Effect of A Propeller Duct On AUV Maneuverability [PDF]

Citation preview

Ocean Engineering 42 (2012) 61–70



Contents lists available at SciVerse ScienceDirect



Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng



Effect of a propeller duct on AUV maneuverability E.A. de Barros n, J.L.D. Dantas ~ Paulo. Av. Prof. Mello Moraes, 2231, 05508-900 SP, Brazil Department of Mechatronics Engineering and Mechanical Systems, University of Sao



a r t i c l e i n f o



abstract



Article history: Received 6 January 2011 Accepted 2 January 2012 Editor-in-Chief: A.I. Incecik Available online 25 January 2012



A number of autonomous underwater vehicles, AUV, are equipped with commercial ducted propellers, most of them produced originally for the remote operated vehicle, ROV, industry. However, AUVs and ROVs are supposed to work quite differently since the ROV operates in almost the bollard pull condition, while the AUV works at larger cruising speeds. Moreover, they can have an influence in the maneuverability of AUV due to the lift the duct generates in the most distant place of the vehicle’s center of mass. In this work, it is proposed the modeling of the hydrodynamic forces and moment on a duct propeller according to a numerical (CFD) simulation, and analytical and semi-empirical, ASE, approaches. Predicted values are compared to experimental results produced in a towing tank. Results confirm the advantages of the symbiosis between CFD and ASE methods for modeling the influence of the propeller duct in the AUV maneuverability. & 2012 Elsevier Ltd. All rights reserved.



Keywords: AUV Ducted propeller Maneuverability CFD Hydrodynamic coefficients Prediction method



1. Introduction A number of autonomous underwater vehicles, AUVs, are equipped with commercial ducted propellers, most of them produced originally for the operation in remote operated vehicles, ROVs. However, AUVs and ROVs are supposed to work quite differently since the ROV operates in almost the bollard pull condition, while the AUV works at larger cruising speeds. Ducts can help the AUV to accelerate from zero to cruising speed. At cruising speed, however, the duct drag effect may cancel or even surpass the additional thrust it produces. Moreover, the duct also contributes to increase the damping effect during manoeuvres. Considering its common location far behind the vehicle center of gravity, the duct effect on the vehicle maneuverability can be quite significant. There is a lack of works on the evaluation of the duct effect on maneuverability for this kind of vehicle. Van Gusteren and van Gusteren (1972) has proposed an analytical estimation method for predicting the effect of the ducted propeller on the steering of ships. Minsaas et al. (1973) have analyzed experimentally the effect of duct propellers on de maneuvering of tankers. Considering the combination of duct and a body of revolution, Falca~ o de Campos (1983), based on numerical flow simulation tools, has analyzed the effect of the duct on the flow at the stern of the hull, however, only the zero angle of attack case was considered. Lift, drag and moment coefficients for the duct alone case have been computed by analytical formulas derived from theoretical



n



Corresponding author.Tel.: þ 55 11 3091 5761; fax: þ3091 5471. E-mail address: [email protected] (E.A. de Barros).



0029-8018/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2012.01.014



results that were validated experimentally for some duct profiles investigated by Morgan and Caster (1965). Considering the numerical simulation, there are a number of works on the application of inviscid flow modeling to the duct propeller analysis. The works of Lewis and Ryan (1972), Gibson and Lewis (1973) were based on the placement of singularities for modeling the duct and the actuator disk, which represents the propeller. Falca~ o de Campos (1983) introduced numerical methods for accounting shear flow effects. Surface panel methods have been developed as well for modeling the duct and the propeller blades (Kerwin et al., 1987; Baltazar and Falca~ o de Campos, 2009). Vortex lattice methods were applied for analyzing the unsteady cavitating performance of ducted propellers subject to nonaxisymmetric inflows (Kinnas et al., 2005). Methods based on the Reynolds Average Navier Stokes, RANS, formulation have been applied also to the duct propellers analysis in order to treat explicitly the viscous effects. Hoekstra (2006) has investigated the duct profiles 19A and 37 for the zero angle of attack case, modeling the propeller as an actuator disk, and obtained good agreement with the experimental results. A number of authors have applied numerical tools to predict added masses, static forces and moments, and the wake field of submarines and other underwater vehicles. In the work of Vaz et al. (2010), two different CFD (computational fluid dynamic) solvers were used for testing a number of turbulence models related to static RANS, applying the American Society of Mechanical Engineers numerical verification and validation methodology, the ‘‘ASME V&V’’. Unsteady RANS and the Large Eddy Simulation formulation were tested as well. The flow simulations were related to two configurations of submarines (with and without the sail and control surfaces).



