Experimental determination of variation of hydrofoil flutter speed with mass ratio

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7.

AR,CF-k&

EXPERIMENTAL DETERMINATION OF

VARIATION OF HYDROFOIL FLUTTER SPEED

WITH MASS RATIO

by Guido E. Ransleben, Jr. FINAL REPORT Contract No. N00014-69-C-0219 SwRI Project 02-2584 Prepared for

Department of the Navy

Naval Ship Research and Development Center Washington, D. C. 20007

April 1970

This research was sponsored by the

H yd rom ech a n ics Laboratory

of the Naval Ship Research and Development Center under Naval Ship Systems Command

Subproject SS 4606, Task 1703

This document has been approved for public release and sale;

its distribution is unlimited

Lab. Y, Snhe. :1",77,1101UW/4V4Z

Tec1,1r.^7,',1:;/'

Delft

SOUTHWEST RESEARCH INSTITUTE

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EXPERIMENTAL DETERMINATION OF

VARIATION OF HYDROFOIL FLUTTER SPEED

WITH MASS RATIO

by Guido E. Ransleben, Jr. FINAL REPORT Contract No. N00014-69-C-0219 SwRI Project 02-2584 Prepared for

April 1970

This research was sponsored by the Hydromechanics Laboratory

of the Naval Ship Research and Development Center under Naval Ship Systems Command

Subproject SS 4606, Task 1703

This document has been approved for public release and sale;

its distribution is unlimited

Reproduction in whole or in part is permitted for any purpose of the United States Government

Approved:

H. Norman Abramson, Director

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ABSTRACT

A description of the design and fabrication of a family of four hydro-foil flutter models is given. These models had identical geometric and

elastic properties, differing only in mass ratio (0. 2 < < 1.0). The heaviest was a direct half-scale model of an earlier flutter model.

A flutter point was approached to within an estimated 1 /2 knot with the heavier model, and it was near the value predicted by scaling

considera-tions. No flutter points were measured with the three remaining models, however, as the torsional divergence speed was lower than flutter speeds for them. This was rather unexpected, as the elastic axis was at the quarter-chord--usually considered to be far enough forward to ensure a high divergence speed.

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TABLE OF CONTENTS. Page INTRODUCTION IL DESIGN 2, Gene ral 2 Model Spar 3 Model Segments 4 Support System

FABRICATION AND ASSEMBLY 9

A. Spars

Segments

9,

10

C. Ballasting and Assembly 10

D,, Support System 12,

IV. TEST PROCEDURE 13

A. General 1,3

B. Frequency Measurements 13

C., Tunnel Tests 13'

CONCLUSIONS AND RECOMMENDATIONS

REFERENCES 16

TABLE AND ILLUSTRATIONS 17

1

6

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I. INTRODUCTION

The state-of-the-art with respect to the flutter of hydrofoils and other lifting surfaces in water is still in an uncertain state of development. Several theoretical treatments have been made in the past few years, most

of which are in poor agreement as mass ratios (ratio of the mass of the structure to that of the surrounding cylinder of water) near or less than

unity.

Until recently, these treatments have agreed to the extent that they all predicted an asymptotic increase in flutter speeds at these low mass ratios--differing mainly in the values of mass ratio at which the sharp

upturn begins, Yates, however, in 1968 presented in a theoryl* which showed an increase in flutter speed with decreasing mass ratio only to a peak, and then a sharp downturn towards zero velocity at zero mass ratio. This theory was applied by Yates to the SwRI flutter model of 19632 and

yielded a conservative prediction on that model of mass ratio p, = 0. 99, before peaking at a mass ratio p, ".=. 0. 3, as mass ratio was decreased.

A hindrance to evaluation of these theories has been the lack of

sufficient experimental flutter points for purposes of correlation. Few well-defined experimental points have been measured experimentally with models of well-determined properties.

The purposes of the present program were twofold.

First, a family

of four models was fabricated to determine the effect of mass ratio on

flutter speeds, to low enough values of mass ratio to check the Yates theory. The second purpose was to check the validity of scaling, since the heaviest model was to be a half-scale model of the 1963 SwRI model. 2

As shall be described later in this report, the second objective was met but the first was not, as the torsional divergence speed unfortunately turned out to be lower than the flutter speeds of the three lighter models.

This report describes the design and fabrication of the models.

Since the test data were collected and are being reduced by NSRDC personnel,

only a brief description of the test program will be given here. The results

will be published later as an NSRDC Technical Report.

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II, DESIGN

A. General

The four models were to be identical except for mass ratio, the

heaviest one being a half-scale model of the flutter model which was success-fully tested in 1963, under Contract Nonr-3335(00), 2 The geometric

proper-ties were therefore predetermined (Fig. 1). Thus, the models were designed

as straight rectangular foils of semispan 5 times the semichord, with a

NASA 16-012 airfoil section. The elastic axis was fixed at the quarter-chord, (a = -1/2), and the center of gravity at 51.2-percent chord, from which the

nondimensional c, g0 location xa = 0,524. The design radius of gyration about the elastic axis (rab) was 2,135 in., from which the square of the

non-dimensional radius of gyration ra2 = 0. 507.

