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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER 511 Experimental and Numerical Investigation of the Unsteady Flow around a Propeller P.G.Esposito, F.Salvatore, F.Di Felice, G.Ingenito (Istituto Nazionale per Studi ed Esperienze di Architettura Navale, Italy), G.Caprino (Centre per gli Studi di Tecnica Navale, Italy) ABSTRACT In the present paper the analysis of the flow around the propeller of a twin screw vessel is performed both experimentally by LDV measurements and numerically by a potential flow solver. The velocity fields obtained through the experimental survey have been used to assess the accuracy of the solver for the application to modern propellers, featuring rather extreme geometries and large pitch variations. The results show that, in spite of the approximations introduced, the solver is able to capture the main features of the flow. The combined use of numerical and experimental tools reveals itself as a fundamental step for a deep comprehension of phenomena taking place in modern ship units. INTRODUCTION Large fast vessels represent a severe challenge to ship designer in the quest for outstanding calm-water performance. The hydrodynamic optimization of the propeller being an essential step of this pursue, the need of reliable and effective tools for the analysis of propeller flow is much felt. The typical configuration is a twin screw controllable pitch propeller with quite a long shaft, due to the gradual rise of the keel in the aftbody, and a set of shaft brackets with a L arrangement so that the vertical bracket is in the shaft wake. The request of large thrust and the constraint on the maximum diameter posed by tip clearance naturally lead to high expanded area ratios; rather extreme skew distributions are adopted to decrease induced pressure pulses, while large pitch variations allow to avoid excessive loading at the propeller tip. Time honored computer codes based on lifting surface theory are inadequate to deal with the new propulsive configurations and are currently in the process to be replaced by panel methods, which provide a fully three dimensional model of blade geometry. On the other hand, the complexity of the unsteady phenomena involved requires a thorough validation of such codes in operating conditions. To this end, high quality experimental data of the flow around the propeller are needed. A joint effort within the framework of the national research program has been undertaken by INSEAN and CETENA to achieve a better physical understanding of the unsteady effects on propeller performance through model tests in the circulating water channel and the application of an unsteady panel code, described in Esposito and Giordani (2000). Flow field survey has been performed upstream and downstream the propeller by using Laser Doppler Velocimetry (LDV). LDV is a key technique for investigating the complex flow around propellers and many studies are available for uniform inflow, see e. g., Min (1978), Kobayashi (1982), Cenedese et al. (1985), Jessup (1989), and for axisymmetric inflow by Hayun and Patel (1991). However, very few studies of propellers operating in non uniform inflow are available, since the experimental analysis is particularly onerous, requiring several days of facility occupancy and a huge amount of data to be processed. The experimental technique adopted for the present measurements allows the reconstruction of the three dimensional velocity field in phase with the propeller. The high level of detail reached by these measurements represents a powerful tool for the analysis of the complex phenomena taking place in propeller-hull-appendage interaction. In addition to the experimental investigations, a theoretical analysis of the flow field around the propeller has been performed by using a Boundary Ele the authoritative version for attribution.

