13-12-2012, 04:13 PM
A generic methodology for determination of drag coefficient of an aerostat envelope using CFD
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Introduction
An aerostat is an aerodynamically shaped body that is tethered to the ground. An Aerostat is filled with a ‘lighter
than air’ gas, and thus generates static lift due to buoyancy. The primary requirements of an aerostat are high
payload capacity, low blow-by, and sufficient stability and fast response to winds. The total lift that is produced by
buoyancy and aerodynamic forces is balanced by the weight of the aerostat, the tether force and the payload. The
buoyancy depends solely on the volume of LTA gas contained in the envelope. To increase the payload that can be
carried by an envelope of fixed volume, either the weight of the aerostat has to be reduced or the tether force has to
be reduced.
The weight of the envelope depends on its total surface area and the density of the material that is used for
manufacturing the aerostat. Thus, to reduce the weight of the aerostat, its surface area should be reduced. Selection
of the proper geometry of the hull can reduce the surface area of the hull for the same volume. However the surface
area alone does not decide the shape of the envelope as there are other considerations such as stresses generated and
drag produced in the aerostat. When stress is low, thinner fabrics with lesser density can be used for manufacturing
the aerostat. Another method to reduce the weight of the envelope is to use patches of thicker and denser material in
highly stressed regions and thinner materials for other regions.
Blow-by is the longitudinal displacement of the aerostat brought about by ambient winds. Such movement is
undesirable, as it induces errors in the station keeping and reduces the effective operational altitude of the aerostat. If
drag on the aerostat is high, longer tether has to be used to maintain the altitude, as shown in Fig. 1, thus drag also
has a weight penalty attached to it.
Drag minimization of axi-symmetric bodies
In most cases, aerostat envelopes can be assumed to be axi-symmetric bodies of revolution. Many studies, both
experimental1-3, and computational4-9 for obtaining low drag shapes of such bodies for various applications and
Reynolds number regimes have been reported in literature. One of the most important considerations in interpreting
the results of these studies is the characteristic length that is used to define the Reynolds number of the envelope.
Though V1/3 is usually used as the characteristic length, in some cases the Reynolds number reported is based on
envelope length L. Transition Reynolds number depends on the choice of characteristic lengths. Similarly, the
definition of coefficient of drag CD can also be based on total surface area of the body S, or the reference area
equivalent to V2/3.
CFD techniques for shape optimization of axi-symmetric bodies
Parsons and Goodson4 were the first to report application of numerical optimization techniques for shape
optimization of axi-symmetric bodies. They represented the body by eight parameters, and coupled a boundary-layer
method to a panel code. Pinebrook8 has also carried out studies on drag minimization of bodies of revolution.
Dodbele et al.6 used the coordinate points defining the geometry of a fuselage as the design vector and the location
of the transition point as the objective function to be maximized. The fact that drag reduction by modification of
shape primarily involves increasing the extent of laminar flow justifies selection of location of transition point as
objective function.
In contrast, Zedan et al.5 used an inverse method for drag minimization of axi-symmetric bodies (such as
airplane fuselages) by shaping. In this approach, a favorable velocity distribution was specified, and the shape of the
body that produced this distribution was obtained. The fuselage designed showed a long region with a favorable
pressure gradient in its forward part. It was stated that this should result in laminar flow up to 70 % of the body
length at medium and large Reynolds numbers. Coiro and Nicolosi7 have also reported some results related to
Natural Laminar Flow on aircraft fuselages. In this method, a linearly varying doublet distribution is placed along
the axis of the body such that the stagnation streamline gives the shape of the body. Starting with an initial guess
shape, the strength of the singularities is varied until the velocity distribution over the shape matches the prescribed
velocity distribution. This method is better than usual optimization methods as the physics of transition delay is not
masked. It also involves less computational resources; however, it involves a lot of experience to decide the required
velocity distribution.
Multidisciplinary approach to envelope shape optimization
Kanikdale et al.14 have attempted a multidisciplinary approach to shape optimization of airships envelopes. They
have defined a generic envelope profile in terms of a combination of two cubic-splines, with a spherical cap in the
front portion, and a parabolic shape in the end, as shown in Fig. 5. The selection of a spherical cap for the enables
the shape to be compatible with the spherical mooring cups that are in use in the winching and mooring systems of
aerostats. A parabola was selected for the rear portion to make attachment of fins easier.