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  • 1. Published in Ingenieria Naval November 2009 FROM TVF PROPELLERS TO THE LAST GENERATION OF CLT PROPELLER Evolution of the design process Dr. Gonzalo Perez Gomez naval architect and retired profesor of ETSI Navales de Madrid. † To the memory of Don Ramon Ruiz-Fornells doctor naval architect, whose tireless andenthusiastic support made possible the realization of this tenacious research. 1. SUMMARY The historical evolution of theoretical principles explaining the performance of this type ofpropellers and allowing them to be designed, is described. To make easier the understanding of the text, mathematical formulation any has-been omitted.In reference list, all mathematical developments are included. The link between existing analyze theoretical principles and propeller geometry has been standedout. 1
  • 2. INDEX CONTENTS Page1. SUMMARY 12. INTRODUCTION 33. CORRELATION BETWEEN THE EFFICIENCY OF A PROPELLER AND THE MAGNITUDES 3 OF THE PROPELLER INDUCED VELOCITIES4. PRESENTATION OF TVF PROPELLERS 45. LERBS LIFTING LINE THEORY AND TVF PROPELLERS 46. NEW MOMENTUM THEORY AND CLT PROPELLERS 67. RENEWED LIFTING LINE THEORY AND LATEST GENERATION OF CLT PROPELLER 98. REFERENCES 11 2
  • 3. 2. INTRODUCTION References (1) and (2) are the theoretical principles of the most modern and advancedprocedure, which exists at present to project as accurately as any type of propeller and in particularthe most recent version of CLT propeller. Its differences with the propeller project procedure which has been using so far are verynoticeable. For this reason it has been considered appropriate in the present study justify thereasons for this development. In my 70 years of age and due to my deep dedication to the University, I feel the need to makeavailable to the profession the knowledge learned during my self-didactic work in the field ofpropellers. I was worried too, by de fact that in the future, merits of CLT propellers could be judgedusing our theoretical developments published before 2004. My expertise in this field of hydrodynamics was started around 1970, when Don Ramón RuizFornells (Technical Director) and I (Head of Section for Hydrodynamics) worked in AESA. In tose daysthe design of the propellers were done by the model basins, and for AESA was critical the period oftime necessary to have fully defined the constructive drawings of the propeller of a new building. It was completely normal that in any experimental program would need to be designed andtested over two propellers, which, sometimes, for planning reasons became irremediable have tolaunch the ship without propeller, placing in the stern bearing a blind flange. As a result, Ramon decided that in AESA, besides making the design of hull form, we designed thepropeller, to save time and try to improve the quality of the designs. The price of fuel was very high, and the ship owners in addition to seeking the best prices onconstruction, highly valued that offers with a reduced fuel consumption. The shipyards competed inthe optimization of the ship design and in particular hull lines, and the ship propulsion. The above facts allow the understanding that were initiate a very difficult specialization, whichwas very exciting for me, because of my teaching at the University in the subject Resistance andShip Propulsion. The effort to implement the service of propellers design give us the enough creativity to try toimprove the quality of future ship propellers. 3. CORRELATION BETWEEN THE EFFICIENCY OF A PROPELLER AND THE MAGNITUDESOF THE PROPELLER INDUCED VELOCITIES Let us consider a generic propeller blades anular section. The water falls on it at some angle withthe plane perpendicular to the shaft line. This angle is called the hydrodynamic pitch angle, and is aconsequence of the relative velocity of water relative to the propeller plan and of the inducedvelocity. The forces acting on the propeller blades annular section are: the lift force, which isperpendicular to the direction of incoming water, and viscous resistance, which is opposite to thevelocity of incoming water. 3
