Simulation of a Launch and Recovery of an UUV to an

2009
Master’s Thesis in
Naval Architecture
Simulation of a Launch and
Recovery of an UUV to an
Submarine
Robert Fedor
KTH Marina System
2009-10-21
Acknowledgments
I wish to extend the outermost thanks to ASC Pty Ltd and Hans Wicklander for giving
me the opportunity to conduct this study at location in Adelaide, Australia. Also
thanks to Patrick Marshallsay, Sean Williams and Per Dahlander who guided me with
their expertise in the field. Christine Philippou without you I would have been lost in
the office. Richard Hejde, Roger Carlsson, Anders Folbert and Paul Plant for your
input and friendship.
Jens Fellenius and Lynda Curtis for your hospitality, friendship and above all help
with my living arrangements. Marucs Leach and Brant Oxlade for teaching me how to
surf. My family for their support throughout my studies with a special thought to my
late father Henry Fedor, who tragically passed away during the course of this study,
may you rest in peace.
2
Abstract
Studies of the flow field surrounding submarines are a common practise, usually to be
able to lower the underwater signature of the vessel. In this report the study has
focused on mapping the forces the flow field and boundary layer exerts on an
adjacent, much smaller, vehicle trying to dock with the submarine. From requirements
defined by ASC Pty Ltd the recovery procedure have to be conducted while at speed.
The submarine was modelled and simulated in a CFD tool with the Unmanned
Underwater Vehicle at different locations along the hull of submarine. The simulation
showed that the boundary layer and vortices surrounding the submarine are highly
complex. With the CFD code and present computing power available at the time of
this report it was impossible to accurate map the flow. However it is shown that the
forces fluctuate almost chaotically and with current manoeuvrability technology and
recovery systems for Unmanned Underwater Vehicles it is highly unlikely that a safe
docking could be conducted at speed.
3
Sammanfattning
Studier av vattnets flöde kring ubåtar är vanligt förekommande, vanligtvis för att
minska den akustiska signaturen hos farkosten. Denna studie fokuserar på att försöka
kartlägga den turbulens och de krafter som uppkommer i gränsskiktet och flödet kring
en ubåt när en mindre farkost försöker docka till den. Enligt kravspecifikationen
definierad av ASC Pty Ltd så måste den tänkta dockningen ske i fart.
Ubåten har modellerats och simuleras i ett CFD-verktyg tillsammans med en
obemannad undervattensrobot placerad på olika platser utmed ubåtens skrov.
Resultatet från simuleringarna visade att gränsskiktet och turbulensen kring ubåten är
mycket komplext. Med den CFD kod och datorkraft som fanns tillgänglig för
författaren vid tillfället för studien var det omöjligt att kartlägga flödet i detalj. Det
visar sig dock att krafterna har en näst intill kaotisk fluktuation och i relation med
dagens manövreringsförmåga hos obemannade undervattensfarkoster samt de
dockningssystem som finns tillgängliga är det högst osannolikt att en säker dockning
skulle kunna utföras i fart.
4
Table of contents
1
INTRODUCTION......................................................................................................................... 9
1.1 SCOPE ......................................................................................................................................... 9
1.1.1
Limitations ........................................................................................................................ 9
2
APPROACH TO THE FLUID DYNAMIC PROBLEM......................................................... 11
2.1 THE MODEL .............................................................................................................................. 11
2.2 THE DARPA SUBOFF PROJECT .............................................................................................. 12
2.2.1
Axisymmetric Hull .......................................................................................................... 12
2.2.2
Sail.................................................................................................................................. 12
2.3 GOVERNING EQUATIONS ........................................................................................................... 12
2.4 FLOW AROUND A SUBMARINE ................................................................................................... 13
2.4.1
Boundary layer ............................................................................................................... 13
2.4.2
Tip and Junction flows at the sail ................................................................................... 13
2.5 CHOICE OF POSITIONS ............................................................................................................... 14
3
CFD AND THE STAR-CCM+ CODE ...................................................................................... 17
3.1 STAR CCM+ (THE CODE) .......................................................................................................... 17
3.1.1
The mesh ......................................................................................................................... 17
3.1.2
AMG SIMPLE Solver...................................................................................................... 19
3.2 REYNOLDS-AVERAGED NAVIER-STOKES (RANS).................................................................... 20
3.3 TURBULENCE MODELS.............................................................................................................. 21
3.4 DETACHED EDDY SIMULATION (DES)...................................................................................... 22
3.5 UNCERTAINTY ANALYSIS OF THE PROBLEM AND CODE ............................................................. 22
3.5.1
Scaling of CFD model .................................................................................................... 24
3.5.2
Presentation and reduction of Data................................................................................ 26
3.5.3
Grid size and dependence study...................................................................................... 27
3.5.4
Deciding the Time-step for the DES simulation.............................................................. 29
3.5.5
Steady modelling of a unsteady problem ........................................................................ 30
4
SIMULATION PROCESS ......................................................................................................... 32
5
NUMERICAL PROCEDURE, RESULT AND DISCUSSION............................................... 33
5.1
5.2
5.3
5.4
6
FLOW FIELD IN GENERAL (TIME DEPENDENT ANALYSIS) ........................................................... 34
POSITION 1 [X = 0.14LSUB] ......................................................................................................... 34
POSITION 2 [X = 0.23LSUB] ......................................................................................................... 36
POSITION 3 AND 4 ..................................................................................................................... 39
UUVS AND LARS IN SHORT .................................................................................................. 45
6.1 THE US NAVY UUV MASTER PLAN (UUVMP) ....................................................................... 45
6.2 UUV’S ...................................................................................................................................... 47
6.2.1
Navigation ...................................................................................................................... 47
6.2.2
Guidance and Communication ....................................................................................... 47
6.2.3
Propulsion and Endurance ............................................................................................. 48
6.2.4
Stability........................................................................................................................... 48
6.2.5
Control............................................................................................................................ 49
6.2.6
Categories....................................................................................................................... 52
6.2.7
Discussion....................................................................................................................... 53
6.3 LAUNCH AND RECOVERY SYSTEMS .......................................................................................... 53
6.3.1
Funnel/Cone Recovery Systems ...................................................................................... 53
6.3.2
Belly mounted Stinger / Buoy Vertical Pole ................................................................... 54
6.3.3
Universal Launch and Recovery Module........................................................................ 55
6.3.4
Sea Owl SUBROV........................................................................................................... 56
6.3.5
Boeing Torpedo mounted retractable arm...................................................................... 57
6.3.6
Reverse Funnel Recovery – Authors suggestion ............................................................. 58
7
CONCLUSION ........................................................................................................................... 59
8
FURTHER WORK ..................................................................................................................... 60
5
9
REFERENCES............................................................................................................................ 61
6
Nomenclature
Symbol
Unit
[kg/m3]
[Pa s]
[–]
[s]
[m/s]
Description
Density
Viscosity
Under relaxation factor
Time step
Turbulent inertia tensor
 x , Lcell
B
CD
CFL
D
F
FB
g
G, CoG
IXX
K2
LAR, LFR
Lsub
LUUV
M
p
p*
[r/s2]
[r]
[m/s]
[m]
[–]
[–]
[–]
[m]
[N]
[N]
[m/s2]
[–]
[m4]
[–]
[m]
[m]
[m]
[–]
[Pa]
[Pa]
p´
[Pa]
Angular acceleration roll
Euler angle of roll
Velocity of fluid
Grid/Cell size
Centre of Buoyancy
Axial Force Coefficient
Courant-Friedrich-Lewy
Diameter
Force
Buoyancy force
Gravity
Centre of Gravity
Mass moment of inertia, roll
Form factor by Jackson
Section Length
Length of submarine
Length UUV
Metacentre
Pressure
Guessed pressure
Correction pressure,
Fluctuating component of pressure
Improved pressure
Reynolds number
Strouhal number (~0.2)
Free stream velocity of fluid
Maximum velocity of fluid
Cell volume
Kinematic viscosity
Height of sail
Boundary layer thickness



t
uiu j
p

v , [u,v,w]
new
p
Re
St
U∞
Umax
V
v
zsail
δ
[Pa]
[–]
[–]
[m/s]
[m/s]
[m3]
[m2/s]
[m]
[m]
7
Acronyms and Abbreviations
ADCP
API
AUV
AUVG
CAD
CFD
DARPA
DES
DSTO
DTMB
DTRC
ITTC
LARS
LES
NGS
RAN
RANS
ROV
UUV
UUVMP
Acoustic Doppler Current Profiler
Application Programming Interface
Autonomous Undersea Vehicle
Autonomous Undersea Vehicle Glider
Computer Aided Design
Computational Fluid Dynamics
Defence Advanced Research Projects Agency (US)
Detached Eddy Simulation
Defence Science and Technology Organisation
David Taylor Model Basin
David Taylor Research Center
International Towing Tank Conference
Launch and Recovery System
Large Eddy Simulation
Next Generation Submarine
Royal Australian Navy
Reynolds-Averaged Navier-Stokes
Remotely Operated Vehicle
Unmanned Undersea Vehicle
United States UUV Master Plan
8
1 Introduction
There are two leading trends in the submarine and military industry that are growing
rapidly. The first one is to put more of the payloads outside the pressure hull on the
next generation submarines. The second one is to increase the safety of the personnel
by using autonomous vehicles on dangerous tasks, such as mine counter measurement
and Intelligence, Surveillance and Reconnaissance missions, rather than humans. Due
to this there is an interest in conducting an investigation of where and how an
Unmanned Undersea Vehicle (UUV) could be recovered to a submarine.
A submarine displaces thousands of tonnes of water and is surrounded by turbulent
fluid while travelling through the water. Why a study of the wake and the fluid around
the submarine is needed to fully comprehend the difficulties involved in recovering a
UUV to a submarine. Hence, the goal of this study is to investigate whether a
recovery of a UUV at speed is feasible, by its own control or with help from a Launch
and Recovery System.
The investigation is performed by conducting a series of simulations of an UUV
docking to a submarine using a Computational Fluid Dynamics (CFD) tool. Using a
CFD tool is cost efficient compared to full scale experiments but the results from the
simulations needs to be verified to some degree by experimental data.
1.1 Scope
The goals of the study which is outlined on a requirement specification given by
ASC Pty Ltd to the author are as follows:




