Aerodynamic design has always been a timely and expensive process specially when using experimental tools and in the final stages of design, refining the details of the configuration. Also, taking advantage of aerodynamic interferences of different components involves setting up various models which increases again the financial burden. CFD simulations with large number of grid points are a real competent for experiment if it is carefully set up. This procedure is followed in this study to simulate the aerodynamic interferences of parts of a flying boat in the vicinity of the ground.
Flying vehicles in vicinity of ground (wing in ground effect, WIG) are more
efficient aerodynamically, Kornev and Matveev (2003)
and have consequently attracted the interest of designers. It has long been
recognised that flight close to a boundary surface is more aerodynamically efficient
than flight in the freestream. This has led to the design and construction of
craft specifically intended to operate close to the ground and fly in ground
effect. A great range of Wing in Ground (WIGs) effect craft have been manufactured
ranging from 2 seat recreational vehicles to 500 tonne warcraft. In addition
to the aerial transportation in ground effect, there has been interest on high
speed trains moving on air gap (Cho et al., 2001;
Kohama and Watanable, 1998; Moon et
al., 2005). Ground affects lift and other aerodynamic forces to a large
extent, (Kim and Geropp, 1998; Zhang
et al., 2004) and these effects come through a complicated process
of deformation and displacement of vortices (Florent et
al., 2000; Zhang and Zerihan, 2003; Engels
et al., 2004).
Recent studies of ground effect are limited to two-dimensional cases or three
dimensional flows around some specific components (Kim and
Geropp, 1998; Zhu et al., 2002). The complex
configuration of flying boat (Fig. 1) can only be properly
modeled using multi-blocked structured grid that is used in this study.
Even small experience in solving complicated flow problems warrants that a
good grid comprises half of what is required for a good solution. Due to the
complexity of the configuration, Fig. 1 and possible separation
of the viscous flow in various regions, application of a structured grid especially
close to boundaries is preferred to the unstructured grid. The properties of
a good grid includes uniformity, smoothness and near orthogonality to boundaries
(Zhu et al., 2002) and no single-block grid can
provide all of these simultaneously, therefore, multi-block grid is applied
in this study (Radespiel, 1987; Rakowitz
and Eisfeld, 2003).
||Different blocks in vicinity of the body used for structured
However, at the interface of different blocks discontinuities in position
and slope of grid lines should be avoided in order to resolve all the details
of the flow and maintain a high convergence rate of the solution at the same
time (Jie and Jou, 2008; Martins et
The configuration properties (Fig. 1) include swept back vertical tail, high taper ratio wing with swept forward trailing edge among the others. Therefore, three main blocks, about upper-body, lower-body and side-body plus wing choosed and divided into smaller blocks of 800 altogether (Fig. 2).
(a) Structured grid in the junction of fuselage and wing,
(b) Structured grid in nose and canopy), (c) structured grid at the junction
of wing trailing edge, vertical tail and fuselage and (d) structured grid
at the junction of vertical and horizontal tails
||Unstructured grid on the tip of tail
||Unstructured grid on the tip of winglet
These large numbers of blocks are used to maintain smooth transition e.g.,
when connecting grids from swept forward trailing edge of the wing to the horizontal
tail. Also some of the blocks are there to keep the near orthogonality of grids
to the boundary. The resulted grid is smooth and uniform (Fig.
In few regions of the flow field use of unstructured grid is inevitable. Although,
these regions are small and quite few, this flexibility warrants the grid quality
in more important regions. These regions contain tips of wing, winglet, control
surfaces and horizontal tail (Fig. 4, 5).
Proper distribution of grid points on different edges provides the required
control of the uniformity and smoothness.
GOVERNING EQUATIONS AND BOUNDARY CONDITIONS
Reynolds averaged, incompressible, steady-state Navier-Stokes equations are:
||Different boundary conditions
where, u, v and w are velocity components of velocity vector, ,
in x, y and z directions, respectively. The p and ρ are pressure and density
and τij are different components of stress tensors as:
Two equation k-ε turbulence modeling is used to determine μt in terms of kinetic energy, k and dissipation, ε as:
Figure 6 shows half of the airplane and the domain for an angle of attack problem. As can be shown in Fig. 6, on some of the boundary planes velocity and turbulent properties are defined and on the downstream plane pressure is set. Water surface is modeled as a planar surface with zero shear stress. In this way of modeling, the water surface, the effect of air flow on free surface deformation and wave production is neglected.
As mentioned before, simple algorithm along with the first order upwind method is used to discretize the momentum and the mass conservation equations.
||Grid study results and aerodynamic coefficients
|Since, this is a quite known procedure no further explanation
A grid study including 1.5, 4 and 6.5 million grid points carried out and the results are shown in Table 1. In Table 1, lift and drag coefficients, lift over drag and the relevant errors are presented. The error is the relative percent error in results with respect to the final row. It is seen that both 4.5 and 6.5 million grid points are fine enough to provide the coefficients with acceptable error. However, y+, i.e., the normalized non-dimensional distance to the wall is only within the acceptable range for the last grid case. Since, the logarithmic velocity profile is applied in the boundary region the proper range of y+ for the first grid point should be between 50 and 500. Therefore, the last grid case of Table 1 is used to resolve the following flow fields.