  • 4. Projecting these forces in the direction of the shaft line and its perpendicular, it is concluded thatthe net thrust exerted by the ring section increases as the hydrodynamic pitch angle decreases, orwhat is the same, when the induced velocity components decrease. The projection of these forces on the direction perpendicular to the axis decreases, when theinduced velocity decreases. Clearly, therefore, can be concluded that the efficincy of the propeller blades annular sectionsgrows, when the components of the induced velocities decreases. In paragraph 2.7.3.4 of ref. (12), these arguments are fully developed. 4. PRESENTATION OF THE TVF PROPELLERS In ref. (3) it was proposed to improve the performance of the propellers by growingmonotonously geometric pitches of the tip sections, and placing a cylindrical tip plates at the endsof the blades. That conclusion was reached in seeking the type of circulation radial distribution that wouldoptimize the propulsive efficiency of the ship. The used mathematical developments were at a rudimentary theory of propeller blades elements,wich incorporated some additional errors to the criticism in ref. (1). To test the feasibility of these ideas, was conducted in the El Pardo Model Basin a pilot programusing a stock propeller model of Kaplan type, whose geometrical pitches were increasedmonotonically from the hub to the ends of the blades. At this propeller model were set forthdifferent types of tip plates and performed with it, propeller open water test. Although not known at that time, the important effect of scale that affect the results of propelleropen wáter tests, findings obtained were enough stimulants like to go on developing the proposedidea. Ramons support was decisive. I want to emphasize that since then it was fixed in our minds the wrong concept that thegeometrical pitched of TVF propellers end sections should be increased monotonically to improuvethe propeller efficiency. 5. LERBS LIFTING LINE THEORY AND TVF PROPELLERS To prove the feasible to design conventional propellers of ships that were built in AESA, and inorder to design new TVF propellers I conduct a study on the state of the art of the procedures usedthen by the model basin, to the design of propellers. Immediately concluded that the proceduresused by the model basins had an empirical nature, and had no publications in which fully describethe sequence of calculations necessary for the project of a propeller. At that time the six major factories of AESA were fully occupied, thus, the number of model testprograms that I had to manage was very high, and this forced us that in order to make our designsfor conventional and TVF propellers we had to make test orders in the main European model basins. 4
  • 5. This activity allowed and forced me to hold technical discussions with leading European experts inhydrodynamics, leading to the conclusion that I had no other recourse that to develop our owncomputer programs. Therefore, I decided that it was essential to study deeply the paper of Lerbsquoted in ref. (8) of our ref. (1). The effort to understand the paper of Lerbs allowed us to correct and generalize that theory tomake our designs of conventional and TVF propellers, ref. (5). In order to define the three-dimensional geometry of the propellers, I develop a new theory ofcascades, which turned out to be remarkably accurate and valid for any type of propeller (see chap. 4ref. (12)). It was also necessary that I developed an analytical procedure for checking the mechanicalstrength of the blades of any type of propeller. Once the computer program was ready we designed, with the aid of some chemical, conventionaland TVFpropellers. Many propellers were tested and built to full scale whose performance wasreasonably satisfactory. In order to extrapolate at full-scale model test results, was necessary to assess the scale effect ofviscous resistance of the propeller blades. In paragraph 11.3.4.2. Ref. (12) describes the programdeveloped, and which was subsequently accepted as basic in the R + D + i described in ref. (13). At this point, we should remember that Lerbs mathematical developments, based on theassumption that the velocities induced on the propeller disc have values equal to half thecorresponding values at infinity downstream (hypothesis that the propeller is moderately loaded). Our effort was aimed at getting that at the propeller disk the induced velocities were as small aspossible. It happens, however, that in accordance with Lerbs developments, the induced velocities atinfinity downstream would also be small, so that the thrust of the propeller would be too small andthe same would happen to the efficiency of the propeller. This paradox was a result of not taking into account in the arguments the existence of radialcontraction of the liquid vein that passes through the propeller disk. Although the omission of the influence of contraction of the vein did not invalidate completelysettled our developments, it was inevitable to have to try to introduce such influence on thecalculation of induced velocities. The procedure developed was a mixture tedious, of Lerbs analyticalsolution, and an a iterative numerical integration program, which is to define the equilibriumpositions of free vortices, discretized then and calculate the induced velocities by applying the Biot-Savart law. See ref. (6) or paragraph 3.5.13. Ref. (12). It was obvious that they were exhausted the possibilities of application of Lerbs induction factorsin the design of TVF propellers. Were published or presented at various conferences, many informative technical papers of thebrilliant successes had been achieved at full scale. In the design of TVF propellers theoreticalresources were used combined with the inevitable weightings of empirical nature (chemistry). Since being introduced TVF propellers, we claimed always that excited vibration levels on the hull,for these propellers, would be reduced due to the lack of blade tip-vortex. Obviously, the smalleroptimal diameter of TVF propellers was also working. 5
