Hydroelastic Considerations in Ship Panel Design

M.E. McCormick, Ph.D., Sc.D., R. Bhattacharyya, Dr. Ing., and S.E. Mouring, Ph.D.

Hydroelastic Considerations in Ship Panel Design ABSTRACT Panels and all other structural components of surface ships and submarines vibrate when the vessel is underway. The vibratory motions are primarily excited by the power plant. At operational (design) speeds, panels vibrate in their fundamental modes and those associated with their higher harmonic frequencies. The panel motions have rather well-defined energy spectra, which depend on both the structural design, position of the panel and the rotational speed of the single or multiple power plants. The panel motions will interact with the vortices in the adjacent turbulent boundary layer. The interaction can result in either an increase in the frictional drag or a decrease. Because of this, the argument is made that the designs of the panels and their support systems should include considerations of this hydroelastic effect.

Introduction he frictional resistance of a surface ship or a submarine is a major consideration in the design of the power plant of these vessels. This component of resistance includes contributions from the boundary layer and the wake. The nature of the flow in the boundary layer plays a part in determining the position of the flow separation and, hence, the size of the wake. In addition, the transition from laminar to turbulent flow in the boundary layer occurs near the bow at operational or design speeds. Hence, most of the hull is enveloped in a turbulent boundary layer. Hull panels vibrate beneath the turbulent boundary layer in the longitudinal, transverse and normal directions when the vehicle is underway. These vibrations are primarily due to the power plant of the vessel. In this paper, the possible effects of the forced vibrations on the adjacent boundary layer are examined, and considerations of these hydroelastic effects in the panellsupport structural system are discussed.

Review of Hydroelastic Studies Let us first state that the term “hydroelastic” is used in this paper to indicate stable fluid-structure interactions. Unstable interactions, such as panel flutter, are not included in the discussions herein. The effect of stable active-panel motions on boundary layer turbulence has received little attention. Consideration of this phenomenon could be important in the hydrodynamic design of a ship or submarine, as discussed by McCormick and Mouring (1993, 1995). Most of the past studies of boundary layer-structure interaction stems from an interest in self-noise, or radiated sound. It has been recognized that the boundary layer turbulence could excite various modes of hull panels which, in turn, radiate sound. In the 195Os, primarily due to self-noise problems of submarines, attention was directed at the phenomenon of turbulent boundary layer-induced vibrations. Two significant works of that decade resulted in the papers of Lyon (1956) and Dyer (1959). In the 196Os, many papers on the subject appeared, including those by el Baroudi et al. (1963), Maestrello (19651, McCormick (1966) and Izzo (1969). The field of study of boundary layer-induced vibrations gave rise to the study of drag reduction by compliant surfaces. An excellent summary of this drag reduction technique is presented in the book edited by Bushel1 and Hefner (1989). Studies of compliant structure drag reduction were also being performed in the former Soviet Union by Levina (1977) and others. The publications resulting from most of these studies have not been translated into English. The assumption in this paper concerning the “compliance” of the panels is that the primary panel motions are caused by the power plant and not by the turbulence. Hence, the feedback effect is considered in the fluid-structure problem to be of second order.

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Hydroelastic Considerations in Ship Panel Design

Nature of Boundary Layer Turbulence In order to understand the effects of panel motions on boundary layers, we must first understand the nature of boundary layer turbulence. Over the length of a long hull, where the pressure gradient in the flow direction is small, the boundary layer can be approximated by that on a flat plate in a zero pressure gradient. We assume that this approximation is valid since there are many publications devoted to the nature of turbulent boundary layers on flat plates. Several of these summarize the significant theoretical and experimental works on the subject. These include the book edited by Kline and Afgan (1988), and the papers by Fiedler (1988), Bernard et al. (1990) and Bushnell (1991). The most important to the present study is the information on coherent structures in the turbulent boundary layer. These structures are recognized as the primary contributors of turbulent energy. The term coherent structure includes several vorticular structures, including rectilinear vortices, horseshoe vortices and streaks. These three coherent structures a r e simply different stages of a single structure (the rectilinear vortex), as illustrated in Figure 1. That vortex forms and absorbs energy from some external source over its travel length. Some transverse portions absorb more energy than others. These higher-energy portions grow rapidly and migrate ahead of the lower-energy portions and away from the panel. As they migrate, the higher-energy portion of the vortex is deformed and takes on a “horseshoe” shape. When the external flow velocity is high, then the horseshoe vortex is stretched and becomes a “streak,” i.e., an elongated horseshoe. Whether a horseshoe or a streak, the