In order to ensure that flutter speeds for the models would be within the 50-knot capacity of the 36-in, water tunnel, a velocity scale of one-half of the original model's flutter speed was arbitrarily chosen for the heavy model, so that it should flutter at about 24 knots.

The heavy model had to have the same mass ratio (m/Trpb2) as the original, and operate at the same reduced frequencies (k = bw/U). Gravity

and water density, of course, were also the same as the original model. Combinations of the above fixed or arbitrary model-to-original parameter

ratios yield the remaining scale ratios. Thus, all frequencies are the same

as the original model, the mass per unit span is 1/4 of the original, and the bending and torsional stiffnesses, El and GJ, are 1/64 of the original.

The resulting design properties common to all four of the models are summarized as follows:

Parameter Definition Model Value

a dimensionless distance from

midchord to elastic axis, positive aft

semichord, inches

r2 dimensionless square of radius

a _{of gyration about elastic axis}

xa dimensionless c, g0 location

aft of elastic axis

El bending stiffness, lb-in2

-0. 500 3 0. 507 0. 524 53, 100 1

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The design mass ratio (m/Trpb2) for the heavy model was 0.99. Mass

ratios for the other three models were arbitrarily chosen at 0. 20, 0.40, and

0.65. It was not possible, however, to obtain the latter value with available materials; the final value for this model was approximately 0.46.

In order to preserve the greatest possible similarity with the original model, these models had the same number of rigid segments (15) attached

to a single spar.

The spar extended past the root end of the models, to be clamped in a housing flush with the bottom of a reflection plate. The housing could

rotate within an enclosure on top of the reflection plate, to allow trimming the angle of attack to zero. Provision was also made inside the enclosure for exciting the models by twisting the model tip through a rod and suddenly

releasing it. The resulting oscillatory decay was recorded during the tests, for damping versus velocity measurements.

The support system, consisting of the enclosure, housing and reflec-tion plate, was designed to attach to an existing bracket inside the open jet test section of the NSRDC 36-in, water tunnel, so that the model tip was located at the tunnel centerline.

Design of individual elements is detailed in the following sections.

B. Model Spar

An H-beam type of spar similar to that of the original model would not have been practical for these models, as the flanges would have to be exceedingly thin in order to obtain the proper stiffnesses. The final con-figuration of the spar (Fig. 2) consisted of two spanwise bending members connected by torque bars, all machined from a solid bar. Sizing of the

members was determined experimentally, as the torsional stiffness of this type of construction is difficult to calculate. An exciter rod was fastened to the spar tip, and run freely through the spar, for excitation by twisting and suddenly releasing the spar tip.

With the elastic axis (spar centerline) at the quarter-chord, torsional divergence was thought not to be a problem (particularly since this was not a problem with the original model), but the small section necessary to obtain the proper stiffnesses was potentially subject to failure in bending due to lift forces induced by small misalignments to the flow (angle of attack other than zero) or by twisting the tip for excitation of the models.

Spanwise lift distributions due to angle of attack (Fig. 3) and to tip twist (Fig, 4) were calculated by the Anderson Method, as outlined by Abbott and Von Doenhoff3, so that the strength requirements of the spar could be

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determined, Angles of attack and tip twist angles which generate yield stresses in bending due to these lift distributions are plotted, for several values of yield stress, versus velocity in Figures 5 and 6.

It is readily apparent that, even for very small angles, high values

of yield strength are required near the maximum tunnel speed of 50 knots.

A maraging steel with a yield strength of 350, 000 psi was therefore selected for the model spars. Even for this strength, the tip twist angle was restricted

to 2 degrees, and possible misalignment to 1 degree at the higher tunnel speeds, to allow a margin of safety. Provision was made, however, for tip twist angles of up to 5 degrees at the lower speed range (up to 20 knots).

C. Model Segments

It was felt that the simplest way to fabricate the segments would be to cast them as solid sections, adding ballast to obtain the correct c, g. and radius of gyration, It then remained only to find materials of the proper densities which would, after ballasting, yield the desired mass ratios,

The segments were designed as shown in Figure 7. The pattern was

made slightly oversize, particularly at the trailing edge, to allow for final

finishing to a smooth contour after assembly of the segments on the spar. The width of the segments was approximately 15/16 inch. Since the

segments were mounted on 1-in, centers, a 1/16-in, gap was left between

segments, to be sealed after assembly with an RTV silicone compound.

A cored hole was provided to just slip over the spar for a 1/4-in.

width at the segment center and leave clearance over the spar from the

center to each side, The segments were bonded to the spar with an epoxy

adhesive. With this configuration, addition of the segments to the spar

would have a minimal effect on the spar stiffnesses.

