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VALIDATION OF TAB ASSISTED CONTROL SURFACE COMPUTATION 474
Validation of Tab Assisted Control Surface Computation
C.-H.Sung, B.Rhee, I.-Y.Koh (Naval Surface Warfare Center, Carderock Division, USA)
ABSTRACT
A numerical procedure for the prediction of the forces and moments of a tab assisted control surface (TAC) has been
developed. The control surface consists of a stern stabilizer, a flap, and a tab. The numerical procedure is based on
solving the incompressible Reynolds-averaged Navier-Stokes equations coupled with several two-equation turbulence
models. Some features of the numerical method used have been highlighted. In particular, the preconditioning method,
multigrid method, and nonreflecting far field boundary condition have been discussed. The wall boundary condition for
the specific dissipation rate which is important in obtaining good convergence for the -ω equation turbulence model have
also been briefly discussed. Computed results of the lift and drag coefficients of the control surface, flap torque
coefficients and tab torque coefficients at various angles of attack of the stabilizer and of flap angles and tab angles have
been predicted within 10 percent from the measured values even at high angles of attack at 15 degrees. The discrepancies
of the torque coefficients of flap and tab are somewhat higher particularly at high flap and torque deflections. There are
two reasons for these higher discrepancies. The first reason is that the turbulence models are inherently weak in the flow
regime where separation is severe, and the second is that the grid solution in both the flap and tab gap is not sufficient.
These will be the topics for future investigations.
INTRODUCTION
A control surface here will be defined as consisting of a stern stabilizer, a flap and a tab. The stabilizer maybe fixed
or movable but the flap and tab are always movable. Control surfaces have at least three major functions applicable to
both aircraft and marine vehicles. (1) The stabilizer, flap, and tab can be aligned to form a high cambered control surface
to increase the lift significantly. In the aerospace industry, this is the so called high-lift multi-element airfoil (or wing). (2)
Control surfaces are normally designed to provide adequate lift at lower speed operation, but undesirable excessive
control may occur at high speed. A smoother control at high speed may be achieved by keeping the stabilizer fixed and
using the flap and/or tab for control. (3) At high speed, an excessively large torque can arise in the stabilizer. This large
torque can be reduced by deflecting the flap and/or tab in the direction opposite to the direction of the angle of attack of
the incoming flow.
The purpose of this paper is to report the progress made in the development of a predictive capability of the forces
and moments of the tab assisted control surface (TAC). The design of efficient and desirable control surfaces by applying
the predictive capability developed here is left for future work.
There is an extensive experimental and computational literature on the high-lift multi-element airfoil (wing). Many
references can be found in [1]. There is an extensive set of data of a NACA 0015 airfoil with a flap and a tab measured by
Sears et al. [2]. For marine applications, work on relatively low aspect ratio control surfaces (sternplanes or rudders) is
mostly experimental. Very little computational work has appeared in the literature. Forces and moments on control
surfaces (no flap nor tab) have been measured by Whicker et al. [3] and those on a flapped control surface (no tab) have
been measured by Bowers [4]. Water tunnel experiments on a series of 12 rudders with systematic variations of flap area
and flap balance have been performed by Kerwin et al. [5]. Three variations of skeg-rudders (i.e., fixed main control
surfaces with movable flaps) have been investigated in a wind tunnel [6]. The effect of gaps between the rudder and the
skeg has also been investigated. It has been observed that the effect of the gap is insignificant. Unlike the case in
aerospace industry, there are not many computational papers on control surfaces. Recently, Soding [7] discussed the
application of potential theory in rudder flow predictions. The effects of flaps and tabs were not discussed. Computations
for
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VALIDATION OF TAB ASSISTED CONTROL SURFACE COMPUTATION 475
rudders (no flap nor tab) based on solving the Reynolds-averaged Navier-Stokes (RANS) equations with a k-ε turbulence
model have been reported by Chau [8]. The 3D computations to be reported will be compared with the data to be reported
in [9]. Implicit in all the investigations discussed so far was the assumption that the control surface was operating in a
uniform flow without the influence of the hull boundary layer, the horse-shoe vortex shed by appendages or the propeller.