head of the structure can eventually “burst,” after which the energy of the structure is randomly disbursed in the flow. This bursting causes the outer “edge” of the boundary layer to be wavy. The formation of the vortices in the boundary layer is also random in both time and space.

Analysis of Compliant Panel Effect on the Drag TIME-AVERAGED BOUNDARY LAYER PROPERTIES In this section, results of both the origmal analyses outlined by McCormick and Mouring (1993) and modified by McCormick and Mouring (1995) are presented here (without derivation) to support the argument that power plant induced hull panel motions can “positively” affect the boundary layer turbulence, so as to reduce the friction on the hull. From those references, the kinetic energy in a convecting two-dimensional vortex within a semicircular fluid boundary over a rigid panel is

E,

=

2.61 Kpcya

(1)

where: K is a constant p is the mass-density of the water c is the convection speed of the vortex in the flow direction y is the vorticity a is the radius of the semicircular bounding streamline From Equation (l),we see that the kinetic energy of the vortex is linearly proportional to both the convection speed and the radius. Hence, any external influence on the vortex that can reduce its size must absorb energy. If the plate length in the flow direction is L , then the time of travel of the vortex over the plate is 1 2

t,=

J-: L.’

See Figure 2 for the notation. von Karman (1921) found that the time-averaged velocity profile outside the wall layer is well-represented by the seventh-power law, for Reynolds numbers to 10’. That is, the time-averaged velocity varies in the direction away from the panel according to I i

-

u

a.

b.

C .

F I G U R E 1. Phases of the morphological transformation

of a coherent structure in a turbulent boundary layer. The formed vortex (a) first becomes a horseshoe vortex (b) and (c), then a streak (d) and, finally, the head of the streak “bursts” (e). 62

u

=

d.

where the overhead bar indicates time-averaging and, referring to Figure 3 6 is the boundary layer thickness z is the coordinate normal to the panel

U is the free-stream velocity (ship velocity) September 1997

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Hydroelastic Considerations in Ship Panel Design

F I G U R E 2. Sketch of a Convecting Semicircular Vortex

See the book by Schlichting (1960) for details. The shear stress on the panel corresponding to the velocity distribution in Equation ( 3 ) is found to be T,,

=

0.0225 pv'"U7'"(8)-'"

(4)

where v is the kinematic viscosity of the fluid. The resulting boundary layer-induced drag on the rigid panel located at 5 = 1 from the leading edge of the long plate composed of the panels (or bow of the ship, as in Figure 4) is

F,

=

0.097pU2 (AS),

(5)

where, from Schlichting (1960), the time-averaged boundary layer thickness in 1 < < 1 + L is

<

(6)

Over the panel, the change in the boundary layer thickness is (A%,

=

E,,,

-

6,

(7)

F I G U R E 4. Sketch of a panel of a ship hull. The origin of 6 is the vertical plane through the water plane at the bow.

