US2283956A - Cavitation retarding blade and a method of delaying the occurrence of cavitation to increased blade velocities - Google Patents

Description

May 26, 1942 l L. P. SMITH 2,283,956 CAVITATION RE RDING BLADE AND A METHOD OF DELAYING OCCURRENCE OF CAVITATION TO INC REASED BLADE VELOCITI Filed June 21, l937 TRAIL/N6 5045 FIG 2 I INVENTOR LYBRAND I? SMITH ATTORNEY Patented May 26, 1942 UNITED STATE S PATENT OFFICE CAVITATION RETARDING BLADE AND A METHOD OF DELAYING THE OCCURRENCE OF CAVITATION TO INCREASED BLADE VELOCITIES Lybrand P. Smith, United States Navy Application June 21, 1937, Serial No. 149,543

' 6 Claims. (01. 170-159) (Granted under the act of March a, 1883, is

amended April 30, 1928;370 0. 0.157) 1 the pressure in the free stream and hence suction is present. The-suction side of the blade with which the present invention is concerned is the back of the bladeythe face of the blade bein the pressure side. Thus, when considering a marine propeller the face denotes the driving face or that which pushes the water astern when the propeller is in motion, while the work back naturally denotes the surface opposite the face.

Whenever pressure on the back or suction side is reduced to vapor pressure, the water in that location boils and the blade will be in burbling cavitation.

Although back cavitation cannot be eliminated its development can, nevertheless, be delayed or deferred and this I accomplish in a new and novel manner based on my researches on this subject. The usual pressure distribution on the suction or backside of the blade shows-a suction increasing from the leading edge to a more or less vision of a. new and novel back configuration which will insure the maintenance of theaforesaid pressure distribution. The present invention is restricted solely to blades adapted for movement in a liquid fluid 'medium and is notconcerned with aerial propellers. For what is sometimes called burbling" in aerodynamics is a phenomenon totally different from the burbling cavitation encountered in connection with marine propeller and water turbine blades.

Marine propellers are usually designed with reference to developed sections of the blade taken along a flow line, a flow line being the path traced across the blade by any droplet of water which'just grazes the leading edge and remains in contact with the blade until it leaves the trailing edge. If, therefore, a cross section of the blade is taken at the flow line and developed on a plane, a developed section will be formed. In'the specification and claims hereinafter, the term developed blade section will be used in the sense here described.

As illustrating the formation of a developed section in the case of conventional marine proprominent peak and gradually declining towards 4 the trailing edge. Obviously before the blade can suction will have reached vaporpressure and burbling cavitation willexist. If, however, the suction were distributed substantially uniformly over the back 'of the blade, thus avoiding any appreciable peak,'the same total lift could be exerted .without the suction reaching vapor pressure. Thus, under these conditions the blade would resist and delaythe occurrence of burbling cavitation. Eventually, as the'speed of the blade is augmented its suction will increase until vapor pressure is reached. This, however, will occur practically simultaneously over the whole blade with the result that burbling cavitation will'take place over theentire blade back or suction side from leading to trailing edge. a

My invention thus contemplates a method of delaying the occurrence of burbling cavitation on the back of marine propellegoreavater iurbine blades by maintaining a-substantially uniform pressure distribution thereover as well as the probe producing its maximum lift the peak of the peller and propeller type turbine blades, it is noted that the flow line of these-blades lies approximately on the surface of a cylinder, the axis of which conincides with the propeller 'or turbine shaft. If, therefore, a section of either blade is cut at the desired'radius by the concentric cylinder and developed on a plane, a developed blade section will be formed.

I have discovered that my new and novel blade, if it is to maintain a substantially uniform pressure distribution on the back thereof and thereby delay the occurrence of burbling cavitation, must have aback which in any developed section of the blade is substantially elliptical in shape or closely approximates that of an ellipse.

The method of arriving at this developed blade section will be pointed out in detail hereinafter.

In the light of the foregoing, it is clear that it is an object of my invention to provide a blade adapted for movement in a liquid fluid medium the back of which is of such a configuration as to delay the occurrence of burbling cavitation;

and that it is another object of my invention to provide a method of delaying the occurrence of burbling cavitation occasioned by the movement Avantages of this invention will be readily appreciated as the same becomes better understood by reference to the following detailed description panying sheet of drawings wherein:

Fig. 1 shows superimposed on one another for comparison purposes developed sections of a blade with a standard, prior art. ogival or circular arc back; the new elliptical back; a new quasi-elliptical back approximately half way between the first two backs; and a new quasielliptical back with ordinates greater than the ellipse of theelliptical back at all points except at the ends and the middle Fig. 2 shows a developed section of any of the novel forms of my blade with minor modifications which it may be desirable to make near the leading and trailing edges; and V Fig. 3 shows a developedblade section which is used in the formulation of a general equation employed in arriving at the developed blade section of the present invention.