In order to determine the material densities required to obtain the

desired mass ratios, several trial segments were cast and finished to final

contour. A dummy spar section of 1-in. width was machined and inserted

into each of these segments, which were then weighed, balanced to determine

the c. go , and swung as pendulums to determine the radius of gyration about

the c. g. Average values thus determined were Ws = 2, 57w + 0. 06 8, 03w + 0. 09 2057w + O. 06 20 57w [2 + (3, 13 -7s)2] + 000061 + 0. 06 (Tcs - 1050)2

,

2. 57w + 0. 06 (1) (2) s (3),

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where

Ws - weight of segment and spar, lb

- specific weight of segment material, lb/in3

- c g. location of segment and spar, inches aft of leading edge

rs- - radius of gyration of segment and spar about c. g. , in.

The desired final values for c. g. location and radius of gyration are XT- = 3. 073 in.

= 2, 085 in2

4 = 4. 56

in2 where

XT- - c. g. location of total configuration (including ballast), aft of

leading edge

rT - radius of gyration of total configuration about c. g. rT - radius of gyration of total configuration about c/4

Referring to Figure 8, the ballast required to satisfy the c. g. and radius of gyration is determined as follows:

dEWE = dsWs , where ds = 3. 073 - )7s ds = _dB W_s TT-T2 = 2. 085 WT = 2.085 (Ws + WE) = W5(F2s + + WBdi (6) from which _2 2 ds 2 2. 085 (Ws + Ws) = Ws(rs + ds) + Ws dB CLB 5 (7) or = - (4) (5)

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or

W5ds(dB)2 + W5[(72s + d2s) - 2. 085] (dB) - 2,085 Wsds = 0 (8)

Equation (8) is a quadratic which may be solved for the value of dB. The weight of ballast, WB, required is then determined from Equation (5), and the total weight, WT, is determined from the sum of Ws and Wg. The

resulting mass ratio, then, is

WT WT

=

g-rrpb2 1,020

Figure 9 is a plot of mass ratio versus material specific weight as determined from the above relations. From this plot, the mixtures for the various model segments were derived. For the model of mass ratio p, = 0, 99, the material must have a specific weight of about 0,36 lb/in3. This was

determined to be satisfied by an alloy of 73 percent lead and 27 percent tin. The p, = 0. 20 specific weight must be about 0.028 lb/in3. Stycast 1091 SI,

an Emerson & Cuming syntactic foam (modified epoxy filled with glass

microballoons) has just this value, and was used as received, The p, = 0,40

specific weight is about 0.113 lb/in3. A mixture of 46 percent Rezoline F/933A modified epoxy and 54 percent lead powder was selected for this

density. For the remaining model, it had been planned to use 1.J. = 0. 65. The

practical highest specific weight for the lead-filled plastics, however, is about 0.15 lb/in3 which results in pi 0. 50 (adding more lead powder results in a nonpourable mixture). The lowest specific weight with the lead-tin alloys is about 0.26 lb/in3, which results in p. z 0. 75. The range 0. 50 < p.

<0.75 can therefore not be met with these materials. A mixture of 41 percent Rezoline 30/932B and 59 percent lead powder was used, resulting in p. 0. 46.

Support System

The support system had to perform four functions: (1) rigidly canti-lever support the models in the open-jet test section of the NSRDC 36-in. water tunnel, (2) provide a reflection plane at the model root, (3) provide a

capability of trimming the models to a nominal zero angle of attack, and (4) provide a means of exciting the models by deflection and sudden release, for decay measurements.

The basic structure of the system (see Figs. 10 and 11) was designed as an aluminum weldment enclosure with a NASA 16-022 airfoil cross section, with removable access panels on both sides. Stiffened aluminum wide-flange

beams welded to the top of the enclosure were mated to an existing bracket inside the test section for support. A reflection plate made of hard-coated aluminum tooling plate was bolted to the bottom of the enclosure with

counter-sunk flat-head screws. All edges of this plate were bevelled on the top side to a sharp edge, to minimize cavitation on the lower surface,

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A turntable, made of 17-4PH stainless steel, was set into a housing, also made of 17-4PH, mounted in the floor of the enclosure, so that the lower surface of the turntable was flush with the lower surface of the

reflec-tion plate, as shown in Figure 12. A rectangular hole in the center of the

turntable received the model spar, which was clamped in place with a separate block and set screws, as shown in Figure 13.

The housing in which the turntable rotated was coated with a D. 0006-in. coating of Teflon®*. The fit between the turntable and coated housing was tight

enough to 'just allow rotation without rattling laterally. A spring-loaded

Teflon® seal was provided to prevent leakage between the turntable and housing into the enclosure.