The expression in Equation (5) shows that drag is directly proportional to the change in the boundary layer thickness over the length of the panel. Hence, any energy source that causes an increase in the downstream thickness will increase the drag. If the panel is active (excited by the power plant), then its vibratory motions may cause either an increase in the downstream boundary layer thickness, thus increasing the drag, or a decrease in the thickness, in which case the drag is reduced. PANEL MODES

Consider the active panel illustrated in Figure 5. In the illustration we see that the panel length is L, the width is W and the displacement of an element of the panel from the coordinate plane is T. The panel is assumed to be excited by some external driving force at its edges. To avoid the feedback problem, the panel is assumed not excited by the turbulent pressure fluctuations in the boundary layer. The panel is assumed to be clamped on the edges. We assume a Galerkm-type solution of the equation of motion in the z-direction, which is M*v

-q =

c B,,,.X,Jx) YAY)

(8)

mY,O

n, n

Laura and Duran (1975) approximate the spacial functions of Equation (8) by X , ( x ) Y,(y) = (ax"

+ p xL +

1) (cu'y4

X , ( x ) Y,(y)

= ( a x4

+

p xL

+

1) (E' y"

+

B'yZ

+

1)

+ K' y4 + yL)

(9) (10)

etc., where, from the boundary conditions for a clamped plate, F I G U R E 3. Time-Averaged Velocity Profile in a Turbulent Boundary Layer NAVAL ENGINEERS JOURNAL

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Hydroelastic Consideralions in Ship Panel Design

ALTERATION OF THE TURBULENT BOUNDARY LAYER BY THE PANEL MOTIONS Our analysis is directed toward that portion of the energy available that is absorbed by the passing vorticular structures at a point on the panel. For the sake of illustration, the analysis is confined to two-dimensional motions of the panel. McCormick and Mouring (1993, 1995) derive the expression for the energy available from a point on the active panel over a time t,]. That expression is

where the single subscript of B indicates the fundamental two-dimensional mode. The mathematical expression for the energy absorbed by the adjacent vortex passing over the point on the panel is found by using Duncan’s (1986) pressure expression. The resulting expression for the energy absorbed (per unit area of plate) by the boundary layer at the interface is the following:

F I G U R E 5.

Notation for the Panel Vibrations

and

The time function in Equation (8) depends on the nature of the excitation. Assume that the exciting force on the plate is both uniform and sinusoidal in time. That is, F(x,y,t) = F (t) = F,, cos(w, t )

(13)

where w, is the circular frequency of the excitation. The amplitude of the forcing function is absorbed in the modal coefficient, B, The expression for the response of the plate in Equation (8) is M L

rl =

c B,,,

,J,,,(X)

nr

Y,,W COS(O

McCormick and Mouring (1993, 1995) assume that fluid motions induced by the panel motions are irrotational. With this assumption, they find that the energy transferred to the fluid is obtained from

E,,

=

0.309pw,’BB,,WL

(15)

From this result, we see that the energy transferred can be increased by increasing either the length or width of the panel. 64

In Equation (17) the coefficient C,,(w,) is called the “receptivity” coefficient. This coefficient determines the amount of energy absorbed by the vorticular structure as it passes a point on the active surface. This coefficient and the function (f) of travel distance x over the plate and time of travel tDmust be determined experimentally, although McCormick and Mouring (1993, 1995) give a mathematical expression for the function. For very low frequencies, we would expect little of the energy to be transferred to the far field of the fluid. For high frequencies, most of the energy would be kept in the near field, near the boundary layer. From the mathematical expression of (f) derived by McCormick and Mouring (1993, 1995), there is also a “sympathetic” frequency condition when w, = m / l 2 a , which is similar to a resonant condition. The purpose of this paper is to lay a foundation for further studies in turbulent boundary layer changes through the design of panel structures, with the ultimate goal of reducing the frictional resistance at operational ship speeds. For this reason, the energy expression is left in the form of Equation (17).