What the effect the boundary layer around the submarine, and the wake
trailing the sail, has on the UUV.
Where on the submarine is a recovery is most favourable?
Whether these forces are so large that the submarine cannot compensate for
them itself?
How a Launch and Recovery System should be constructed to accommodate
the need for a safe docking procedure.
The report focuses on the complexity of the flow surrounding a submarine and the
difficulties simulating it. The reader will get a general explanation how the flow field
around a generic submarine develops and later presented with the results from full
sized computer simulations with a UUV in close proximity to the Submarine.
A literature study containing detailed information about UUVs and Launch and
Recovery Systems (LARS) is presented to the reader. In these chapters different types
of UUVs and LARS are identified and categorised. The study is conducted to
highlight present and past problems with UUV recovery procedures.
1.1.1 Limitations
There are a few limitations that were decided on during the literature study;
9




The submarine model that all simulations are conducted with is decided to be
similar to a normal sized diesel electric submarine or more specifically 87.12
meters in length and 10.1 meters diameter.
During the literature study it was identified that most submarines cannot, or
are reluctant, to travel below 2 knots. At the same time most UUVs cannot
exceed 5 knots. Therefore a single recovery speed of 3 knots is chosen.
There was originally intended that a set of simulations where to be made for
different angles of attack for the submarine to the free streaming fluid.
However only one set of simulations is made at a zero degree angle of attack.
Because of limitations in the CFD tool only simulations of static problems are
made.
Further limitations and constraints concerning the modelling of the problem in the
Computational Fluid Dynamics software will be explained in chapter 3.
10
2 Approach to the Fluid Dynamic problem
In order to determine the best location for recovery it is necessary to know how a flow
field around a submarine behaves. One way of achieving this is to construct a scale
model of the body in question and conduct a series of flow experiments. This is a time
consuming, expensive but well-established approach. In recent decades however, with
the exponential increase of computing power and improvements in numerical
algorithms, Computational Fluid Dynamics (CFD) has gained increasingly favour.
Using CFD an operator can relatively straightforward construct a virtual towing tank
or wind tunnel. Used in conjuncture with Computer Aided Design (CAD) the operator
can construct and modify complex geometries and perform a series of simulations
covering a wide range of flow conditions.
A warning hand is raised though; it is an easy pitfall to think that CFD is the solution
to all fluid dynamic problems. Still even with increasingly computing power a direct
numerical solution of a problem will probably not be feasible until earliest 2080,
(Spalart, 2000). To overcome this problem a lot of different approaches to model the
turbulence and average solutions has seen the light of day.
2.1 The Model
The DTMB model 5470 configured with bare hull and sail as the only appendage is
used as the starting point. The aft control surfaces are omitted from the model as they
are considered not to have any significant effect on the UUV, whereas their inclusion
would negatively impact on the computer resources required.
Figure 1 show the geometry used during this study. The model used in the simulations
is scaled twenty times in order to mimic a diesel electric submarine displacing about
7000 tons. Further discussion of the effect of scaling is contained in section 3.5.1. The
questions asked and answered during this study is:
1. What is the most favourable location on the submarine to launch and recover a
UUV?
2. What characteristics does the flow around submarine take at “recovery
speed”?
3. What pressures and velocities act on the UUV in the turbulent wake and
boundary layer of the submarine?
Question 1 and 2 can relatively easily be extracted from a steady-state simulation
using a CFD code. Question three however is more challenging. Ideally one would
use an overset grid approach, (CFD-Online, the free CFD reference, 2006), which
would allow the two bodies to move through the computational space independently
of one another. Unfortunately, such facilities are not yet readily available in
commercial CFD codes. Therefore, for each recovery position, a series of steady-state
simulations were performed with the UUV located at various positions along its
trajectory. The process was automated by writing a Java macro script to perform the
processing required at each point on the trajectory, and running the various
simulations sequentially in batch mode using a Python script to control the process.
The procedure is described further in chapter 4.
11
2.2 The DARPA SUBOFF Project
It is essential to be able to verify the results gained from the simulations. One way is
to compare the results with experiments made in controlled environments, such as a
wind tunnel or towing basin. Therefore information is available in the public domain
from experiments performed on hulls, airfoils and submarines. In this study the
DARPA SUBOFF Project is chosen for validating purposes.
The Defence Advanced Research Projects Agency (DARPA) is the central research
and development organization for the United States Department of Defence. In the
end of the 1980’s there was an initiative taken by DARPA to develop an experimental
database for CFD code validation. The experiments were held at the David Taylor
Model Basin (DTMB) in Bethesda, Maryland. Two models were built, DTMB Model
no. 5470 and 5471, which differed only in the location of the surface pressure taps.
Model no. 5470 was designed for towing tank experiments while model no. 5471 was
designed for the wind tunnel. The details of the models and their configurations are
described in (Groves, Huang, & Chang, 1989).
2.2.1 Axisymmetric Hull
The DARPA models have an axisymmetric hull with an overall length of 4.356 m and
a maximum diameter of 0.508 m. The characteristic length used to reduce the results
to non-dimensional form is 4.261 m or ~0.978 L. The hull is composed of a fore-body,
a parallel middle-body, an after-body, and an aft-body cap of 1.016 m, 2.229 m, 1.111
m and 0.095 m respectively, see Figure 1. Full geometrical details are contained in
(Groves, Huang, & Chang, 1989). The coordinate system adopted in the present study
is shown in Figure 17.
Figure 1 – DTMB model no. 5470, Hull + Sail configuration
2.2.2 Sail
The sail is located on the hull at top dead centre with its leading edge positioned at
x = 0.924 m (.2121 Lsub) and trailing edge at x = 1.293 m (.2968 Lsub). A cap is
attached to the top of the sail at height of 0.460 m (zsail), from the hull, and is a 2:1
elliptical cross-sectional shape. The sail and cap profile are found in (Groves, Huang,
& Chang, 1989).
2.3 Governing equations
The governing equations for fluid flow, which describe the conservation of fluid mass
and momentum, are the equation of continuity and the Navier-Stokes equations. The
derivation of the Navier-Stokes equations begins with the conservation of mass,
12
momentum and energy being written for an arbitrary control volume, and can be
followed in full in (Versteeg & Malalasekera, 2007). If we instead consider that we
have an incompressible Newtonian fluid with constant density, ρ, and constant
viscosity, μ, then we can express the Navier-Stokes equations in its most general form
by equation (12.1),
 v