By formulating a general equation for determining the location of the first appearance of burbling cavitation I have been enabled to arrive at the equation which expresses the conditions under which the pressure on the suction or back side of the blade will be approximately uniform. Since a' short method in the formulation of the general equation is desired,anumber of simplifications are made, which a priori were believed to be reasonable and aposteriori were found to be Justified. These simplifications are as follows. Only the case of uniform motion is considered. Over the pertinent area from near the leading edge to near the trailing edge the velocity relative to the blade is considered uniform. Over the pertinent area the stream lines are considered approximately'paraliel to each other. The following physical statements are V=velccity and direction of P relative to'the blade. The direction must obviously be tangent to the blade. Note that on the suction side of the blade V must always be greater than w, being compounded of W plus the circulation velocity.

S=the velocity of P in space.

N=the component of S which is normal to the blade.

considered correct for the present purpose. Liquid in which a body is submerged exerts a pressure on it. The pressure can be considered as.

being-exerted by the liquid particles in immediate contact with the approximately stagnant boundary layer of liquid that clings tothe-body.

The particles outside those mentioned above merely increase or decrease the pressure on the latter; and, if the stream lines are approximately parallel. do not change the relative pressure exerted by a particle in contact with the body (or boundary layer) as it flows past the body. Consequently, if the relative pressure exerted on a body by a particle which fiowspast it but always in contact with it (or the boundary layer) is determined, the loeation'of the lowest pressure can be determined. It a particle. of liquid is being accelerated a force is involved. I In the case of a submerged propeller blade the forces of gravity and cohesion can be ignored and, therefore, the remainingforce is a difference in pressure. A particle of liquid moving relative to but in contact with a submerged body has no' relative velocity towards or away from that body. but may wards the body, it indicates that the pressure at the body is less than-in the surrounding liquid:

' and'vice versa.

Reference is now made to Fig. 3 of the drawing w to show the manner employed in formulating the general equation by "which the location of the first appearance of burbling cavitation is deterblade.

.o=angle between V and W .(reversed).

p=angle between S and V.

Since V is always greater than W on the suction side, N must always lie between W and S; though mathematically it would make, no difference on which side of S, N lies; for in any case:

1v=s sin ,9 Eq. 1 Now by a law of trigonometry; Y

' sin B sin 0 2 Therefore: v

. I sin fl=- 2 0 q-- Hence:

N=W sin 0 1 Eq; 4 The rate of change of N with respect to 0 is:

dN 1 W cos 0 Eq. 5

Now:

d0 V Eq. 6

Multiplying Equations 5 and 6, we get:

dN da dN WV cos 0 w m-ar -R 7 But g dt

=the component of acceleration in space normal is the result of a pressure at the blade above or 4 below that of the surrounding fluid. The total pressure at the blade is the pressure of the surrounding fluid plus or minus this acceleration pressure. Whether or not burbling occurs depends upon the total pressure at the blade.

From a consideration of the general equation Eq. 8 'it can be shown that. underusual operating conditions, burbling cavitation'on the back of a blade will begin, in the case of an ogival blade,-at a point on the back where the curvature tion should give an approximately uniform suc-' of the blade is tangent to the direction of motion of the blade relative to undisturbed water; and, in the case of airfoil blades, burbling cavitation will begin forward of that point of tangency. The

reason for this difierence is stated in section 4C of my article entitled Cavitation on marine propellers appearing in the Transactions of the American Society of Mechanical Engineers, vol. 59, No. 5, July 1937, pages 409-431. Theimportant thing, however, to note in connection with the present invention'is that the acceleration A varies over these blade sections withthe result that there cannot be a substantially uniform suction on the blade backs. This necessarily. follows from the fact that an acceleration pressure corresponds to each acceleration and that the total pressure at the blade is the pressure of the surrounding fluid plus or minus this acceleration pressure. Whether or not burblingoccurs depend upon the total pressure at the blade.

If now the pressure distribution on the suction side or back of the blade is to be approximately uniform,. the acceleration pressure and hence A must be constant with the result that the general equation Eq. 8 hereinbefore' discussed takes the form cos constant In this latter equation R at any point on the back of the blade is the radius of curvature of the developed section at this point, and 0 is the angle between the tangent to the blade at that point and the direction of flow of the undisturbed water relative to the blade, the tangent of course lying in the plane of thedeveloped section. If on a developed section of the blade the curve of the back thereof be represented by the equation then equation 9 can be put'into the diiierential form; a

. 1 l= a* e en" Q] a.

. y 17: Equation 11 has not been solved, but I have studied it thoroughly and recognize it represents a figure strongly resembling an ellipse.

=constant Eq. 11

'Thus, consider a conventional blade wherein any developed section thereof shows a circular arc backas at I (Fig. 1) which has come to'be designated an ogival back in the marine propeller art. A little consideration will make it clear that,since in this case R is constant,

' cos is not constant but decreases from a maximumvalue in. the middle: of the blinds: to minimum values'at the leading and! trailing edges. Since the suction decreases with decreasing, values of cos 0 R issolbwimm that'mmitm evmana appteln um Ag; dufi, inom-aniuaitnum in with 1111 nae'flm lim- Wm v i h'ualmu:

One of these simplifying assumptions was that from near the leading edge to near the trailin edge the velocity vector of a liquid particle in contact with the boundary layer was constant in magnitude though of course varying in direction.