62



E.A. de Barros, J.L.D. Dantas / Ocean Engineering 42 (2012) 61–70



Recently, CFD methods were used to predict the stability derivatives of AUVs. For example, in the works of Tyagi and Sen (2006) and Jagadeesh et al. (2009) the forces and moments acting upon the AUVs hulls, when they are inclined to the flow (i.e. have an angle of attack), are compared with those obtained in experimental tests in the towing tank. Phillips et al. (2007) applied CFD methods for predicting the dynamic stability derivatives of the Autosub AUV. The turning manoeuvre was simulated, and the computed efforts were compared to those ones obtained during towing tank tests with a planar motion mechanism (Kimber and Scrimshaw, 1994). Tang et al. (2009) also used CFD methods in the prediction of hydrodynamics coefficients of AUVs in block-type shapes. The validation was done by comparison of the vehicle trajectory obtained in simulations and manoeuvres performed in the field. In addition to the identification of hydrodynamic coefficients, the CFD tools are also used to optimize the shape of AUVs (Yamamoto, 2007; Inoue et al., 2010), performance of AUV propellers (Husaini et al., 2008), and to examine the efforts upon AUV hull during the docking process (Wu, 2010). The economy of computational resources and expertise in numerical models make the analytical and semi-empirical methods, ASE, still an interesting alternative to the CFD approaches. The calculation of hydrodynamic derivatives yield approximate results that can be used to predict maneuverability characteristics, select hydroplanes, and investigate control strategies at an early stage of vehicle design. ASE methods are directly focused on the estimation of parameters such as added mass and inertias (acceleration related coefficients), linear and non-linear damping coefficients (related to velocities), and control action related parameters. Advanced approaches to AUV design may also involve combined plant/controller optimization, where prediction methods of hydrodynamic derivatives play an important role (Silvestre et al., 1998). The ASE approach to derivatives estimation provides an analytical formulation based on physical concepts that can help in the interpretation of experimental and CFD results as well as in defining uncertainty intervals for hydrodynamic parameters in order to help the design of robust control systems. On the other hand, some elements of the numerical simulations can be used to improve the ASE predictions. For instance, the flow visualization at the stern of an AUV bare hull was used for improving the normal force prediction in de Barros et al. (2008a). In the work of Jeans et al. (2010) the CFD simulations were applied for modeling the hydrodynamic impulse, which was used for estimating the normal force distribution along axisymmetric hulls at incidence.



This work proposes the combination of CFD and ASE approaches applied to a different problem: the prediction of static efforts acting upon the AUV bare hull combined with a propeller duct. The main motivation of this study is to achieve a method of modeling the effects of the duct on the AUV for manoeuvre simulation and control system design. During investigations on the modeling and control of AUV dynamics, it is common to refer to the hydrodynamic derivatives in the equations of motion. Methods for predicting those parameters may include analytical and semi-empirical, ASE, formula based on the vehicle geometry and mass distribution. In de Barros et al. (2008a), the duct effect on those derivatives was included by the addition of the ASE formula proposed by Morgan and Caster (1965), without considering the interaction between hull and duct. Moreover, the formula adopted had not been tested for a typical accelerating duct such as the 19A. In this work, a CFD technique is used for simulating the flow around a propeller duct at different angles of attack. The numerical predictions are validated according to experimental results for the duct alone case. In a next phase, the interaction between the duct and the bare hull wake is investigated. The vehicle considered is an AUV, which was investigated previously (de Barros et al., 2008a, b). Predictions based on CFD, ASE and on the combination of both approaches are compared to those ones produced during experiments in a towing tank.



2. Numerical model The solver adopted in CFD simulations is the Ansys Fluent 12.1, using the ‘‘k-o shear stress transport’’ turbulence model (Menter, 1994), due to the good results obtained in former investigations (de Barros et al., 2008a). Moreover, in Phillips et al. (2010), the k-o shear stress transport was the 2-equation model, which provided the best prediction of efforts and vortice distribution around a submarine vehicle. A slightly better result was produced by the Reynolds Stress Method. However, its computational cost is much higher, and the method convergence is more unstable when compared to the ‘‘k-o’’ model. Considering the meshing generation, grids around the duct alone and for the hull-duct combination are similar, both having the same kind of elements and are distributed using the O-topology. The grid space was decomposed into three regions: a boundary layer region, the space closely around the vehicle (Fig. 1) or duct, and the outer region. All three regions included only hexagonal elements, the size of which was increased from the body surface to the outer region according to an exponential law. The thickness of the closest elements to the vehicle were



Fig. 1. Mesh generated closed to the bare-hull and duct, using hexaedral elemets with O-topology.