 v v   p   2 v   g
 t


(12.1)
where v is the flow velocity vector and p the pressure. The Navier–Stokes equations
are strictly a statement of the conservation of momentum and to fully describe the
fluid flow you need more information, boundary conditions etc. Regardless of the
assumptions made, a statement of the conservation of mass is generally necessary.
This is achieved through the mass continuity equation, given in its most general form
for an incompressible fluid in equation (12.2).
v  0
(12.2)
2.4 Flow around a submarine
Before delving into the numerical approach to fluid dynamics an overview of the flow
around a submarine is explained. When an object travels through water it displaces
water. This in turn constructs complex flow patterns around the submarine as whole
but also the obstacles that are attached to the hull, such as the tower, arrays etc.
2.4.1 Boundary layer
In this study all simulations are conducted at a Reynolds number is in the order of
Re ≈ 150E6 for the submarine, hence the submarine are surrounded by a turbulent
boundary layer. The axisymmetric and slender shape of the submarine prevents the
boundary layer from separation until it reaches the negative shaped after-body.
2.4.2 Tip and Junction flows at the sail
Junction flow occurs when the boundary layer on a surface encounters an obstacle
attached to that surface, (Simpson, 2001). The resulting flow fields are complex and
feature three-dimensional separating flow. The stream wise adverse pressure gradients
cause the boundary layer to separate and form multiple horseshoe vortices. Figure 2
shows a schematic view of a simplified junction flow and wing tip vortex shedding.
The separation line that wraps around the sail has its origin at a stagnation point in
front of the sail. The stagnation point is the separating point between the relatively
undisturbed flow upstream of the obstacle, and the complex flow region that develops
around and downstream of the obstacle. Generally these vortices are highly unstable
and break up to form a highly turbulent wake downstream of the obstacle. The
vortices that trail from the top of the sail arise from separating flow that occurs as a
result of the adverse pressure gradient downstream and upstream flow regions. These
vortices are referred to in the following discussion as “wing-tip” vortices.
13
Figure 2 – Simplified illustration of the flow around the sail
2.5 Choice of positions
Initially three candidate positions where selected. After assessing the output data from
these simulations, the strength of the tip vortices was found to be greater than
expected and it became apparent that further information of the wake characteristics
was needed. Therefore the investigation was extended to include one extra recovery
position aft of the sail, and also to include an un-steady simulation with no UUV
present, in order to fully understand the wake characteristics and flow aft of the sail.
The resulting four recovery positions are shown in Figure 3.
Figure 3 – The positions on the Submarine where recovery simulations where made.
It was concluded at an early stage that it would be inadvisable to consider any
recovery positions in the aft part of the submarine due to the adverse flow
characteristics present in this region. As shown in (Huang, et al., 1992) the stern part
of the submarine is dominated by a quickly thickening boundary layer and two contrarotating vortices. The thickening boundary layer is the result of the separation of the
boundary layer that occurs due to the adverse pressure that develops from the point
14
that separates the middle body and aft part of the submarine, as explained in
chapter 2.4.1.
Figure 4 – Presentation of velocity profiles and an approximate illustration of the thickening
boundary layer in the aft region. Based on data extracted from velocity profiles at
x = [75 80 85 90 95] per cent of model length.
Figure 4 further shows that the boundary layer thickness upstream of the afterbody of
the submarine does not exceed 0.6-0.9 meters, which is in good agreement with
predictions made by the Power-Law theory for turbulent boundary layers on two
dimensional flat plates, as formulated by Prandtl (White, 1991). This expression
estimates a boundary layer thickness of about 0.55 meter in this region. The power
law relationship takes the form:
.
  0.16
x
1
 0.55m
(12.3)
Re x 7
Further upstream within the wake the sail, the flow is dominated by two contra
rotating horseshoe vortices close to the hull, accompanied by two tip vortices. The
nature of the flow within this region is shown clearly in Figure 5, and the existing
vortex structures could potentially cause a problem for the recovery of UUV’s within
this region. Since there are clear logistical advantages in launching and recovering a
UUV within this region, a decision was made to investigate the resulting flow forces
on a UUV deployed within this region.
15
Figure 5 – Vortices generated by the sail at x = 0.5L, illustrated as in-plane velocity i.e. u = 0. The
white streamlines together with black arrows define the direction and the colour the velocity of
the fluid.
16
3 CFD and the Star-CCM+ code
Computation Fluid Dynamics provides a means of simulating flows of moderate
complexity using computational methods, generally without recourse to experimental
techniques. A CFD code comprises three main elements: a pre-processor, a solver and
a post-processor:
Pre-processor
Pre-processing is the part where an operator defines the geometry of the
region; the computational domain of the model. Furthermore a discretization
of the problem is necessary because the partial differential equations that
describes a fluid flow are non linear and an analytical solution is almost never
present, which is why the domain is divided into a number of smaller subdomains, often referred to as a mesh (or grid) of cells. The problem can hereon
after be solved numerically over the grid. A selection of what physical or
chemical phenomena that needs to be modelled has to be made and finally
define the fluid properties and appropriate boundary conditions.
Solver
The most well-established numerical solution technique is the finite volume
method. Its numerical algorithm first discretizes the integral form of the
governing equations and applies the discrete versions to each cell. The
objective is to obtain a set of linear algebraic equations, with the total number
of unknowns in each equation system corresponding to the number of cells in
the grid. The resulting equations are then solved by an iterative method.
Post-Processor
A Post-processor gives the ability to visualize the solution by different kinds
of plots, both 2D and 3D. Also many CFD codes include animation tools for
dynamic result display.
3.1 Star CCM+ (the code)
The code used during this study is the Star CCM+ (version 3.04.008) from
CD-Adapco. Star CCM+ use an “Algebraic MultiGrid Semi-Implicit Method for
Pressure-Linked Equations solver” (AMG SIMPLE) when solving the discretized
linear system iteratively. Star CCM+ also provides a powerful semi-automatic
meshing tool which allows the operator to generate both surface and volume mesh.
The mesh is automatically generated upon the operator’s inputs and are valid and of
good quality. Furthermore Star CCM+ has the ability to automatically wrap surfaces
in order to ensure a complete closed model.
3.1.1 The mesh
The volume mesh is the mathematical description of the space or geometry of the
problem, (CD-adapco, 2008). It consists of three basic mesh entities, vertices, faces
and cells. Where, a vertex is a point in space defined by a position vector. A face
comprises an ordered collection of vertices such that they define a surface in threedimensional space and a cell is an ordered collection of faces that define a closed
volume in space, se figure 6.
17
Figure 6 – Illustration of vertex, face and cell respectively
One of the hardest and most time consuming parts of a CFD simulation is the mesh
generation. The refinement of the mesh has a major effect on the accuracy of the
solution and one could say that the greater amount of cells the better chance of
obtaining a good result. Though the denser the mesh the more computing power and
time it takes to generate and calculate the problem. Furthermore the mesh also needs
to be valid, no open faces, and of high quality to produce an accurate solution. A non
uniform grid is almost always the optimal one with a denser mesh at complex areas
and a coarser one in other areas. An example of a non uniform grid is shown in Figure
7.
Figure 7 – Non uniform grid
However, it is getting more common with intelligent meshing tools that are able to,
with relatively little human intervention, construct high quality valid meshes.
Star CCM+ offers three different types of volume mesh; tetrahedral, polyhedral and
trimmed mesh. The tetrahedral meshing model use tetrahedral shaped cells and is the
model that is fastest and uses the least amount of memory out of the three provided.
However, the tetrahedral model needs approximately five to eight times more cells to
produce the same accuracy as the equivalent polyhedral or trimmed cell mesh.
The polyhedral meshing model use polyhedral shaped cells and provides the operator
with a balanced solution for complex mesh generations problems. As for the
tetrahedral model, the polyhedral mesh model is directly dependant on the quality of
the starting surface triangulation. In other words, a bad quality starting surface will
lead to a bad quality volume mesh.
The trimmed cell mesher provides a robust method of producing a high quality grid
that consists of predominantly hexahedral cells with trimmed cells next to the surface.
It combines a hexahedral mesh with automatic curvature and proximity refinement
and, most importantly, surface quality independence in a single meshing scheme. Of
the three models the trimmer meshing model is more likely to produce a good quality
18
mesh for most situations, which is why it was chosen for this study. In Figure 8, the
three types of mesh models are illustrated.
Figure 8 – Three types of volume meshing, from left to right; tetrahedral, polyhedral and
trimmer respectively.
Image Copyright© CD-Adapco.
3.1.2 AMG SIMPLE Solver
The SIMPLE solver was originally put forward by Patankar and Spalding in 1972 and
is essentially implementing a guess-and-correct procedure. A short description of the
algorithm will now follow, for a complete derivative of the SIMPLE algorithm see
(Versteeg & Malalasekera, 2007). A SIMPLE calculation is initiated by first guessing
a pressure field p*. Then by using the discretized momentum equation and the guessed
pressure field it yields the velocity components v*, where v* is the guessed velocity
field vector in a Cartesian system. After which a correction p’ as the difference
between the correct pressure field p and the guessed pressure field p* is defined, so
that;
p  p *  p
(13.1)
A similar definition is done for the velocity field with v’. The correct pressure and
velocity fields in the governing equations are substituted for equation (13.1) and by
using the discretized continuity equation the mass fluxes at all faces are calculated.
The continuity equation is then rewritten so the pressure correction coefficient p’ can
be extracted. The new pressure field is then calculated by correcting the “old” one
with the newly extracted correction factor. However, the solution is prone to diverge
unless some under-relaxation is used during the iterative process so the new,
improved, pressure pnew are obtained with;
pnew  p *  p
(13.2)
Where, ω is the under-relaxation factor for pressure. Usually the under-relaxation
factor is changed over the total time of simulation. A ω equal to one is often too large
when the guessed pressure field p* is far from the final solution, which is why the
operator normally start with a low under-relaxation factor and gradually increase it to
one. With the new pressure field a corrected mass flux for the faces are calculated,
and from the mass flux the corrected cell velocities can be obtained with;
v new  v * 
19
V p 
a vp
(13.3)
Where, p’ is the gradient of the corrected pressure, a vp is the vector of central
coefficients for the discretized linear system representing the velocity equations and V
is the cell volume.
Star CCM+ uses a Multigrid method spanning the SIMPLE solver to speed up the
process of finding a solution. Instead of visiting each cell in sequence and updating
the values of pressure and velocity a Multigrid solver agglomerates cells to form
several coarse grid levels. It then performs a number of cycles with the SIMPLE
solver over the original fine layer (known as smoothing). After which the solution is
transferred to the next in line coarser level (known as restriction) where the cycling is
repeated and yet again the residuals are transferred to the next in line coarser grid
level. The restriction process continues until the Multigrid solver reaches the coarsest
level, where it turns and repeats the process of transferring solutions and performing
the cycles, but to the finer level (known as prolongation). The solution is prolongated
until the finest level is reached and the whole process is repeated until satisfactory
convergence is reached, se Figure 9.
Figure 9 – Schematics of a Multigrid process
There are two branches of Multigrid methods; Full Geometric Multigrid and
Algebraic Multigrid. Star CCM+ use the latter branch and it has the advantage of
performing the agglomeration without taking the geometry into account from the
finest level. In other word, the new coefficient matrix representing the coarser levels
consists of specially chosen coefficients from the original grid which means that no
new discretization is required and the grid does not need to be stored in the virtual
memory.
3.2 Reynolds-Averaged Navier-Stokes (RANS)
The numerical solution of the Navier-Stokes equations for turbulence in an
incompressible Newtonian fluid with constant viscosity is extremely difficult to solve
for and it take an almost indefinite fine mesh to find a solution which means that the
computational time becomes infeasible for calculation. To counter this, time-averaged
equation such as the Reynolds-Averaged Navier-Stokes equations are used in
practical CFD applications when modelling turbulent flows. The RANS equations can
be obtained by decompose the velocity and pressure into a mean and fluctuating
component, equation (13.4);
v  v  v
p  P  p
20
(13.4)
where v and v´ are the mean (time-averaged) and fluctuating velocity vectors in a
Cartesian system, and P and p´ are the mean and fluctuating component of pressure.
By substituting these expressions into the continuity equation, (12.2), and take the
time average of the entire equation we get (13.5),
v  0
(13.5)
where, v is the time-averaged velocity component in a Cartesian system. If we now
attempt the same procedure and substituting (13.4) into the nonlinear Navier-Stokes
equations, (12.1), and use the time average, we obtain equation (13.6).

 v

 v v   p  2 v   g  
uiuj
x j
 t

 

(13.6)
Thus the mean momentum equation has an additional term involving the turbulent
inertia tensor uiuj also known as the Reynolds Stress tensor. This term is never
negligible in any turbulent flow and is the source of the analytical difficulties because
its analytical form is not known a priori. Essentially the time averaging has added nine
new unknown variables (tensor components) that can be defined only by detailed
knowledge of the turbulent structure, which is not known. The problem being that the
Reynolds stresses are not only related to fluid physical properties but also to local
flow conditions such as; velocity, geometry, surface roughness and upstream history,
and no physical laws are available to resolve this dilemma, (White, 1991).
One way to get around this dilemma is to model the turbulence by using an
appropriate turbulence model.
3.3 Turbulence Models
As discussed above, the challenge with acquiring a high-quality solution by using the
RANS equations is to model the Reynolds stress tensor satisfactory. This is done
using turbulence models. It is widely acknowledged that turbulence models are
inexact representations of the physical phenomena being modelled and no single
turbulence model is the best for every flow simulation, (CD-adapco, 2008). Star
CCM+ come bundled with four major classes of turbulence models