A retainer plate was bolted to the turntable and bore on the 'Teflon®

coated top edge of the housing. ,A swivel nut attached to this plate was engaged by a lead screw driven by a gear motor through a universal joint,

for trimming the angle of attack. The trim range was approximately 3 degrees each side of a nominal zero angle. Micro switches were mounted on the floor of the enclosure, and adjusted to trip when contacted by a cam on the retainer plate just before any portion of the plate or exciter motor mounted on it would

contact either *side of the enclosure.. This would light an indicator lamp in a remote control box outside the test section.

As shown in Figure 1, when the model spar was mounted in the turn-table, the square end of the exciter rod projected into a square socket in a shaft inside the turntable. An, aluminum crank was mounted near the top of this shaft. Another crank was mounted on the 'vertical shaft of a' gearmotor attached to the turntable retainer plate (so the relation between the two

cranks 'would not change with trim changes). As the crank on the gearmotor rotated, it would engage the end of the crank on the exciter shaft, deflecting

it. This would twist the exciter rod and the model tip., As rotation continued,.

the cranks would suddenly disengage, allowing a free oscillatory decay of the model in torsion and bending (at finite tunnel speeds, twisting the tip induced bending in the spar due to lift forces).. The centerline of the gear-motor crank was off the exciter crank centerline, so that two deflection ,amplitude,s were obtainable by simply reversing the exciter motor.

A remote control box was provided outside the test section, connected to the enclosure by a cable which was fed through stuffing boxes in the tunnel. wall and top of the enclosure. 'This box contained switches for controlling the trim and exciter motors,, and all the indicator lamps.

,A float switch 'was mounted in the aft end of the enclosure, to light an indicator lamp if a leak should develop. allowing water to enter the enclosure.

The strain gage leads were fed up, through a hole in the turntable,

through a stuffing box at the top of the hole, and connected to a terminal

*Tradename of E. I. du Pont.,

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board on a bulkhead. Cables from this terminal board were fed through stuffing boxes in the top of the enclosure and tunnel wall, to the signal

con-ditioning equipment, All conditioning and recording equipment was furnished

by NSRDC.

An air hose was connected to the enclosure and fed through the tunnel wall to a regulating system, also provided by NSRDC. This system maintained air pressure in the enclosure and model slightly above the test section

pres-sure, in order to minimize leakage into the enclosure or model, should any

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FABRICATION AND ASSEMBLY

A. Spars

The spars were machined, while in the annealed condition, from 1-1/4-in. -diameter bar of VASCOMAX 350 CVM, a maraging steel. The

first step was to gun-drill the 5/16-in. -diameter hole lengthwise through

each bar. The bars were then sawed and machined to the overall dimensions, centered on the hole. The rectangular cutouts were machined in the first

spar on a milling machine at the SwRI central machine shop, so an immediate check of the actual bending and torsion stiffnesses could be made. Four

other spars were then sent out to have the cutouts machined by an electric discharge (EDM) process. This was done by Metem, Inc., in Tulsa, Okla-homa. One of these four was inadvertently ruined during the EDM process, so the original machined spar had to be used on one of the models. Fortunately, the differences in the spars were negligible, in both geometry and stiffness.

An exciter rod, made from 1/4-in. -diameter drill rod, was installed

in each spar, as shown in Figure 2. A square was machined on each end of

the rod. The 5/16-in. -diameter hole in the tip end of the spars was broached

square, after which the spars were precipitation hardened. Steel spacers

were cut to fill the gap between this broached hole and the square on one end of the rod. This assembly was bonded with epoxy into the spar tip. Two

nylon bushings provided the only other support for the rod, one near the root and the other at midspan. The rod was thus free to rotate relative to the spar everywhere except at the tip, but was constrained to bend with the spar. The rod projected from the root end of the spar to allow it to be engaged by the exciter crank. Due to the difference in torsional stiffness between the rod and the spar, it was necessary to twist the root end of the rod through approximately five times the desired spar tip twist angle.

Average stiffnesses of the bare spars, with exciter rods installed,

were

El = 54, 030 lb-in2 GJ = 14, 050 lb-in2

The average bending stiffness was 1. 8 percent higher than the desired final model stiffness, while the average torsion stiffness was 7. 5 percent lower than the desired final model stiffness. These values were deemed satisfactory, since it was anticipated from past experience with similar

models that addition of the segments would have a negligible effect on bending stiffness, but would increase the torsional stiffness between 5 and 10 percent.

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Se gm ent s

A single master half pattern and a three-piece core were machined from Mild steel. A plastic mold was prepared from the master pattern, and two plastic halves cast. These were then joined to make a full pattern which was perfectly symmetric. This pattern was used for all the segment molds. The heavy (la = 0. 99) model was to be cast of a lead-tin alloy, so plaster molds were made for these segments. The remaining models were all to

be filled plastics, so plastic molds were prepared for these. The

three-piece steel core was used in the plaster mold while pouring the lead-tin

segments. Casting these one at a time was not too time-consuming, as

several could be cast in one day. Since the plastic segments required

over-night curing, it was not practicable to cast one at a time. A total of eight

molds was made for these. A core mold was made, in which to cast

dupli-cate cores of a low-melting tin-bismuth alloy, Cerrolow 117., Three batches Of each model mixture were cast, from which the best 15 of the resulting 14 segments could be chosen for each model. After curing, the cores were melted out of the segments in warm water.