E.A. de Barros, J.L.D. Dantas / Ocean Engineering 42 (2012) 61–70



defined according to the boundary layer size of similar axisymmetric bodies (ESDU, 1978). The outer region is a rectangular volume for the hull-duct combination, whose length is 15 times the vehicle length (26.0 m), the height is about 85 times the vehicle diameter (20.0 m) and the width is about 25times the vehicle diameter (6.0 m). In the simulations considering the duct alone, taking the chord length as unit, the outer region has 100 units length (7.5 m), a height of 80 units (6.0 m) and a 20 units width (1.5 m), resulting in a mesh with 1.5 million elements. Since the hull and duct are axisymmetric bodies, and subjected only to a variation in the angle of attack, a grid including just half body was considered, in order to save computational resources. In the near-wall region (i.e. close to the body or the duct external surface), the chosen turbulence model use the so called Enchanced Wall Function, that requires a minimum spacing between grid elements in order to correct model the viscous sublayer in the boundary layer. The size of these elements are given in function of the non-dimensional wall distance y þ , representative of the local Reynolds number, and must be as close to 1 as possible (Fluent, 2005). This parameter is defined as yþ ¼



ryun m



ð1Þ



pffiffiffiffiffiffiffiffiffiffiffi where, y is the distance to the body surface; un ¼ tw =r, is the friction velocity; tw is the shear stress at the body surface; r is the density of the fluid, m is the local dynamic viscosity of the fluid. In the space closely around the bodies, the grid refinement depends on how intensively the flow is disturbed. This means that the size of the elements needs to be decreased where flow separation and vortices occur, compared to other areas where minor



63



perturbations are observed. For the case of hull-duct combination the propeller boss was represented in the grid. Moreover, a conical body, connecting the hull base and the propeller hub, was also included. The analysis of the mesh refinement influence on the computed results is based on the ‘‘ASME V&V’’, as applied by Ec- a et al. (2010). The same procedure is used to define the uncertainty level of the CFD calculation, which is represented by the corresponding bar for each computed point in Figs. 3–5, 8, and 12. During the application of such methodology, five different grids have been tested for the flow simulation around each body (see Tables 1–4). The grid index (hi) is used to express the degree of mesh refinement in each case. It is a geometric parameter adopted for defining the typical cell size of a grid (Ec- a et al., 2010). The grid index is defined in this work as the first cell thickness, i.e. the distance of the closest grid node to the body surface. The grid index ratio is then calculated by the ratio between the grid index for each case, to that one corresponding to the first case.



Table 1 Bare-hull mesh properties. Total Number of elements



First cell Thickness (hi) (mm)



yþ Mean value



Grid Index ratio (hi/h1)



Case 1 Case 2



2008108 1807332



0.050 0.071



0.87 1.25



Case 3 Case 4



1650662 1468441



0.010 0.141



1.75 2.50



Case 5



1385595



0.200



3.50



1 pffiffiffi 2 2 pffiffiffi 2 2 4



Fig. 2. Lift and moment coefficient slope in function of the duct chord-diameter ratio, predicted by the analytical and semi-empirical formula presented in Morgan and Caster (1965).



Fig. 3. Lift force (a) and pitch moment (b) coefficient on the Clark-Y duct with t/c¼ 0.117, and Dd/cd ¼ 1.5, calculated in the duct leading edge.



64



E.A. de Barros, J.L.D. Dantas / Ocean Engineering 42 (2012) 61–70



Table 2 Bare-hull with duct mesh properties. Total number of elements



First cell thickness (hi) (mm)



yþ mean value



Grid index ratio (hi/h1)



Case 1 Case 2



2306423 2220223



0.040 0.056



0.68 0.95



Case 3 Case 4



2111227 2015283



0.080 0.113



1.34 1.98



Case 5



1929083



0.160



2.80



1 pffiffiffi 2 2 pffiffiffi 2 2 4



Total number of elements



First cell thickness (hi) (mm)



yþ mean value



Grid index ratio (hi/h1)



1459968 1436640 1404960 1383840 1297440



0.015 0.020 0.025 0.030 0.050



0.63 0.85 1.07 1.23 2.00



1.00 1.33 1.67 2.00 3.33



Table 3 19A Duct mesh properties.