Spalart-Allmaras models are a good choice for applications that has mild
separation and a largely attached boundary layer. A typical example is a flow
over a wing
K-Epsilon models provide a good compromise between robustness,
computational cost and accuracy. Generally well suited for applications that
contain complex recirculation, with or without heat transfer.
K-Omega models are similar to K-Epsilon models but have seen most
application in the aerospace industry, and are therefore recommended as an
alternative to the Spalart-Allmaras models for similar types of applications.
Reynolds stress transport models are the most complex and computationally
expensive models of the four. They are recommended for situations in which
the turbulence is strongly anisotropic.
21
From works by and discussion with Dr. Patrick Marshallsay at ASC Pty Ltd the
Abe-Kondoh-Nagano (AKN) Low-Reynolds K-Epsilon model was chosen as the
turbulence model for the simulations during this study. The AKN model is developed
to be used when calculating complex turbulent flow with separation and heat transfer.
The simulations done by Dr. Marshallsay showed that the AKN model performed well
in comparison with other turbulence models.
3.4 Detached Eddy Simulation (DES)
RANS together with turbulence models suffers from the inexact representation of the
time-dependent physical phenomena. A different approach is using Detached Eddy
Simulation, which is a hybrid modelling approach that combines features of
Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES)1. DES
uses a RANS solution in regions close to solid boundaries as well as where the
turbulent length scale is smaller than the grid dimension and treat the rest of the flow
in a LES manner. Therefore a DES model is not as demanding as a pure LES and
reduces the cost of computation. However just as in any CFD model DES is not an
answer to all turbulence problems; it must be cautioned that the creation of suitable
grids is a difficult task.
Hence, it needs a lot of careful preparation to run a DES simulation with special care
taking when considering mesh size and time step, further discussed in chapters 3.5.3.2
and 3.5.4.
3.5 Uncertainty analysis of the problem and code
The ITTC (International Towing Tank Conference) recommended procedures from
1999, (ITTC, 1999), contain guidelines for a general uncertainty analysis in CFD. It is
divided into four parts:
1. Preparation; which involves the selection of the CFD code and the
specification of objectives, geometry, conditions and available benchmark
information.
2. Verification; which amongst other is defined as a process for assessing
simulation numerical uncertainties. This includes a grid dependence study and,
for a transient solution, a time-step dependence study.
3. Validation; which is defined as a process for assessing simulation modelling
uncertainty by using experimental data as a reference.
4. Documentation; which is a detailed presentation of the CFD code (equations,
initial and boundary conditions, modelling and numerical methods),
objectives, geometry, conditions, verification, validation and analysis.
This study is sponsored by ASC Pty Ltd and a continuation of a previously conducted
work by Dr. Patrick Marshallsay. Therefore much of the preparatory work contained
in the ITTC recommended procedures is taken from the work made by Marshallsay.
In (Marshallsay, 2008) Marshallsay compares data extracted from simulating a
1
Large Eddy Simulation model is a time-dependent simulation which implicates
Kolmogorov’s theory of self similarity that the large eddies of the flow are dependent
on the geometry while the smaller are more universal in character. Thus an explicit
solution of the large eddies is possible while the smaller eddies can be solved
implicitly using a subgrid-scale model (SGS). (Versteeg & Malalasekera, 2007).
22
DTMB model no. 5470, using only a bare hull, with data from experiments in (Roddy,
1990) and (Huang, et al., 1992). Two different turbulence models were assessed, the
v2-f model and the SST k-ω model. The results, shown in Figure 10 and Figure 11,
show that predictions of skin friction and surface pressure coefficients made by the
SST k-ω model are in close agreement with the experimental measurements
undertaken at DTRC. The results from the v2-f model on the other hand are clearly
unacceptable. This latter model is known to suffer from realizability problems,
(Svenningsson & Davidson, 2003), and is arguably not yet sufficiently mature for
industrial applications.
Figure 10 – Comparison between Skin Friction Coefficient estimated using CFD and
experimental measurements made at the David Taylor Research Centre (DTRC),(Marshallsay,
2008).
Figure 11 – Comparison between Pressure Coefficient distribution estimated using CFD and
experimental measurements made at the David Taylor Research Centre (DTRC),(Marshallsay,
2008).
As explained in chapter 3.3 the author used the AKN k-ε turbulence model described
in (Abe, Kondoh, & Nagano, 1993) rather than the SST k-ω turbulence model. This
was decided after personal communications with Dr Marshallsay who found that the
23
data collected from the AKN k-ε model simulations are in closer agreement with
experimental data than the data from the SST k-ω model simulations.
3.5.1 Scaling of CFD model
In order of reducing the scale errors when calculating the forces and moments that act
on a UUV when it enters an area in near proximity to the submarine all simulations
was made in as near full size scale as possible. After consulting the supervising group
at ASC Pty Ltd (Dahlander, Williams, & Marshallsay, 2008) it was concluded that an
optimal size is most likely longer than the Collins class, which extends 77 meters, but
less than 100 meters long.
Scaling is done either by keeping the Froude’s number or the Reynolds number static
for both the model and full-scale submarine. The Froude’s number is derived from
wave resistance and therefore not applicable in this case, why scaling using a static
Reynolds number is implemented.
Roddy concludes in (Roddy, 1990) that scale effects between models and full-scale
submarines are negligible if experiments are made at or above a Reynolds number of
10E6 – 15E6. Scaling the DTMB model twenty times the size of the submarine reaches
87.12 meters, which in turn means that the Reynolds number exceeds 10E6 – 15E6 as
long as you keep the speed of the free flowing fluid above ~0.2 m/s.
Scaling the SUBOFF model twenty times generates a Reynolds number of roughly
Re ≈ 150E6 if one use a inflow speed of u = 1.54333 m/s, which equals 3 knots. To
maintain Reynolds number for the smaller model an inflow speed of u = 31.618 m/s is
needed. The drag of the two models is compared in order to verify the scaling of the
submarine model. Table 1 displays the resulting comparison between the two
simulations.
Table 1 – Comparison of Axial Force Coefficient
Re ≈ 150E6
Axial Force Coefficient
Fpressure  Fshear
C D
1
2
(  ref vref
L2 )
2
Model
Full-scale
0.790E-3
0.799E-3
Figure 12 and figure 13 shows the pressure- and skin friction coefficient distribution
over the hull at the lower mean line for both the Full-scale and model simulations,
respectively. When compared it is clear that the scaling effects are negligible.
24
Pressure Coefficient at Re  150E6
1
Fullscale
Model
0.8
Cp = p-pref/0.5refv2ref
0.6
0.4
0.2
0
-0.2
-0.4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Distance from bow [x/L]
0.8
0.9
1
Figure 12 – Pressure coefficient distribution at the lower mean line for the model and full-scale.
Skin Friction Coefficient at Re  150E6
-3
3.5
x 10
Fullscale
Model
3
Cf = w/(0.5refv2ref)
2.5
2
1.5
1
0.5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Distance from bow [x/L]
0.8
0.9
1
Figure 13 – Skin friction coefficient distribution at the lower mean line for the model and fullscale.
3.5.1.1 Drag predictions
The drag coefficient extracted from the simulations of the SUBOFF differ with ~5%
from the data collected in (Roddy, 1990) during his towing tank experiments. Even
though Roddy have not presented any uncertainty analysis for the present
configuration of the SUBOFF mode does he however give an approximate margin of
error of about 4-10% on the different derivatives of motion on a fully appended
SUBOFF model. Moreover in (Pankajakshan, Remotigue, Taylor, Jiang, Briley, &
Whitfield, 2003) a margin of error of 10% is presented.
25
The drag coefficient has also been compared to a semi-empirical method proposed in
(Jackson, 1992) and differs by a great margin. Jackson’s method is to be used on a
submarine that consists of three sections; a super elliptical bow, a parallel middle
section and a super parabolic stern, which the SUBOFF model clearly not consists off,
Figure 1. Further Jackson’s method uses a form factor, K2, to calculate the drag due to
pressure distribution throughout the hull. The form factor being a function of the
shape functions and wetted surface coefficient of the different sections respectively,
equation (14.1).
K 2  ( LAR  LFR ) - LAR  Cws , A - LFR  Cws , F , where
LiR 
Li
, and
Di
Cws,A 
(14.1)
Aws ,i
  Di
Where, LAR and LFR is the length of the sections, respectively. Di is the maximum
diameter for the section and Aws,i, is the wetted surface area for the section. The
subscript ‘i’ denotes the current section. In table 2 a comparison is shown with the
different methods used.
Table 2 – Comparison of Axial Force Coefficient.
Axial Force
Coefficient
Roddy
RANS
K-ε AKN
Jackson
CD
1.160E-3
1.101E-3
10.69E-3
3.5.2 Presentation and reduction of Data
The data is either presented in tabular form or in a plot. The tabular data is rounded
down to three working decimals. The force and moment coefficients presented in
chapter 5, Numerical Procedure, Result and Discussion, are all averaged over fifty
iterations of raw data. This is done because the forces and moments acting on the
vehicle did not converge at every single simulation. An example of this is shown in
Figure 14 where the top row contain all data collected from one of the simulations
conducted aft of the sail. The lower row on the other hand holds the last 50 iterations
from where the mean value was calculated.
26
x 10
Lift Force Coefficient Position 17
-4
4
-4
-6
-8
0
-1
0
200
-4
x 10
400
600
Iterations
800
1000
Lift Force Coefficient Position 17
200
x 10
400
600
Iterations
800
-2
Side Force Coefficient Position 17
6.4
750
x 10
800
850
Iterations
900
950
5.8
700
1000
Yaw Moment Coefficient Position 17
750
-5
7.4
2.6
-2.7
6.6
6
-6
-2
6.8
6.2
-3.5
700
1000
Pitch Moment Coefficient Position 17
7
-3
0
x 10
7.2
-2.5
-5
2.8
-5
7.4
-1.5
-3
-4
Yaw Moment Coefficient Position 17
-1
1
-2
-10
x 10
-0.5
Moment Coefficient
Force Coefficient
Force Coefficient
-5
0
2
-2
-2.65
Side Force Coefficient Position 17
3
0
-12
x 10
Moment Coefficient
-4
2
x 10
800
850
Iterations
900
950
1000
Pitch Moment Coefficient Position 17
7.2
-4
2.4
7
2.2
-2.85
2
1.8
1.6
1.4
Moment Coefficient
-2.8
-6
Moment Coefficient
Force Coefficient
Force Coefficient
-2.75
-8
-10
6.8
6.6
6.4
6.2
1.2
-2.9
-12
6
1
-2.95
950
960
970
980
Iterations
990
1000
0.8
950
960
970
980
Iterations
990
1000
-14
950
960
970
980
Iterations
990
1000
5.8
950
960
970
980
Iterations
990
Figure 14 – Example of data reduction for a simulation
3.5.3 Grid size and dependence study
A grid dependence study is necessary for validation that the amount of cells in the
grid yield a close enough solution of the problem. It is however a delicate procedure
of choosing just the right amount of cells that the solution is accurate enough but do
not take a lifetime to converge. The methodology of a grid dependence study is
straightforward. One only has to increase the density of the grid until no significant
difference is longer observed in the converged solution.
Most of the dependence study has already been done in this study by Dr. Patrick
Marshallsay. Marshallsay has in his works concluded that the AKN Low-Reynolds
K-Epsilon model with approximately two million cells gives a sufficient solution
compared to converging time when conducting simulations on the SUBOFF model.
With this in mind this study instead focuses on the grid on and surrounding the UUV.
Position 4d was chosen to where a grid dependence study is carried out. At this
position the UUV has just entered the heavy turbulent area just aft of the sail. It was
chosen because at this position the fluid is very complex and consists of small vortices
that can only be discovered with a fine grid.
In Star CCM+ one can add volume shapes to the continuum and define grid
generation rules for them. A block volume was added spanning the area in front and
aft of the sail where the length scales of the grid could be varied. Figure 15 shows
this together with a before and after image of the grid.
27
1000
Figure 15 – Before and after image of the added volume shape increasing the density of the grid
The characteristic length of the cells in the coarse simulation was set to a cell size of
Lcell  4.82  10 3 Lsub  0.42 meter, while the finer simulation used half that size,
Lcell  2.41  10 3 Lsub  0.21 meter. The result did show a small difference between the
two simulations but judging the fact that the finer mesh used almost twice the
computing time to converge, the coarser grid size was chosen.
3.5.3.1 Surface grid problems with the UUV Control Surfaces
One problem did arise with the grid. Caution should be taken when using results from
simulations where the external force acting on the UUV is weak. The surface grid on
the control surfaces of the UUV is not optimal and adds noise in the solution. A
solution to this is to remove the control surfaces but they are needed to give the model
an accurate representation of an ordinary UUV.
3.5.3.2 Deciding grid size for the DES simulation
For the DES to act as a LES and detect all eddies in the wake area of the sail the mesh
needs to be fine, but how do one determine what is fine enough? One way of doing it
is to analytically estimate the smallest and largest vortices in the wake. It is a rule of
thumb that the largest vortices behind a wing can be as long as the cord of the wing,
which can be applied here because it is the area behind the sail that is of interest. To
28
determine the smallest ones one can use the Kolmogorov micro scales, which is a
theory suggested by Andrey Kolmogorov in 1941, (Versteeg & Malalasekera, 2007).
Kolmogorov suggested that the smallest scales of turbulence are universal and that
they depend only of the fluids viscosity and the average rate of energy dissipation per
unit mass. By using the Kolmogorov scale, equation (14.2), the smallest vortices
would be in the order of 1E-5 m.
 v 3 
L 3 
 U 
1
4
 7.071 10 19  0.1 


