# Encyclopedia of Ocean Engineering

Living Edition
| Editors: Weicheng Cui, Shixiao Fu, Zhiqiang Hu

# AUV/ROV/HOV Resistance

• Zhe Jiang
• Pengfei Sun
Living reference work entry
DOI: https://doi.org/10.1007/978-981-10-6963-5_263-1

## Definition

When the underwater vehicles such as AUVs/ROVs/HOVs or submersibles navigate in the sea, they will inevitably suffer the resistance of the water as they move in the water fluid medium. Therefore, the reaction force of the water on the hull is called the resistance. The resistance of the submersible is usually divided into the resistance of the bare hull and the resistance of appendage (Renilson 2015). Appendage resistance refers to the increase in the resistance value of the appendage structure, such as rudders, stabilizers, manipulators, thrusters, etc., which overhung on the naked hull. From the mechanical point of view, the resistance of the submersible consists of the frictional resistance because of the tangential force along the surface of the hull and the pressure resistance because of normal force which is exerted on the surface of the hull. Unlike the ship hull, since the submersible does not have a free surface, the pressure resistance exists only in the composition of the viscous pressure resistance, and there is no wave-making resistance.

## Scientific Fundamentals

### Method for Studying the Submersible Resistance

Methods for studying the resistance of submersibles include theoretical analysis, experimental research, and numerical calculation (Sheng 2003). Theoretical analysis can only be applied to simple problems and qualitative analysis because of the simplification of the object. Experimental method has the characteristics of strong authenticity and high reliability relative to theoretical research; but due to the cost, project duration, and other constraints, experimental method is generally only used to validate the results of numerical methods. The towing tank test and wind tunnel test are the mostly used experimental methods currently. In recent years, with the rapid development of computer technology, computational fluid of dynamics (CFD) method in the hydrodynamic performance of submersibles are applied in more and more applications. Compared to traditional theoretical and experimental methods, CFD methods have the advantages of short time consumption and low cost.

### Classification of Submersible Resistance

There are many appendage structures on the surface of the submersible, including the rudder, manipulator, thruster, underwater camera, underwater lighting, sampling basket, etc., so the submersible resistance can usually be divided into the resistance of the bare hull and the resistance of appendage according to the structure of the submersible.

From mechanical point of view, the main source of resistance of the submersible under water is the tangential force along the surface of the hull and the normal force which is perpendicular to the surface of the submersible, which are the frictional resistance and the viscous pressure resistance respectively.

According to the boundary layer theory, a boundary layer is formed on the surface when the viscous water flows through the submersible, and the rate of change of the fluid velocity in the boundary layer is prominent. According to the Newton internal friction law, the frictional shear stress on the surface of the submersible is great, so the resultant force of these frictional shear forces is the frictional resistance of the submersible. In scientific research, the frictional resistance can be thought of as the sum of the smooth plate frictional resistance with the same wetted surface, the same length and speed, and the additional frictional resistance after considering the tortuosity and roughness. In the theoretical study, scholars often use the formula to estimate the frictional resistance. After comparing with the experimental data, it can be proved that these formulas have appropriate precision within limits.

The viscous pressure resistance is another component of the resistance of the submersible, in essence, due to the viscosity of the fluid. It is known from the theory of fluid mechanics that a lot of vortices appear in the rear part of the hull when boundary-layer separation occurs, causing a difference in fore and aft pressure, which causes resistance. This resistance is called viscosity pressure resistance. Sometimes, it is also referred as vortex resistance. There are various methods for measuring the viscosity pressure resistance, and the most commonly used method is the wake pressure measurement method. In the actual research, in order to avoid the tediousness of the experiments and to obtain the value of the viscosity pressure resistance, the Froude two-dimension method and the three-dimensional method which is proposed in the 1950s can be used.

### Factors Affecting the Resistance of the Submersible

The hull form is the most important factor which is affecting the resistance performance of the submersible. The following two parameters are the most sensitive parts of the resistance performance of the submersible (Renilson 2015).
1. 1.

L/D: Aspect ratio. Where L is the submarine length, D is the diameter.

2. 2.

$${C}_P=\frac{\nabla }{A_ML}$$: Prismatic coefficient. Where ▽ is the volume of the submarine and AM is midships cross-sectional area.

In addition, the fore body form, the parallel middle body length and shape, and the aft body form all affect the resistance performance of the submersible.

## Key Applications

Studying the resistance performance of the submersible is of great significance for improving the cruising speed for AUV/ROV/HOV.

### Methods on Measuring Submersible Resistance

There are generally three methods to measure the drag of submersible: empirical equation estimation, model test method, and computational fluid dynamics (CFD) method. In different design phases of submersible, different methods are used.

