Title:
Cavitation retarding blade and a method of delaying the occurrence of cavitation to increased blade velocities
United States Patent 2283956


Abstract:
My invention relates to a marine propeller or water turbine blade and more particularly to such a blade wherein the back or suction side is of such configuration as to retard or delay the formation of burbling cavitation to increased blade velocities. In addition, the invention also contemplates...



Inventors:
Smith, Lybrand P.
Application Number:
US14954337A
Publication Date:
05/26/1942
Filing Date:
06/21/1937
Assignee:
Smith, Lybrand P.
Primary Class:
Other Classes:
415/914
International Classes:
B63H1/12; F03B3/12; F03B11/04
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Description:

My invention relates to a marine propeller or water turbine blade and more particularly to such a blade wherein the back or suction side is of such configuration as to retard or delay the formation of burbling cavitation to increased blade velocities. In addition, the invention also contemplates a method of retarding or delaying the occurrence of burbling cavitation to increased blade velocities.

On one side of the blades of a marine propeller or water turbine the pressure is reduced below 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 blade; the face of the blade being 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 back side of the blade shows a suction increasing from the leading edge to a more or less prominent peak and gradually declining towards the trailing edge. Obviously before the blade can be producing its maximum lift the peak of the suction will have reached vapor pressure and burbling cavitation will exist. 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 delay the 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 the entire blade back or suction side from leading to trailing edge.

My invention thus contemplates a method of delaying the occurrence of burbling cavitation on the back of marine propeller or-water turbine blades by maintaining a-substantially uniform pressure distribution thereover as well as the provision of a new and novel back configuration which will insure the maintenance of the aforesaid pressure distribution. The present invention is restricted solely to blades adapted for movement in a liquid fluid medium and is not concerned 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 propeller 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 a back 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 45 adapted for movement in a liquid fluid medium the back of which is qf 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 of a blade in a liquid fluid medium.

Other objects and many or the attendant ad-antages of this invention will be readily appreciated as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying sheet of drawings wherein: Pig. 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 the elliptical 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 Fig. 3 shows a developed blade section which i 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, a number of simplifications are made, which a priori were believed to be reasonable and a posteriori 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 parallel to each other. The following physical statements are 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 to the 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 flows past it but always in contact with it (or the boundary layer) is determined, the location of the lowest pressure can be determined. If a particle of liquid is being ed a r in o h se accelerated a force is involved. In the case of a submerged propeller blade the forces of gravity and cohesion can be ignored and, therefore, the remaining force is a difference in pressure. A particle of liquid moving relative to but in contact with a submerged body has no relative ve- 60 The acceleration locity towards or away from that body, but may be accelerated relatively to the undisturbed fluid and this acceleration may be relatively towards or away from the body. If the acceleration is towards 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 to show the manner employed in formulating the general equation by which the location of the first appearance of burbling cavitation is determined.

Let the figure be the developed section of a blade.

Let P=a particle of fluid moving relative to but always in contact with the blade.

R=radius of curvature of the blade the point thereof touched by the fluid particle P.

Po=position of P when moving parallel to the direction of the motion of the blade in space; 1. e., Po is the "point of tangency" where the curve of the back of the blade is tangent to the direction of motion W, and where 0=0.

Ro=radius of curvature of the blade at point Po.

W=velocity and direction of the blade in space, 1. e., relative to the undisturbed fluid.

V=veloclty and direction of P relative to the blade. The direction must obviously be tahgent 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.

.=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: N=S sin p Eq. 1 Now by a law of trigonometry: W _Eq. 2 sin p sin e Therefore: sin Eq. 3 Hence: N=W sin 0 Eq. 4 The rate of change of N with respect to o is: dN = W cos 0 Eq. 5 Now: d VEq.

di E. Multiplying Equations 5 and 6, we get: dNX d dN WV cos Eq. 7 de X Eq R But dN dt -the component of acceleration in space normal 55 =the component of acceleration in space normal 5 to the blade, so denoting this acceleration by A we have: WV cosEq. 8 R dN dt is the result of a pressure at the blade above or 65 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 de70 pends upon the total pressure at the blade.