1.5433


1
4
 1 105 m
(14.2)
Where v is the fluids kinematic viscosity, δ the boundary layer thickness on the sail
and U∞ is the free stream flow. The maximum boundary layer thickness on the sail
was approximated using both the analytical power law and a visual measurement in
the CFD code to ~0.1 m. The kinematic viscosity used is the default for H20 in the
CFD code.
Of course using a mesh size of 1E-5 m would create a mesh so fine that it would not be
feasible to solve it in this lifetime. Instead after a couple of tries with different sizes a
mesh size of 0.14 m in the area aft of the sail was chosen, which created roughly 3.3
million cells. Usually, during a steady simulation, the computing power allowed up to
5 million cells without the simulation being too time consuming but in this case with
much iteration over several time steps it was decided that a finer mesh than the one
chosen would take too long to solve. This meant that only vortices of a size ~0.14 m
or greater was detected by the CFD code.
3.5.4 Deciding the Time-step for the DES simulation
Just as choosing a mesh size the selection of time step is an engineering judgment,
and a difficult one. The most common approach one would take is suggested in the
CFD code user guide, (Cummings, Morton, & McDaniel, 2008), the Strouhal number.
The Strouhal number, St, is a dimensionless number for determine cylinder shedding
frequency. Normally the St is ~0.2 which is valid for most cylinders ranging in
Reynolds number from 100 to 106. Using this approach and with the added “rule of
thumb” that one need approximate 5 to 10 iterations for every period one would get a
time step of 0.4 seconds, (14.3),
f 
St  U  0.2 1.543

