Transactions on the Built Environment vol 11, 1995 WIT Press, ISSN

Transcription

1 An experimental and numerical investigation of turbulent flows around a ship-like body with and without propeller M. Abdel-Maksoud*, H. Brandt*, H.Nowackf, G. Tzabiras* *Schiffbau-VersucksanstaltPotsdam GmbH, Germany ^Technical University of Berlin, Berlin, Germany "National Technical University of Athens, Heroon Polytechniou 9, Zografou 57 73, Athens, Greece Abstract The present work deals with an experimental and numerical study of the turbulent flow around a submerged body of revolution with a propeller in operation. The numerical solution of the corresponding Reynolds equations is based on the finite volume approach in connection with the k - 5 turbulence model. Two different techniques are used to solve the Reynolds equations numerically. The calculated profiles of the mean velocities and pressure coefficients are compared with the measurements for different propeller loading conditions. Also included is a comparison of experimental and numerical data for the case without propeller. The stern geometry of the model was selected to provide separated flow just before the propeller plane. The goal of the study is to determine the influence of the propeller loading on the separated flow around the stern of the model. Introduction Although the interaction between propeller and hull has been studied in various investigations, the effect of a full stern geometry on the velocity distribution and the pressure field at different propeller loading conditions is not yet adequately understood. The effect of the propeller on the boundary layer parameters of axisymmetric bodies was investigated by Hucho[l], Nagamatsu et al.[2] and Huang et al.[3]. Moreover, Rood et al.[4] studied the interaction between a propeller and a body of revolution with appendages. An extensive experimental program concerning the flow around an axisymmetric body with propeller was performed by Hyun[5] at the Iowa Institute of Hydraulic Research (IIHR). Concerning the theoretical treatment, potential flow assumptions were used in many investigations dealing with the interaction between propeller and hull. A detailed description can be found in Nowacki[6] and in Nakatake et al.[7]. Moreover, many advanced methods for calculating the turbulent flow in the stern re-

2 00 Marine Technology and Transportation gion have been used to predict the combined hull-propeller flow field. The approximation of the propeller effect on the viscous flow as an external force (body force approximation) was successfully used in many numerical investigations, see Schetz et al.[8], Stern et al.[9], Tzabiras[0] and Abdel-Maksoud et al.[ll]. 2 Experimental study The experimental part of the study was conducted in the cavitation tunnel of the Technical University of Berlin. The measuring section is 700 mm deep, 000 mm wide and 3750 mm long. Since the subject of the experiment was a submerged body, the deformation of the free surface of the water was suppressed by using a solid plate to cover the measuring section. The investigated model in the present study was an axisymmetric body. The advantage of using a body of revolution as a ship-like body was the possibility of reducing the problem to an axisymmetric one. Thus, a very fine grid resolution could be applied in the numerical simulation which is essential for a sufficiently accurate calculation of separated flows. The geometry of the axisymmetric body consisted of three mathematically defined parts. The nose and stern were elliptic with an axis ratio of.6 : and 3:, respectively. The middle part of the model was cylindrical with a diameter of 250 mm. The total length of the model L was 590 mm. The geometry of the stern was extended to form a smooth passage to the propeller hub. The ratio of the cross section area of the model to the water tunnel was Therefore, in all theoretical investigations the wall effect had to be considered. The propeller was selected from the Newton-Rader series, Newton et al.[2]. It had the following characteristics: diameter D= 52mm, pitch ratio P/D=.33, Profile type Newton-Rader, hub ratio d/d= 0.9, number of blades Z= 3, and area ratio AE/AQ = The ratio of the propeller diameter to model diameter was 0.6. At the self propulsion point, the propeller was lightly loaded. The propeller was driven using a propeller dynamometer mounted behind the model, see Fig.. The gap between the model and the propeller was one millimeter only. The advantage of this configuration was the possibility to measure the model resistance and the propeller thrust independently. A detailed description of the experiments can be found in Abdel-Maksoud[3]. The experiments were carried out at two Reynolds numbers, that is, 6.7 x 0^ and.0 x 0" and for three thrust loading conditions, namely C^h- 0.38, 0.76 and The following measurements were conducted: model resistance with and without propeller, thrust and moment of the propeller in the wake of the model and in an open water test, pressure distribution on the surface of the model, velocity profiles in the stern region with and without propeller. 2. Description of the experiments The model resistance was measured with a six component dynamometer, which was mounted outside (above) the measuring section. The measurements were carried out twice. In thefirstrun the upstream velocity of the circulating