Flow field at zero angle of attack in ground and out of ground effect: When the body is set at zero angle of attack, the wing will be at 8 degrees with respect to the free stream. A comparison of aerodynamic coefficients in ground and out of ground is presented in the followings. In free flight, the lift, drag and pitching moment coefficients about the leading edge are 0.564, 0.098 and 0.089, respectively. When the flight height (height of the wing trailing edge above ground) is 30% of the root chord, these coefficients change to 0.693, 0.0967 and 0.1383. This indicates a noticeable. i.e., 23% increase in lift and 25% increase of aerodynamic efficiency or lift/drag which is expectable. However, the drastic increase in pitching moment with flight height, i.e., 55% needs more explanation as follows. Although, the symmetric airfoil of horizontal tail is set at zero degrees of angle of attack, it produces a coefficient of lift equal to -0.0569 which is 10% of the total of lift in free flight condition. This downward force is mainly caused by the interference of the main wing to a large extent and to the vertical tail to a lesser extent. When the boat flies close to the ground at the mentioned height the horizontal tail tends to produce positive lift, due to ground, which results in a less net negative lift, i.e., a coefficient of lift equal to -0.0476 or 6.8% of the total lift. This noticeable change in lift of horizontal tail produces due amount of change in pitching moment coefficient during take-off.
||Variation of CM versus AOA and distance from ground
||Variation of CL versus AOA and distance from ground
The next important effect of ground is on the body drag. The body has a boat-tail
shape from its maximum cross section tapered to the end. This part produces
a propulsive force (negative drag) in free flight. In addition to this part,
the same effect is generated by a step located in the lower part of the body.
It is interesting that step drag force in free flight becomes a propulsive component
in vicinity of the ground and hence contributes to higher lift/drag in ground
effect. The high setting of wing at 8 degrees angle of attack enhances this
effect by generating a high pressure area around body and beneath the wing.
The overall effects of ground on various aerodynamic coefficients with angle
of attack are shown in Fig. 7-10. The same
trend is seen in Fig. 7-10; however, the
nonlinearity o f lift variation with angle of attack even in 6 degrees range
of variation is noticeable (Fig. 10).
||Variation of CD versus AOA and distance from ground
||Variation of L/D versus AOA and distance from ground
This is mainly due
to the interaction of vortices coming off from wing tips and other parts of
the configuration, explained in the followings.
Comparison between the experimental lift and drag of a flying boat that is
available in high performance Computer Center of Shiraz University (HPCC) and
the numeric results of this study is done. Experimental lift and drag coefficients
for the case h/c = 0.3 are 1.1 and 0.158, respectively which shows a deflection
of 3.6 and 15.6% according to Fig. 8 and 9.
This deflection is in acceptable range for numerical calculations.
The effect of winglet in ground and out-of-ground effect: The cases
discussed up to now had no winglet. In Fig. 11, the path
lines from different parts of the whole configuration including winglet are
||Path lines of a flying boat
||Pressure distribution in cross section with 15 cm distance
The interaction of vortices with each other and with the main flow field
is quite strong.
Addition of winglet to the configuration in free flight increase the lift coefficient by 36%, the pitching moment coefficient by 22% and lift over drag by 2.8%. It is interesting that the winglet increases the downward lift of the horizontal tail by 14%. This increase in negative lift is due to the effect of stronger tip vortices and the downwash induced by vortices, (Fig. 11). Addition of winglet in presence of ground increases the lift by 32%, pitching moment by 17% and aerodynamic efficiency by 26%. These numbers show that the winglet influence reduces as the flying-boat decreases its height.
Figure 12 and 13 show the pressure contours
at two span wise sections of wing and horizontal tail. The pressure underneath
the horizontal tail is negative due to wing effect and this pressure change
is enhanced by the presence of the vertical tail. This increase is due to the
vertical tail effect.
||Pressure distribution in cross section with 1 m distance from
In overall, if the flying-boat increases its height above
the ground a nose up pitching moment would apply on the plane due to increased
negative tail lift which is mainly due to interferences.
Configuration tuning would take the best advantage of ground effect in increasing lift and aerodynamic efficiency. Strong interference of wing and the horizontal tail produces a large pitching moment amplified in ground effect. Winglet has a broad effect on performance of all parts, even on the canopy lift at upstream (not mentioned in the text). However, the main effect would be to increase the lift and aerodynamic efficiency, which is more pronounced in free flight than in ground presence. The interference of wing and vertical tail on horizontal tail is a net downward force on tail. As this force increases with increasing the height a nose up moment would assist the take-off.