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER 512 ment Method (BEM) for the velocity potential. By comparing the numerical results with the experimental findings, the capability of a potential flow model to study the wake past a propeller in the non uniform flow induced by a ship hull is addressed. In literature, many works dealing with the prediction of marine propeller performance by BEM are available. Unsteady flow analyses are given, e. g., by Kinnas et al. (1990), Koyama (1992), Hoshino (1993). In these formulations the shape of the wake is prescribed either from blade pitch distribution or by using semiempirical models. Such approaches do not allow accurate predictions of the trailing vorticity path and hence of the flow field downstream the propeller. In order to overcome these limitations, the shape of the wake must be determined as a part of the flow field solution. Theoretical models in which the propeller wake is aligned with flow velocity are proposed by Greeley and Kerwin (1982) and Pyo and Kinnas (1997). In the present approach a Langrangian wake-alignment procedure is used. In order to reduce the computational effort, a two-step technique is proposed. The wake shape is assumed to be slightly affected by the circumferential variations of the incoming flow. Hence, a steady-flow wake alignment analysis is performed by using as input an axisymmetric inflow obtained by considering the circunferential average of the hull wake on the propeller disk. Next, the computed wake surface is used as input of a prescribed wake unsteady flow computation in which the actual non uniform inflow is used. EXPERIMENTAL ANALYSIS Experimental setup Measurements have been carried out at the INSEAN free surface Circulating Water Channel, having a test section of 10 mÃ3.6 mÃ2.25 m; the maximum flow speed is 5 m/s, and pressure may be reduced to 4 KPa. Figure 1: Sketch of the hull model. Figure 2: View of the model installed in the water channel. The hull model is represented by the starboard half of a twin screw vessel and it is 6.4 m long, while the propeller has a diameter DP=275 mm. The propeller and the aft region between the transom and the 8/20 station are scaled by factor Î»=20. The fore region is shrinked in the longitudinal direction in order to fit into the channel test section while preserving the sectional area distribution (see Fig. 1). The four-bladed, adjustable-pitch, highly skewed propeller is installed on an open shaft supported by two bearings that are attached to the hull by shaft brackets. Figure 2 shows a view of the model with the propeller installed. Fig. 3 shows a sketch of the experimental setup. Flow velocity components are measured by means of a two component back scatter LDV system, in which a 5 W Argon laser produces a radiation that is collimated by an underwater fiber optic probe in the measurement point. The frequency shift, required for the velocity versus ambiguity removal, is provided by a 40 MHz Bragg cell. Real time analysis of the the authoritative version for attribution.

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER 513 Doppler signal is performed by two TSI IFA 550 processors. Only two velocity components can be measured simultaneously, thus two optical configurations are adopted for resolving the three dimensional velocity field and measuring respectively the longitudinal/vertical and the transversal/vertical velocity components. Therefore, particular care is required in the initial location of the measurement volume to reduce positioning errors of the two optical configurations. The initial position of the probe volume is fixed with an accuracy of about 0.5 mm. The underwater probe is set up on a computer-controlled traversing system, which permits to get a displacement accuracy of 0.1 mm in all directions and to achieve a high automation of the LDV system. Figure 3: Sketch of the experimental setup. A rotary incremental 3600 pulse per revolution encoder supplies the actual propeller position with an angular accuracy of 0.2Â°. Signals from the encoder are processed by a synchronizer which provides the propeller angular position to a two-bytes digital port available on the LDV master processor. In order to improve the processor data rate and to reduce the time acquisition length per point, the channel water is seeded upstream the ship model with titanium dioxide (TiO2) particles by using a special seeding rake device. Data acquisition is accomplished by using a low-end personal computer, whereas the post processing analysis requires several GBytes of data storage. First, the hull nominal wake is measured on the propeller disk. The operating propeller condition is analyzed on two transverse measurement planes placed upstream and downstream the propeller. On each plane, 400 measurement points are distributed by a Cartesian grid within a circular area of diameter DM=316.25 mm =1.15DP. A grid spacing of 12 mm in both horizontal and vertical directions is sufficient to have a good resolution in the tip vortex regions; a higher grid resolution is used in the wake regions of the brackets. Measured data are post-processed in order to obtain velocity fields with angular resolution of 2Â°. Phase sampling technique The application of flow measurement techniques with operating propeller is complicated by the flow unsteadiness also in a frame of reference that rotates with the propeller. As a consequence, experimental techniques for open water propellers based only on radial movements of the measurement volume, like those described in Min (1978), Kobayashi (1982), Cenedese et al. (1985), Jessup (1989), are not valid and a different approach is required. In particular, measurements covering all the investigated disk must be taken at different propeller angular positions. In addition, the acquisition time must be so long to provide a sufficient number of samples to make possible statistical data post-processing. In the present work, the Tracking Triggering Technique (TTT) proposed by Stella et al. (1998) is utilized. Velocity samples are acquired when Doppler signal is detected on the corresponding LDV system channel. Next, each LDV sample is tagged with the angular propeller position at the measurement time by means of an encoder-synchronizer system and then stored in the PC memory. This process is repeated independently for both LDV channels because it is experienced that Doppler burst are not necessarily detected simultaneously. In the post processing phase, data averaging is performed. A slotting technique is required because LDV samples are not equally spaced in time (burst detection in the measurement point is a random event) and classical ensemble averaging is not possible. Therefore, each sample is rearranged in angular slots of constant width. By evaluating averages at each slot, values of velocity components at any angular position are obtained. The choice of the slot width is critical for this kind of analysis as described by Stella et al. (2000). In fact, a compromise should be obtained between the need to increase the angular resolution (to capture velocity fluctuations) and to have an adequate number of samples (required for statistical consistency). For instance, the standard slotting procedure- N contiguous slots of constant width from 0Â° to 360Â°âprovides poor statistical processing accuracy. Hence, more complex the authoritative version for attribution.