3 Marine Technology and Transportation 0 water of the tunnel was increased from 3 to 6.5 m/s in steps of 0.5 m/s. In the second run, the measurements were conducted by reducing the upstream velocity in the same way. The propeller dynamometer H34 of Kempf and Remmers company was used to measure the propeller characteristics in the wake of the model. An open water test was also carried out. The propeller thrust and torque were measured for a constant upstream velocity and a varying number of revolutions. The pressure distribution on the surface of the model was measured at 9 positions in the horizontal symmetry plane. The positions X/L= 0.0, 0.032, 0.057, 0.093,0.54,0.283,0.66,0.773,0.87,0.98,0.95,0.957 and were selected. The measurements of the velocity profiles were taken using a 5 mw one-component He-Ne-Laser Doppler-Velocimeter (LDV). After measuring the velocity distribution in the stern region of the model, seven positions were chosen to measure the velocity profiles, namely X/L= 0.882, 0.933, 0.969, 0.979, 0.99,0.996 and 0.999, see Fig. 2. The measurements were carried out in the horizontal plane of symmetry. The traverse system for moving the measuring head was mounted above the measuring section. It had three degrees of freedom, two longitudinal and one rotational. The measuring head 60X0 from Dantec company was employed. The laser beam was transmitted to the measuring head by means of a glassfibercable. A beam expander was used to get a suitable measuring volume dimensions at the required measuring distance. The front lens had a focus length of 30 mm in air. The measuring volume was 75 // mm long and 0.63 mm wide (in air). At every point, the velocity was measured using three different angles (-45,0,+45 ). The measured component at 0 was the axial velocity component u (parallel to the symmetry line). The measurement of the other two velocity components at (-45,+45 ) were used to evaluat<mhe_radial velocity component r. The Reynolds stresses were also evaluated (?/%, v'* and wv). The measured data were not corrected for the BIAS effect, i. e. the fast particles pass more frequently through the measuring volume than the slower ones, thereby shifting the mean value of the velocity upwards. 2.2 Accuracy of the measurements By repeating the resistance measurements the maximum deviation of the drag was found to be accurate to ± 2%. The symmetry of the flow was checked using pressure measurements at two sections at X/L= 0.54 and The deviation on the same plane, vertical or horizontal, was within ± O.OlCp. The deviation between the vertical and the horizontal planes was ± 0.025Cp. The LDV measuring head was adjusted using a traverse system. The accuracy of the two longitudinal components of this system was 0.0 mm and the rotational one is 0.5 degree. The accuracy of the adjustment of the LDV measuring volume relative the model was 0. mm, which was also the nearest position of the measuring volume to the model, (both laser beams were adjusted tangentially to the

4 02 Marine Technology and Transportation surface of the body of revolution). The deviations of the velocity components u and v were ± % and ±.2% respectively. 3 Description of the numerical methods Two different numerical methods were used to calculate the turbulent flow field at the stern of the model with and without propeller in operation. The flow was considered stationary, incompressible and axisymmetric with non-zero circumferential velocity. The continuity equation and the time averaged Navier-Stokes (Reynolds equations) are written in their differential form using cylindrical polar coordinates (x,r,0): + V^ = o (i) 0z r <9r.Xr/m%) #P <9 / _2\ # \ r + 5 = -if + i" l-m^ j + -ir -^^^) + A (2) 0r a? c/z\ / ror 9(/)% ' i dx 7" d 4- ( d(rpv*) 8r dp /)W^ d + dr * r dx ox (-puv) --(-pw^ \ ritn\ (3) _ ;;- = f%%;) (4)? r or r oz (-r^uw) -- (-/?uu;) + /m rc/r r The k-e eddy viscosity model was used to calculate the Reynolds stresses in equations 2-4. Normally, in an axisymmetric flow the circumferential velocity w is equal zero. However, due to the propeller torque this component is non-zero and should be considered in the calculations. The terms /& and fm in equations (2) and (4) represent the forces on the fluid due to propeller thrust T and torque Q. They act as external body forces in the momentum equations. The terms /& and fm are non-zero only in the control volumes of the propeller plane. (5) Q = Q r/mr^r (6) In the above expressions C^ and C$ are constants, which can be calculated from the integrated results of the thrust and torque of the propeller. r/> and r^ are the hub and the propeller diameter. A lifting line code, which is based on the method of Oossanen[4], the induction factors from Lerbs and the lifting surface corrections from Morgan was