 0.229 Hz  T  4.37 s
L
1.35
(14.3)
where St is the Strouhal number, U∞ is the free stream velocity and L is a
characteristic length, in this case the width of the sail. However because the
simulations conducted during this study are run at a Reynolds number of well above
106 and that experimental data has showed that the Strouhal number can reach St ≥ 10
in high Reynolds flow, (Cummings, Morton, & McDaniel, 2008), other approaches of
deciding time step where looked at.
(Cummings, Morton, & McDaniel, 2008) discuss different approaches used to
determine an accurate time step. Cummings et al. also proposed an iterative approach
or a poor man’s “steepest descent” method, as they wish to call it, for choosing a time
step. In which one compares the wave number (inverse Strouhal number) against
29
several converged solutions with different time steps and grid sizes. The problem with
Cummings et al. approach is the time consumption, their experiment needed six
simulations before a small enough time step was conceived, all which took 50 CPU
hours each to reach convergence, this by using a mere 0.1 million cells and eight
parallel processors working together in a cluster. During the present study a cluster of
four CPU’s where used and a mesh of roughly 3 million cells, which is why
Cummings et al. approach is ruled out as a decider.
Further Cummings et al. discuss the approach made by other researchers in the field.
(Spalart, 2001) uses the Courant-Friedrichs-Lewy condition (CFL condition), which
can be explained as the ratio of the distance a wave-like disturbance travels in a time
step to the grid size, Equation (14.4),
CFL 
U max  t
CFL  x
 t 
x
U max
(14.4)
where CFL is a non-dimensionalized number, suggested to be approximately one by
Spalart for accurate prediction of large eddies. Umax is the maximum velocity
measured in the area of interest (normally Umax ≈ 2U∞, where U∞ is the free stream
velocity), Δx is the grid size and Δt is the time step needed. Another approach
*
introducing a non-dimensional time step Δt* ( t  t  U  l , where l is a
characteristic length of the vehicle, in this case the length of the sail) is used by
(Strelets, 2001), (Görtz, 2003) and (Schiavetta, Badcock, & Cummings, 2007) in their
studies of massively separated flows. Table 3 shows the time step required when
predicted by the different methods explained above.
Table 3 – Comparison between different methods for time step prediction.
Method
Δt
[s]
Strelets
Δt*= 0.025
Δt*
Görtz
Δt*= 0.006
.120
0.029
Strouhal
Schiavetta
Δt*= 0.01
CFL
Spalart
CFL ≈ 1
0.048
0.045
4.37
St = 0.2
As shown in table 4 the time step predictions by the different models vary quite a lot.
The author choose the method suggested by Strelets because the time step was
decided to be small enough for accurate prediction of large eddies and still large
enough so that the simulation would not take too long2. However, due to an error
made by the author the time step was set to 0.13 seconds and not 0.12, this was
determined not to have any significant effect on the result of the simulation so no
attempts for correcting it where made later.
3.5.5 Steady modelling of a unsteady problem
Simulating a clearly unsteady problem with a steady model is strongly recommended
against in the user manual of the CFD code, (CD-adapco, 2008). However if used the
CFD code will average the results in a similar matter to time averaged results that
could be extracted from a proper transient simulation. The problem arising with
2
It took roughly 350 CPU hours, divided over 4 CPU’s, i.e. just under 4 days, to simulate
approximately 180 seconds.
30
simulating an unsteady problem with a steady model is that the result from the steady
simulation will be equivalent to using an extremely inaccurate time step in transient
simulation. Essentially the CFD code will over the iterations use something similar to
a local time step that is smaller where the mesh is fine and larger where the mesh is
coarse.
Hence the results presented below from the steady simulations are to some stage
incorrect and should not be treated as an absolute fact. The problem lies within the
small unsteady vortices. Even though the primary vortices could be stable to some
extent, the secondary or tertiary vortices are unstable and very difficult to average
over a period of time. Their contribution in terms of force on the UUV is however
small compared to the larger vortices. For this reasons, the force- and momentcoefficients extracted from the simulations are determined to be accurate enough for
this investigation.
31
4 Simulation process
Star-CCM+ has the ability to be started in macro mode without using the graphical
user interface. It requires that the macro scripts are written in Java and the program
comes bundled with its own Java Application Programming Interface (API). In order
to be more versatile and easier make changes to specific runs several macros is
written, each with a specific purpose and input data. Spanning this, a Python script is
written to control the sequence of which positions and what type of simulations is
performed. The process is visualised in Figure 16.
Figure 16 – Overview of the simulation process
Where,
1. Translate the UUV to the given position and constructed the grid.
2. A less accurate but converged solution is firstly obtained with a first-order
segregated solver and with the under-relaxation factor set to a low value. This
is a common procedure if a more accurate converged second-order solution is
unobtainable at first, (CD-adapco, 2008).
3. After a converged solution is found the script switches to the more accurate
second-order solver and high under-relaxation factors. Thus resulting in an
accurate and converged solution.
4. This step extracted coefficients from the solution into raw data files.
5. The data was lastly imported into MATLAB for post-processing.
32
5 Numerical Procedure, Result and Discussion
In this chapter all results extracted from the simulations is presented and discussed.
All simulations used the same Cartesian coordinate system, with its origin situated at
the front tip of the submarine with the X, Y and Z axis directed horizontal positive aft,
horizontal positive port and vertical positive up respectively, as shown in Figure 17.
All forces and moments coefficients presented below are displayed in this coordinate
system, with the force and moment coefficients acting on the UUV at its centre of
gravity, which is situated at x = 0.375 LUUV from the front, (Prestero, 2002).
Figure 17 – Coordinate system on the REMUS 600 UUV and the continuum as whole,
respectively.
However when the UUVs distance from the hull is presented, the author uses the
distance from body to body. Reason being so the reader can easier tell whether the
UUV has entered the turbulent boundary layer or not.
The UUV used during the simulations is based on the REMUS 600 with a total length
of 3.25 meter and a diameter of 0.35 meter. A total of 26 static simulations have been
conducted divided over the four positions discussed in chapter 2.5. For each
simulation the UUV had to be placed at its location, after which the continuum was
meshed and the solution calculated. After the data was extracted to post processing
the UUV was translated to its new location and a new mesh and solution was
generated and calculated. All locations simulated at are displayed in Table 4. For
position 1 and 2 the distance from the hull is non-dimensionalized by the boundary
layer thickness but at positions 3 and 4 the sail height is used. This because at the
former locations the boundary layer is the dominant turbulence factor whiles at the
latter ones the sail is the origin of the dominant turbulence.
33
Table 4 – Overview of all simulated locations. Note that position 1 and 2 are non-dimensionalized
by boundary layer thickness while at 3 and 4 the height of the sail is used.
1
2
3
1/δ
a
b
c
d
e
f
g
h
i
j
4.8
3.3
2.5
4
1/Zsail
5.7
2.9
1.5
0.8
1.12
1.05
0.98
0.87
0.54
0.30
0.23
0.11
0.07
1.55
1.12
1.05
0.98
0.87
0.54
0.30
0.23
0.11
0.07
5.1 Flow field in general (time dependent analysis)
The simulations presented below are all conducted so both the submarine and the
UUV are fixed in space with the fluid flowing around them and a time-averaged
solution is calculated. The reason, as explained in chapter 3.5.5, is that the CFD code
at the time of this study did not support dynamic meshes and therefore it was
impossible to simulate a “live” recovery of an UUV. One consequence of this is that
all the calculations of pressure, vorticity and fluid direction is averaged over time,
hence it is difficult to draw any definite conclusions how much the force exerted from
the fluid on the UUV fluctuates over time. Thus an un-steady simulation with only the
submarine present in the continua was conducted.
The turbulence model chosen was Detached Eddy Simulation, DES, which in some
cases can result in the best of both worlds between Reynolds averaged Navier-Stokes
(RANS) and Large Eddy Simulation (LES) turbulence models. However the
simulation was conducted with a too coarse grid for the DES to function properly.
Instead of showing a vortex shedding and turbulence that changed over time a timeaveraged RANS solution appeared.
5.2 Position 1 [x = 0.14Lsub]
Position 1 is the only position investigating conditions in front of the sail. This region
consists of a laminar flow with a small turbulent boundary layer. At this position the
submarine’s hull is cone shaped which produces a favourable pressure gradient that
hinders the boundary layer growth. Furthermore the cone shape increases the fluid
velocity and decrease the pressure at this position. In theory the best solution would
be to control the UUV so that the fluid attacks it head on at all time which minimizes
the rudder movements during the recovery procedure. This is however very difficult
so the UUV is simulated fixed parallel to the free stream and not the hull, as shown in
Figure 18.
34
Figure 18 – The direction of fluid, illustrated by black streamlines, at the bow with UUV at close
location to the hull at position 1.
In conclusion, three simulations where conducted at this position, at increasing
distances from the hull, shown in Figure 19. The distances from the hull to the
vehicles centre of gravity and stern are presented in Table 5. The centre of gravity of
the UUV is not within the boundary layer at any time but the aft of the vehicle enters
the turbulent area in simulation 1c.
Figure 19 – The UUV location at the three simulations, respectively, at [x, y] = [0.14Lsub, 0]
Table 5 – Distances from the hull where the UUV where situated at position 1
non-dimensionalized by boundary layer thickness δ.
a
b
c
CoG
4.8
3.3
2.5
Stern
3.2
1.7
0.9
Figure 20 shows the resulting force and moment on the UUV. As expected the side
force- and yaw moments are both very small because of the uniform UUV body. The
increase is most likely due to noise. The lift force coefficient shows that the UUV is
repelled by the fluid flowing around the bow of the submarine. As the vehicles
approach each other a squat effect due to the two objects pressure fields give way to a
decrease. A similar conclusion can be drawn for the pitch moment coefficient which
increases as the UUV approach.
35
Figure 20 – Force and Moment acting on the REMUS 600 at Position 1. The dots represent one
simulation each and the Y Axis shows the distance from the hull of the submarine to the CoG of
the UUV. Left and bottom axis are non-dimensionalized.
5.3 Position 2 [x = 0.23Lsub]
In these simulations the UUV is positioned next to the submarine’s sail. Except for the
horse-shoe vortices and the turbulent boundary layer the region is dominated by a
steady non turbulent flow. The sail is situated at the intersection between the bow and
the parallel middle section which means that the fluid is still flowing with an angle
slightly outward from the centre of the hull, see Figure 21. Four simulations are
conducted at this position all located along a straight line at 15 degrees from the upper
mean line of the submarine, see Figure 22. The distances outwards from the hull are
chosen in relation to the boundary layer thickness at this position and are presented in
Table 6.
36
Figure 21 – Direction of the fluid and its magnitude at position 2 – CoG, viewed from aft. The
arrows represent the direction of the fluid (u = 0) and the background colour represent its
magnitude.
Figure 22 – Locations of the simulations at position 2, viewed from front.
Table 6 – Distances from the hull where the UUV where situated at position 2
non-dimensionalized by boundary layer thickness δ.
a
b
c
d
5.7
2.9
1.5
0.8
The reason why the UUV only partly enters the boundary layer is solely because it is
not thick enough and that the UUVs control surface would collide with the hull of the
submarine before it would enter the turbulent boundary layer area.
37
In Figure 23 where the forces and moments acting on the UUV is shown one can see
that all of the forces and moments are following a distinctive pattern as the smaller
vehicle approaches the hull of the Submarine. There is a force repelling the UUV
which is increasing until it enters the boundary layer and one of the horse-shoe
vortices where a decrease of the force occurs. It is more likely that the decrease is due
to the fluids directional change in the horse-shoe vortex than the interaction between
the two objects pressure fields.
Figure 23 – Force and Moment acting on the REMUS 600 at Position 2. The dots represent one
simulation each and the Y Axis shows the distance from the hull of the submarine to the CoG of
the UUV. Left and bottom axis are non-dimensionalized.
The Side Force Coefficient plot’s shape is similar to the Lift Force Coefficient. In this
case the forces acting on the UUV are inflicted by the horse-shoe vortex which at first
pushes it toward the sail of the submarine but when the UUV get situated inside the
vortex the force decrease again.