In the next section, the governing equations of the incompressible RANS equations and the turbulence models will
be described. The numerical method used will be discussed next. Only some special features of the numerical schemes
will be highlighted omitting most of the details. The experiment performed on the TAC control surface with a flap and a
tab will be described and the comparison between computations and measurements will then be discussed. Finally, some
conclusions will be mentioned.
GOVERNING EQUATIONS
The incompressible Reynolds-averaged Navier-Stokes (RANS) equations and a nonlinear -ω turbulence model
must be solved. The nonlinear -ω model used here is a standard -ω turbulence model developed by Wilcox [10]
coupled with a nonlinear Reynolds stress model.
(1)
(2)
(3)
(4)
where uj is the Cartesian velocity component, is the pressure p divided by a constant density ρ, is the
turbulent kinetic energy, ω is the specific dissipation rate, ν is the kinematic viscosity, νt is the eddy viscosity given as /ω
and τij is the Reynolds stress tensor. A quadratic Reynolds stress model developed by Speziale [11] will be used here, and
an explicit expression can be found there. Standard modeling coefficients are used: β*=0.09, β=3/40, α=5/9 and
σk=σω=1/2.
NUMERICAL METHOD
The incompressible RANS equations are solved by the artificial compressibility approach first proposed by Chorin
[12] and subsequently generalized and improved by Turkel [13]. A finite volume method is used. The mean flow (i.e.,
Eqns (1) and (2)) is spatially discretized by a second-order accurate central difference method with fourth-order accurate
dissipation terms. The logic for using the fourth-order accurate dissipation terms is twofold. During the early stage of time
stepping, the fourth-order accurate dissipation terms act to suppress spurious oscillations thus enabling convergence to be
reached. But once the convergence is achieved; however, their contribution the solution is negligible because they are
fourth order accurate compared to the second-order accurate spatial discretization scheme. Several upwind schemes have
been suggested by Yee [14]. The reason for using an upwind scheme, not a central difference scheme, to solve the
turbulent flow equations is that the flux matrix is already diagonal; therefore there is no additional cost in doing a
characteristic formulation. The time stepping is based on an explicit one-step multi-stage Runge-Kutta method to reach a
steady-state solution. This approach is not only applicable to the steady state solutions but can also be extended in a very
simple manner to solve the time dependent equations. Some discussion of this extension can be found in the papers by
James on [15] and Liu et al. [16]. Several convergence acceleration techniques including multigrid, local time step,
implicit residual smoothing, preconditioning and bulk viscosity damping have been implemented. To handle complex
geometry, the multi-block grid structure is adopted.
These numerical techniques have been implemented in a code named IFLOW, which is an abbreviation for
Incompressible FLOW. IFLOW is intended to be a production code for solving 2D, 3D, steady and unsteady problems.
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The code is highly modular in structure so that different turbulence models and higher order schemes can be easily
implemented. Some special features of the numerical schemes used will be highlighted. However, detailed derivations
will be mostly omitted.
Preconditioned Method
The preconditioned method is developed based on a system of hyperbolic equations, but the idea goes back to the
effort to reduce the condition number

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VALIDATION OF TAB ASSISTED CONTROL SURFACE COMPUTATION 476
of a matrix in linear algebra. For hyperbolic equations, the objective is to make the various speeds of different wave
modes more or less the same so that convergence can be significantly accelerated. This is particularly important if the
artificial compressibility approach is adopted to solve incompressible flows. The reason is that the sound speed, which is
one of the wave modes in the incompressible flow, propagates much faster than the fluid speed. The result is a very slow
convergence as often encountered in the attempts to compute low Mach number flows using a compressible flow code.