5 Marine Technology and Transportation 03 implemented for the present investigation. To test the reliability of the lifting line code, numerical results were compared to the measured propeller characteristics in the open water test. A quite satisfactory agreement was observed. The differential equations (2) to (4) and the k-e equations were integrated using a control volume approximation and resulting non-linear algebraic equations of elliptic type. Two different methods were used in this study. Thefirstone uses the method of Tzabiras[0]. A detailed description of the second method is given in Abdel-Maksoud[l ]. The major differences between the two codes stem from the integration procedure. Thefirstmethod uses a staggered grid while the second method employs a collocated one. While in the second code the momentum and the k-e equations are solved in their elliptic form, thefirstcode uses a marching procedure to solve the Reynolds and k-e equations. In both methods the SIMPLE algorithm is applied, which obtains a pressure correction equation by combining the continuity and momentum equations. In the two methods the pressure correction equation is treated as fully elliptic. According to this procedure an iterative solution is followed: The momentum and the turbulence model equations are solved and the pressure field is corrected to satisfy local continuity. The procedure is repeated until convergence is achieved for all variables. In thefirstmethod, the flow around the body is divided in two regions surrounding the front and the rear part, see Tzabiras[0]. An orthogonal curvilinear C-type grid and curvilinear velocity components were applied in the front region. The number of nodes used in this region was (300 x 65 ). In the second computional region, covering the flow field around the rear part of the body, a non-orthogonal grid (290 x 90 ) was adapted, see Fig. 3. To achieve convergence without the body forces from the propeller, 000 iterations were required. After that, only 20 iterations were necessary for the propeller effect. In the second method an adaptive non-orthogonal grid with 48 x 65 nodes was used, see Fig. 4. The inlet plane of the calculation domain was located at X/L= 0.9. The required inlet data at this position were calculated using the Cebeci method, which agrees well with the measured data at this position. After 300 iterations the convergence criterion was met. 4 Results and discussion The calculated pressure distribution, velocity profiles and the model resistance are compared with the measured data. The results without propeller are presented in Figs. 5 and 6, and the results for one propeller loading condition, CTH.= 0.76 at Rn =.0 x 0?, are given in Figs. 7 and 8. The other results are summarized in the Figs. 9 and 0. The velocity profiles were normalized using the upstream velocity U^. The velocity diagrams include the velocity components (u/u^) and (vlu^) in x and r directions. The vertical axis of thefigurepresents the distance in (mm) from the body surface. It is known that the circumferential velocity component (wlu^) is non-zero