#### Empirical Equation Estimation (Cui et al. 2018)

For submersibles moving underwater, if the depth exceeds one coxswain, the total resistance can be expressed as:
$${R}_t={R}_f+{R}_{pv}+{R}_{ap}=\frac{1}{2}\rho {V}^2\left({C}_f+\Delta {C}_f+{C}_{pv}+{C}_{ap}\right)$$
(1)

In the formula, “Rt” is the total resistance.

Rf” is the frictional resistance.

Rpv” is the viscous pressure resistance.

Rap” is the appendage resistance.

ρ” is the fluid density.

V” is the submersible speed.

Cf” is the frictional resistance coefficient.

“ΔCf” is the roughness coefficient.

Cpv” is the viscous pressure resistance coefficient.

Cap” is appendage resistance coefficient.
1. (1)

Empirical formula for calculating frictional resistance

The following three formulas can be used to calculate the friction resistance of submersible.
1. 1.
Schoenherr formula
$$\frac{0.242}{\sqrt{C_f}}=\mathit{\lg}\left({R}_e{C}_f\right)$$
(2)
When Re > 106–109, the formula is equal to:
$${C}_f=\frac{0.4631}{{\left(\mathit{\lg}{R}_e\right)}^{2.6}}$$
(3)

2. 2.
ITTC formula
$${C}_f=\frac{0.075}{{\left(\mathit{\lg}{R}_e-2\right)}^2}$$
(4)

3. 3.
Prandtl-Schlichting formula
$${C}_f=\frac{0.455}{{\left(\mathit{\lg}{R}_e\right)}^{2.58}}$$
(5)

2. (2)
Empirical formula for calculating viscous pressure resistance
$${C}_{pv}={C}_{\phi}\bullet K\bullet \frac{A}{S}$$
(6)

In the formula, K = f(B/H).

S” is the wetted surface area.

Cϕ” can be expressed as follow:
$${C}_{\upphi}=f\left({L}_A/{A}^{\frac{1}{2}},\phi \right)$$
(7)

LA” is the length of outlet section;

ϕ” is the longitudinal prismatic coefficient, ϕ =/L · A.

A” is the midship section area.

3. (3)

Empirical formula for calculating appendage resistance

The appendage resistance can be expressed as follows:
$${C}_{ap}=\sum {C}_{scf}\bullet \frac{S_{SC}}{S}+{K}_{SC}\bullet {C}_{pv}$$
(8)

In the formula, “Cscf” is frictional resistance coefficient on control surface.

SSC” is the wetted surface area on control surfaces.

KSC” is the empirical coefficient.

Cpv” is viscous pressure resistance coefficient on naked bodies.

#### The Towing Tank Test

The towing tank test is one of the most used experimental methods to obtain the resistance of underwater vehicles, ships, etc. Due to the limitation of facilities of any towing tanks, scaled-sized models are generally used instead of real size models. In the towing test, the scaled model is usually mounted on the trailer through the support rod, and the resistance of the model is measured in all directions through the movement of the trailer, which simulates the movement of the submersible. The real body resistance can be converted by the model resistance through the similarity laws. Froude similarity theory is often used for resistance conversion in engineering experiments. A towing tank test of a full ocean depth submersible is shown in Fig. 1 (Jiang 2016).

#### Resistance Analysis Using Computational Fluid Dynamics (CFD) Method

Empirical equation estimation has poor adaptability varying with different shapes and characteristics of different types of submersibles. Towing tank model test is costly and time consuming. Compared to experimental method, using CFD analysis in the resistance analysis will be much faster and require relatively low cost. In addition, in principle it is possible to use CFD to obtain results at full-scale Reynolds numbers, something which is not possible using model experiments. On the other hand, the analysis object can be modeled according to the shape or molded lines of it, and even appendages or local contour can be simulated in a CFD analysis; the results obtained through CFD analysis will be more accurate and reliable compared to using empirical equation estimation. Therefore, the CFD method is usually adopted to conduct flow field simulation, especially in the early stage of submersibles’ design, and numerical calculation model is built in CFD software to obtain submersibles’ resistance.

## References

1. Cui W, Guo W, Wang F, Jiang Z, Luo G, Pan B (2018) Submersible technology and application. Shanghai Scientific and Technical Publishers, ShanghaiGoogle Scholar
2. Jiang Z (2016) Hydrodynamic performance test analysis report of the 11000-meter manned submersible [R]. Technical report. Hadal Science and Technology Center, Shanghai Ocean University, ShanghaiGoogle Scholar
3. Renilson M (2015) Submarine hydrodynamics. Springer Briefs in applied sciences and technology, SwitzerlandGoogle Scholar
4. Sheng Z (2003) Principles of ship. Shanghai Jiao Tong University Press, ShanghaiGoogle Scholar