Case Case Case Case Case



1 2 3 4 5



Table 4 Clark Y duct mesh properties.



Case Case Case Case Case



1 2 3 4 5



Total number of elements



First cell thickness (hi) (mm)



yþ mean value



Grid index ratio (hi/h1)



1470544 1308414 1145768 1016808 920234



0.020 0.035 0.050 0.065 0.080



0.45 0.78 1.10 1.42 1.77



1.00 1.75 2.50 3.25 4.00



3. Preliminary tests This study started with the application of the flow numerical simulation on duct profiles that have been used in experiments reported in the literature. After comparing the measured results on lift and moment coefficients with those ones predicted by CFD, it was possible to proceed with more confidence on the numerical approach. The flow around the Clark-Y duct was simulated, adopting the value 0.117 for the thickness to chord ratio. This was the profile chosen by Morgan and Caster (1965) for validating the analytical and semi-empirical approach developed for estimating lift and pitch moment coefficients (see Fig. 2). This profile was tested experimentally by Fletcher (1957) in a wind tunnel for a number of different diameter/chord ratios. In Fig. 3(a), the experimental results reported by Fletcher (1957) are included, as well as those generated by CFD, adopting air as the fluid. Additionally, results obtained in CFD using water, and the analytical prediction proposed by Morgan and Caster (1965) are also presented. Except for the angle of attack range where stall occurs (i.e., between 15 and 20 degrees), a fair agreement between experiment and CFD based estimations can be observed. Even better results can be observed in the prediction of the moment coefficient, as indicated in Fig. 3(b). The center of pressure location is better predicted by the CFD estimations when compared to the analytical formula derived by Morgan and Caster (1965), as can be observed in Fig. 4. There is still a discrepancy between experiment and the results derived by both approaches in the stall region. However, in the higher angle



Fig. 4. Hydrodynamic center position as a function of the angle of attack for the Clark Y duct, with t/c¼ 0.117, and Dd/cd ¼ 1.5.



of attack range the CFD predictions clearly follow the experimental values closer than the original analytical prediction. Therefore, it seems that the adopted turbulence model could not correctly identify the duct stall. It is believed that the complex flow at the stall condition may exhibit pressure gradients large enough so that the isotropic turbulent viscosity (Boussisneq hypothesis), which is implicit in the ‘‘k-o’’ model, can no longer be assumed. Using a more complex CFD model, that do not use the RANS (Reynolds Averaged Navier-Stokes) approach, like the transients ‘‘Large Eddy Simulation’’ or the ‘‘Detatched Eddy Simulation’’, could be further tried, at a much larger computational cost, in order to improve the predictions at the stall region. However, considering the estimation of stability derivatives, this phase of the investigation was focused on the agreement between experiment and calculation in the range of 0 to 151. Taking into account the agreement between predicted and experimental results up to this phase, it was decided to keep the ‘‘k-o’’ model in the next tests with the 19A duct, which was combined later to the AUV bare hull for tank tests. The 19A duct profile is more usual in marine applications nowadays than the others presented in the previous section. The analytical and semi-empirical predictions (see Fig. 2) produced by Morgan and Caster (1965) and validated using the previous profiles were also applied to this case. The results were compared to the ones generated by CFD. The duct dimensions were defined in order to fit it to the AUV stern: the diameter is 150 mm and the duct chord is 75 mm. Results showing the ASE and CFD predictions are presented in Fig. 5a and b. For the normal force and pitch moment coefficients, it is observed a dead band in the range of 0 to 31 of angle of attack. This can be explained by the significant slope of the external side of the duct, which results in a large incidence angle at small angles of attack, producing the stall effect (Fig. 6a). As the angle of attack is increased, the flow lines tend to be aligned with the duct profile at the lower part, producing lift in that region (Fig. 6b). Deducing the dead band effect from the ASE calculations, it is possible to observe a good agreement between ASE and CFD normal force predictions for all the angle of attack range considered. In the case of the moment coefficient, the agreement is restricted to the linear angle of attack range. This may be explained by the viscous drag on the upper side, which is responsible for the change in the total pressure center location.



E.A. de Barros, J.L.D. Dantas / Ocean Engineering 42 (2012) 61–70



65



Fig. 5. Comparison of the normal force (a) and pitch moment (b) coefficient estimated by CFD and ASE formulation (Morgan and Caster, 1965) for the 19A duct profile.



Fig. 6. Streamlines of the flow around the duct with 01 (a) and 251 (b) of angle of attack.



