# Effect of Reynolds number on flow behavior and pressure drag of axisymmetric conical boattails at low speeds

- 69 Downloads

### Abstract

The effect of Reynolds number on flow behaviors and pressure drag around axisymmetric conical boattails was experimentally investigated at low-speed conditions. Four conical boattails with slant angles of 12°, 16°, 20°, and 22° were studied. The Reynolds number ranged from 4.34 × 10^{4} to 8.89 × 10^{4} based on the model diameter. The global-luminescent-oil-film skin-friction measurement was employed to analyze the surface skin-friction topology. Quantitative skin-friction values at the centerline were obtained in this study. The results show that a separation bubble can be formed on boattail surfaces at angles from 12° to 20°. However, at a boattail angle of 22°, flow is fully separated near the boattail shoulder. The integrated afterbody pressure drag indicated that, at angles of 12°, 16°, and 22°, the Reynolds number has very small effect on the afterbody drag, while, at 20° the drag coefficient decrease was relatively large with increasing Reynolds number. We believe that this study provided the first results for a boattail angle of 20° and we observed that the size of the separation bubble decreased as the Reynolds number increased. The effect of the separation bubble on the pressure distribution was also examined in detail.

### Graphical abstract

## Notes

### Acknowledgements

This work was supported by Kakenhi Grant 16H04582 from the Japan Society for the Promotion of Science and by Presto Grant JPMJPR1678 from the Japan Science and Technology Agency.