The preconditioned mean flow (i.e., Eqns (1) and (2)) can be written in the conservative form as
(5)
where the preconditioned matrix Po and the three components of fluxes F, G, and H are defined as
(6)
(7)
where α, β−2 and γ are preconditioning parameters, τij, I, j=x, y, z, are Reynolds stresses. For mathematical analysis, it
is easier to write Eqn (5) in a non-conservative form. Neglecting the viscous terms, it can be derived as:
(8)
−1 is different from the
The explicit forms of matrices A, B, and C are omitted here. The preconditioning matrix P
previous one Po−I and is given by
(9)
The condition a=γ ensures the system of partial differential equations is well posed. However, the implication of
well posedness in the case of numerical solution is not clear. In this paper, it is α=γ=0 and
(10)
Through rather tedious algebraic manipulations, the eigenvalues and left and right eigenfunctions can be found. The
maximum of eigenvalues is used to define a local time step. The eigenfunctions are of no use to central difference
schemes except for establishing a nonreflecting boundary condition at far field. The final system of equations to be solved
in the conservative form is
Since the formulation is based on hyperbolic equation only, viscous terms should be added to the fluxes F, G and H
as shown in Eqn (7). The right-hand side of Eqn (11) is the fourth-order matrix dissipation terms. The
(11)
matrix dissipation gives the most accurate solution but is less stable because a smaller amount of dissipation is
added. As a compromise between accuracy and robustness, vector dissipation is adopted in this paper. For vector
dissipation, matrices PA, PB and PC are replaced by their corresponding radius spectra. In the curvilinear coordinates, ξI,
I=1, 2, 3, the maximum eigenvalue in the i-direction is given by
(12)
Multigrid Method
Multigrid is one of the most effective methods to accelerate the rate of convergence and should be used routinely in
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every production code. The approach in IFLOW substantially follows the ideas of Brandt [17] and James on [18]. Several
variations including V-, W-and F-cycles have been implemented. In general, W-and F-cycles are more efficient, but not
significantly so. More levels of multigrid cost a little more but are more efficient. For simplicity, most computations
performed with IFLOW use three levels of multigrid in the V-cycle. The multigrid method is used routinely in IFLOW.
For large scale computations on complex geometries, computational startup is often jumpy. For a smoother start, a
multigrid starting procedure is used. Consider a 3-level multigrid computation: A 2-level

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VALIDATION OF TAB ASSISTED CONTROL SURFACE COMPUTATION 477
multigrid consisting of the medium and coarse grids is run for about 50 cycles. The solution is then interpolated to the
fine grid to start the 3-level multigrid computation. In general, a solution adequate for engineering applications can be
achieved in 100–500 multigrid cycles. This efficiency is at least as good as the best Computational Fluid Dynamics
(CFD) codes available but is far from the Textbook Multigrid Efficiency (TME, less than 10 cycles) advocated by Achie
Brandt [19]. Achieving TME is a noble goal, and will have a significant impact on engineering applications of CFD.
Boundary Conditions
Only the solid wall and the farfield boundary conditions need to be discussed. At the wall, the three components of
velocity and the turbulent kinetic energy are set equal to zero, the pressure p is derived from assumption that the
pressure gradient normal to the wall is zero. Finally, the wall boundary condition of specific dissipation rate ω originally
given by Wilcox (p. 148 in [10]) is modified as
(13)
where Ωw is the vorticity at the wall and ao is a constant varying from a value of 6 given by Wilcox to 20. The choice
of ao may vary the convergence rate slightly but once convergence is achieved, the solution is about the same. The
motivation in deriving the modified wall boundary condition (13) is to get rid of the requirement that the first grid normal
distance must be given. The non-dimensional normal distance y+ requirement creates a difficulty for coarser grids because
the first grid normal distances tend to be too large in the coarse grids. With Eqn (13), the normal distance does not appear
and the y+ of the first grid normal distance of the finest mesh should be of the order 1 or 2.