4. Duct body combination The combination of bare hull and the 19A propeller duct is tested in the CFD simulations and experimental trials in a towing tank. Flow simulations of the duct-body combination indicate an important consequence of the bare hull effect on the incidence at the duct. Flow lines converge following the duct profile shape, and the stall is no longer observed at the low angles of attack (Fig. 7). Fig. 8a and b show the comparison between experimental results and the CFD predicted normal force and moment coefficients as function of the angle of attack. The AUV Reynolds number based on the vehicle length is 1.8  106. The agreement between numerical and experimental results is very good, particularly in the linear range. Analytical and semi-empirical predictions applied to the normal force and moment in the bare hull, and in the body with duct are also represented in the figures, for comparison. The bare hull prediction was based on the ASE expressions presented in formulas (2)–(8). The body with duct case was considered by the simple addition of the bare hull contribution to that one provided by the duct alone, as shown in Fig. 2. In this last case, no interference between the flows at the hull and duct was considered. As expected, the experimental results lie between both curves. In the sequel, it is shown that the hull-duct interaction can



be taken into account by the prediction of the wake coefficient, improving the ASE estimation. The dead band in the normal force, as predicted by the CFD simulation, is not observed for the duct body combination. The next phase in the duct body combination study is the prediction of the efforts based on analytical and semi-empirical models, and the comparison to the experimental results. The bare hull force and moment were predicted based on a modification of the slender body theory, and related formula derived by Munk (1923), and Hoak and Finck (1978). Results were experimentally validated (de Barros et al., 2008a). The proposed formula for the bare hull normal force coefficient, CN(a), is given by C N ðaÞ ¼ ðK 2 K 1 ÞC Np ðaÞð1sink aÞ þ C Nv ðaÞ,



ð2Þ



The coefficients CNp(a) and CNv(a) denote the contribution of potential and viscous terms, respectively. In the equation above C Np ðaÞ ¼



Sn sinð2aÞ Sref



ð3Þ



and C Nv ðaÞ ¼ ZC dn



Sp sin2 a Sref



ð4Þ



where, Sn is the sectional area in a station at a longitudinal distance xn0 from the nose tip. The coefficients K1 and K2 are,



66



E.A. de Barros, J.L.D. Dantas / Ocean Engineering 42 (2012) 61–70



Fig. 7. Streamlines of the flow in the duct with and without the presence of the bare hull.



Fig. 8. Comparison of normal force (a) and pitch moment (b) coefficients of body-duct combination.



respectively, the longitudinal and transversal apparent mass factors (Munk, 1923). The factor (1sinka) is related to the boundary layer thickening, vorticity and cross-flow separation in the bare hull (de Barros et al., 2008b). For the hull shape considered, k¼1.3 was adopted. The parameter Sp is the planform area at the xy plane (Fig. 9), and Sref is the reference area (taken as L2 in this work). The coefficient Z is a correction factor, equal to the ratio of C dn for a finite length cylinder to that for an infinite cylinder. This parameter is a function of the fineness ratio L/d (Jorgensen, 1977), where L is the body length and d is the body maximum diameter. The distance xn0 is the average value between the hull length and x0. The parameter x0 is adopted by the Datcom handbook (Hoak and Finck, 1978), as the axial distance between the nose and the station, which the flow can no longer be considered as potential. The semiempirical expression for estimating x0 is given by x0 ¼ 0:378Lþ 0:527x1



ð5Þ



where x1 is the coordinate where the body profile has the most negative slope in the aft direction. The parameter xn0 is adopted as a better approximation than x0 calculated by (5), since it takes into account that a significant portion of the flow at the stern can be considered as potential, according to



Fig. 9. Definition of the considered coordinated system.



the flow visualization in Fig. 10a (de Barros et al., 2008a). The numerical flow simulations also indicate that the presence of the duct does not provoke a change in the position of such station at the stern (Fig. 10b). In fact, the velocity profile at the stern suffers no significant change because of the presence of the duct (Fig. 11). The moment coefficient Cm is defined by Cm ¼



Z 0



xn0



cN ðxÞðxm xÞdx



ð6Þ



E.A. de Barros, J.L.D. Dantas / Ocean Engineering 42 (2012) 61–70



67



Fig. 10. Comparison of the flow streamlines and the station where the flow can no longer be considered as potential (x0) for the bare hull alone and in the presence of the duct, for some angles of attack (a).



