candidate design for model testing.Although a model of the final ship design is still tested in a towing tank, the testing sequence and content have changed significantly over the last few years. Traditionally, unless the new ship design was close to an experimental series or a known parent ship, the design process incorporated many model tests. The process has been one of design, test, redesign, test etc. sometimes involving more than 10 models each with slight variations. This is no longer feasible due to time-to-market requirements from ship owners and no longer necessary thanks to CFD developments. Combining CAD (computer-aided design) to generate new hull shapes in concert with CFD to analyze these hull shapes allows for rapid design explorations without model testing. CFD allows the preselection of the most promising design. Then often only one or two models are actually tested to validate the intended performance features in the design and to get a power prediction accepted in practice as highly accurate. As a consequence of this practice, model tests for shipyard customers have declined considerably since the 1980s. This was partially compensated by more sophisticated and detailed tests funded from research projects to validate and calibrate CFD methods. One of the biggest problems for predicting ship seakeeping is determining the nature of the sea: how to predict and model it, for both experimental and computational analyses. Many long-term predictions of the sea require a Fourier decomposition of the sea and ship responses with an inherent assumption that the sea and the responses are moderately small, while the physics of many seakeeping problems is highly non-linear. Nevertheless, seakeeping predictions are often considered to be less important or covered by empirical safety factors where losses of ships are shrugged off as acts of God, until they occur so often or involve such spectacular losses of life that safety factors and other regulations are adjusted to a stricter level. Seakeeping is largely not understood by ship owners and global sea margins of, e.g., 15% to finely tuned (1%) power predictions irrespective of the individual design are not uncommon.</p>
<p>5.1. Governing equationsFor assessing the thrust provided by the proposed wind harnessing solutions, there was used the ANSYS CFX, CFD code. The set of equations solved by ANSYS CFX are the unsteady Navier-Stokes equations in their conservation form.The instantaneous equation of mass, momentum, and energy conservation are presented. For turbulent flows, the instantaneous equations are averaged leading to additional terms.- the continuity equation (5.1.)- the momentum equations (5.2.)Where the stress tensor, , is related to the strain rate, by: (5.3.)- the total energy equation (5.4.)where htot is the total enthalpy, related to the static enthalpy h(T,p) by: (5.5.)Where the term represents the work due to viscous stresses and is called the viscous work term. This models the internal heating by viscosity in the fluid, and is negligible in most flows. The term represents the work due to external momentum sources and is currently neglected.The transport equations described above must be augmented with constitutive equations of state for density and for enthalpy in order to form a closed system. In the most general case, these state equations have the form: (5.6.) (5.7.) (5.8.)In the ANSYS CFX code, the Redlich Kwong equation of state is available as a built-in option for simulating real gases. It is also available through several pre-supplied CFX-TASC flow RGP files. The Vukalovich Virial equation of state is also available but currently only by using CFX-TASC flow RGP tables.Cubic equations of state are a convenient mean for predicting real fluid behavior. They are highly useful from an engineering standpoint because they generally only require that you know the fluid critical point properties, and for some versions, the acentric factor. These properties are well known for many pure substances or can be estimated if not available. They are called cubic equations of state because, when rearranged as a function volume they are cubic in volume. This means that cubic state equations can be used to predict both liquid and vapor volumes at a given pressure and temperature. Generally the lowest root is the liquid volume and the higher root is the vapor volume. Four versions of cubic state equations are available: Standard Redlich Kwong, Aungier Redlich Kwong, Soave Redlich Kwong, and Peng Robinson. The Redlich-Kwong equation of state was first published in 1949 and is considered one of the most accurate two-parameter corresponding states equations of state. More recently, Aungier (1995) [54] has modified the Redlich-Kwong equation of state so that it