At the far field, the gradients of the three components of velocity and the gradients of the two turbulence quantities
and ω are set to zero. The pressure is obtained by a non-reflecting condition discussed by Hedstrom [20], Rudy and
Strikverda [21] and Sung [22]. This is one of the most important boundary conditions for external flows and will be
outlined. The idea is based on the characteristic formulation of hyperbolic equations, such that the outgoing solution
modes will not be reflected back into the computational domain to corrupt the solution. To do this, the time derivatives of
the characteristic variables corresponding to the positive eigenvalue λ+ at the left boundary and the negative
eigenvalue λ_ at the right boundary are set equal to zero, i.e.,
(14)
(15)
R−1 R−1
q is the vector defined in Eqn (7) and is the matrix of the left eigenvectors. The matrix is quite complex for
general preconditioning. But for the simpler case of non-symmetric preconditioning, Eqn (14) is quite simple and is given
as Eqn (17) is used as the outflow far field boundary
(16)
(17)
condition of P* after the three components of velocity are specified.
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Two-Equation Turbulence Models
Several two-equation turbulence models have been implemented in the general-purpose code named IFLOW. It is
well known that the convergence of the two-equation turbulence models is rather temperamental. Two techniques have
been used in IFLOW and as a result the same convergence rate as in the case of the Baldwin-Lomax turbulence model has
been achieved. One of the techniques is the point-implicit method for source terms. Here, the positive part of the source
term is treated explicitly, the negative part implicitly. This technique is in fact quite widely used. The other technique is to
establish a lower bound for the specific dissipation rate ω by the Schwartz inequality. To illustrate the method, it is
sufficient to consider a linear Reynolds stress model

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VALIDATION OF TAB ASSISTED CONTROL SURFACE COMPUTATION 478
(18)
By Schwartz inequality, it can be shown that
(19)
Taking square of the both sides of Eqn (18) gives
(20)
A lower bound for ω is then obtained by combining Eqns (19) and (20) as
(21)
The proportionality factor in Eqn (21) can be taken as a value in the neighborhood of 2. Different values for this
factor can affect the convergence rate. But once the convergence is achieved, they all give about the same solution. The
value used in this paper is 2.1.
DESCRIPTION OF EXPERIMENT
As mentioned earlier, the control surface model consists of a stabilizer, a plain flap and a plain tab as show in
Figure 1. The control surface has NACA 0018 airfoil sections. Specifically, the tip chordlength is 8.40 in., root
chordlenght is 10.66 in., span is 8.44 in.. Both flap and tab gaps are 1/16 in. with the flap gap widened at both ends. At the
root section, the flap hinge axis is located at 7.63 in. and the tab hinge axis is at 9.70 in.. The entire control surface model
is mounted on a pedestal to place the model outside of any test section boundary layer.
The control surface model was tested in the semi-closed jet test section of the 24 in. water tunnel at David Taylor
Model Basin. The test section is 21 in. high by 27 in. wide with an area contraction ratio of 8.1. The control surface model
was hung vertically from the top. The strain-gaged stabilizer and flap dynomometers measured lift, drag, and torque about
their respective hinge axes. The tab dynamometer measured only torque about its hinge. But since the tab dynamometer
was fastened to the flap, the flap dynamometer measured the combined loads of the flap and the tab. The nominal test
speed was 10.9 to 12.0 ft/s.
Fig 1. Grid used in the computation of flow over an NACA 0018 airfoil with flap and tab
Based on a mean chordlength of 9.53 in., the Reynolds number is 9.7 x 105. Forces and moments of the TAC model
under various combinations of the angles of attack of the stabilizer and the deflections of the flap and the tab were
measured. The angle of attack of the stabilizer varied from −15 to +15 degrees, flap deflection from −27 to +27, and the
tab deflection from −60 to +60. The values of lift, drag, and torque coefficients are based on the mean chordlength.
Corrrections due to blockage, wall, and pedestal were made. The net blockage effects of the model on velocity were about
1.2% for the whole range of angles of attack. The true angle of attack of the model was 3.5% higher than the measured
value. The corrected values will be used for comparison with the computed results.
