Abstract    This paper presents 2-D finite volume method for computation of viscous drag based on Reynolds-averaged Navier-Stokes (RANS) equations. Computations are performed on bare submarine hull DREA and six axisymmetric bodies of revolution with a number of length-diameter (L/D) ratios ranging from 4 to 10. Both structured and unstructured grids are used to discretize the domain around the bodies. Different turbulence models have been tested to simulate turbulent flow. Finally, results computed by 2-D method are compared with published experimental results and found satisfactory.

Keywords    axisymmetric body of revolution, underwater vehicle, viscous drag, CFD, turbulence model

چکیده    چكيده اين مقاله براي محاسبه گرانروي درگ به روش حجم محدود بر اساس معادلات رينولدز- متوسط ناويه استوكس (RANS) بصورت دو بعدي را نشان ميدهد. محاسبات بر روي زيردريايي برهنه(DREA) و جسم شش بعدي حاصل از دوران با نسبت طول به قطر (L/D) 4 تا 10 صورت گرفته است. دامنه اطراف اجسام با هر دو شبكه شكل يافته و يا شكل نيافته منقطع شده است. براي آزمون صحت مدل سازي جريان آشفته از مدل هاي مختلف آشفته استفاده گرديد. مقايسه نتايج پيش بيني شده از روش 2 بعدي با نتايج آزمايشي/عددي همخواني مطلوبي داشته است.

References      1.          Patel, V. C., Chen, H.C., “Flow over tail and in wake of axisymmetric bodies: review of the state of the art­”, Journal of Ship Research, Vol. 30, No. 3, (1986), pp. 202-314. 2.          Choi, S. K., Chen, C. J., “Laminar and turbulent flows past two dimensional and axisymmetric bodies”, Iowa Institute of Hydraulic Research, IIHR Report 334-II (1990). 3.          Sarkar, T., Sayer P. G., Fraser, S. M., “A study of autonomous underwater vehicle hull forms using computational fluid dynamics”, International Journal for Numerical Methods in Fluids, Vol.  25, (1997), pp. 1301-1313. 4.          Lam, C.K.G., Bremhorst, K., “A modified form of the k-ε model for predicting wall turbulence”, ASME Journal Fluid Engineering, Vo.103, (1981), pp. 456. 5.          Baker, C., “Estimating drag forces on submarine hulls”, Report DRDC Atlantic CR 2004-125, Defence R&D Canada – Atlantic, (2004). 6.          Gertler, M., “Resistance experiments on a systematic series of streamlined bodies of revolution for application to the design of high speed submarines”, DTMB Report C-297 (1950). 7.          Menter, F. R., “Two-equation eddy-viscosity turbulence models for engineering applications”. AIAA Journal, Vol. 32(8),  (1994), pp.1598-1605. 8.          Schlichting, H., “Boundary Layer Theory”, McGraw-Hill, New York, (1966). 9.          Versteeg, H. K., Malalasekera, W., “An Introduction to Computational Fluid Dynamics The Finite Volume Method”, Longman Scientific and Technical, U.K. (1995). 10.       Cebeci, T., Shao, J.R., Kafyeke, F., Laurendeau, E., “Computational Fluid Dynamics for Engineers”, Horizons Publishing Inc., Long Beach, California (2005). 11.       Department of Research and Development Canada- Atlanta, National Defense, “Wind Tunnel Test of the DREA Six Meter long Submarine Model- Force Data analysis”, Ottawa, (1988). 12.       White, N. M., “A comparison between a simple drag formula and experimental drag data for bodies of revolution”, DTNSRDC Report 77-0028 (1977). 13.       Lin, C.W., Percival, S. and Gotimer, E.H., “Viscous Drag Calculations for Ship Hull Geometry”, Technical Report, Design Evaluation Branch, Hydromechanics Directorate, David Taylor Model Basin, Carderock Division Naval Surface Warfare Center, Bethesda, MD USA, (1995)