  • 6. Because of my activities at the University, I had begun serious study of the propeller momentumtheory by finding that it incorporated some mistakes, I set out to correct. 6. NEW MOMENTUM THEORY AND THE CLT PROPELLERS Having become convinced that it was imperative to take into account in design calculations, theinfluence of radial contraction of the liquid vein, it made sense to pass this influence in defining thethree-dimensional geometry of the propeller. Premature and forced retirement of Ramon and other executives of AESA, was associated withthe onset of labor problems for those who had been his closest collaborators, so I decided tocontinue my career out of AESA. In ref. (11) includes the text of my patent application of CLTpropellers. The CLT name attributed to this type of propeller, comes from the features claimed in thepatent application, "Contracted Loaded Tip Propeller." Reference (4) corresponds to the publication that is designated for the first time, this type ofpropeller with the name CLT Once out of AESA, promoted the creation of Sistemar, among others, Don Ramon Ruiz-Fornells,Don José María Rotaeche, Don Juan González-Adalid, and me. Later on joined us Don Alfonso Alfaro,Don Javier Ferrer, and Don Gerardo Bonnin. The momentum theory is characterized by modeling the action exerted by the propeller on thesurrounding water. In this theory the action of the propeller disk is modeled using an actuator diskthat causes in the wáter a discontinuity in the axial distribution of pressure field. Upstream produces some depression edp, while downstream there is an excess of pression (1-e)dp, where dp total magnitude of the jump of pressure, which is linearly related to the thrust exertedby the propeller. Applying Bernoullis theorem, it is posible to relate the pressure field, with the field of the axialcomponents of water velocites. In the original version of this theory, it was wrongly concluded that the magnitude of the axialcomponent of induced velocity in the disk of the propeller was equal to half the magnitude of thiscomponent at the infinite downstream. In ref. (8) I showed that this conclusion was wrong and I deduced the right expressions of theaxial components of the velocities induced in the actuator disk, dependent of coefficient e and, andat infinite downstream, dependent only of the thrust of the propeller. The energy balance, with which it was intended to calculate the angular components of theinduced velocities in the original momentum theory was totally wrong, and I correct it (ref. (7), fromthe 1982 edition), ref. (9), ref. (10), ref. (12) (3.8)). Corrections on the momentum theory encouraged me to call the new developments newmomentum theory. In the case of conventional propellers, when one could accept the hypothesis were moderatelyloaded, one could assume that the axial component of induced velocity in the disk of the propeller, 6
  • 7. had a value equal to half the corresponding value at infinite downstream, thereby circumventing theneed to attach a value to the factor e. When it was not a conventional propeller moderately loaded, I found that e factor remainedalmost constant at 0.4167. We note with great satisfaction that with the procedure developed for the calculation of inducedvelocities was achieved to predict the efficiency and the geometric pitches of conventionalpropellers, without resort to any further empirical support. There is a copious list of referencesjustifing the excellent results obtained. Analyzing the expression of the efficiency of a propeller blades annular section is concluded thatthis increases as the factor e decreases. On the other hand when e decrease the pressure increasesin the pressure side of the propeller blades and the pressure decreases in the suction side ofpropeller blades. I found no valid analytical expression allows us to calculate the value of the factor e that shouldbe introduced in the calculations, when designing a CLT propeller for a given radial loadingdistribution. To design CLT propellers were available only the recommendation that the factor e should be assmall as possible, or what is the same, to be achieved, the pressure in the pressure side of thepropeller blades to be as large as possible. In ref. (12) are include the most important developments that have been created to discernwhether a given value