provides much better accuracy near the critical point. The Aungier form of this equation of state is the default cubic equation used by ANSYS CFX. The Peng Robinson and Soave Redlich Kwong equation of state were developed to overcome the shortcomings of the Redlich Kwong equations to accurately predict liquid properties and vapor-liquid equilibrium.The Redlich Kwong variants of the cubic equations of state are written as: (5.9.)where is the specific volume.In order to provide a full description of the gas properties, the flow solver must also calculate enthalpy and entropy. These are evaluated using slight variations on the general relationships for enthalpy and entropy that were presented in the previous section on variable definitions. The variations depend on the zero pressure, ideal gas, specific heat capacity and derivatives of the equation of state. The zero pressure specific heat capacity must be supplied to ANSYS CFX while the derivatives are analytically evaluated. Internal energy is calculated as a function of temperature and volume (T,v) by integrating from the reference state (Tref, vref) along path 'amnc' (see diagram below) to the required state (T,v) using the following differential relationship: (5.10.)</p>
<p>Figure 5.1. Energy development on T-v coordinatesFirst, the energy change is calculated at constant temperature from the reference volume to infinite volume (ideal gas state), then the energy change is evaluated at constant volume using the ideal gas cv. The final integration, also at constant temperature, subtracts the energy change from infinite volume to the required volume. In integral form, the energy change along this path is: (5.11.)Once the internal energy is known, then enthalpy is evaluated from internal energy: (5.12.)The entropy change is similarly evaluated: (5.13.)where is the zero pressure ideal gas specific heat capacity. By default, ANSYS CFX uses a 4th order polynomial for this and requires that coefficients of that polynomial are available. These coefficients are tabulated in various references including Poling et al [55].In addition, a suitable reference state must be selected to carry out the integrations. The selection of this state is arbitrary, and can be set by the user, but by default, ANSYS CFX uses the normal boiling temperature (which is provided) as the reference temperature and the reference pressure is set to the value of the vapor pressure at the normal boiling point. The reference enthalpy and entropy are set to zero at this point by default, but can also be overridden if desired.Other properties, such as the specific heat capacity at constant volume, can be evaluated from the internal energy. For example, the Redlich Kwong model uses: (5.14.)where u0 is the ideal gas portion of the internal energy: (5.15.)specific heat capacity at constant pressure, cp, is calculated from cv using: (5.16.)where and are the volume expansivity and isothermal compressibility, respectively. These two values are functions of derivatives of the equation of state and are given by: (5.17.) (5.18.)5.2. Modelling similitude principlesFor the following simulations, which served for assessing the thrust force determined by the wind, when using different wind harnessing solutions, in order to overcome the challenges imposed by the existing computational power, it was necessary to develop scale models (at 1:100 scale).Modeling and simulation techniques have widely become instrumental in the design and development stage of many advanced technology programs. They play an essential part in allowing a great variety of design concepts to be generated and tested without having to rely on physical prototypes. Therefore, they help companies maintain their competitiveness by expediting the design and redesign processes of their engineered products to efficiently keep up with the frequently changing, and stringent needs in the market [36].In the initial design process, engineers often make use of modeling and simulation techniques along with their hands-on experience to evolve their product into its optimum, subject to possibly many specifications. Some of these specifications inevitably have to be later modified according to such stringent market needs. While these modifications render the optimal original design no longer optimal for the new application, some desirable properties of the original design may still have to be sustained and then migrated to the new design.Scaling differs from traditional engineering system design optimization in its strong emphasis on minimal modifications. In scaling an internal combustion engine to meet higher power demands, for instance, one typically seeks to change only a few engine parameters (e.g., number of cylinders or displacement per cylinder) to meet the new