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER 514 slotting procedures are to be implemented in order to guarantee statistical requirements and angular resolution, also in the case of critical data rate conditions. Three independent slotting procedures are used in the post-processing phase: overlapping, blade slotting and weighted slotting. The overlapping procedure provides partial overlapping, wide, for contiguous slots. Hence, any sample in the overlapping area increases the two overlapped slots statistical population simultaneously, with statistical processing advantages. The blade slotting procedure is based on the assumption that all the propeller blades are identical both in mechanical and in geometrical terms. By this assumption, the velocity field at any measurement point is a periodic function of time with blade frequency. Thus, the slotting procedure can be limited inside a circular sector of width 360Â°/Z, where Z is the number of blades. A given slot, with center in the angular position Î¸i and width will contain all the velocity samples acquired when the angular position is Î¸=Î¸i+2Ïn/Z, (n=0, 1, â¦Z). Hence, the sample population of each slot is increased by a factor corresponding to the propeller blade number. In the weighted slotting procedure a weighted average is introduced in the statistical analysis so that the influence of each sample decreases by a prescribed law (linear or Gaussian) as the distance from the slotting center increases, with accuracy improvement. In the present analysis, statistical evaluation is performed by using a blade slotting technique with 360 overlapped slots of amplitude and weighted averaging by Gaussian law. In such way 150Ã·200 samples per slot are collected; in addition, angular resolution is adequate to describe flow regions with high gradients. THEORETICAL ANALYSIS Governing equations In the following, a frame of reference (Oxyz) that is fixed with the propeller (hereafter referred to as the rotating frame of reference), as shown in Fig. 4, is considered. The hull-induced wake is prescribed in the propeller disk as vW=vW(Î¸, r), where Î¸ and r are polar coordinates in the propeller disk plane. Hence, the flow incoming to the propeller in the rotating frame of reference is (1) where â¦=(â¦, 0, 0) is the angular velocity of the propeller. Figure 4: Frame of reference. The perturbation induced by the propeller to the velocity field is assumed to be irrotational, and hence it can be expressed in terms of a scalar potential. Denoting by the perturbation velocity potential, the total velocity field in the rotating frame of reference is given by (2) Under the assumption of incompressible flow, the velocity potential satisfies the Laplace equation, (3) where denotes the unbounded fluid region surrounding the propeller and its trailing wake. As usual in potential flow analyses of lifting bodies, the wake is included by assuming that the vorticity generated on each blade is shed into a zero thickness layer which is replaced by a discontinuity surface for the velocity potential. The pressure field in is given by the Bernoulli equation that, in the rotating frame of reference, reads (4) where q= Ç q Ç , Ï I= Ç vI Ç , p0 is the undisturbed flow pressure and Ï is the fluid density. In order to solve Eq. (3), boundary conditions must be imposed on On the propeller surface the impermeability condition yields q Â· n=0, and recalling Eq. (2), the authoritative version for attribution. (5)