Discussion and Conclusion Vibrating panels on surface ships and submarines are a fact of life. There have been a number of successes in quieting the near-field noise radiating from these panels. However, the fact remains that the panels still vibrate in response to excitations by power plants. Since hull vibraSeptember 1997

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Hydroelastic Considerations in Ship Panel Design

tions are a reality, it is recommended that panel vibrations be considered in hydrodynamic designs. The authors believe that this can be accomplished without compromising the structural integrity (strength or fatigue) of vessels. Simply put, the thickness, length and width of panels can be designed to reduce the frictional drag on ships at operational speeds. In order to accomplish this design optimization, much more information is required concerning vibrating panel effects on boundary layers. At the present time, there is no clear picture of the effects of active panels on boundary layer turbulence. That is, it is not clear whether vibrating panels increase or decrease surface ship drag. There are two theoretical approaches to the problem that could improve our knowledge of the phenomenon. The first can be considered to be microscopic in nature and concentrates on the formation, convection and alteration of the coherent structures in boundary layers adjacent to active panels. There is much information concerning coherent structures on rigid panels, but little exists on the subject of coherent structures on active panels. The second approach can be considered to be macroscopic, concentrating on the actual drag reduction or drag increase caused by active panels. From the mathematical results presented herein, we conclude the following: A. From Equation (1):when panel motions are such that the size of the boundary layer vortices are reduced, the panel absorbs hydrodynamic energy. B. From Equation (5): if the panel motions can retard the growth of the boundary layer over the panel, then the drag on the panel will also be reduced. It then follows that if the drag reduction results in a few percent reduction in fuel consumption at operational speeds, the design effort could be cost-effective. C. From Equation (15): the energy transferred from the vibrating panel to the boundary layer is proportional to both the length and width of the panel. Hence, the plate size can be altered to obtain a hydroelastically optimal design. There are no significant experimental data available to determine the functional form of the receptivity coefficient of Equation (17). That is, the dependence of the coefficient on the driving frequency is unknown. Possibly, some frequencies could reduce the effects of the coherent structures on the surface drag, while others could result in an increase in drag. In addition to the excitation frequency, there may be a phase relationship between the plate motions and the fluid pressure oscillations at a point. All of these aspects of active-panel effects on the boundary layer structures should be determined by experimental studies. 4REFERENCES H e r n a r d , L). C . , F. H. H a r l o w , R. M . R a n e u z a h n and C. Zemack, “Spectral Transport Model for Turbulence,” Los Alarnos National Lab. Rept. LA-11821-MS, UK-910, July 1990. Bushnell, D. M., “Turbulence Modeling in Aerodynamic Shear NAVAL E N G I N E E R S J O U R N A L