'Ballasting and Assembly

At least 210 to 24 segments were cast of each of the four materials.,

After trimming all flash, sprues, and risers from the segments, and

finish-ing the width on each, 'they were each weighed, the c, g. located, and the volume measured by submerging in water so the density could be determined.

Three representative segments Of each material (light, heavy,. and

median) were selected to determine the effects of finishing the contour and

addition of silicone sealing material on the final properties of the segments. The exact weight, co g. locations, and radius of gyration of these segments with the dummy spar section were measured before and after finishing to

final contour and addition of a bead of sealant around the edges. Ballast requirements were determined individually for the segments from Equa-tions (4) to (8),, and averaged for the three segments of each material. These average ballast weights and locations were then used for all the segments of

each model. The ballastweights as cut accounted for the weight of material

removed from the segments to accommodate them. Tungsten rod was used as ballast on all the models, and glued into holes drilled in the segments.

A single rod of 0.40-in. 'diameter was used in the three plasticmodels.

Two rods of 0. 25-in, diameter were used in the lead-tin model, as the

further aft location did not permit use of the larger diameter. The fifteen

most uniform segments of each material were drilled and ballasted, then weighed, and the c. g. location and radius of gyration measured. 'Corrections for trimming and addition of sealant, as determined from the three samples

of each material, were applied to obtain the final properties. These

correc-tions were all within 1 percent on final weight and c., g. location, and varied from 1 to 1. 6 percent on radius of gyration.

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The spars were instrumented with two strain gage bridges near the root, one being sensitive to bending moments, and the other to torsional moments. The root segment was hollowed out sufficiently to clear the wiring

to these gages.

The root segments were first slid over and cemented to the spars, and held in position until cured. All the remaining segments were then "stacked" onto the spars with adhesive, then held in final position until

cured. After curing, the contour of the entire model was finished by hand filing and sanding.

A closure plate of 0.032-in. -thick aluminum was cemented to the tip segment to cover the spar tip and ballast hole. Two tapped holes were pro-vided in the tip; one into the end of the exciter rod, and the other into the

segment. These holes permitted attachment of a loading plate for

determina-tion of final model stiffnesses, and a shaker attachment block for impedance

measurements at NSRDC. They were plugged with RTV silicone when the

models were installed in the tunnel.

The final step in assembly of the models was to seal the gaps with an

RTV silicone compound. This was applied with a hypodermic syringe.

All glue joints in the models were bonded with Scotchweld 1838B /A, a 3M modified epoxy product. The RTV compound used for sealing the gaps

was SILASTIC RTV 731, a Dow-Corning product.

Figure 14 shows one of the spars and associated ballasted segments before assembly. Figure 15 shows the lead-tin model and one of the plastic

models following completion.

Stiffness measurements of the completed models were made by clamp-ing them horizontally and obtainclamp-ing load-deflection measurements. A loadclamp-ing plate was attached to the model tip. Weights were first hung directly under the spar centerline to determine bending stiffness, With a knife-edge support on the spar centerline, the weights were hung 5 in. forward of the spar, to

determine torsional stiffness. Five increments of weight, up to 15 lb, were

used, and the resulting tip deflections measured with dial indicators. The

stiffnesses El and GJ were then calculated from cantilever beam formulas.

Measured final parameters of the models are listed in Table I. The

lead-tin model (p. = O. 96) came out with somewhat higher stiffnesses,

particu-larly in torsion, than the others, This is believed due to an extra liberal

application of adhesive on this model, which may have partially filled the clearance between segments and spar.

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D. Support System

Fabrication of the support system was straightforward, and need not be discussed in detail. All of the fabrication was done in the SwRI central

machine shop. The only outside work involved hard coating the reflection

plate and Teflon® coating the turntable housing.

One additional item was added after assembling the system. _Backlash in the trim motor, universal joint, and swivel nut added up to an excessive slope in rotation of the turntable. _{To correct this, an aluminum block was} bolted to the retainer plate, and a coil compression spring with a rate of appxoimately 200 lb/in, was inserted between this block and one of the

enclosure bulkheads with a preload of about 100 lb. This kept the trim sys-tem jammed to one of its extremes of backlash.

Figure 16 shows the support system with the cover plates removed from one side to show the interior.

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IV. TEST PROCEDURE

A. General

Since the data were collected and are being processed by NSRDC personnel, this report will not detail the results of the tests and preliminary frequency measurements. All of these data will be published as an NSRDC

Technical Report.

Only a brief description of the test procedures as participated in by the author and a SwRI technician will be given here. The tests were made in February 1970.