This assumption was merely a device to render the mathematics tractable. As a matter both of theory and of physical fact it is known, however, that the magnitude of that vector varies also, being less near the leading and trailing edges. The shortening of this vector would therefore decrease the suction near the leading and trailingedges. To offset or prevent decreased suction from this cause, a value of cos 0 is needed which increases near the edges. As pointed out hereinbefore the ellipse has such characteristics.

Thus, by purely theoretical, a priori reasoning, I was led to the conclusion that an elliptical back on any developed blade section would produce a practically uniform suction and would resist the onset of burbling cavitation longer than either the standard ogival back generally used or the airfoil backsometimes used. By blade with an airfoil back is meant a blade whose suction side has a shape similar to that generally used on the suction side of airplane wings.

Following this theoretical reasoning, a number of foils were made, the developed sections .of which had elliptical backs and the pressure distribution measured experimentally in a wind tunnel. Up to about a 6 angle of attack they had a substantially uniform suction over the back with no prominent peak of suction thus differing markedly from either the conventional ogival or airfoil backs. Since a marine propeller rarely reaches an angle'of attack as great as 5, except at the moment of starting, this was satisfactory.

Next .a standardi model. marine screw propeller, which suitered. badly from: cavitation, was duplicatedi in every noanect except the new propeilen'wasi provided with back: which. appeared elliptieall i'm in their: develhnedl cross sections;v 'Ilhlsruuvell 1m waa them.

tested! i'm a variable pressure water lit. nesistedl burbli'ng: in than; the standard prior: anti pmpellbm; emit, at: the: slim ratios practicall fair pm; time new,-

wherein the backs were substantially elliptical in shape in their developed cross sections accomplish the purpose of the present invention, but

pended described.

also blades wherein the backs in their developed cross sections closely approximated an ellipse.

In Fig. 1 of the drawing there are shown superimposed on one another for comparison and clarifying purposes four developed sections taken respectivelyon four separate blades at the same but any convenient radius. The blades may form a part of a marine screw propeller or a water turbine screw propeller; and their curved section portions in all cases denote the backor suction side of the blade.

The standard, prior art, ogival back is indicated by the reference character I; and the elliptical back of the present invention by the reference character 2. Quasi-elliptical backs 3 and 4 which closely ap proximate that of the. ellipse 2 are also considered novel and satisfy the requirements of the present invention. It will be observed that the quasi-elliptical back 3 lies approximately halfway between the prior art ogival back I and the trueelliptical back 2 and represents an approximate solution of Equation 11 set forth hereinbefore. The quasi-elliptical back 4 has ordinates greater than those of the ellipse at all points except at the ends and middle of the latter. This back 4 is intended to give an even closer approximation to a substantially uniform suction than is obtained by the ellipse '2. .In Fig. 2 of the drawing there are shown minor modifications which maybe made near the leading and trailing edges of any of my new and novel blade forms in order to further improve their operating characteristics. If it is found desirable to modify any of my novel blade sections in the manner depicted in Fig. 2 it will be seen that the blade as modified has for its major portion an ellipf tical or quasielliptical back. 4

In Figs. 1 and 2 of the drawing the pressure side or face [of the various developed blade sections are shownas formed by the major axis of The .invention herein described and claimed may be-used and/or manufactured by or for the Govemment of the United States of- America for governmental purposes without the payment of any royalties thereon or therefor.

I claim:

1. A blade adapted for movement in a liquid fluid medium, said blade having a back which in any developed section of theblade lies at least for its major portion substantially along a curve represented by the differential equation dy a +(s) 1 whereby to provide a back which delays the occurrence of burbling cavitation.

2. A blade adapted for movement in a liquid fluid medium, said blade having a back which in any developed section of the blade lies at least for its major portion substantially along a curve the ordinates of which are greater than those of an ellipse at all points except at the ends and middle of the latter.

3. A blade adapted for movement in a liquid fluid medium, saidblade in any developed section thereof having a back which lies at least for its major portion along an ellipm and a face which lies at least for its major portion along the major axis of the ellipse.

4. A blade adapted formovement in a liquid fluid medium, said blade having a back which in any developed section of the blade has at least a partthereof substantially defined by the major portion of a semi-ellipse which has for its base the major axis of the ellipse.

5. A blade adapted for movement in a liquid fluid medium, said blade having a back which .in any developed section of the blade has at Jugate diameter inclined to the major axis, for

example, at an angle representing the average angle of attack; a chord parallel to the conjugate diameter; or 'a curved line to give the slightly concave pressure face sometimes used.

According to the provisions of the patent statutes I have set forth the principle and mode.

ellipse.

least a part thereof substantially deflned by the major portion of a semi-quasi ellipse, the major axis of which coincides with the major axis of an ellipse andthe end and middle ordinates of which are those of the ellipse.

6. A blade adapted for "movement in a liquid fluid medium, said blade having a back which in any developedsection of the blade has at least a part thereof substantially defined by the major portion 'of a semi-quasi ellipse which has for its base the major axis of an ellipse and which has an ordinate at its middle which is that of said LYBRAND B. SMITH.

claims the invention may be practiced otherwise than as-speciflcally illustrated and

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