• International Journal of Technology (IJTech)
  • Vol 10, No 4 (2019)

Resistance Characteristics of Submerged Projectile with Bow Variation based on Hull Envelope Equation using Steady RANS Simulation

Resistance Characteristics of Submerged Projectile with Bow Variation based on Hull Envelope Equation using Steady RANS Simulation

Title: Resistance Characteristics of Submerged Projectile with Bow Variation based on Hull Envelope Equation using Steady RANS Simulation
Yanuar , Ibadurrahman , Syifa Alfiah Andini Putri

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Yanuar., Ibadurrahman., Putri, S.A.A. 2019. Resistance Characteristics of Submerged Projectile with Bow Variation based on Hull Envelope Equation using Steady RANS Simulation. International Journal of Technology. Volume 10(4), pp. 677-688

Yanuar Department of Mechanical Engineering, Faculty of Engineering, Universitas Indonesia, Kampus UI Depok, Depok 16424, Indonesia
Ibadurrahman Department of Mechanical Engineering, Faculty of Engineering, Universitas Indonesia, Kampus UI Depok, Depok 16424, Indonesia
Syifa Alfiah Andini Putri Department of Mechanical Engineering, Faculty of Engineering, Universitas Indonesia, Kampus UI Depok, Depok 16424, Indonesia
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Resistance Characteristics of Submerged Projectile with Bow Variation based on Hull Envelope Equation using Steady RANS Simulation

This paper investigates the influence of the forebody of a projectile-shaped model without appendages and propulsion system in a submerged condition. The commercial steady RANS code, ANSYS Fluent, was used to conduct the simulations, and the forebody was varied based on the Hull Envelope equation. From the results, the model with nf = 2.75 was the optimum design according to the bow efficiency coefficient. However, the model with a blunt form (nf = 1) produced the lowest drag because it had the least wet surface area. For models with high nf, a high accelerating flow led to a low-pressure condition after the impact of the fluid on the fore end. This soaring pressure difference caused a flow separation, and therefore the fullness of the forebody affected the fluid flow around the body: the alteration of pressure, the flow speed, and friction as the primary component of resistance.

Bow shape; Hull envelope coefficient; Resistance characteristic; Steady RANS; Submerged projectile


The resistance of a submerged object has a significant influence on its speed and acoustic signature, and hence its endurance. Viscous resistance is the only component of total drag on a deeply submerged object and is divided into two elements: skin-friction resistance and form (viscous pressure) resistance (Renilson, 2015). One way to reduce these resistances in the initial design stage is to consider the hull form of the vehicle in terms of its hydrodynamic aspect (Joubert, 2004).

Generally, the hull of a submerged object or submarine consists of three sections: the forebody, middle body and aft body (Burcher & Rydill, 1994). The “Hull Envelope” formula, the first developed equation for a true teardrsop shape, is essential in the concept design stage (Jackson, 1992). Other designers have used different hull form equations for submerged objects or submarines, but they have still been associated with the teardrop shape (Kormilitsin & Khalizev, 2001). The forebody of a submerged object determines the stagnation point (location and pressure) of the flow. Moreover, the bow shape has a significant influence on the behavior of fluid flow around and after it, thus affecting the effectiveness of sensitive equipment in it, e.g. acoustic or navigation equipment.

Following previous studies, an experiment on a submerged spheroid was conducted by Farell et al. (1973) in order to examine the influence of body form on the resistance components.  Besides,  a wind-tunnel experiment on a high-speed underwater object reasonably demonstrated that an ellipsoidal nose profile could improve hydrodynamic performance (Suman et al., 2010). A wind-tunnel observation of a submersible vehicle also showed a typical flow separation in the symmetric bow of a submarine model with an angle-of-attack variation (Saeidinezhad et al., 2015).

The use of Computational Fluid Dynamics (CFD) has gained increasing favor in recent decades, during which time computing power and improvements in numerical algorithms have been improving significantly; Using CFD could straightforwardly construct a virtual towing tank or wind tunnel (Yang & Löhner, 2003; Toxopeus, 2008; Fedor, 2009; Gross et al., 2011). The commercial CFD code ANSYS had been used to investigate an autonomous underwater vehicle and has resulted in a propeller race deduction (Rattanasiri et al., 2015). Another CFD approach showed that the elliptical submarine nose-shape was preferred for an initial design (Moonesun et al., 2016). Furthermore, Siswantara et al. (2016) have proven that the CFD method could be used for various digester designs to find that which is optimal in terms of slurry flow; they modelled in two dimensions to reduce the complexity of the calculations.

Investigation of a moving submerged object has focused mainly on achieving an optimum design by identifying the body form. Work using 2D steady-state flow RANS (Reynold Averaged Navier-Stokes) with variants of forebody shape and the speed range is well underway; the commercial CFD software ANSYS Fluent had been utilized in this study. The objective of this paper is to examine the characteristics of resistance and flow influenced by the bow form. The result may help designers at a concept design phase. The scope of the study focuses only on the forebody form of a projectile-like object in deeply submerged conditions, with the only drag components considered important being skin friction and viscous pressure resistance.


The design of a submerged object depends on hydrodynamic aspects; the forebody is one of the critical concerns since flow of fluid toward the bow influences the remaining body. In this paper, CFD simulations of 2D submerged projectile models were conducted to examine this issue. The results provide a reasonable estimate of the resistance and flow characteristics of the models.

The model with nf = 1 produced the lowest total drag since its wet surface area was smaller than that of the other models. However, the ellipse models attained better flow properties, and that with nf = 2.75 was designated as the optimum design according to the bow efficiency coefficient. The pressure point on the front end became extensive for higher nf models, thus making the pressure difference rise dramatically. On the ellipse models, the flow velocity increased from a point one-fifth along the bow length after the high pressure on the front end when the bow-head displaced the fluid. Subsequently, the rising velocity of the flow reduced the fluid pressure, thus creating a slight separation

The study has shown that a simplified CFD method using a commercial code could be a functional assessment of designing a submerged object at the initial stage. The optimum design based on the results of this study is suitable for projectile-shaped objects in deeply submerged conditions, such as submarines and torpedoes. Any consideration omitted from this paper may slightly revise the results.

Furthermore, involving additional analysis, such as the relation of the fluid around the bow to propulsion efficiency, would be considered worthy of examination, since the form of a hull affects the wake formation behind the self-propulsion object, as well as its resistance (Suastika et al., 2017).


This work is sponsored by the Ministry of Research, Technology, and Education of Republic Indonesia (NKB-1791/UN2.R3.1/HKP.05.00/2019).


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