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER 515 where n is the outward unit normal to Boundary conditions for on the wake surface are determined by applying mass and momentum conservation laws across the surface. One obtains (6) where the symbol â denotes the jump across upper and lower sides of the wake. Applying the Bernoulli equation (4) on the two sides of the wake and recalling Eqs. (6), yields (7) where qW denotes the averaged flow velocity on the two sides of the wake. Equation (7) means that the potential discontinuity is convected along wake streamlines with velocity qW. Hence, the potential discontinuity at an arbitrary wake point xW and time t may be expressed as (8) where xWTE is the trailing edge wake point lying on the same streamline as xW, whereas ÏW denotes the convection time from xWTE to xW. A further condition on is required in order to assure that no finite pressure jump may exist at the blade trailing edge (Kutta condition). Following Morino et al. (1975), this is equivalent to impose (9) where and denote, respectively, blade trailing edge points on suction and pressure sides. Boundary integral formulation In the present approach, the Laplace equation for is solved by means of a boundary integral formulation. By recalling the first of Eqs. (6), the application of third Green's identity gives (10) where G=â1/4Ï Ç xây Ç is the Green's function of the Laplacian operator in an unbounded three dimensional domain; in addition, E=0, 1/2, 1 if x is inside, on, or outside respectively. If x is on Eq. (10) represents a Fredholm integral equation of the second kind for in which on is known from Eq. (5), and on is expressed in terms of on by combining Eqs. (8) and (9). The perturbation velocity may be evaluated by taking the gradient of both sides of Eq. (10), as (11) where â x is the gradient operator acting on x. Once on is known from the solution of Eq. (10), the equation above provides an explicit representation of the perturbation velocity field. Wake analysis In both Eqs. (10) and (11) the location of the wake surface is not known a priori and should be either prescribed or determined as a part of the flow field solution. In order to determine the location of the condition that all the wake points move according to the local flow velocity is applied. Such procedure is referred to as wake alignment, and it stems from Eqs. (6) and (7). In the present work a Lagrangian scheme is used: the location xW of an arbitrary wake point changes with time as (12) However, the inclusion of a wake alignment procedure into a boundary element analysis of unsteady propeller flows produces time consuming computations. In fact, Eq. (12) requires at each time step the evaluation of the velocity q at all the wake nodes (see below). In order to reduce the computational effort, a two-step technique is used. First, a steady flow wake alignment analysis is performed by using as input an axially symmetric inflow which is obtained by averaging in circumferential direction the non uniform hull-induced inflow (cfr. Eq. (1)) the authoritative version for attribution. (13) with (14)

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER 516 Next, the computed wake surface is used as input of an unsteady flow computation with prescribed wake in which the non uniform inflow vI is used. Discretization A numerical solution of the boundary integral formulation for the velocity potential outlined above is obtained here by using a boundary element method. The propeller surface and the wake are divided into hyperboloidal quadrilateral elements. The angular extension of wake elements is constant and is given by âÎ¸W=â¦ât, where ât denotes the time step. The distribution of over is evaluated by enforcing Eq. (10) in discretized form at each centroid on the propeller surface (collocation points). Flow quantities are assumed to be constant on each element. Denoting by NP the number of elements on the propeller surface, and by NW the number of elements on the wake, one obtains (15) where Î´ij=1 if i=j and Î´ij=0 otherwise, and (16) denote the influence at xi of, respectively, sources and doublets distributed on the j-th surface element on or Next, by discretizing Eq. (11) at an arbitrary field point xi one obtains (17) where (18) The evaluation of source and doublet coefficients in Eqs. (16) and (18) is performed analytically as in Morino et al. (1975). On the other hand, the analytical evaluation of the doublet coefficients in the wake is based on the equivalence between a piecewise constant distribution of doublets and a vortex lattice (see Campbell (1973), for details). Specifically, one has (19) where r=yâx, and r= Ç r Ç . Hence, the velocity induced by a constant doublet distribution on a quadrilateral element is equivalent to that induced by a square vortex ring lying on the panel edges. In order to avoid numerical instabilities, a finite vortex core is utilized. This denotes a flow region where the intensity of the velocity induced by the vortex at a given point is linearly proportional to the distance from the vortex axis. A physical motivation of the vortex core may be given in terms of viscous flow effects. In order to stress the analogy with viscous flows, a variable vortex core radius is used, where rÎµ0 is the vortex core radius at trailing edge, ârÎµ is a growth factor and s is the arclength in streamwise direction. Solution procedure First, a flow-aligned wake surface is determined by using the circumferentially averaged inflow given in Eqs. (13) and (14). In such conditions, the flow is steady in the rotating frame of reference. Wake alignment is achieved through an iterative procedure. As initial guess, the wake shape is prescribed as a helical surface that leaves the trailing edge tangent to the mean line of each radial blade section; wake pitch varies linearly until an ultimate constant value equal to the propeller mean geometrical pitch is reached. By using Eq. (5), with vI replaced by Eq. (15) is solved to obtain on Next, the perturbation velocity is computed by Eq. (17), and the total velocity follows from Eq. (2). Hence, the location of each wake node is updated by the authoritative version for attribution. using Eq. (12) in discretized form. At the k-th step of the iterative process, we obtain1 (20) where is the average between velocity values at the two locations and (21) 1For simplicity of notation, Eqs. (20) and (21) are referred to wake elements lying on the same row in streamwise direction, and m=1 labels wake elements at trailing edge.