DISCUSSION OF RESULTS
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Convergence and Grid-Independent Solution
As Computational Fluid Dynamics (CFD) plays an increasingly important role in practical engineering applications,
it is important to have some idea about how accurate and reliable the computed solutions are. It is possible to perform
meaningful error analysis on a simple problem in a Cartesian computational domain with a uniform grid for inviscid or
laminar flows. However, it is not possible to analyze the order of accuracy of a spatial discretization scheme in a highly
stretched computational domain in a curvilinear coordinate system. The situation

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VALIDATION OF TAB ASSISTED CONTROL SURFACE COMPUTATION 479
becomes much worse with the additional complication from turbulence models. Efforts to quantify the errors in RANS
computations for practical problem shave produced dubious results. Nevertheless, attempts must be made to establish
confidence in the RANS solutions. The most important thing to do is to assure that the solution is monotonically
convergent. But this is not sufficient. It is well known that a nonphysical converged solution can be obtained. For
example, one can construct a coarse grid for a turbulent flow about a body with the nondimensional first grid normal
distance to the wall y+ on the order of several hundred and obtain a very nicely converged solution. But the solution will
not be close to the real physics because a turbulent boundary layer can not be developed for such a large y+ for a
conventional two-equation turbulence model. To resolve this difficulty, a sequence of finer grids must be used until the
change in the solution due to the grid refinement is small enough to be acceptable to engineering requirement. Thus a
careful check of convergence history and mesh refinement to obtain a grid-independent solution are the most effective
approach to establish confidence in the results. Other researchers as in e.g., [23] have adopted a similar view.
A C-grid with four blocks was used in the computation. The first block wraps around the entire control surface, the
second block is on top of the control surface, the third covers the gap between the stabilizer and the flap and the final
block covers the gap between the flap and the tab. The water tunnel is not modeled in the computation. A total of three
meshes were considered. The coarse mesh consists of 112x28x20, 44x8x8, 8x8x12, and 8x8x12 grid cells for the first,
second, third, and fourth block, respectively. This mesh consists of a total of about 65K grid cells. The medium mesh
doubles the number of grid cells in each curvilinear coordinate direction of each block and has a total number of grid cells
of about half a million. The fine mesh will have the number of grid cells increased by 50 percent in each direction of each
block of the medium mesh, giving a total number of grid cells of about 1.6 millions. It will be seen that the solutions
obtained by the fine and the medium mesh are almost identical, indicating that a grid independent solution has been
achieved.
The boundary conditions imposed are the following. The farfield boundary conditions at both the upper and lower
wakes are zero gradient for the three components of the Cartesian velocity, the turbulence quantities and ω, and the
nonreflecting boundary condition for the pressure. The nonreflecting boundary condition is important for good
convergence and accuracy as mentioned earlier. On the outflow boundary at the top of the computational domain are
imposed fixed values for the three components of the Cartesian velocity, the two turbulence quantities and ω, and zero
gradient of the pressure. Because of the presence of the pedestal, the symmetric boundary condition is applied at the
bottom of the computational domain. Non-slip boundary condition for the velocity and zero gradient for the pressure are
applied at the wall boundary. The turbulent kinetic energy vanishes at the wall and the dissipation rate at the wall has
been described earlier. For other boundaries such as between grid blocks and the interface between the upper and the
lower wake, exact boundary conditions are applied.
Some typical convergence histories of the root-mean-square of pressure for the case without flap and tab deflections
and the case with 20 degrees deflections for both flap and tab are shown in Figure 2, where residue is defined as the root-
mean-square value of the difference between the current calculated pressure and the last calculated one. It can be seen that
flap and tab deflections do not seem to affect convergence rate. The residues for both cases drop more than three orders of
magnitude in 200 multigrid cycles. The forces and moments become steady at about 200 multigrid cycles. It should be
noted that the drop in the residue due to the multigrid starting procedure has not been included in Figure 2. This explains
why logic10 (residue) starts at somewhere between −1 and −2, instead of 0.
Fig 2. Root-mean square residue of pressure vs. multigrid cycles
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VALIDATION OF TAB ASSISTED CONTROL SURFACE COMPUTATION 480
Forces and Moments
In the following discussion, the medium grid with a total of about half a million grid cells was used for the computed
results. The grid consists of four blocks with grid size of 224x56x40, 88x16x16, 16x16x24, and 16x16x24. The Reynolds
number based on the mean chordlength is 9.7x105. The coefficients of the forces and moments are also defined using the
mean chordlength as the characteristic length. The lift and drag coefficients will be defined as the total forces applied to
the entire control surface. The flap torque coefficient will include both the torque applied to the flap and the tab while the
tab torque coefficient will include the torque applied to the tab alone.