of the e coefficient it is admissible for some propeller blades anular section.Speculative resources are also included to deduce the value of the most appropriate e coefficientassociated with a given radial loading distribution. At this point, it is essential to establish, that to qualify a design procedure as consistent, it shouldrequire at least that it be exempt from empirical calibrations, the design speed be achieved in reality,and that geometrical pitches and the camber – chord ratios be appropriate. In the present case, by a process of trial and error, to predict correctly the design speed, it wasconcluded that an e factor should be used, ranging between 0.12 and 0.2, depending on the type ofship. Under these conditions the geometric pitches were prohibitive. To perform the detailed design of the propeller it was used a value of e factor close to 0.09. Thespeed prediction was extremly optimistic and the propeller rpm was light. To correct this inconvenient, when it was defined the geometry of the propeller blades annularsections, the cambers-chords ratios were reduced and consequently the geometrical pitches wereincreased. Thus the right revolutions of the propeller were obtained, but the propeller blades annularsections work very far from the free-sock entrance conditions. Having in mind the objective to get radial loading distributions with a significant excess ofpressure on the pressure side of propeller blades, still were using radial geometrical pitchesdistributions which monotonically increased geometrical pitches toward the ends of the blades. The resulting propeller efficiency depended on the value assigned to the e factor and if thegradient of the radial distribution of geometrical pitches be adequate for design conditions of the 7
  • 8. propeller in question. A low gradient may not generate the necessary over pressure, and an excessivegradient could lead to inadmissible flow separations in extreme annular sections, and increasing theviscous resistance of the propeller blades in this región. As regards the cavitación behavior of the propeller, apart from the boundary conditions, thedesigns had to favor the lowest underpressure existing upstream, due to the low value of the factore, and against the flow separation produced in the tip sections of the propeller, as a consecuence ofthe excessive angle of attack. Besides the risk of vibration excitation, highest risk in relation to the cavitation behavior of thepropeller was due to the possibility that the separated flow existing in the tip sections could returnon the blades causing cloud cavitation, with the consequent erosion. To successfully conduct the CLT propeller cavitation tests, it was necessary to develop the specialprocedure described in ref. (13) to take into account the scale effect that affects to the viscousresistance of the propeller blades in the model field and to the value of the a factor during thecavitation test. The number of CLT propellers built and designed with the help of the new momentum theory hasbeen very high. And there were also some results obtained at full scale, seemingly inexplicable, butwhich can be justified taking into account the foregoing arguments. I must place on record the great support received from Don Ramón López Diaz-Delgado TechnicalDirectorof Navantia who incorporated to us to a numerous research programs led brilliantly by DonMariano Perez Sobrino in which we cooperate with experts from Navantia of CEHIPAR, TSI and othercompanies. It has also been very important the support received from Don José Luis Cerezo Preysler and DonAntonio Sanchez Jauregui, both from the Gerencia del Sector Naval, at the time. In ref. (13) it is described the programs of R & D & i in Spain have helped establish theexperimental technique of CLT propellers. The numerous cavitation tests carried out on programs of R + D + i that have been made with CLTpropellers have revealed that the tip sections of these propellers have important flow separation,which can cause cloud cavitation. In several CLT propellers that have been built, erosions have appeared in the tip sections of theblades. In order to try to avoid the risk of cloud cavitation, I proposed that in the future, the end sectionsof the blades had a negative rake, in order to hinder, return on the propeller blade, of separatedcavitating flow. Due to the evidence that, without doubt, the propellers designed using the procedure describedare too loaded at the tips of the blades, I since 2003, strongly recommend, unsuccessfully, toSistemar to modify the design procedure that it was being used. 8