where xm is the axial distance from the nose tip to the center of rotation and cN ðxÞ ¼ ðK 2 K 1 Þsinð2aÞ



dSðxÞ ð1sink aÞ þ 2ZC d sin2 ðaÞrðxÞ dx



ð7Þ



with r(x) denoting the cross section radius at the axial distance x from the nose tip and S(x) is the corresponding cross-sectional area. From formulas (6) and (7), the final expression for the moment coefficient results  n n n  V S ðx0 xm Þ Sp xm xc  2 sin ðaÞ, sinð2aÞð1sink aÞ þ ZC dn 2 Cm ¼ 3 L L L ð8Þ where Sn is the cross-sectional area at the station distant xn0 from the nose, xm is the axial distance from the nose tip to the center of



rotation, and Vn is the volume between the nose tip and such station. The parameter xc is the axial distance from the nose tip to the centroid of the bare-hull planform area at the xy plane. The prediction of the normal force for the combination should take into account the effect of the hull wake at the duct location. The ratio between the dynamic pressures at the duct and that of the undisturbed flow defines the efficiency factor as follows:



Zo ¼



q V2 V 2 ð1oÞ2 ¼ 2 ¼ 1 2 ¼ ð1oÞ2 q1 V1 V1



ð9Þ



The wake coefficient, o, was estimated by two different approaches. The first one is an ASE method. Jackson (1992) presented a formula for estimating the wake coefficient based on the relationship between the bow and stern surface areas in



68



E.A. de Barros, J.L.D. Dantas / Ocean Engineering 42 (2012) 61–70



Fig. 11. Comparison of the velocity profile in the bare hull tail with and without the presence of the duct. The angle of attack is zero.



the case of typical submarine hull geometries. The wake coefficient is calculated from the expression



The duct normal force is composed by the lift and drag forces. Expressing them in the non-dimensional form it follows:



0:01382 D D ð1oÞ ¼ 0:3674þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ 0:008406 þ 1:6732 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , d ðL=dÞK o d ðL=dÞK o



C NDuct ðaÞ ¼ C LDuct ðaÞcos aC DDuct sin a where, C LDuct ðaÞ is given by



ð10Þ where L is the hull length, d is the hull maximum diameter, and D is the propeller diameter. The coefficient Ko is proportional to the wetted surface area coefficients of the forebody and afterbody, as follows: K o ¼ 62:4C wsf 3:6C wsa



ð11Þ



C wsf ¼



Sf



pdLf



,



ð12Þ



and C wsa ¼



C LDuct ðaÞ ¼



dC LDuct a da



Sa



ð13Þ



pdLa



where Sf, Lf are the forebody wetted area and length respectively, while Sa, La are the same parameters related to the afterbody. The second approach for estimating the wake coefficient is based on the velocity distribution at the duct station produced by the numerical flow simulation. Considering the flow around the bare hull (without the presence of the duct), the velocity field was estimated by the CFD just at the zero incidence case by a single 2-D simulation. An average value was calculated from the velocity distribution at the station relative to the virtual location of the duct hydrodynamic center (taken at 25% of its chord length from the leading edge). R ro R ro r VðrÞrdr r i VðrÞrdr V ¼ V 1 ð1oÞ ¼ iR ro ¼ ð14Þ 2 r 2 Þ ð1=2Þðr rdr o i r i



where ri is taken as the propeller boss radius (0.015 m), and r0 is the duct external radius (0.0908 m) at the hydrodynamic center position. According to numerical predictions, the velocity distribution at the body stern is not significantly affected by the presence of the duct, as indicated by Fig. 11. The presence of the duct should not affect as well the approximation to the station of the body where the flow ceases to be considered potential (see Fig. 10). Therefore, it is possible to consider the summation of the normal force generated on the bare hull (Eq. (2)) to the duct contribution multiplied by the efficiency factor defined in Eq. (9).



ð16Þ



The lift slope coefficient (dC LDuct =da) is given in Fig. 2a. The drag coefficient was adopted as the experimental value presented by Morgan and Caster (1965) for the forward thrust increase type of duct C DDuct ¼ 0:48



where,



ð15Þ



C d Rd



ð17Þ



L2



For composing the moment coefficient, it was assumed the algebraic summation of the bare hull contribution (Eq. (9)) to the duct contribution calculated as follows: C mDuct ðaÞ ¼ C NDuct ðaÞZo