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Flow: Status and Problems,” Proceedings, 29th Aerospace Meeting (AIAA), Paper 91-0214, January 1991. Bushnell, D. M. and J. N. Hefner, editors, Viscous Drag Keduction in Boundary Layers, Progress in Astronautics and Aeronautics (AIAA), Vol. 123, 1989. Duncan, J. H., “The Response of an Incompressible, Viscoelastic Coating to Pressure Fluctuations in a Turbulent Boundary Layer,” Journal of Fluid Mechanics, Vol. 171, 1986, pp. 339-363. Dyer, I., “Response of Plates to a Decaying and Convecting Random Pressure Field,” Journal of the Acoustical Society of America, Vol. 31, No. 7, July 1959, pp. 922-928. el Baroudi, M. Y., “Turbulence-Induced Panel Vibrations,” University of Toronto, UTIAS Report 98, February 1963. Fiedler, H. E., “Coherent Structures in Turbulent Flows,” Progress Aerospace Science, Vol. 25, 1988, pp. 231-269. Izzo, A. J., “An Experimental Investigation of the Turbulent Characteristics of a Boundary Layer over a Vibrating Plate,” General DynamicsiElectric Boat SUBIC Report U417-69-049, May 1963. Kline, S. J. and N. H. Afgan, editors, “Near-Wall Turbulence,” Proceedings, Zoran Zaric Memorial Conference, Dubrovnik, Yugoslavia. Published by Hemisphere Publishing Co., New York. 1988. Laura, F! A. A. and R. Duran, “Vibrations of a Clamped Rectangular Plate,” Journal of Sound and Vibration, Vol. 42, 1975, pp. 129-135. Levina, S. M., “The Effect of Elastic Boundary Compliance on the Spectrum of Pressure Fluctuations in a Turbulent Flow,” Fluid Mechanics-Soviet Research, Vol. 6, No. 2, March-April 1977, pp. 128-140. Lyon, R. H., “Response of Strings to Noise Fields,” Journal of the Acoustical Society of America, Vol. 28, No. 3, May 1956, pp. 391-398. Maestraello, L., “Measurements of Panel Response to Turbulent Boundary-Layer Excitation,” A I A A Journal, Vol. 3, No. 2, February 1966, pp. 359-361.McCormick, M. E., “Turbulent Boundary-Layer Induced Vibrations of Ribbons,” David Taylor Model Basin Rept. AVL-136.943, August 1966. McCormick, M. E. and S. E. Mouring, “On the Effects of ActiveSurface Motions on Coherent Turbulent Boundary Layers,” U. S. Naval Academy E n p e e r i n g Report EW-21-93, November 1993. McCormick, M. E. and S. E. Mouring, “On the Hydrodynamic Design of Active Panels of Marine Vehicles,” Journal of Offshore Mechanics and Arctic Engineering, (ASME), Vol. 117, No. 4, November 1995, pp. 290-294. Schlichting, H., Boundary Layer Theory, McGraw-Hill Book Co. 1960. von Karman, T., “Uber laminare und turbulente Reibung,” Zeitschriftfiir angewandte Mathematik und Mechanik, 1921, p. 233. Dr. Michael E. McCormick is a research professor of civil engineering at The Johns Hopkins University. Before joining the Hopkins faculty in 1994, he was a professor of ocean engineering for twenb-five years at the U.S. Naval Academy. I n addition, he has held full-time faculty positions at Swarthmore College, Trinity College (Hartford) and the Catholic University of America. He was also a hydrodynamicist at the David Taylor Model Basin for more than four years. Prof: McCormick received his undergraduate degree in mathematics and physics from American University, a masters degree in applied mechanics and a Ph.D. 65

Hydroelastic Considerations in Ship Panel Design

in mcchanical cnginecringfrom Catholic Universi&, a Ph.U. in civil engineering und a Sc.D. in engineering science from Trinity Colkgc in Dublin, Ireland. He has over 100 publications including two books in the areas of ocean engineering wave mechanics und ocean wuve energy conversion. He has also edited two books deuling with occan engineering. I n addition, he is co-editor of both thp journal, Ocean Engineering, and the Elsevier book series in ocean engineering.

Dr. Rameswar Bhattacharyya is professor of naval architecture ut the US.Naval Aademy, where he has served f i r

twenty-six years, and adjunct pro&ssor of mechanical engineering at The Johns Hopkins University. Prior to joining the Naval Acadcmy faculty, he was a faculty member in the Department of Naval Architecture und Marine Engineering at the University of Michigan. His rcsearch experience includes ten years at both the Lubecker Flender- Werke und the Hamburg Shio Model Basin in Germun.y. His research has led to numerous publications including two books, one in the area of ship dynamics and the other in

66

the area of computer-aided sh$ design. Prof: Bhattacharyya received his undergraduate degree in naval architecture from the Indian Institute of Technoloa, and his doctorate in engineering from the Technical University of Hanoves Germany. I n addition, he holds a n honorary doctorate from the University of I/eracruz. With Prof. McCormick, he co-edits both the journal, Ocean Engineering, and the E lsevier book series in ocean engineering. Dr. Sarah E. Mouring is a n assistant Professor of ocean engineering at the U.S. Naval Academy. Her research has concentrated on both the reliability of structures and ocean engineering, and naval architecture applications of composite materials. Professor Mouring received her zlndergruduate degree in civil engineering from the University of Delaware. Her master’s degree and Ph.D.. both in civil engineering, were earned at The Johns Hopkins University. Her research has resulted in numerous publications. She holds membershtjx and committee positions in several professional organizations, and is a technical panel member for the National Scieme Foundation.

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