  • 9. 7. RENEWED LIFTING LINE THEORY AND THE LAST GENERATION CLT PROPELLER At University, during 2003-2004, in addition to being professor of Resistance of Ship Propulsion Ialso was profesor of graduate course in Advanced Procedures to Design Ship Propellers. I proposed to the students that we would do a small research project, once complete it would bepublished in Ingenieria Naval. As at the time I was immersed in developing a new propeller designprocedure, I proposed then to perform the work described in ref. (1). I imposed the condition thatthey should make their own computer program, in order that the effort to be done by then, wouldresult for them useful. I looked to find an alternative and more accurate design procedure, to the new momentumtheory. The looked design procedure must connet the shape of radial loading distribution with thepropeller open water efficiency, and must allow to the designer to obtain geometrical pitchesdistribution decresing towards the blade tips. In ref. (1) emphasizes that the Goldstein theory had the attractive of working with an infinitenumber of blades, and considering that the vortices are threaded into a cylinder of infinite length.Due to this, the calculation of induced velocities is simplified significantly. The influence of contraction of the liquid vein is automaticly taken into account, since the inducedvelocities are calculated at the infinite downstream, once the free vortices adopt their equilibriumpositions on a cylinder. The components of induced velocities correspondic to the propeller disck are calculatedrespectively by applying the continuity equation and the conservation of angular momentumbetween the the propeller disk and the infinite downstream. In ref. (1) it was demostrated tha a new design procedure for conventional propellers had beenobtained correcting adequately the traditional Goldstein procedure. The asumption that it is posibleto replace a finite number of propeller blades by a infinite number of blades were pruved to becorrect. Also it was proved that the new procedure is compareble, in the case of conventionalpropellers, to the new momentum theory. In ref. (2) was presented the generalization of this procedure for the case of CLT propellers. It is introduced as input the radial distribution of circulation. In the case of conventionalpropellers, necessarily, such distribution ends in a null value at the tip of the blades. The calculation process does not require the introduction of any empirical weighting, andcalculation results are excellent, and the prediction of the speed of project is very precise andgeometric pitchs are also successful. The advantage of this project procedure (ref. (1) and ref. (2)), to be called the renewed lifting linetheory, over the new momentum theory lies in that in the case of conventional propellers, it must nobe assumed if the propeller is moderately loaded or not, when calculating the axial componentinduced velocity. The importance of the load of the propeller it is automatically taken into account inthe results of the calculations. To ensure that a propeller has a high efficiency, its induced velocities must be smaller than in thecase of a conventional propeller. In ref. (2) it is justified the hydrodynamic model of systen of radial 9
  • 10. and free vortex that has to manage to get induced velocities only produced by a fraction of theordinates of the radial circulation distribution. Also it is justified the need of having to install a tip plates on the ends of the propeller blades,with the aim of reaching a non-zero circulation in the blades tips. Naturally, as in the case of new momentum theory, the size of the tip plates must be appropriatein order to reach the intended circulation at the ends of the blades. I must correct the contents of ref. (2), with respect to the component of the radial distribution ofthe circulation that ends with a nonzero value at the ends of the blades. This may also have anonzero value at the propeller hub, without the viscous resistance of the blades is seen unfavorablyaffected. I have found that making this component maintains a constant value radially from the hub to theends of the blades, the results of the calculations, besides being very precise, are very accurate. The radial distribution of geometrical pitchs, which are obtained using this method of project isvery different from that obtained using the new momentum theory. The pitchs of the end sections ofthe blades decrease monotonously to the ends of the blades. The marked differences in their geometry show the birth of a new generation of CLT propellers. From the appearance of the radial circulation distribution is easy to conclude that the endsections of the blades are downloaded, as intended. This procedure does not require empirical correction coefficients, and their results are excellent,both as regards the prediction of the ship velocity, as the radial distribution of geometrical pitches. The annular sections of the blades can operate in conditions as close as you want to the onescorresponding to free shock entrance. From the point