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER 517 Figure 5: Computed wake surface. and Î± â [0, 1] is a weight factor (in the present analysis, Î±=1/2). The quantity represents here a relaxation parameter. The alignment procedure is applied only in the wake portion close to the propeller (near wake), whereas the remaining portion (far wake) is determined as a helical surface with prescribed pitch, smoothly connected to the near wake. This yields a reduction of the computational effort, and enhances the robustness of the numerical procedure. Once the wake surface is updated, wake coefficients Dij are re-computed and a new distribution of on is obtained by Eq. (15). The process is repeated until convergence of wake node locations is achieved. As a convergence criterion, the root mean square of the displacement of all wake nodes between two subsequent steps must be smaller than a fixed value (5 Â· 10â4 in present calculations). A sample view of the computed wake surface is shown in Fig. 5. The unsteady flow solution is obtained by solving Eq. (15) in which the non uniform inflow vI is used in the impermeability condition on in addition, the computed flow-aligned wake geometry is used. The pressure distribution on is obtained by the Bernoulli equation (4). Next, unsteady forces acting on the propeller are computed by pressure integration over A simple viscosity correction is introduced by evaluating the friction coefficient Cf according to the Prandtl-Schlichting friction line formula. FLOW FIELD INVESTIGATIONS Tests have been carried out with propeller angular velocity of 7.7 rps and channel upstream velocity of 2.4 m/s, corresponding to an advance ratio J=1.133 and a blade Reynolds number at r=0.7R, Re0.7= 3.7 Â· 105. The aim of the experimental investigations is twofold: â¢ the measurement of the nominal wake to be used as input of the BEM code; â¢ the study of the velocity field upstream and downstream the propeller. All the measurements are taken for two different appendage configurations: vertical bracket at an angle of attack of 0Â° (configuration A) or 7Â° (configuration B) with respect to the x axis. In both cases, the horizontal bracket is at zero angle of attack with respect to the x axis. In the following, all plots show the right inward rotating propeller as seen from the stern. Hull nominal wake Figure 6 depicts the velocity field on the propeller disk by means of contour levels of the axial component and vector plot of the crossflow for the two different bracket configurations. The perturbation induced by the hull and its appendages is mainly concentrated in the top left portion of the propeller disk area, where the two brackets are located; in that region, the effect of the hull boundary layer, the wakes of the brackets and of the shaft are clearly identified. In the other regions of the investigated area the perturbation induced by the hull reduces to a flow inclination due to the rise of the keel in the aft region (see Fig. 2). The low velocity region covering a wide sector around Î¸=0Â° is strongly affected by the angle of attack of the vertical bracket. In fact, in the case of configuration B, the bracket induces a flow acceleration and improves wake uniformity in the outer region, whereas a larger flow separation is observed close to the shaft, compared to configuration A. Similar considerations arise from the analysis of the crossflow. In particular, the upward flow inclination due to the keel shape in the aft region is apparent. In addition, it may be noted a vortex pair in the shaft wake region that is more pronounced in the case of Configuration B (Fig. 6, right). Flow field around the propeller The velocity field with operating propeller is studied in two transverse planes located upstream at x=â0.245DP, and downstream at x=0.371DP. Due to flow periodicity, results are shown in the range 0Â°â¤Î¸â¤90Â°. Experimental results are compared to theoretical predictions. The capability of present numerical the authoritative version for attribution.

