An investigation of free surface effects on drag and lift coefficients of an autonomous underwater vehicle (AUV) using computational and experimental fluid dynamics methods

Abstract

In the present paper, in order to investigate the effect of free surface on drag and lift coefficients of an Autonomous Underwater vehicle,¹ two phase flow Reynolds Averaged Navier–Stokes (RANS) equations were solved using computational fluid dynamics. The numerical results were compared with those obtained from both numerical single phase flow simulations and the experiments conducted in the towing tank of the Subsea R&D Center at Isfahan University of Technology, using a 1:1 scale model of AUV developed in this center. The study was conducted at various submergence depths ranging from 0.87 to 5.22 of the AUV diameter and at the speeds of 1.5 and 2.5 m/s (corresponding to Reynolds numbers of 1.9 and 3.17 million, respectively). The variation of drag and lift coefficients of the AUV with the submergence depth were shown to be very sensitive to the AUV speed.

Introduction

To investigate the hydrodynamics performance of submersible vehicles, the dynamics governing equations must be solved. However, since the forces and moments in these equations are expressed in terms of hydrodynamics coefficients, these coefficients should be provided as a priori. There are a number of experimental, semi-experimental and numerical methods which can be used to calculate the hydrodynamics coefficients of submersible vehicles. These coefficients are normally obtained for an infinite domain, assuming that these vehicles operate very far from the free surface. To calculate the hydrodynamics coefficients of a submersible vehicle numerically by using computational fluid dynamics, it is easy to define an infinite medium by specifying proper boundary conditions. The governing equations can then be solved numerically to obtain forces and moments required to calculate the hydrodynamics coefficients. The effect of free surface in this case is not, therefore, considered in the numerical calculation of these coefficients.

To calculate the hydrodynamics coefficients of a submersible vehicle experimentally, various experiments should be conducted in a towing tank. To calculate the drag and lift coefficients, for example, a scaled model of the vehicle must be towed in a towing tank at various constant speeds. The axial and lateral forces required to tow the vehicle at each speed should be measured. The scale effect should also be considered when the hydrodynamics coefficients are calculated experimentally. Since the hydrodynamics coefficients are supposed to be calculated for a submersible vehicle which normally operates at deep waters, the main question in these experiments is that at what depth, the model should be towed in order to eliminate the water-free surface effects on the measured hydrodynamics coefficients.

On the other hand, when a submersible vehicle approaches the free surface, the calculated coefficients obtained for an infinite domain are not suitable for investigating the stability and maneuverability of the submersible vehicle. The dynamics of the vehicle, in this case, is influenced by the surface effects and the wave produced by the motion of the vehicle. Both cases described above show the importance of predicting the hydrodynamics coefficients of a submersible vehicle as a function of the vehicle distance from the free surface.

The drag coefficient of submersed bodies has been studied by many researchers. Ming et al. (2009) and Wei-yun Shao (Shao et al., 2013), for example, used single phase flow numerical simulations to model the flow past stationary vertical and yawed cylinders, respectively. The fluid flow structure around a cylinder and its force coefficients were also experimentally studied by Malavasi and Guadagnini (2009) in some experiments with a water channel under various flow conditions and elevations of the cylinder above a channel floor. A notable number of works have been reported on predicting the hydrodynamics coefficients of submersible vehicles in an infinite domain; this can be seen, for example, in Mansoorzadeh et al. (2013), Lee et al. (2011), Phillips et al. (2010), Jones et al. (2002), Ross et al. (2004), Tang et al. (2009), Aage (1994), and Ridley et al. (2001). Despite numerous numerical studies on hydrodynamics coefficients of submersible vehicles in the single phase flow, comparatively, little attention has been directed to two phase flow studies in which the effect of free surface on forces and moments of these vehicles can be addressed. Due to the complexity of the two phase flow problems, only a few researchers have used analytical methods to solve the governing equations, this can, for example, be seen in Hajmohammadi et al. (2014) and Hajmohammadi and Nourazar (2014). Therefore, most works on two phase flow problems that have addressed the hydrodynamics coefficients have been performed by either numerical or experimental methods.

A number of works have been conducted over the past few decades on predicting the forces and moments on surface and submerged vehicles due to waves. Wiley (1994), for example, used a linear wave theory and slender body theory for a stationary AUV to predict the force and moments due to wave. Milgram (2007) also used the strip theory to determine the response of a streamlined AUV subjected to waves. Malik et al. (2013) applied the panel method used in the commercial CFD code and Ansys AQWA to compute wave forces in both frequency and time domains. The previously mentioned works are some examples of the studies conducted on the effects of regular waves on the force and moments of a surface or submerged vehicle. More references on similar works can be found in papers published by the above references. To study the effect of waves on the force and moments of an AUV in the previous works, the assumptions of potential flow, slender body and small amplitude motions had to be made. Accuracy of the results obtained from the above works, therefore, depends on the validity of the assumptions. Strip theory, for example, cannot give accurate hull pressure predictions when the slenderness of the vessel is decreased. The results are also valid for only regular waves with small amplitudes.

Jagadeesh and Murali (2010) and Jagadeesh et al. (2009) are among the few researchers who used Reynolds Averaged Navier–Stokes (RANS) equations to study the surface influence on the hydrodynamics coefficients of an axisymmetrical underwater body at calm water. They compared results obtained for hydrodynamic forces and moments using various turbulence models together with the Volume of Fluid (VOF) model. They also compared the numerical results with the corresponding experimental results conducted in a towing tank. Their AUV geometry lacked any control surfaces. Therefore, they managed to use a relatively small number of mesh elements (0.46 million elements) to obtain the results. However, the results obtained for an AUV without any control surfaces might not be fully applicable for a real AUV.

In this paper, a numerical investigation based on computational fluid dynamics was performed using Reynolds Averaged Navier–Stokes equations in order to study the effect of free surface on the drag and lift coefficients of an AUV model at various depths of submergences. It is worth mentioning that since the main aim of this work was to investigate the effect of free surface on the hull of the AUV, the upper fin (rudder) was removed from the AUV in both numerical and experimental studies. Therefore, our model had one vertical control surface fin (rudder) at the bottom and two horizontal fins (stern). A schematic of the AUV model used for the current study is shown in Fig. 1.

A set of two phase flow numerical simulations was performed for AUV model located at various distances from the water-free surface, at two different AUV speeds, namely at its nominal speed of 1.5 m/s and at 2.5 m/s, to study the effect of the increase in AUV speed on the results. The obtained two phase flow results were compared with the corresponding results obtained from single phase flow simulations performed for an infinite domain. The numerical results obtained from the simulations were then compared with the available experimental results conducted in the Subsea Research and Development Center at Isfahan University of Technology (IUT), Isfahan, Iran.