Frequency Measurements

Upon arrival at NSRDC, the support system was mounted in an inverted position on a rigid test fixture. The models were installed in sequence into the support system for impedance measurements. A shaker with impedance head was suspended on strings so that it lined up with an attachment block

bolted to the model tip. The mass of the shaker and block, however, proved to be so large relative to that of the model that the natural frequencies and mode shapes were significantly affected.

The shaker was therefore replaced by a noncontacting electromagnet suspended close to the model near the tip. The coupling between the magnet

and the steel spar was sufficient to excite the resonant frequencies of the model when the magnet excitation frequency was tuned. Several "in air" modes were determined in this manner for each model, in terms of frequency and nodal lines, but damping could not be measured.

Tunnel Tests

After installing the support system in the open-jet test section of the NSRDC 36-in, water tunnel, model No. 1 (f.i= 0. 96) was installed. The first

bending and torsional frequencies in water at zero speed were determined by operating the exciter, and decay measurements were obtained as well.

The tunnel speed was then increased in 5-knot increments to 15 knots. At each speed, a decay record was made and immediately reduced in order to keep a running track of the damping versus velocity relation. Since

damp-ing appeared to be approachdamp-ing a peak at 15 knots, further speed increments were reduced to 1, 1/2, and, finally, 1/4 knot. The damping was decreasing

rapidly beyond 20 knots, and finally was reduced to less than the zero-speed

value at 24 knots. Extrapolating the damping curve indicated zero damping (flutter) would occur at about 24-1/2 to 24-3/4 knots. The tests on this

13

'B.,

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model were then stopped in order to save the model for possible further

testing.

Model No. 2 (p,. 0.46) was next installed. A prediction of 43 knots had been made for the flutter speed of this model, but this was never reached. The records were indicating that the torsional moment was increasing expo-nentially for the same excitation deflection, instead of remaining essentially constant, so it was realized that a divergence speed was being approached. The decision was made to proceed in order to find out if flutter or divergence would come first. The model diverged at 36 knots. The divergence speed would be the same for all the models, since it is a static hydroelastic

phenom-enon and all the models have the same elastic properties, so it was pointless

to attempt to run Model No. 3 as its flutter speed should be even higher than

that of Model No, 2. Since the Yates theory indicated that the flutter speed

of Model No. 4 (p, = 0.20) may be as low as that of Model No. 1, it was

decided to test it to at least 30 knots to see if it would approach flutter in that range. Up to 30 knots, however, damping was still increasing and was far past the peak damping of Model No, 1. No further tests were made at

this time.

Flutter analyses of the models were made at SwRI by Chu, using the method outlined as Case 6C in Reference 4 and the measured model

param-eters. The calculated flutter speed for the No 1 model was 23,5 knots,

which compares well with the apparent experimental speed of 24-1/2 to 24-3/4 knots,

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V. CONCLUSIONS AND RECOMMENDATIONS

It is immediately apparent that freedom from divergence cannot be taken for granted in models designed to be flexible enough to flutter within facility capabilities, even for elastic axis locations at the quarter-chord.

If divergence speeds are to be well above the facility maximum speed, it is essential that the elastic axis for flutter models be located at or ahead of the hydrodynamic center. For finite span models, this point may be sig-nificantly ahead of the quarter-chord.

This makes the design of models for flutter research quite difficult, particularly for the type of models used in this program (lumped elements on a separate spar), as space limitations for a spar near the leading edge of commonly used sections are critical.

The present models can be altered for useful testing, if the flutter speed can be reduced below the divergence speed, or if the divergence speed can be increased beyond the maximum facility speed.

The flutter speed can be reduced by attaching pod-like masses at the

model tip, with far aft c. g. locations. The divergence speed could be

increased by cutting back the leading edge of the models. This would move

the elastic axis farther forward on the remaining chord length, at the cost of winding up with a blunter leading edge.

The complexity of these models results in high fabrication costs. In order to obtain a large number of experimental flutter points for correlation with theory, it would be highly desirable to investigate other construction techniques which would reduce the fabrication labor. Such an investigation

should stress concepts which may simultaneously simplify fabrication and result in higher divergence speeds. This combination must be achieved in order to enable parametric variations involving large numbers of data points.

(20)

REFERENCES

Yates, E.G. , Jr. , "Flutter Prediction at Low Mass-Density Ratios

with Application to the Finite-Span Noncavitating Hydrofoil, "

Pre-sented at the ALAS Third Marine Systems and ASW Meeting, San

Diego, California, April 29-May 1,, 1968,, AIAA Paper No. 68-472,

2.

Abramson, H. N. and Ransleben, G. E, Jr.,

An Experimental

Investigation of Flutter of a Fully Submerged Subcavitating Hydrofoil," Tech. Report No. 4, Contract Nonr-3335(00), Southwest Research Institute, 15 December 1963. Also, ALAA Jour. Aircraft, 2, 5,

pp. 439-442, Sept.-Oct. 1965.