power demands while retaining the remaining desirable engine characteristics. This can only be possible if such desirable characteristics are invariant with respect to the parameter or combination of parameters used for scaling. From a conceptual standpoint, therefore, scaling is essentially a search for invariance, and every scaling algorithm should be based on a principle of invariance (a.k.a., a similarity principle). Many different similarity principles exist in the literature, each of which can be interpreted as a metric quantifying whether or not two systems are similar. First, geometric similarity [40, 41] defines the conditions under which two objects are similar in shape. Further, kinematic and dynamic similarities [40-42] define the conditions under which the two objects undergo similar motions, and experience similar forces during those motions, respectively. In particular, these similarity conditions designate the values at which the properties (e.g., length, density, pressure, etc.) associated with one object has to be with respect to the other object. This notion of dynamic similarity or dynamic similitude (these two terms will be used interchangeably in this dissertation) is applicable to any energetic system in any domain (e.g., mechanical, thermofluidic, electromagnetic, etc.) because the notions of force and motion are equivalent to those of the power variables (i.e., effort and flow) in system dynamics [43]. In spite of the long history of these similarity principles, they still remain very useful especially when the basic laws of governing systems are known, but their solutions are difficult to obtain [44]. Due to the wide applicability mentioned above, several scaling approaches appear in the literature have utilized these similitude principles, especially dynamic similitude (e.g., [41, 42, 45-47]). Nevertheless, such similitude-based scaling approaches still have the following shortcomings. First, similitude-based scaling often turns out to be too restrictive because it may be infeasible to follow all of the conditions designated by a given similitude principle exactly (e.g., [42, 47-50]). This infeasibility can be, for instance, due to some physical constraints present in the scaling problem (e.g., material constraints in structural testing).Second of all, dynamic similitude is a discrete principle of invariance, that is, two system designs either satisfy the conditions of similitude or not at all. As a result, whenever similitude is not feasible, one cannot assess the degree to which the two designs are close to satisfying the discrete definition of exact dynamic similitude. </p>
<p>5.3. Assessment of the thrust force provided by the wind harnessing solutionsBy having in mind the wind harnessing solutions presented in chapter 4, two solutions were developed; the first one consists in a rigid sail system, fitted in the ships hull.The hulls dimensions were considered to be those specified in table 2.1. The added rigid sail will provide an active surface of 3 x 387,52 m2 (figure 5.2.), with the sails height of 42.998m.The second solution consists in a sky sail, mounted in the ships bow (figure 5.3.).</p>
<p>Figure 5.3. The sky sail assembly, scale 1:1</p>
<p>Figure 5.4. Sky sail, scale 1:1Figure 5.5. Sky sail, scale 1:63</p>
<p>Invoking theBuckingham theoremshows that the system can be described with two dimensionless numbers and one independent variable [52]. Dimensional analysisis used to rearrange the units to form theReynolds number (Re) andPressure coefficient(CP). These dimensionless numbers account for all the variables listed above exceptthe thrust force, which will be the assessed by simulation. Since the dimensionless parameters will stay constant for both the simulation and the real application, they will be used to formulate scaling laws for the test:(5.19.)(5.20.)For estimating the wind velocity, in the both cases, rigid sail and sky sail, it was considered the Beaufort scale [104].Table 5.1. The wind velocity, on the Beaufort scaleBeaufort numberDescriptionWind speedWave heightSea conditions</p>
<p>0Calm< 1knot0mFlat</p>
<p>< 0.3m/s</p>
<p>1Light air13 knot00.2 mRipples without crests.</p>
<p>0.31.5m/s</p>
<p>2Light breeze46 knot0.20.5 mSmall wavelets. Crests of glassy appearance, not breaking</p>
<p>1.63.4m/s</p>
<p>3Gentle breeze710 knot0.51 mLarge wavelets. Crests begin to break; scattered whitecaps</p>
<p>3.55.4m/s</p>
<p>4Moderate breeze1116 knot12 mSmall waves with breaking crests. Fairly frequent whitecaps.</p>
<p>5.57.9m/s</p>
<p>5Fresh breeze1721 knot23 mModerate waves of some length. Many whitecaps. Small amounts of spray.</p>
<p>8.010.7m/s</p>
<p>6Strong breeze2227 knot34 mLong waves begin to form. White foa...</p>

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