Figure 3 shows the comparison between measurement and computation of the lift coefficient as the angle of attack of
the stabilizer varies from −6 to +15 degrees with no deflections for both flap and tab. The error bars on the data show
10% discrepancy in measurements. The lift coefficient is almost linear indicating insignificant viscous effect in this range
of angles of attack. Both the predictions by the fine and the medium grids agree well with the measurement. However, the
coarse grid prediction starts to deviate form the measurement by more than 10% after an angle of attack of 9 degrees,
indicating insufficient grid resolution.
Figure 3. Comparison of calculated and measured lift coefficients with flap and tab at zero deflection
Figure 4 shows the comparison of the drag coefficient under the conditions as similar to those in Figure 3. Although
a grid independent solution has been achieved between the fine and the medium grids, the drag coefficient is
overpredicted by more than 20% in the neighborhood of the zero angle of attack and within 10% for greater than 10
degrees. The coarse grid prediction is even worse, again due to insufficient grid resolution. The effect on lift coefficient of
varying the flap deflection from −15 degrees to +15 degrees is shown in Figure 5, where angle of attack for the stern
stabilizer remains zero.
Figure 4. Comparison of calculated and measured Fig 5. Comparison of calculated and measured lift
drag coefficients with flap and tab at zero deflection coefficients with stern stabilizer and tab at zero
deflection
A grid independent solution has been achieved between the fine and the medium grid up to 10 degrees of flap
deflection. At 15 degrees of flap deflection, the fine grid prediction is still within 10% of the measured values but the
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medium grid prediction

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VALIDATION OF TAB ASSISTED CONTROL SURFACE COMPUTATION 481
degenerates rapidly. The coarse grid prediction is inadequate beyond 5 degrees of flap deflection. One physical feature is
worthy of mentioning. Consider a lift coefficient of 0.2 [Fig 3]. This lift can be achieved by an angle of attack of slightly
less than 6 degrees of the entire control surface. It can also be achieved by a flap deflection of about 10 degrees but at a
much smaller torque requirement. This is the essence of using a flap and also a tab which would be discussed later.
Finally, the effect on lift, flap torque, and tab torque coefficients of varying the tab deflection from—60 degrees to
+60 degrees are presented in Figures 6 through 8, respectively. Here, the stabilizer is at zero angle of attack and the flap
has no deflection.
Figure 6. Comparison of calculated and measured lift Figure 7. Comparison of calculated and measured
coefficients with stern stabilizer and flap at zero flap torque coefficients with stern stabilizer and flap
deflection at zero deflection
A grid independent solution has not been obtained in the calculation of the lift coefficient as shown in Figure 6.
However, the prediction of the lift from the fine grid is within 10% of measurement even at high tab deflection of 60
degrees. There is one discrepancy when tab deflection is less than 10 degrees. The slope of the measured lift is linear near
zero tab deflection but is not zero. The predicted slope is almost zero when tab deflection is less than 10 degrees. If the
measurement were correct, the discrepancy could be explained as insufficient grid resolution around the tab. The small
increase in the lift due to a small tab deflection has not been picked up even by a grid as large as 1.6 million grid cells. It
was mentioned earlier than a lift coefficient of 0.2 can be achieved by either an angle of attack of about 6 degrees of the
entire control surface or by a flap deflection of about 10 degrees. This lift can also be obtained by a tab deflection of 40
degrees with even smaller tab torque requirement. The comparison of the flap torque coefficient is shown in Figure 7. It
has a similar characteristic as the lift coefficient shown in Figure 6. A grid independent solution has not been achieved at
high tab deflection, and the slope near zero tab deflection is much flatter than the measurement. The predicted slope of the
tab torque coefficient near zero tab deflection seems to agree better with the measurement but the predicted torque
coefficient at high tab deflection deviates from the measurement by more than 10%. It should be noted that the tab torque
coefficient is smaller than the flap torque coefficient by approximately one order of magnitude. This is the main reason
that the tab assisted control surface is of great practical interest.