of view of excitation of vibrations on the hullthis procedure has the following advantages over the new momentum theory: The end sections of the propeller blades are much more downloaded, thus the excitation of vibrations caused by phenomena of flow separation are lower. The station more loaded it is not the blade tip but another station close to 0.7, and therefore farther from the hull. The annular sections are operating in conditions closer to those of free- shock entrance, and the camber-chord ratios are very close to the optimum, thereby decreasing the extent of the sheet cavitation. It is important to mention also that the quality of the preliminary design that are obtained bycombining the design procedure with the theory of Lerbs equivalent profile (ref. (2)) is excellent. Theresults obtained are very close to those of the detailed design. I must place on record that, I was able to make a design of a new generation CLT propeller, whichwas tested and the results were excellent. Its ship speed exceeded by 3.22% to the corresponding to a conventional propeller alternative.The speed prediction was diferent from the one corresponding to the extrapolation of model test in 10
  • 11. a 0.77%, and the prediction of ship velocity obtained from the preliminary design disagree with theone obtained from the extrapolation of model test in 0.22%. Geometrical pitch corresponding to station 0.7 disagreed with the needed in 1.8%, and thegeometrical pitch predicted in the preliminary design disagreed with the required in 5%. CLT propellers are becoming popular today. Reference (14) is an excellent example of theapproach to the study of their behavior with the aid of CFD. This work includes the discussion I hadwith authors, courtesy of Don Antonio Sanchez-Caja. He hoped that the new design resources that have been developed will be useful to theprofession, and I hope that in future the justification of the merits of CLT propellers are made takinginto account the content of this contribution. 8. REFERENCES 1. Pérez Gómez, G., Souto Iglesias, A., López Pavón, C., González Pastor, D., ¨Corrección yrecuperación de la teoría de Goldstein para el proyecto de hélices ¨. Ingeniería Naval. Nov. 2004. 2. Pérez Gómez, G., ¨Utilidad de la teoría renovada de las líneas sustentadoras para realizar eldiseño de hélices con carga en los extremos de las palas, y para estimar el rendimiento de cualquierhélice al efectuar su anteproyecto ¨. Ingeniería Naval. Marzo 2007. 3. Pérez Gómez, G., ¨Una innovación en el proyecto de hélices ¨. Ingeniería Naval. 1976. 4. Pérez Gómez, G., González – Adalid, J. ¨Comportamiento del Sesermendi Barri dotadoalternativamente de una hélice convencional en tobera y de una hélice CLT ¨. Rotación ¨. Julio 1987. 5. Pérez Gómez., y Baquerizo Briones, I. ¨Análisis de las contribuciones de Lerbs, de Morgan yde Wrench sobre la teoría de las líneas sustentadoras, enmiendas a sus resultados yperfeccionamiento de las mismas¨. Ingeniería Naval, Mayo 1978. 6. Pérez Gómez, G., González Linares., and Baquerizo Briones,I., “Some Improvements ofTraditional Lifting Line Theory for Ship Propellers”. International Shipbuilding Progress, July 1980. 7. Pérez Gómez. G., “Conferencias sobre Teoría del Buque¨ ETSI Navales de Madrid. Sucesivasediciones desde 1973. 8. Pérez Gómez. G., ¨ Correcciones a la teoría clásica de la impulsión y habilitación de la mismapara el diseño de propulsores¨. Ingeniería Naval. Enero 1983. 9. Pérez Gómez. G., Pérez Gómez, G., Baquerizo Briones, I., González Adalid, j .,¨ Aplicacionesde la nueva teoría de la impulsión al diseño de propulsores ¨ .ingeniería Naval. Julio 1983. 10. Pérez Gómez. G., Application of a New Momentum Theory to the Design of Highly EfficientPropellers¨ WENT, Paris julio 1984. 11. Pérez Gómez. G., ¨ Solicitud de patente de invención referente a los propulsores de losbuques caracterizados por la incorporación en las secciones extremas de unas placas tangentes a la 11
  • 12. superficie de revolución que encierra a la vena liquida que atraviesa al propulsor, con lo cual el radiodel extremo del borde de salida ha de ser menor que el radio correspondiente al borde de entrada.Etc…¨. Registro de la Propiedad Industrial. 13 de Agosto de 1985. 12. Pérez Gómez. G., González Adalid, J. ¨ Detailed Design of Ship Propellers¨. Libro editado porFondo Editorial de Ingeniería Naval. Madrid 1998. 13. Pérez Gómez, G., Pérez Sobrino, M., González Adalid, J., García Gómez, A., Masip Hidalgo,J., Quereda Laviña, R., Minguito Cardeña, E., Beltrán Palomo, P., ¨Un hito español en la propulsiónnaval. Rentabilidad de un amplio programa de I+D+ i ¨´. Ingeniería Naval .Junio 2006. 14. Sánchez-Caja, A., Sipia, T.P., Pylkkanem, J.V., ¨Simulation of the Incompressible Flow aroundan Enplate Propeller Using a RANSE Solver ¨, 26 Symposium on Naval Hydrodynamics, Roma 17-22Sept. 2006. 12