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER 518 results to agree with measurements is affected by some basic approximations. First, the measured hull wake is used as an input in the numerical analysis to compute the inflow vW (see Eq. (2)), and no attempt is made to determine the correction due to propeller suction effects (effective wake). In fact, while theoretical models to infer the effective wake from nominal wake surveys have been developed for single screw vessels by e. g. Huang and Groves (1980), similar approaches for twin screw vessels with appendages are not available to the authors' knowledge. In addition, the dependence of the inflow with respect to the axial abscissa x is not taken into account; thus, values measured at the propeller disk (x=0) are assumed to be constant at any x in the computational domain. Furthermore, the effect of the inclined flow induced by the rise of the keel in the aft region is neglected in the modeling of the propeller wake. Figure 6: Hull nominal wake. The numerical results presented here are obtained by using 48Ã24 elements on each blade surface and 12Ã88 elements on each hub sector between two adjacent blades. Wake elements with angular extension of 6Â° are used, and two wake turns are considered in the calculations (with wake alignment limited to one turn). These values provide results whose dependence on discretization parameters is negligible. Downstream plane First flow measurements and theoretical predictions downstream the propeller are considered. Here, the flow field is characterized by the propeller trailing vorticity path. Investigations in this region are of basic importance due to the close relationships between trailing wake shedding and thrust generation by the propeller. The trace of the wake in the investigated plane may be determined from the analysis of the turbulence intensity of the measured axial velocity component. Figure 7 shows turbulence levels in the measurement plane at Î¸=0Â°, 30Â° and 60Â°, for both configurations A and B. Traces of the wake surface predicted by the BEM code are also drawn in Fig. 7 by dashed white lines. The agreement in wake locations between experiments and theoretical predictions is good. In particular, both shapes and angular locations of the wake traces are accurately predicted by the present unsteady flow wake alignment approach. The locations of the four wake tip vortices are indicated by high turbulence cores; differences of turbulence intensity among the tip vortices reflects the unsteadiness of the flow, whereas the wake confinement inside the propeller disk circle (represented by a black line) reveals the contraction of the stream tube downstream the propeller. The effect of vorticity diffusion is apparent from the thickness of the measured wake. In addition, the strong effect of the hub wake with very high turbulence levels is appreciated. The results in Fig. 7 show that the present theoretical model is capable to accurately predict the trailing wake shedding process. This proves that the approximated representation of the incoming flow vI discussed above has only a minor impact on the solution. On the other hand, the numerical evaluation of the velocity field, based on the hypothesis of negligible streamwise variations of the nominal wake, shows some drawbacks. In fact, by comparing experimental and theoretical results, some discrepancies in terms of velocity intensity predictions are observed. This is shown in Fig. 8 that depicts the axial velocity the authoritative version for attribution.

About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. simulations on the downstream measurement plane. EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER Figure 7: Experimental turbulence levels of the axial velocity component and location of the trailing wake by numerical 519

About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. Figure 8: Downstream axial velocity component (Configuration A). EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER 520

About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. Figure 9: Downstream axial velocity component (Configuration B). EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER 521

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER 522 component at angular positions Î¸=0Â°, 30Â°, 60Â°, in the case of configuration A. Figure 10: Upstream axial velocity component at Î¸=0Â° (Configuration A). Figure 11: Upstream axial velocity component at Î¸=0Â° (Configuration B). Similar considerations arise from velocity field surveys in the case of bracket configuration B. In particular, the axial velocity component at angular positions Î¸=0Â°, 30Â°, 60Â°, are presented in Fig. 9. A comparison between Fig. 8 and Fig. 9 shows that the velocity field downstream the propeller is slightly affected by the different bracket arrangement used. In fact, both experimental and numerical results show that the perturbation induced by the propeller tends to smooth any difference between the velocity fields incoming to the propeller. Upstream plane Figures 10 and 11 show the axial velocity component in the upstream plane at the representative angular position of Î¸=0Â° for the two bracket arrangements. By comparing the experimental measurements referred to the two configurations, large differences concentrated in the region where vertical bracket and shaft wakes merge are observed. The agreement between measurements and numerical predictions is not satisfactory. This shows that the hypothesis of neglecting the streamwise variation of the hull wake in the computations is not adequate for theoretical analyses of the velocity field upstream the propeller. This effect has been already pointed out in the discussion of results in the downstream plane, but it is more pronounced upstream. If fact, the the authoritative version for attribution.