Figure 8. Comparison of calculated and measured tab torque coefficients with stern stabilizer and flap at zero deflection
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VALIDATION OF TAB ASSISTED CONTROL SURFACE COMPUTATION 482
CONCLUSIONS
A numerical procedure for the prediction of the forces and moments of a tab assisted control surface has been
developed. The procedure is based on solving the incompressible Reynolds-averaged Navier-Stokes equations coupled
with a -ω, turbulence model. Computed results of lift, flap, and tab torque coefficients were compared with the measured
data at a Reynolds number of 9.7x105 based on the mean chordlength. Three meshes with grid size of 65K, one half
million, and 1.6 millions were used to investigate the grid independent solution. A grid independent solution was
achieved in most of the cases except for some cases with high flap and tab deflections. The trend of the changes in the
forces and moments due to the variations in the angle of attack of the stabilizer and the deflection of the flap and tab has
been completely captured. In most cases investigated, the predictions are within 10% of the measurements. Some
exceptions are the tab torque coefficients at high tab deflections and the slopes of the lift and flap torque coefficients near
zero tab deflection. It is suggested that both the turbulence model and the grid resolution need to be improved. The fact
that even with a grid as large as 1.6 million cells, a grid independent solution can only be achieved in most, but not all
cases, indicates that more efficient numerical schemes and turbulence models are urgently needed. Despite all these
limitations, the predictive procedure presented here is already a useful tool for the design of efficient control surfaces.
ACKNOWLEDGMENTS
This work is funded by the Office of Naval Research, Code 333, under the Mechanics and Energy Conversion
Science and Technology Division (PE0602121). Dr Patrick Purtell is the technical monitor of this program. Dr. Nguyen
Thang is the monitor at David Taylor Model Basin. Helpful discussions of experiment and measured data with Mr. David
Bochinski at David Taylor Model Basin are gratefully acknowledged. Computer resources provided by the Department of
Defense High Performance Computing Modernization Office (DOD-HPCMC) at NAVO and the Arctic Region
Supercompting Center in Fairbank, AK are also gratefully acknowledged.
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VALIDATION OF TAB ASSISTED CONTROL SURFACE COMPUTATION 484
DISCUSSION
Y.Tahara
Oskaka Prefecture University
Japan
In your computation, laminar-to-turbulent flow transition was not considered, although your experimental condition
(i.e., Re≈106) apparently implies that there exists laminar-flow region on the wing (stabilizer in your definition) surface.
Inclusion of the effects is generally essential for accurate prediction of hydrodynamic forces especially for drag
component [Tahara et al., 1998, 2000]. In addition, the conventional two equation model used in your work may not be
suitable for the purpose.
REFERENCES:
Tahara, Y., et al., “An Application of RaNS Equation Method to Strut/Bulb Configuration of America's Cup Sailing Yacht and Comparison with
Experiments,” J. Kansai Society of Naval Architects, No. 230, 1998, pp. 163–171.
Tahara, Y., et al., “Development of Ballast Bulb for IACC Sailing Yacht—Especially for Investigation on Basic Low Drag Form,” J. Kansai Society of
Naval Architects, No. 234, 2000, pp. 51–59
AUTHOR'S REPLY
Due to a relatively high turbulence level in a water tunnel, early experimental tests indicated that the flow was
turbulent at a Reynolds number of about one million based on a mean chordlength of 9.53 inches. For this reason,
computations were made assuming the flow was completely turbulent. Transition from laminar to turbulence was not
considered. Admittedly, turbulence models are not perfect for a complex flow such as the one investigated here. However,
the −ω turbulence model used here worked quite satisfactorily in our opinion. It is believed that further improvement of
accuracy can be made by increasing the grid size, particularly in the leeward side of the flow region. This will be
investigated in the future.
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