Abbott, I. HI, and Von Doenhoff, A. E., Theory of Wing Sections,, Dover Publications, 1959, Ed.,, pp., 9-19,

Chu, W. H., and Abramson, H. N.,: "Further Calculations of the

Flutter Speed of a Fully Submerged Subcavitating Hydrofoil, " AIAA

J. Hydronautics, 3, 4,, pp. 168-174, October 1969.,

3

(21)

TABLE AND ILLUSTRATIONS

(22)

Description

Individual Parameters:

TABLE I

FINAL MODEL PARAMETERS

Parameters Common to All Models:

Symbol Model Value

Nondimensional distance from midchord to elastic axis,

positive aft a -0. 50

Semichord, in. b 3. 00

Semispan, in.

Symbol

15,00

Numerical Value, Model No.

1 2 3 4 2 ra xa 0. 0. 508 524 O. 503 0. 523 O. 511 0. 528 0. 506 0. 523 J. 0. 963 O. 455 0. 395 0. 202 El 56, 900 55, 300 55, 800 56, 700 GJ 19, 200 16, 420 16,440 15, 630 Description Nondimensional square of radius of gyration about elastic axis

Nondimensional

loca-tion of c, g. from elastic axis, positive aft

Mass ratio = m

Trp62 Bending stiffness, lb-in2 Torsional stiffness, lb-in2

(23)

.L2

C/4 = 012

z

= C/2 =

Figure 1. Model Geometric Pa ra meters,

b = ₁₂ 1/16 ( TY P. ) 15/16 ( TYP. ) .032 TH IC K ALUM. PLATE NASA 16 - 012 AIRFOIL SECT! ON 2707

//

1/32

(24)

!I

75 1.00 17.969 14.969 A 11 ii Ii A SQUARE END

EXCITER ROD ( 1/4 D. DRILL ROD )

.438 .125 ( TYP.) 1.00 ( TYP.) B

.159

.420

Figure 2. Model Spar Configuration

5/16 D.

DRILL THRU SECTION A-A

Steel spacers bonded between square end of exciter rod and

5/16 sq. hole in spar.

SECTION B- B

2708

.875

(25)

CI 0.08 0.07 0.06 0.05 aROOT 0.04 (PER DEGREE) 0.03 0.02 0.01

-ROOT V = 44.3% SEMIS PAN_ ( 6.645 inches ) CL

a--

0.0634/deg. I I i 20 40 60

PERCENT SEMI S PAN

1

80 100

2709

Figure 3. Spanwise Static Lift Distribution Due To Angle Of Attack

(26)

CA 0.040 0.035 0.030 0.025 aTIP 0.020 (PER DEGREE) 0.015 0.010 0.005

-I i V' = 55% SEMI SPAN ( 8.25 inches) CL - 0.027/deg. "TIP , I I I 20 40 60

PERCENT SEMI S PAN

1

80 100

2 710

Figure 4. Spanwise Static Lift Distribution Due To Twisted Tip

-^

(27)

10.0 6. 0 4.0 0.4 0.2 0 feet/sec 1111111M11011111111

WIIMINIM

INOMILWRIM -2

!

11111NLVME

1111111OPAYM,9%.

11111E1ts

1 \

1

'7Dk

i

1'f'. .1 ' . -90.', .

k

OM

1 I

s

_., '' '.

I

1

1111.1111INIZI

IMMENILIN

1111'

MOM

1

11

:_

-MI

-1111

[0 1 20 40 '60 I 10 10 20 30 40 50 knots 'VELOC ITY 2711

(28)

10.0

6.0

2.0

0.4

0.2

Figure 6. Tip Twist Angie To Cause Spar TO Yield In Bending

feet /sec

niiMINIVII

LI1111111,11010k,

lik11111111,%..

inaimmrsi

_

111i

111111,11NUI

'

4

, ° ..

1,'?

1

1. t_. ___J.. r

A

1

1 1.

Iii

, ,I -9,,t 1 ,

1

k

a,

i

1

IiIi

1

II

i 1 i i -_-L'jJ -40 ! 1-61 20

r I

10 20 30 40 50 knots VELOCITY

via

I

(29)

L--

1.50

A 7

7==Z7--- x' --a101 .25 SECTION A - A .420

Figure 7. Model Segment Details

NACA 16-012 AIRFOIL SECTION 2713

T

6.00

-.875

(30)

C/4 111 . mS dB WT = Ws +WB = 2.085 2714 1Figure 8.

Notation For Determination Of Ballast Requirements

1.50

= 3'073

(31)

U' CD Cil CD C:, I....J cp r..) .4.. crN oo

-

-MASS RATIO OF BALLASTED SEGMENT,

ii -pmb2 1 STYCAST 1090 SI

=

1 II II CD

PP

N.) -r=. .1 CD C.) Cr, I l I I

46% REZOL I N F1933 A - 54 % LEAD POWDER

41% REZOL I N 30/932 B - 59 % LEAD POWDER

(32)

EXCITER MOTOR

REFLECTION PLATE

NSRDC TUNNEL BRACKET

AIR HOSE

EXCITER CRANKS

POWER AND STRAIN GAGE CABLES

MODEL

FIGURE

10.