From a consideration of the general equation Eq. 8 it can be shown that, under usual operating conditions, burbling cavitation on the back of a blade will begin, in the case of an ogival 75 blade, at a point on the back where the curvature 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 difference 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. The important thing, however, to note in connection with the present invention is that the acceleration A varies over these blade sections with the 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 burbling 'occurs depends 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 cs= constant Eq. 9 R In this latter equation R at any point on the back 30 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 the developed section. If on a developed section of the blade the curve of the back thereof be represented by the equation y-=f(x) Eq. 10 then equation 9 can be put into the differential form: 1 rl -r1/2 d2y [1+ -dX2]2 2 _L - P = constant Eq. 11 4 1+ 1 M d2y d2 50 Equation 11 has not been solved, but I have studied it thoroughly and recognize it represents a figure strongly resembling an ellipse.

Thus, consider a conventional blade wherein any developed section thereof shows a circular arc back as 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 0 R is not constant but decreases from a maximum value in the middle: of the Wlah to, minimum values at the leadsig and trailing edges. Since 65 the suction decreases with decreasing values of cos 0 R h701 its iis abRius that am oaiswia wack eamnne Bare it evma as appmMiimately unifnom satiinm iii tUmi. As waftir&tf ouf JImnh&iimMM, ma asbadism in2= acnfmtlin with NiwBlmlitim 111tefbl aw e to Bf MoW agot xm 2lWfi=GaRlud am a eoDluMeteO& 8- 7 tion should give an approximately uniform suction. I then analyzed the ellipse and found also that in its case cos 0 R is not constant but instead of decreasing from the center of any developed section towards the edges of the blade, it increases. Hence the solution of Equation 11 would be between a circular arc and an ellipse. But before undertaking the labor of solving such a differential equation as Equatioh 11 the simplifying assumptions heretofore mentioned in connection with the formulation of the general equation were re-examined.

One of these simplifying assumptions was that from near the leading edge to near the trailing 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 trailing-edges. To offset or prevent decreased suction from this cause, a value of cos 0 R 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 back sometimes 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 suffered badly from burbiig eavitation, was duplicated in. every mespect except the new propeller was; provided with backs whkth appeared ellipticall fi shae~ ink their developed cross sectionsi. This- novell pPmresllr was them testedl in a variable' pressure water- thaneiL It resistedl burbling aGsamitaflin longer thanm the standard4 prior art propelltr,; alp, at the sip ratios. practical foir popefins;. thte imw,ampili had equalozrskIb emlbnIae effenim.ie M t zmneasatingm~ coditlims andl malntedly greater efCEnyR in thei Gastvtfita G condiMtnm . "When this new, arnilc novell pmnpellir waa fftlsLy fnoiadl faht endatiuaom Br yedUitag ttake asut me em ites =antium siAte tsU a suffiuslrita Ibw vaultu ilkt nihlel ie tBi mmanomr pliedl wAdlrillttBimlianailJy inBEr O tte enteainE lIat. Nbitt'mbratijB ipingntel viBte$ wherein the backs were substantially elliptical in shape in their developed cross sections accomplish the purpose of the present invention, but 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 respectively on 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 back or 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 approximate 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 true elliptical 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 may be 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 elliptical or quasi-elliptical back. In Figs. 1 and 2 of the drawing the pressure side or face 5 of the various developed blade sections are shown as formed by the major axis of the ellipse. For practical reasons this is believed desirable. But there is nothing to prevent the use of a chord parallel to the major axis; a conjugate 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 of operation of my invention and have illustrated and described what I now consider to represent 53 its best embodiment. However, I desire to have it understood that within the scope of the appended claims the invention may be practiced otherwise than as -specifically illustrated and described.

The .invention herein described and claimed may be used and/or manufactured by or for the Government 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 the blade lies at least for its major portion substantially along a curve represented by the differential equation d2y dr- " - constant 1+ Jd 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, said blade in any developed section thereof having a back which lies at least for its major portion along an ellipse and a face which lies at least for its major portion along the major axis of the ellipse.

4. 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 least a part thereof 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 least a part thereof substantially defined by the major portion of a semi-quasi ellipse, the major axis of which coincides with the major axis of an ellipse and the 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 developed section 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 ellipse.

LYBRAND P. SMITH.