## References

- Bader P, Pscherning M, Sanz W, Woisetschlager J, Heitmeir F, Meile W, Brenn G (2016) Flat-plate boundary layers in accelerated flow. In: Proceedings of ASME Turbo Expo 2016: turbine technical conference and exposition, Seoul, South Korea, GT2016-56044Google Scholar
- Boutilier MSH, Yarusevych S (2012) Parametric study of separation and transition characteristics over an airfoil at low Reynolds numbers. Exp Fluids 52:1491–1506CrossRefGoogle Scholar
- Braslow AL, Knox EC (1958) Simplified methods for determination of critical height of distributed roughness particles for boundary-layer transition at Mach numbers from 0 to 5. National Advisory Committee for Aeronautics NASA technical Note no 4363Google Scholar
- Britcher CP, Alcorn CW (1990) Interference-free measurements of the subsonic aerodynamics of slanted-base ogive cylinders. AIAA J 29(4):520–525CrossRefGoogle Scholar
- Brunn A, Nitsche W (2006) Active control of turbulent separated flows over slanted surfaces. Inter J Heat Fluid flow 27:748–755CrossRefGoogle Scholar
- Choi H, Lee J, Park H (2014) Aerodynamics of heavy vehicles. Ann Rev Fluid Mech 46:441–468MathSciNetCrossRefGoogle Scholar
- Compton WB (1974) Effect on base drag of recessing the bases of conical afterbodies at subsonic and transonic speeds. NASA Technical note D-4821Google Scholar
- Compton WB, Runckel JF (1970) Jet effects on the boattail axisal force of conical afterbodies at subsonic and transonic speedsGoogle Scholar
- Dresz DA (1989) Drag measurements on a laminar-flow body of revolution in the 13-inch magnetic suspension and balance system. NASA Technical paper 2895Google Scholar
- Driver DM, Drake A (2008) Skin-friction measurements using oil-film interferometry in NASA’s 11-Foot transonic wind tunnel. AIAA J 46(10):2401–2407CrossRefGoogle Scholar
- Genc MS, Karasu I, Acikel HH (2012) An experimental study on aerodynamics of NACA2415 aerofoil at low Re numbers. Exp Thermal Fluids Scien (39):252–264Google Scholar
- Gillieron P, Chometon F (1999) Modelling of stationary 3D separated air flows around an Ahmed reference model. ESAIM Proc 7:173–182CrossRefGoogle Scholar
- Howard FG, Goodman WL (1984) Axisymmetric bluff-body drag reduction through geometrical modification. J Aircraft 20(6):516–522CrossRefGoogle Scholar
- Ilday O, Acar H, Elbay MK, Atli V (1992) Wakes of three axisymmetric bodies at zero angle of attack. AIAA J 31(6):1152–1154CrossRefGoogle Scholar
- Joseph P, Amandolese X, Aider JL (2012) Drag reduction on the 25 slant angle Ahmed reference body using pulsed jets. Exp Fluids 52:1169–1185CrossRefGoogle Scholar
- Karman Th V (1930) Mechanical similitude and turbulence. NACA Technical Memorandums No 611Google Scholar
- Kendall A, Koochesfahani M (2008) A method for estimating wall friction in turbulent wall-bounded flows. Exp Fluids 44:773–780CrossRefGoogle Scholar
- Kentfield JAC (1984) Short multi-step afterbody fairings. J Aircraft 21(5):351–352CrossRefGoogle Scholar
- Kim D, Lee H, Yi W, Choi H (2016) A bio-inspired device for drag reduction on a three-dimensional model vehicle. Bioinspir Biormim 11:026004CrossRefGoogle Scholar
- Kremheller A, Fasel H (2010) Water tunnel experiments of three-dimensional separation bubbles on a flat plate. AIAA Paper 2010–4738Google Scholar
- Kumar R, Viswanath PR, Prabhu A (2002) Mean and fluctuating pressure in boat-tail separated flows at transonic speeds. J Spacecraft 39(3):430–438CrossRefGoogle Scholar
- Lavrukhin GN, Popovich KF (2009) Aerogasdynamics of jet nozzles vol 2 Flow around the base. Fizmatlit, Moscow
**(in Russian)**Google Scholar - Lee D, Nonomura T, Anyoji M, Aono H, Oyama A, Asai K, Fujii K (2015) Mechanisms of surface pressure distribution within a laminar separation bubble at different Reynolds numbers. Phys Fluids 27:023602CrossRefGoogle Scholar
- Lee T, Nonomura T, Asai K, Liu T (2018) Linear least-squares method for global luminescent oil film skin-friction field analysis. Rev Sci Instrum 89:065106CrossRefGoogle Scholar
- Liu T, Sullivan JP (1998) Luminescent oil-film skin-friction meter. AIAA J 36(8):1460–1465CrossRefGoogle Scholar
- Liu T, Montefort J, Woodiga S, Merati P, Shen L (2008) Global luminescent oil-film skin-friction meter. AIAA J 46(2):476–485CrossRefGoogle Scholar
- Liu T, Woodiga S, Ma T (2011) Skin-friction topology in a region enclosed by penetrable boundary. Exp Fluids 51:1549–1562CrossRefGoogle Scholar