6 04 Marine Technology and Transportation behind the propeller. However, since the aim of this study is the investigation of the effect of the propeller on the flow around the stern before the propeller, where w/uoo =0, the circumferential momentum equation was not considered in every numerical calculation. To study the effect of this assumption, thefirstmethod was used to calculate the flow around the stern of the model while taking into account the circumferential momentum equation as well, see Results without propeller The measured results show separated flow at the positions X/L= 0.959,0.979, 0.99, and The numerical results of both methods in the separated flow region are in good agreement with the measured data, see Fig. 5. The first method shows better results in the wall region than the second one. The difference may be a result of the different grid resolution, (290 x 90 in thefirstmethod and 48 x 7 in the second one). The calculated radial velocity component v is in good agreement with the measurements, except at the positions X/L= and , where there is a strong curvature on the body contour. The turbulence model may be responsible for this deviation, because both methods predicted the same behaviour. The comparison between the numerical and the experimental values of the pressure coefficient without propeller is given in Fig. 6. Good agreement between the calculated and the experimental results can be observed until X/L = Behind this position the calculated values are higher than the measured ones. 4.2 Results with propeller As expected, the experimental results show that the axial velocity component u is increased due to the action of the propeller, see Fig. 7. The differences between the calculated radial component v and its measured values at the positions X/L= and are less than without propeller. It is clear, that the separation point is moved backwards, and the amount of the separated flow is reduced. The pressure coefficient shows the same trend as without propeller but the differences between the calculated and the measured data in the stern region are smaller than without propeller, compare Fig. 6 with 8. The reduction of the separated flow around the stern, due to propeller action, is responsible for better numerical results in the stern region. The effect of the propeller on the flow can be observed as a pressure jump ACV just behind the model, see Fig. 8. The value of ACp is not related to the produced thrust, because it presents only the change of the pressure over the shaft of the propeller dynamometer. The difference in the value and the inclination of ACV between thefirstand the second method is due to the different assumption for the axial thickness of the propeller disc. In the first method, it was taken as one control volume. In the second one, it was assumed to be equal to 80% of the axial distance between the leading and trailing edge of the propeller blade at 0.7R, which means more than one control volume. An investigation on the numerical effects of this assumption will be discussed later. It should be mentioned, that with increasing the propeller loading the perfor-

7 Marine Technology and Transportation 05 resist. measurement 85 N method j 80.8 method Table : Model resistance without propeller deviation ±2% resist. 04 N -4.94% % 05.8 with propeller Cr A =0.3 8 C^=0.76 deviation :h2% % +.73% resist. 8N deviation i:2% +3.86% +2.96% ' mance of the calculation methods are improved as long as the results of the propeller performance program are applicable. The increase of the propeller loading should be coupled with higher grid resolution near the propeller plane, otherwise numerical problems will be occur at the tip and the root of the propeller blade or convergence cannot be achieved at all. Generally, both numerical methods are able to detect the effect of the propeller action on the flow. The acceleration of the flow in the axial direction and the pressure reduction on the stern region are in good agreement with the measured values. 4.3 Resistance The measuring and numerical results of the model resistance with and without propeller are given in table. The calculated results with propeller in operation are in better agreement than without propeller, especially at the self propulsion point CTH =0.38. Probably, the reason is again the reduced amount of separated flow, which leads to better agreement of the calculated and the measured pressure coefficients. Both numerical methods predicted the model resistance with good accuracy. We must keep in mind that the error of the resistance measurement was about ± 2 %. 4.4 Thrust deduction fraction The increase of the model resistance, due to the propeller action, as a function of the thrust loading condition is presented in Fig. 9, where AR = Rwithpropeiier - Rwithoutpropeiier- At R^ =.0 x 0^, the measured thrust deduction fraction at the self propulsion point is The measured results at CTH > 0.5 show, that the increase of the model resistance is nearly a linear function of the thrust loading coefficient. At thrust loading conditions < 0.5, the viscous effect of the separated flow is still important and should be considered. The calculated thrust deduction fraction from both methods is equal The numerical results follow the measured ones, but they are higher than the measurements. The difference is about The reason for this parallel shift is the difference between the calculated and measured model resistance without propeller. The comparison between the numerical and the experimental results shows