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER 523 measurement plane is extremely close to the trailing edges of the brackets; thus the velocity defect of the bracket wakes is stronger and confined in a thinner region than on the propeller disk plane, where the nominal wake used in the computations is measured. Further, this effect is enhanced by the low intensity of the perturbation induced by the propeller. Pressure and performance For the sake of completeness, some additional results obtained by the theoretical analysis are presented. Specifically, Fig 12 shows history of thrust coefficient KT and torque coefficient KQ for both configurations A and B. It may be observed that the stronger shaft wake of configuration B determines higher fluctuations for both KT and KQ than in the case configuration A results. For bracket configuration A, pressure coefficient distributions on the blade surfaces at angular locations Î¸=0Â°, 30Â°, and 60Â° is given by Fig. 13. CONCLUDING REMARKS An experimental and theoretical analysis of the flow field around a four-bladed propeller installed on a twin screw vessel has been presented. Flow field survey upstream and downstream the propeller has been performed by using LDV. Particular attention is payed to set up a procedure suitable for measurements of unsteady velocity fields as is the case of propellers in the wake of a hull. Phase sampling is performed by means of a Tracking Trigger Technique, by which velocity samples are arranged into angular slots according to the propeller position at measurement time. The procedure provides a satisfactory compromise between statistical requirements and angular resolution. The results of the measurement campaign demonstrate the capability of the present LDV phase sampling technique to provide an accurate description of both hull and propeller wakes. The analysis of measured velocity fields is helpful to highlight some important features of the interactions among wakes of the hull appendages and to investigate the flow field in the propeller wake region. In addition, experimental results are used to assess the validity of a theoretical approach based on a boundary element method for the analysis of propellers in non uniform flows. Comparisons with measured velocity fields show that the present theoretical approach provides reasonable predictions of the most relevant flow features in the propeller wake region. In particular, the wake alignment procedure is fully adequate to simulate the trailing vorticity convection process, in which viscosity has a minor influence. Better agreement between theoretical predictions and experimental results could be obtained by taking into account the streamwise variation of the hull wake used in the computations. ACKNOWLEDGMENTS The present work was supported by the Ministero dei Trasporti e della Navigazione in the frame of INSEAN and CETENA Research Programs 1997â99. REFERENCES Campbell, R., 1973, Foundations of Fluid Flow Theory, Addison-Wesley. Cenedese, A., Accardo, L., and Milone, R., 1985, âPhase sampling technique in the analysis of a propeller wake,â in Proc. of the International Conference on Laser Anemometry Advances and Application. Esposito, P.G. and Giordani, A., 2000, âNumerical analysis of non cavitating propeller in uniform and non uniform flow conditions,â in Proc. of the 9th IMAM Congress, pp. B21âB28. Greeley, D.S. and Kerwin, J.E., 1982, âNumerical methods for propeller design and analysis in steady flow,â SNAME Transactions, vol. 90, pp. 416â453. Hayun, B.S. and Patel, V.C., 1991, âMeasurements in the flow around a marine propeller at the stern of an axisymmetric body,â Experiments in Fluids, vol. 11, pp. 105â117. Hoshino, T., 1993, âHydrodynamic analysis of propellers in unsteady flow using a surface panel method,â Journal of The Sociey of Naval Architects of Japan, vol. 174, pp. 71â87. Huang, T.T. and Groves, N.C., 1980, âEffective wake: Theory and experiment,â in Proc. of the Thirteenth Symposium on Naval Hydrodynamics, pp. 651â673. Jessup, S.D., 1989, An Experimental Investigation of Viscous Aspects of Propeller Blade Flow, Ph.D. thesis, The Catholic University of America, Washington, D.C. Kinnas, S., Hsin, C., and Keenan, D., 1990, âA potential based panel method for the unsteady flow around open and ducted propellers,â in Proc. of the Eighteenth Symposium on Naval Hydrodynamics, pp. 677â685. Kobayashi, S., 1982, âPropeller wake survey by laser doppler velocimeter,â in Proc. of the 4th International Symposium on Application of Laser Doppler Anemometry to Fluid Mechanics. the authoritative version for attribution.