The Yaw Moment Coefficient is explained by the route the fluid takes around the sail
of the hull. The front part of the UUV is located so that the fluid is parallel when it
strikes the smaller vehicle, but when the fluid leaves the aft part of the UUV it is
drawn to the centre of the submarine due to the shape of the sail. This is clearly shown
38
at the aft of the UUV in Figure 24, where the separation of the fluid is clearly larger
on the side facing the sail.
The negative Pitch Moment Coefficient is most likely a result of the complexity of the
horseshoe vortex as it propagate throughout the hull of the UUV. A slight decrease in
the negative moment is visible when the vehicle enters the boundary layer which can
be attributed to the pressure field interaction.
Figure 24 – Top view over Pressure and Vorticity distribution, respectively, over the UUV (small
object) and the sail of the submarine at position 2.
Observe that in the lower right image of Figure 24 the origin of the horse-shoe vortex
is visualized as a high level of vorticity.
5.4 Position 3 and 4
Position 3 and 4 are both situated aft of the sail of the submarine to answer whether a
recovery is plausible at all in this region, maybe at a certain distance aft of the sail.
The simulated distances from the submarines hull are directly related to the height of
the sail and specified in Table 7.
39
Table 7 – Distances from the hull at position 3 and 4, respectively.
Non-dimensionalized by sail height (Zsail = 4.41m).
3
a
b
c
d
e
f
g
h
i
j
1.12
1.05
0.98
0.87
0.54
0.30
0.23
0.11
0.07
4
1.55
1.12
1.05
0.98
0.87
0.54
0.30
0.23
0.11
0.07
Position 3 is located so the UUVs bow is x = 0.3Lsail aft of the sail and position 4 is
situated so the UUV has its centre of gravity amidships the submarine. The region aft
of the sail is turbulent and dominated by two pairs of contra-rotating vortices; the
horseshoe- and “wing tip” vortices which both commence from the sail. This is
illustrated in Figure 25 which shows an in plane projection of the fluid,
[u,v,w] = [0,v,w], at position 3 and 4 respectively.
40
Figure 25 – Direction of the fluid and its magnitude at position 3 and 4 respectively. The arrows
and streamlines represent the direction of the fluid and the background colour represents its
magnitude.
Figure 26 shows the lift force and pitch moment coefficients acting on the UUV. It is
visible that both plots follow a similar pattern but the forces and moments are greater
for the position closer the sail. The Lift Force Coefficient plots shows that the UUV is
affected by a small downward force when in the free flowing area above the sail. At
this distance from the hull the attracting force between the objects due to the pressure
field interaction should be next to nothing, therefore the force is most likely due to the
noise created by the UUV’s control surfaces, as explained in chapter 3.5.3.1. The
most interesting observation is when the UUV enters the tip vortices which then exert
41
a repelling force on the smaller vehicle. This force only affects over a short distance
between circa ~1.05 to ~0.7 the height of the sail. It then changes to an attracting
force which increases as the vehicle approach the submarine. The attracting force is
due to the downward direction of the horse-shoe vortices with a small contribution
from the pressure field interaction between the objects.
The Pitch Moment coefficient shows a similar behaviour. In theory the UUV should
attain an increasing positive trim the closer it gets to the submarine, which it also
does. An exception exists when the vehicle pass through the tip vortices where an
irregular much larger moment is present.
Figure 26 – Lift Force and Pitch Moment at position 3 and 4 respectively. The dots represent one
simulation each and the Y Axis shows the distance from the hull of the submarine to the CoG of
the UUV. Left and bottom axis are non-dimensionalized.
Figure 27 illustrates the interaction between the two objects pressure field. Observe
that the dominating low pressure at the stern of the UUV which is causing the positive
trim when the UUV is in close proximity of the submarine.
42
Figure 27 – Interaction of pressure fields between UUV and Submarine in close proximity to each
other at position 4. From left is front, middle and aft of middle-body shown.
43
Figure 28 – Side Force and Yaw Moment Coefficients at position 3 and 4 respectively. The dots
represent one simulation each and the Y Axis shows the distance from the hull of the submarine
to the CoG of the UUV. Left and bottom axis are non-dimensionalized.
In Figure 28 the Side force and Yaw moment coefficients is presented and it is clearly
shown that they are very irregular, almost chaotic. This can be attributed to the
complexity of the vortices which changes characteristic and direction throughout the
vehicles body as the UUV descends towards the hull.
44
6 UUVs and LARS in short
These chapters cover the UUV and LARS technology and their basic theory of control
and communication. A short presentation of most UUV’s and LARS is presented and
a few is discussed in depth. However a lot of information regarding the different
system is company and/or Commonwealth proprietary and is not available to the
public.
There are multiple UUVs on the market today and their numbers are growing. Earlier
there where a clearer distinction between UUV’s for military and civilian use but
lately module based systems with the ability to use “off the shelf” products as payload
modules are becoming more of a standard. A module concept is not only more
versatile but much more cost effective and there are some systems on the market
today that are able to conduct a wide variety of functions. An example of a modular
based system is the AUV 62 from SAAB Underwater Systems; figure 29 shows the
setup for the UUV and all the interchangeable parts.
Figure 29 – Example of a module based system, AUV 62 Sapphires in basic configuration,
Copyright© SAAB Underwater Systems
6.1 The US Navy UUV Master Plan (UUVMP)
In 2004 the US navy released an updated version of its UUV Master Plan, (U.S. Navy,
2004), in which they describe their vision that an UUV can;
“Attack today’s littoral coverage problem and tomorrow’s advanced threat”
Furthermore an UUV can gather, transmit or act on all types of information, from
anywhere to anyone… Deploy or retrieve devices, anyplace, anytime… Engage any
target, bottom, volume, air or space. With minimal risk to US force… at an affordable
cost. Most importantly is of course the cornerstone where cost is not necessarily
monitored in the monetary value of the UUV but also the cost of human lives. Further
the Master Plan categorise UUV/AUV’s into four vehicle classes depending on their
size, which is shown in Table 8.
45
Table 8 – Vehicle classification according to the US UUVMP
Man
Portable
Light
Weight
Vehicle
Heavy
Weight
Vehicle
Displacement
10-50 kg
~250 kg
~1000 kg
~10 000 kg
Endurance
10-20 h
20-40 h
N/A
N/A
Shape /
Diameter
N/A
Torpedo
12.75 in.
Torpedo
21 in.
N/A
Class
Large
Vehicle
The Man Portable class is omitted from this study because firstly its endurance is
determined not sufficient for deployment into littoral zones from a submarine, and
secondly that the Master Plan only identifies the three larger classes as deployable and
recoverable from a submarine. The Large Vehicle class is intended to be used in AntiSubmarine warfare missions thus carrying heavy torpedoes which is why it is simply
too large and heavy to be carried by a medium/large sized diesel electric submarine.
Hence it is omitted from the study.
So, why are UUVs a necessary force multiplier for a Navy? Well, except for being
able to operate in deniable areas there is an obvious important fact;
“Minimizing human casualties during hazardous missions”
Additionally the Master Plan has identified nine functions in which the UUV’s are
superior in use. Four of them however are solely for the large- and man portable class
vehicles and therefore not presented. The five remaining, with a brief explanation, in
prioritized order are;
Intelligence, Surveillance and Reconnaissance (ISR)
UUV’s are perfectly suited for information recovery due to their ability to
operate undetected in littoral areas extending the reach of their host
platforms into previously inaccessible areas.
Mine Countermeasures (MCM)
It is desirable to minimize risk to a fleet operating in a specific area, to do
this time is paramount and it is proven that using a UUV is far more time
efficient than any human diver.
Oceanography
Knowledge of the operating environment is of key importance and
conventional data collection is commonly dependent on hull mounted or
towed systems. UUV’s permits characterizations of greater areas at less
cost and also perform reconnaissance in a near shore environment while its
host remain at a safe distance.
Communication / Navigation Network Nodes (CN3)
A small vehicle has a greater chance to stay undetected while manoeuvring
to the surface and using a discrete antenna to communicate. An UUV can
also provide a link between a submarine and Global Positioning System
(GPS).
Information Operations (IO)
46
An UUV could be used either as a platform to jam or inject false data into
enemy communication network or secondly as a submarine decoy. An
example of this is the AUV 62 from SAAB Systems which can be fitted
with a payload module containing noise transmitters and echo responders
to mimic the signature of a submarine.
6.2 UUV’s
In this chapter a brief explanation of how an UUV works is presented and discussed.
This is to give the reader a basic understanding of some of the problem involved with
a recovery of an UUV to a submarine whilst at speed.
6.2.1 Navigation
All AUVs use an Inertial Navigation System to navigate in submerged mode. The
works by utilizing motion sensors and computers to keep track of the vehicles
position, orientation and velocity. Usually it is used together with a GPS or another
means of getting an initial position. In this specific case the host’s position is most
likely be programmed in the AUV before the start of the mission. To easier
understand the concept of inertial navigation, one can imagine oneself sitting
blindfolded in the passenger seat of a car trying to navigate by feeling the movements
of the car.
This system is of course not entirely perfect, far from it, and it does experience
internal errors. The AUVs then either resurface in intervals to reacquire an absolute
position by using GPS, or using an Acoustic Doppler Current Profiler (ADCP) the
AUV can bounce sound of the bottom and determine its velocity. According to the
University of Southampton their Autosub, which uses this system, has a navigational
error of 0.1% per travelled distance (Underwater Systems Laboratory at the National
Oceanography Centre, 2007). The Kongsberg group on the other hand claims that
their Hugin and REMUS AUVs have a navigational error less than 0.03% when
following a lawnmower pattern3. This is possible by using a Terrain Contour
Matching navigation system that uses an on board contour map of the terrain and
compares it to the image collected by the vehicles sonar system.
Another way of aiding the Inertial Navigation System is the use of acoustic beacons.
These need to be delivered beforehand at strategic locations or in some cases there are
suggestions that the AUV could place the beacons before conducting its mission, and
to recover them when finished. By using this approach the AUV is constantly updated
with its absolute position which lowers the navigational errors close to zero. However,
the alternative with acoustic beacons might not be optimal if ones intention is to stay
undetected.
6.2.2 Guidance and Communication
When in close proximity to the Submarine the AUV communicates by undersea
acoustic modems. One would hope that the AUV could be remotely controlled from
the host ship while conducting the recovery, but the low bandwidth and time delays
involved with undersea communications currently makes this very difficult. There are
however a few Virtual Tether-solutions on the market that claim a bandwidth close to
3
A lawnmower pattern is the name of the movement pattern an AUV follows when it is surveying an
area, the name given because its resemblance of a person’s movement when moving the lawn.
47
200 Kbits/s. Whether it is failsafe4 enough to actively remotely control the vehicle or
not is not known but it is fast enough to work as a real time positioning for the AUV
relative the submarine during a recovery procedure.
A surfaced AUV can also communicate using the Iridium satellite network or, at a
closer range, using a Wireless Local Area Network (WLAN) connection.
6.2.3 Propulsion and Endurance
Power consumption is of course directly proportional to the shape of a UUV. A long
slender shape is likely to use less energy than a short bulky shape. One consideration
has to be accounted for though: the size of the payload. If the payload is square in
shape then it may be of advantage to use an UUV with a box-like shape with rounded
corners. The circular shape body have to be much larger to contain the payload, with
added wetted surface and drag area as a consequence.
Most torpedo shaped UUVs have a single propeller at the aft. Some torpedo shaped
UUVs use a setup with two contra rotating motor assemblies, this to exert a zero net
torque in order to give the possibility of controlling the vehicle roll (Stevenson &
Hunter, 1994).
6.2.4 Stability
There are two ways for an UUV to maintain a certain depth during its mission. It flies
in either auto depth or auto altitude mode. In auto depth it uses the depth sensor to
calculate its depth and in auto altitude it uses an ADCP and follows the ocean floor
terrain. Auto altitude is by far the most common mission approach.
6.2.4.1 Hydrostatic Stability
For a surfaced vehicle we consider the metacentre height as a measurement on how
stable a certain ship or surfaced undersea vehicle is but as the submarine, or the UUV,