8 06 Marine Technology and Transportation that a great improvement can be achieved by using the viscous flow methods for the prediction of the thrust deduction fraction. 4.5 Wake fraction The wake fraction as a function of the thrust loading condition is presented in Fig. 0. The mean value of the wake fraction over the propeller disc area w can be calculated as follows: (^r~) is the axial velocity component at the position X/ L= 0.999, (2 mm before the leading edge of the propeller blade). x.p is the dimensionless radius of the propeller. It is clear, that the results of the LDV measurements and the numerical results of both numerical methods have the same trends. At zero thrust loading condition, the same results were measured for the two Reynolds numbers (6.7 x 0^ and.0 x 0"). With increasing thrust loading Reynolds number effects increase, too. It should be mentioned, that the measured wake fraction without propeller is higher than at zero thrust loading condition, see Fig. 0. In general, the calculated results of the wake fraction of both methods are lower than the LDV measured values. At the self propulsion point and Reynolds number equal to.0 x 0" the measured wake fraction is The calculated value is in thefirstnumerical method, which is about 6 % lower than the measured value. The predicted wake fraction is 0.46 in the second method with a -3.2 % deviation from the measured one. Without propeller (nominal wake), the difference between the results of both numerical methods and the measurement is-9 96, which is higher than with propeller. Since in propulsion experiments the Reynolds numbers for the model and the ship are different, the velocityfieldsin the propeller plane are different. Under this circumstance, the thrust distribution along the propeller radius is not the same in model and full scale. In model scale the roots of the propeller blades are more loaded than in full scale. In this indirect way, the thrust deduction fraction is affected by the Reynolds number. The large difference between the effective and nominal wake fraction shows that the nominal wake fraction cannot be used for propeller design. However, both numerical methods are able to predict the effective wake fraction with good accuracy, which is essential to design an optimum propeller for a specified afterbody. 4.6 Further numerical investigation The effect of the assumed axial length of the propeller disc A/p and the rotation of the propeller flow on the numerical results was investigated using the first method. Moreover, numerical calculations were performed with and without blockage effect.

9 Marine Technology and Transportation 07 The comparison was made for four values of A/p, namely 3.5, 7.5, 32, 52.5 mm. Within a small value of A/p, a strong increase in pressure must be reached within a short distance. The sudden increase of the pressure causes separation of flow within the propeller plane and affects the calculated total resistance. By increasing the distance A/p to a reasonable value, this problem will disappear. The assumption about the axial expansion of the propeller disc A/p has only restricted effect on the predicted results upstream of the propeller. Mainly in the propeller plane the pressure distribution will be strongly affected, which may be responsible for a small difference in the calculated total resistance. In the investigated cases this was less than %. According to the comparison between the results of the numerical investigation and the measured values, it is recommended to select a value of A/p equal to of the actual axial distance between the leading and trailing edge of the propeller blade at radius 0.7. The Reynolds equations 2,4,4 were solved numerically using thefirstmethod to investigate the effect of the circumferential velocity component on the results. The consideration of the circumferential momentum equation in the solution affected the predicted total resistance by a value, which was less than %. This showes that it was justified to omit the circumferential velocity component in all the numerical investigations. The blockage effect was also studied. The turbulent flow around the model without propeller was calculated with and without blockage effect. Due to the walls of the tunnel the predicted model resistance was 3 % higher than in open water. For this reason, the wall effect was considered in all numerical treatments. 4.7 Conclusion The separated turbulent flow on a ship-like body with and without propeller was investigated both experimentally and numerically. The model resistance, the pressure distribution on the model surface, velocity profiles and the propeller thrust and moment were measured. The results of two different numerical methods for predicting the turbulent flow were presented and discussed. Both methods are able to calculate the turbulent flow on the model with and without propeller and to predict the resistance, thrust deduction fraction and wake fraction. In the separated flow region, the predicted results of both numerical methods for solving the Reynolds equations are in satisfactory agreement with the measured data. In the case with propeller in operation, a good agreement between the measured and the numerical results was achieved, while some differences were found for the case without propeller. Because two different numerical methods show the same tendency, the turbulence model may be responsible for this small deviation.

10 08 Marine Technology and Transportation pressure measuring system res istancc c vnairiomettt ' r dj r i L upstream -~«n cover plate, _-. propeller dynamomter model propeller Figure : Experimental configuration. velocity measurements Hi- pressure measurements Figure 2: Measuring positions on the model surface.

11 Marine Technology and Transportation 09 Figure 3: Numerical grid used in thefirstmethod. propelk-j- Figure 4: Numerical grid used in the second method.