- Mair WA (1969) Reduction of base drag by boat-tailed afterbodies in low speed flow. Aeronaut Q 20:307–320CrossRefGoogle Scholar
- Mariotti A, Buresti G, Gaggini G, Salvetti MV (2017) Separation control and drag reduction for boat-tailed axisymmetric bodies through contoured transverse grooves. J Fluid Mech 832:514–549CrossRefGoogle Scholar
- McQuilling M, Wolff M, Fonov SD, Crafton J, Sondergaard R (2008) An experimental investigation of a low-pressure turbine blade suction surface using a shear and stress sensitive film. Exp Fluids 4(1):73–88CrossRefGoogle Scholar
- Naughton JW, Sheplak M (1996) Modern developments in shear-stress measurement. Prog Aerosp Scie 38:515–570CrossRefGoogle Scholar
- Olson DA, Katz AW, Naguib AM, Koochesfahani MM, Rizzetta DP, Visbal MR (2013) On the challenges in experimental characterization of flow separation over airfoils at low Reynolds number. Exp Fluids 54:1470–1481CrossRefGoogle Scholar
- Presz WM, Pitkin ET (1974) Flow separation over axisymmetric afterbody models. J Aircraft 11(11):677–682CrossRefGoogle Scholar
- Presz WM, Pitkin ET (1976) Analytical model of axisymmetric afterbody flow separation. J Aircraft 13(7):500–505CrossRefGoogle Scholar
- Reda DC, Wilder MC (2001) Shear-sensitive liquid crystal coating method applied through transparent test surfaces. AIAA J 39(1):195–197CrossRefGoogle Scholar
- Roberts WB (1980) Calculation of laminar separation bubbles and their effect on airfoil performance. AIAA J 18(1):25–31CrossRefGoogle Scholar
- Schloemer HH (1967) Effect of pressure gradient turbulent boundary-layer wall-pressure fluctuations. J Acoust Soc Am 42(1):93–113CrossRefGoogle Scholar
- Selig MS, Deters RW, Villiamson GA (2011) Wind tunnel testing airfoils at low Reynolds numbers. AIAA Paper 2011 – 875Google Scholar
- Silhan FV, Cubbage JM (1957) Drag of conical and circular-arc boattail afterbodies at Mach numbers from 0.6 to 1.3. NASA Technical Memorandum RM L56K22Google Scholar
- Silton SI, Dinavahi SPG (2008) Base drag considerations on a 050-caliber Spinning Projectile. AIAA Paper 2008–6739Google Scholar
- Strachan RK, Knowles K, Lawson NJ (2007) The vortex structure behind an Ahmed reference model in the presence of a moving ground plane. Exp Fluids 42:659–669CrossRefGoogle Scholar
- Suliman MA, Mahmoud OK, Al-Sanabawy MA, Abdel-Hamid OE (2009) Computational investigation of base drag reduction for a projectile at different flight regimes. In 13th international conference on aerospace sciences and aviation technology Cairo Egypt ASAT-13-FM-05 May 24–26Google Scholar
- Tani I (1964) Low speed flows involving bubble separations. Progr Aerosp Sci 5:70–103CrossRefGoogle Scholar
- Tran TH, Ambo T, Lee T, Chen L, Nonomura T, Asai K (2018) Effect Boattail angles on the flow pattern on an axisymmetric afterbody at low speed. Exp Thermal Fluid Sci 99:324–335CrossRefGoogle Scholar
- Tripathi A, Manisankar C, Verma SB (2015) Control of base pressure for a boat-tailed axisymmetric afterbody via base geometry modifications. Aerosp Sci Technol 45:284–293CrossRefGoogle Scholar
- Venning J, Jacono DL, Burton D, Thompson M, Sheridan J (2015) The effect of aspect ratio on the wake of the Ahmed body. Exp Fluids 56(6):126CrossRefGoogle Scholar
- Vino G, Watkins S, Mousley P, Watmuff J, Prasad S (2005) Flow structures in the near wake of Ahmed model. J Fluids Struct 20:673–695CrossRefGoogle Scholar
- Viswanath PR, Ramesh G, Madhavan KT (2000) Separation control by tangential blowing inside the bubble. Exp Fluids 29:96–102CrossRefGoogle Scholar
- Westerweel J, Geelhoed PF, Lindken R (2004) Single-pixel resolution ensemble correlation for micro-PIV applications. Exp Fluids 37:375–384CrossRefGoogle Scholar
- Wolfe WP, Oberkampf WL (1985) Drag predictions for projectiles and finned bodies in incompressible flow. J Spacecraft 24(1):14–22CrossRefGoogle Scholar
- Woodiga SA (2013) Global skin-friction diagnostics: the Glof technique and measurements of complex separated flows. PhD Thesis Department of Mechanical and Aeronautical Engineering Western Michigan University USAGoogle Scholar
- Woodiga SA, Liu T (2009) Skin-friction fields on delta wings. Exp Fluids 47:897–911CrossRefGoogle Scholar
- Zhong H, Woodiga S, Wang P, Shang J, Cui X, Wang J, Liu T (2015) Skin-friction topology of wing-body junction flows. Euro J Mech B/Fluids 53:55–67CrossRefGoogle Scholar
- Zilliac GG (1996) Further development of the fringe-imaging skin-friction technique. NASA TM-110425Google Scholar