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER 524 Koyama, K., 1992, âApplication of a panel method to the unsteady hydrodynamic analysis of marine propellers,â in Proc. of the Nineteenth Symposium on Naval Hydrodynamics, pp. 817â836. Min, K.S., 1978, Numerical and Experimental Methods for Prediction of Field Point Velocities Around Propeller Blades, Tech. Rep. 78â12, MIT Department of Ocean Engineering. Morino, L., Chen, L.-T., and Suciu, E., 1975, âSteady and oscillatory subsonic and supersonic aerodynamics around complex configurations,â AIAA Journal, vol. 13, pp. 368â374. Pyo, S. and Kinnas, S., 1997, âPropeller wake sheet roll-up modeling in three dimensions,â Journal of Ship Research, vol. 41, pp. 81â92. Stella, A., Guj, G., Di Felice, F., Elefante, M., and Matera, F., 1998, âPropeller flow field analysis by means of LDV phase sampling techniques,â in Proc. of the 3th International Symposium on Cavitation, pp. 171â188. Stella, A., Guj, G., and F.Di Felice, 2000, âPropeller wake flowfield analysis by means of LDV phase sampling techniques,â Experiments in Fluids, vol. 28, pp. 1â10. Figure 12: History of propeller loads during a revolution: â, configuration A; , configuration B. the authoritative version for attribution.

About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. Figure 13: Pressure coefficient on blade. EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER 525

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE UNSTEADY FLOW AROUND A PROPELLER 526 DISCUSSION T.Hoshino Mitsubishi Heavy Industries, Ltd. Japan The authors should be congratulated for their efforts to measure the complicated flow fields around a propeller operating in non-uniform flow by LDV and develop a panel method with a flow-aligned wake. I have the following questions. (1) Did you compare the calculated flow fields between with flow-aligned wake and without flow-alignment procedure? (2) Where is the remaining wake (far wake) with prescribed pitch starting from? (3) How many calculations are needed to obtain a final convergent solution? AUTHOR'S REPLY The authors wish to thank Dr. Hoshino for submitting his comments and discussion to the paper. In response to his questions the following remarks can be made: 1. Some comparisons concerning the effects of wake alignment have been presented in a previous paper by Esposito and Giordani [1], where the Seiun Maru HSP propellers has been analysed. In Figure 1, the tip vortex line of the prescribed wake is compared to the flow aligned wake. Of course the different position of the wake in the two cases has a strong impact on the flow field on downstream planar sections orthogonal to the axis. Some effects are also apparent in the loads as shown in Figure 2. 2. In the present computation two wake turns are used, with wake alignment limited to the first turn. 3. Our experience showed that the number of iterations needed to reach wake alignment convergence is slightly greater than the number of streamwise elements of the free portion. 1.1. REFERENCES 1. Esposito, P.G., Giordani, A. âNumerical Analysis of Non Cavitating Propeller in Uniform and Non Uniform Flow Conditionâ, Proceedings of the IMAM 2000 Conference, Ischia, Italy, Apr. 2000, pp. B-21:28. 2. Hoshino, T., âHydrodynamic Analysis of Propellers in Unsteady Flow Using a Surface Panel Methosâ, Journal of the Society of Naval Architects of Japan, Vol. 174, 1993, pp. 71:87. Figure 1: Propeller free wake geometry in axysimmetric flow. Figure 2: Single blade contribution to thrust and torque coefficients along a revolution. the authoritative version for attribution.