SIDE VIEW OF SUPPORT SYSTEM

TRIM MOTOR _ 1 el 1 1 1 1 L4 1,_ -f--+ l -± -F ± I-e :i 4 -} (0- (0 i -H : _l; (0_,_/N---0 (0-i$ * i . 1 1 ; ( + ++ Pi + -1-+ ++ + , f iiiiiatillild

I

IN

6) Xlip111.0\11 i +

l- ++

-I-+ -I-+

-I-± + -I I + TURNTABLE 2 716 +

(33)

RETAINER PLATE EXCITER MOTOR EXCITER CRANKS TURNTABLE-11U" JOINT TRIM NUT ---TRIM MOTOR

NN-REFLECTION PLATE LEADSCREW FIGURE II.

PLAN OF SUPPORT SYSTEM INTERIOR

2717

(34)

-Mktg

EXCITER SHAFT

NEEDLE BEARING

MODEL EXCITER ROD MODEL SPAR

SEAL

EXCITER CRANK

SEAL

TEFLON COATED HOUSING

MODEL

Figure 12. Section Through Turntable

BALL BEARING

STRAIN GAGE CABLES

STUFFING BOX

TURNTABLE

RETAINER PLATE

(35)

SPAR

MODEL

SET SCREW AND JAM SCREW

CLAMP PINS

CLAMP BLOCK

Figure 13. Spar Clamp

(36)

V '54 i Miq 1=sz' , .rv=

-FIGURE 14 SPAR AND BALLASTED SEGMENTS BEFORE ASSEMBLY

(37)

-,"0111'

III1111utIV11.l'4,#,[ill

[.[ htle 01411 14/'',14111111,1 11, .1,1,, 11,11/11/11 ;id .1111111 ' 114, 0,11 I o 1'11'6 0,5 , 111v,d11,1i1 1111,0, yt11 1',o] A er[liRJ111 1'rq th ,h111 14114'111," T.11 "' ' 0 11','11'',1°°g111'1,1'1II 0:14 r :1 , 4 1F Ia[I' 114,. 4 1P1t.'11" ..,, Ape 1111jilik. nnn. 11-450 r'", 4 'h:f1/,$ [1111 ' 1IF....11"te 11,,,

(38)

-":4/44.411.411i/o

-,

" _.."44

FIGURE 16. COMPLETED SUPPORT SYSTEM

_

-IF

7 e 4444,4,,

(39)

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UNCLASSIFIED

Security Classification

DOCUMENT CONTROL DATA - R & D

(Security classification of title, body of abstract and indexing annotation must be entered when the overall report is classified)

1. ORIGINATING ACTIVITY (Corporate author) Southwest Research Institute

8500 Culebra Road

San Antonio, Texas 78228

2e. REPORT SECURITY CLASSIFICATION UNCLASSIFIED

2b. GROUP

3. REPORT TITLE

Experimental Determination of Variation of Hydrofoil Flutter

Speed with Mass Ratio

4, DESCRIPTIVE NOTES (Type of report and inclusive dates)

Final Report - March 1, 1969-March 31, 1970

5. AU THORISI (First name, middle initial, last name)

Guido E. Ransleben, Jr. 6. REPORT DATE

April 1970

7a. TOTAL NO. OF PAGES

37

7b. NO. OF REFS

4

Be. CONTRACT OR GRANT NO

N00014-69-C-0219 b. PROJECT NO SS 4606, Task 1703 C. i d.

9e. ORIGINATOR, REPORT NUMBER(S) Final Report

9b. OTHER REPORT NO(S) (Any other numbers that may be assigned

this report)

10. DISTRIBUTION STATEMENT

This document has been approved for public release and sale; its distribution is unlimited.

/I SUPPLEMENTARY NOTES 12 SPONSORING MILITARY ACTIVITY

Naval Ship Research and Development Center

Washington, D. C. 2(5007

of a family of four hydrofoil identical geometric and elastic

< F.1. < 1.0). The heaviest was

model.

an estimated 1/2 knot with the predicted by scaling considerations. three remaining models, however,

than flutter speeds for them. axis was at the

quarter-chord--to ensure a high divergence speed. 13. ABSTRACT

A description of the design and fabrication flutter models is given. These models had properties, differing only in mass ratio (0.2 a direct half-scale model of an earlier flutter

A flutter point was approached to within heavier model, and it was near the value No flutter points were measured with the as the torsional divergence speed was lower This was rather unexpected, as the elastic usually considered to be far enough forward

(47)

UNCLASSIFIED Security Classification

14

KEY WORDS LINK A LINK B LINK C

ROLE WT ROLE WT ROLE WT

,

Hydrofoil

Flutter

Mass Ratio Effects