12 0 Marine Technology and Transportation Y mm J I(> f _ o / I I u/u^ measurement )K )K )K )K v/u^ measurement 0000 first method second method i --^ <^\"\ ^ 0 *k^ & k%, V/Uoo, U/Uo I; ] ; ;.' 4' / Figure 5: Velocity profile at X/L = (without propeller). Cp LOO measurement first method R ==.0x second method X/L Figure 6: Pressure coefficient (without propeller).

13 Marine Technology and Transportation Y mm /, / Jg/LJ^ ^/g/u^ / '\ / c, V a /Uo /Uc0 / \ I v-,' c \! \ \ P- \ \ ^-^ I/U^ measurem ent XX XX \ /U^ measurme^ J rst method second method prope er induced vel. omp. c ^,<^ _4K< ^ / J I i j»/: ' *i ^'" , u/u txi Figure 7: Velocity profile at X/L = (C^A = 0.764) 070 o.8o Figure 8: Pressure coefficient (Cxh = 0.764).

14 2 Marine Technology and Transportation AR/T experiment 0.25 first method second method x Th Figure 9: Influence of the propeller thrust loading on the model resistance. W i, without prop. I g^^-zero thrust I without prop. I l_ I R 0.2 I ^ - ^ I I LI.3.5 c Th Figure 0: Influence of the propeller thrust loading on the wake.

15 Marine Technology and Transportation 3 References [ ] Hucho, W.H., Uber den EinfluB einer Heckschraube auf die Druckverteilung und Grenzschicht am Schiffsrumpf, Bericht 67/5, TH Braunschweig, 967. [2] Nagamatsu, T., Tokunaga, K., Prediction of effective wake distribution for a body of revolution, J. of the Society of Naval Architects of Japan, Vol.43, 978. [3] Huang, T.T., Wang, H.T., Santelli, N., Groves, N.C., Propeller / stern / boundary layer interaction on axisymmetric bodies, theory and experiment, DTNSRDC Report no , 976. [4] Rood, E.P., Anthony, D.G., An experimental investigation of propeller/hull/appendage hydrodynamics interactions, Proc. 7th ONR Symp. on Naval Hydrodynamics, den Haag, 988. [5] Hyun, B.S., Measurements in the flow around a marine propeller at the stern of an axisymmetric body, Ph. D. thesis, University of Iowa, Iowa, 990. [6] Nowacki, H., Analytisch-numerische Methoden zur Untersuchung der Wechselwirkung zwischen Schiff und Propeller, Inst. fur Schiffbau der Uni. Hamburg, Kolloquium 88, 989. [7] Nakatake, K., Ando, J., Mitsunori, M., Masaaki, K., Practical quasicontinuous method to calculate propeller characteristics in uniform inflow, PRADS 92, Newcatle 992. [8] Schetz, J.A., Favin, S., Numerical solution of a body-propeller combination flow including swirl and comparisons with data, J. Hydronautics, Vol.3, 979. [9] Stern, F., Toda, Y., Kim, H.T., Computation of viscous flow around propeller-body configurations, Iowa axisymmetric body, J.S.R., Vol.35, 99. [0] Tzabiras, G.D., A numerical investigation of the Reynolds scale effect on the resistance of bodies of revolution, Ship Technology Research, Vol. 39, 992. [] Abdel-Maksoud, M., Brandt, H., Nowacki, H., Numerical computation of resistance, thrust deduction and wake fraction using a vicous-flow approach, Ship Technology Research Vol. 4, 994. [2] Newton, R.N., Rader, H.P., Performance data of propellers for high speed craft, RINA, 96. [ 3] Abdel-Maksoud, M., Vergleichende experimented und numerische Untersuchungen der turbulenten Stromung am schiffsahnlichen Korper mit und ohne Propeller, VDI-Fortschritt-Bericht, Reihe 7, Nr.207, 992. [4] Oossanen, P.van, Theoretical prediction of cavitation on propellers, Marine Technology, Vol.4, 977.