ðxm xLE Þ dC mDuct þ a L da



ð18Þ



where, xLE is the axial distance from the nose tip to the duct leading edge, and dC mDuct =da is the moment slope coefficient, related to the duct leading edge, as given in Fig. 2b. In Fig. 12a and b the experimental and CFD results are compared to the curves generated by the ASE method. In those figures, the normal force and moment coefficients variation with the angle of attack are displayed according to different conditions. They correspond to the bare hull case, the duct alone case, and the duct-hull combination with and without the influence of the hull wake. All the curves belong to the area defined by the bare hull case, and the curve generated by the algebraic summation of bare hull estimative with the duct alone case. Comparing to the bare hull generated efforts, as expected, the duct contribution is significant, especially for the pitch moment. Two different curves are generated for each estimated value of the wake coefficient. The Jackson method (Eqs. (8) and (9)) produced a wake coefficient equal to 0.22, while the value generated by the analysis of the CFD simulation is 0.36. It can be observed also that the best fit to experimental results, mainly in the moment coefficient, are provided by the ASE using the wake coefficient value estimated through the CFD simulation. 5. Conclusions This paper presented a comparative study of CFD and ASE methods applied to the prediction of normal force and moment



E.A. de Barros, J.L.D. Dantas / Ocean Engineering 42 (2012) 61–70



69



Fig. 12. Normal force (a) and pitch moment (b) coefficient of the bare hull plus duct combination, for values of wake coefficient coming from analytical and numerical methods.



coefficients of a Myring type hull of an AUV combined to a propeller duct. The methods were applied to the body-duct combination. The CFD calculations have produced very good predictions of the normal force and moment coefficients for the bare-hull and duct combination. This makes the information given by the flow visualization and pressure distribution very useful during the selection or tuning of the ASE formulas. The accuracy of the estimations when considering the vehicle length up to a station in between the base and that one suggested by the Datcom approach has not been affected by the duct presence at the stern. The Morgan Caster formulation for the normal force and moment generated by the duct provided good results for the 19A profile. The analysis of the duct-hull combination, as in the case of the bare hull normal force and moment coefficients (de Barros et al., 2008b), shows that combining ASE formula to CFD results can provide qualitative understanding and more physical meaning to experimental and CFD results, using quite simple hydrodynamic concepts. Moreover, the ASE estimation could be improved using a CFD based result based on a single case, without requiring the usual long time and computer resources related to the numerical simulation approaches. Next steps will include the propeller modeling inside the duct under incidence. The inclusion of such effect may change the pressure distribution over the vehicle stern so that the moment coefficient would be affected. However, it is the authors’ belief that changes in the normal force and moment coefficients will be not so significant when compared to the results presented in this work.



References Baltazar, J., Falca~ o de Campos, J.A.C., 2009. On the modelling of the flow in ducted propellers with a panel method. In: Proceedings of the First Symposium in Marine Propulsors. Norway. de Barros, E.A., Pascoal, A., de Sa´, E., 2008a. Investigation of a method for predicting AUV derivatives. Elsevier. Ocean Engineering, pp. 1627–1636. de Barros, E.A., Dantas, J.L.D., Pascoal, A.M., de Sa´, E., 2008b. Investigation of normal force and moment coefficients for an auv at nonlinear angle of attack and sideslip range. IEEE J. Oceanic Eng., 538–549. Ec-a, L., Vaz, G., Hoekstra, M., 2010. Code verification, solution verification and validation in RANS solvers. ASME Conference Proceedings, ASME, vol. 2010, no. 49149, p. 597–605.



ESDU Aerodynamics, 1978. The influence of body geometry and flow conditions on axisymmetric velocity distribution at subcritical Mach numbers. ESDU International, London, UK, Data Item 78037. Falca~ o de Campos, J.A.C., 1983. On the calculation of ducted propeller performance in axisymmetric flows. Ph.D. Thesis. Delft University. Fletcher, H.S., 1957. Experimental investigation of lift, drag, and pitching moment of five annular airfoils. National Advisory Committee for Aeronautics TN 4117. Fluent Inc., 2005. Fluent 6.2 User’s Guide. Fluent Inc. Hoak, D., Finck, 1978. USAF Stability and Control Datcom. Wright-Paterson Air Force Base, Ohio. Hoekstra, M., 2006. A RANS-based analysis tool for ducted propeller systems in open water condition. International Shipbuilding Progress 53, IOS Press, Maritime Research Institute Netherlands, Wageningen, The Netherlands. Husaini, M., Samad, Z., Arshad, M.R., 2008. Optimum Design of URRG-AUV Propeller Using PVL. 2nd Technical Seminar on Underwater System Technology: Breaking New Frontiers 2008. Inoue, T., Suzuki, H., Kitamoto, R., Watanabe, Y., Yoshida, H., 2010. Hull form design of underwater vehicle applying CFD (Computational Fluid Dynamics). IEEE, 1–5. Jackson, H.A., 1992. Fundamental of Submarine Concept Design. SNAME Transactions 100, 419–448. Jagadeesh, P., Murali, K., Idichandy, V.G., 2009. Experimental investigation of hydrodynamic force coefficients over AUV hull form. Ocean Eng. 36 (1), 113–118. Jeans, T.L., Holloway, A.G.L., Watt, G.D., Gerber, A.G.A., 2010. A force estimation method for viscous separated flow over slender axisymmetric bodies with tapered tails. J. Ship Res. 54 (1), 53–67. Jorgensen, L.H., 1977. Prediction of static aerodynamic characteristics for slender bodies alone and with lifting surfaces to very high angles of attack. NASA Technical Report. TR-R-474. Kerwin, E.J., Kinnas, S.A., Lee, J.-T., Shih., W.-Z., 1987. A surface panel method for the hydrodynamic analysis of ducted propellers. SNAME Trans. 95, 93–112. Kimber, N.I., Scrimshaw, K.H., 1994. Hydrodynamic testing of a 3/4 scale Autosub model. In: Oceanology International 94. Kinnas, S.A., Lee, H., Gu, H., Deng, Y., 2005. Prediction of performance and design via optimization of ducted propellers subject to non-axisymmetric inflows. SNAME Trans., 99–121. Lewis, R.I., Ryan, P.G., 1972. Surface vorticity theory for axisymmetric potential flow past annular aerofoils and bodies of revolution with application to ducted propellers and cowls. J. Mech. Eng. Sci. 14 (4). Minsaas, K.J., G.M. Jacobsen, H. Okamoto, 1973. The design of large ducted propellers for optimum efficiency and manoeuvrability. Symposium on Ducted Propellers. The Royal Institution of Naval Architects. pp. 134–160. Menter, F.R., 1994. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. Am. Inst. Aeronaut. Astronaut. 32 (8), 1598–1605. Morgan, W.B., Caster, E.B., 1965. Prediction of Aerodynamic Characteristics of Annular Airfoils. Department of TheNavy, Washington, D.C. Report1830. Munk, M.M., 1923. The Aerodynamic Forces on Airship Hulls. NACA Rep. p. 184. Phillips, A., Furlong, M., Turnock, S., 2007. The use of computational Fluid dynamics to determine the dynamic stability of an autonomous underwater vehicle. In: 10th Numerical Towing Tank Symposium (NuTTS’07). Hamburg, Germany, p. 6. Phillips, A., Furlong, M., Turnock, M., 2010. Influence of turbulence closure models on the vortical flow field around a submarine body undergoing steady drift. J. Mar. Sci. Technol. 15 (3), 201–217. Silvestre, C., Pascoal, A., Kaminer, I., and Healey, A., 1998. Combined plant/ controller optimization with application to autonomous underwater vehicles. In: Proceedings of the Control Applied Marine System, Fukuoka, Japan. pp. 361–366.



70



E.A. de Barros, J.L.D. Dantas / Ocean Engineering 42 (2012) 61–70



Tang, S., Ura, T., Nakatani, T., Thornton, B., Jiang, T., 2009. Estimation of the hydrodynamic coefficients of the complex-shaped autonomous underwater vehicle tuna-sand. J. Mar. Sci. Technol. 14 (3), 373–386. Tyagi, A., Sen, D., 2006. Calculation of transverse hydrodynamic coefficients using computational fluid dynamic approach. Ocean Eng. 33 (5–6), 798–809. Van Gusteren, L.A., van Gusteren, F.F., 1972. The effect of a nozzle on steering characteristics. Int. Shipbuilding Prog., 139–151. Vaz, G., Toxopeus, S., Holmes, S., 2010. Calculation of manoeuvring forces on submarines using two viscous-flow solvers. In: OMAE2010. ASME 29th



International Conference on Ocean, Offshore and Arctic Engineering. Shanghai, China, vol. 6, pp. 621–633. Wu, L., 2010. Applying dynamic hybrid grids method to simulate auv docking with a tube. In: Information and Automation (ICIA), 2010 IEEE International Conference. pp. 1363–1366. Yamamoto, I., 2007. Research and development of past, present and future AUV technologies. In: Masterclass in AUV Technology for Polar Science: British Library, (469, 4), pp. 99–102.