descends it is required, for all transversal and longitudinal, that the centre of gravity is
below the centre of buoyancy. It is the size of this distance, BG, which determines the
stability of a submerged vehicle. Figure 30 illustrates the changes of B, G and M in a
surfaced and submerged condition.
Figure 30 – Cross-section of UUV to illustrate the changes in B, G and M between surfaced and
submerged condition.
There is one great advantage with a torpedo shaped vehicle compared to an “odd”
shaped vehicle when considering the hydrostatic stability. If a UUV is subjected to an
4
The AUV will have a fallback mode in case the communication fails for military applications.
48
external force of i.e. vorticity in the wake after a submarine, let us also assume that
this force can be simplified as it would be acting on a single point on the UUV.
Furthermore this point is directed perpendicular upwards to the longitudinal axis, on a
body fixed coordinate system, and situated on the longitudinal centre of gravity. With
these assumptions this force would only inflict movement in roll terms of the UUV.
We are also assuming that it is a static environment so we can make the following
simplifications to the roll equation of motion for an UUV, formulated by (Nahon,
2006), simplified in equation (7.1).
FB  BG sin   F  x  I XX  p
assuming static why,
F
x
p  0  B 
F BG sin 
(7.1)
Where, FB is the buoyancy force,  the Euler angle of roll, F and x is the external
force and its point of action respectively, IXX is the mass moment of inertia in roll for
the UUV and p is the angular acceleration in roll.
We have now determined a relationship between the stability of the submerged
vehicle and the external force acting on it. If we now incorporate this to a torpedo
shaped and an “odd” shaped UUV and have a look at the differences between them,
figure 31, we see that for a torpedo shaped the relation is close to two but for this
particular “odd” shape it is closer to eight. In this case it would take four times the
force to roll the torpedo shaped UUV than it would for the “odd”-shaped one.
Figure 31 – Difference between righting moments to an external force between a torpedo-shaped
and "odd"-shaped UUV.
Figure 31 shows a not so forgiving selection of shape for an “odd”-shaped UUV. The
same rectangular shape rotated 90 degrees in either direction would increase the
stability significantly. The reason why the “odd’-shaped UUV is depicted this way is
because both of the two “odd”-shaped vehicles discussed in this study have this shape.
Another reasoning that promotes a torpedo shaped UUV is its hull smoothness. A
fluid directed toward an object exerts a greater force if the object is flat and
perpendicular than if the object is rounded.
6.2.5 Control
By far most common approach for torpedo shaped UUVs is a propeller at the aft and
two sets of control surfaces working as rudders, either fitted as a cross or in an
49
inverted Y configuration, see Figure 32. Some systems can be fitted with an extra set
of control surfaces at the front for extra manoeuvrability. This leads to the conclusion
that there are very few UUVs on the market today with the ability to hover. There are
however exceptions: The Archerfish, a single shot mine disposal system from
BAE SYSTEMS which instead of a single mounted propeller in the aft has two
thrusters mounted on either side of the body amidships. This gives the Archerfish the
ability to operate in either hover mode or transit mode.
Figure 32 – Example of an inverted Y control surface configuration
Another negative aspect with the rudder configuration as above is the time delay
involved in controlling the vehicle. The slower the vehicle travels the longer time it
takes for the vehicle to respond to a rudder change. This naturally leads to a problem
if the vehicle enters a turbulent area. An example of this is shown in the chapter
relating “Navigation, guidance and control of the Hammerhead AUV” in (Roberts &
Sutton, 2006). In which it took the Hammerhead roughly 45 seconds to stabilize on a
course. The Hammerhead was conducting a circle movement at the surface with a
constant rudder angle of 20 degrees and the time is measured from when the
Hammerhead started its alignment on a specific heading to when it is stabilized. As
shown in figure 33 the rudder command is given at approximately 30 seconds and the
AUV stabilizes at around 60 seconds, the spike at roughly 125 seconds is a response
to a change in the vehicles heading due to surface currents.
Figure 33 – Hammerhead AUV controller trial results: (a) rudder deflections generated and (b)
Hammerhead heading.
Copyright© the Institution of Electrical Engineers
50
An “odd” shaped UUV on the other hand have superior manoeuvrability when
compared. This is necessary if one uses the reasoning mentioned above that it needs a
lot more control interaction to be stable when conducting its missions. Typically an
“odd” shaped UUV uses a set of thrusters at varying locations, instead of a
propeller/rudder combination, for control.
6.2.5.1 Ability to maintain depth
Most UUV’s incorporate a fixed ballast system i.e. external weights that needs to be
calibrated for the salinity and temperature in the mission area. This usually means that
when and if the UUV experiences any local variations in the salinity and temperature
or external forces in the water it has to travel with an angle of attack, use thrusters or
control surfaces to maintain its depth. This of course affects the endurance of the
UUV. Another fact to be taken into account is that most of the UUV’s with fixed
ballast systems are made slightly buoyant, so if there is a mishap it floats to the
surface. This, of course, is a feature that is not desired if your aim is to stay
undetected.
Another way of maintaining altitude or depth is the system that Autonomous
Undersea Vehicle Gliders (AUVG) uses. They have the ability of changing their
buoyancy to descend or ascend and while doing so they use wings to create a lift
which propels them forward, figure 34. There are two kinds of glider to date, they
both have a variable buoyancy system but use different technologies.
Figure 34 – Illustration of an Autonomous Undersea Vehicle Glider’s flight through the water.
6.2.5.1.1 Thermal Glider
This type uses the thermal gradient that is present in the ocean. The sun rays keep the
water warm towards the surface but the water gradually gets cooler at depths, down to
2-4 degrees Celsius. The “Slocum Thermal Glider” from Webb Research Corporation,
(Webb Research Corporation), has wax filled tubes within its body. When the sun and
the surrounding water heats the wax it expands and pushes a mineral oil into bladders
filling them and thus changing the buoyancy of the glider making it sink. When the
wax cools of due to the cooler water the oil retracts from the bladder and the cycle is
complete.
51
6.2.5.1.2 Electric Glider
This system uses a single stroke piston pump which is connected to an electric motor.
Then it either uses it to control the amount of seawater in a bladder situated in the free
flooding compartment of the AUVG or to transfer a fluid, usually mineral oil,
between one bladder in the pressure hull and one in the free flooding part. The
“Slocum Electric Glider” from the Webb Research Corporation, (Webb Research
Corporation), also has the ability to move its battery pack forward or aft to control
pitch.
6.2.6 Categories
There are numerous UUV’s on the market and many of them are very similar in shape
and size. Therefore, as mentioned earlier the UUV’s are divided into two groups,
torpedo- and “odd”-shaped UUV’s. In each chapter a brief presentation of the UUV’s
found and an in depth discussion of an UUV of interest is made.
6.2.6.1 Torpedo Shaped UUV’s
In Table 9 a list with the torpedo shaped vehicles found during the literature study are
presented. Generally a torpedo shaped UUV consists of a bow, a parallel middle
section, and an aft section. Most have the same diameter as a torpedo, 21” or in some
cases less than that. Very seldom they have the ability to hover but need instead a
minimum forward speed of 0.5-1 knot to maintain control. If they don’t maintain this
speed they rise to the surface due to the natural positive buoyancy. In some cases they
have a set of forward hydroplanes but most of the time they rely on aft rudders, in
different configurations. Most of the torpedo shaped vehicles are powered by a
brushless energy efficient “off the shelf” DC motor connected to a two bladed
propeller, which makes it very energy efficient and many manufactures claim their
system can operate autonomously up to and above 50 hours.
Name
REMUS 600
REMUS 6000
HUGIN 1000
HUGIN 3000
HUGIN 4500
Bluefin 12
Bluefin 21
AUV 62 Sapphires
Autosub AUV
Mullaya
Table 9 – Torpedo shaped UUVs
Depl.
Size L/D
Depth
Manufacturer
[kg]
[m]
[m]
240
3.25/0.324
600
885
3.84/0.71
6000
Kongsberg
650
4.5/0.75
1000
1400
5.5/1
3000
1900
6/1
4500
Bluefin Robotics 181.5
3/0.33
200
Corporation
330
3.3/0.53
200
SAAB
1500
7/0.53
200
Uni.Southamton
7/0.9
1600
DSTO
?
?
?
End.
[hrs]
50
22
24
60
78
+15
18
?
+505
?
Comments
As REMUS 6006
6.2.6.2 The REMUS 600
There is one UUV in the torpedo shaped group that is of special interest. Not only
because it is owned and in use by the RAN but also because it is of a typical torpedo
shape and of a size that would be able to dock to an average sized submarine without
any major modifications of the submarine. One major reason is also that the REMUS
was first developed by scientists from Wood Hole Oceanographic Institution (WHOI)
5
The National Oceanography Centre in Southampton claims that the Autosub have up to 144 hours
endurance in optimal conditions, but Autosub has not yet been on a mission exceeding 50 hours.
6
Information gathered from personal communication with Dr. Francis Valentines at the DSTO.
52
in Massachusetts, USA. Due to this there is a lot of publicly available information on
the REMUS control characteristics and different lengths. In 2008 Kongsberg
Maritime A/S acquired the rights to construct and sell the UUV.
6.2.6.3 “Odd”-shaped UUVs
There are still a few “odd”-shaped UUVs on the market today. No detailed
information, on any of the systems, where possible to apprehend even though several
attempts were made by the author. A discussion with Dr. Francis Valentines at the
DSTO revealed that the Wayamba is decommissioned due to instability reasons.
Dr. Valentines also believed that “Odd”-shaped UUVs would more or less be replaced
with the torpedo shaped ones. The Talisman from BAE Systems is apparently still
under development and the information regarding it is mainly speculations. The
information available on public domain at BAE Systems, (BAE Systems), reveals a
hybrid diesel propulsion system and endurance up to 24-hours. Lastly the author did
manage to sign a non disclosure agreement with SAAB Underwater Systems with the
promise that SAAB would supply with detailed specifications, which was
unfortunately never delivered.
6.2.7 Discussion
In general an “odd”-shaped UUV is very sensitive for external forces and therefore its
control systems and acting thrusters needs to be very responsive. This in turn hinders
the operating time. In a scenario where the operating time is the weighing factor then
the torpedo shaped UUV has the clear advantage. On the other hand if operating time
is of less importance and the weighing factor is manoeuvrability then an “odd”-shaped
UUV with several thrusters, such as the SAAB Double Eagle SAROV, has the upper
hand. A torpedo shaped UUV with a rudder configuration in front of the propeller do
not react fast enough to external forces to perform a safe recovery.
As of now none of the UUVs are ideal for a recovery procedure and still perform
operations at great distances and time from its host.
6.3 Launch and Recovery Systems
A number of underwater docking systems have already been developed by the
research community and offshore industry. Although most of them are still at a
concept or prototype stage the most significant ones are described in this section.
6.3.1 Funnel/Cone Recovery Systems
Is by far most common approach to construct a recovery system in the offshore and
military market is to have a funnel guiding the UUV into its stowed position. Usually
the UUV homes in on the funnel or cone by either sonar or a transponder system
using triangulation. All systems on the market today are deployed from surface ships
and used in speeds close to nil. Furthermore according to a representative from the
DSTO, who has seen a couple of the systems in action on the annual AUV Fest7,
claims that they have a pretty low success rate, down to one successful recovery of
every ten tries. Another story is told by Stokey in (Stokey, 1997) where it is claimed
that the cone recovery system for the REMUS UUV vehicles works well. Figure 35
7
AUV Fest is an annual gathering arranged by NOAA Office of Ocean Exploration and Research,
Office of Naval Research and Naval Undersea Warfare Center to demonstrate advanced technology on
AUVs.
53
shows an undersea trial and a concept design of a funnel recovery system mounted on
a submarine. The concept, developed by the BMT Group, is a dry dock situated on the
back of a submarine allowing submariners hands-on handling the UUV while
submerged.
Figure 35 – Concepts of funnel recovery systems
Copyright© BMT Group
The advantages with a funnel recovery system is it simplicity and low cost. The
negative aspects are that it is a relatively large contraption and that it has yet been
proven to work well in non optimal conditions.
6.3.2 Belly mounted Stinger / Buoy Vertical Pole
The Belly mounted Stinger, developed by the Florida Atlantic University’s
Department of Ocean Engineering, and the Buoy Vertical Pole system, from the
Woods Hole Oceanographic institute, works on similar principles. Both systems use a
stinger or vertical pole slides in and get caught by a scissor like construction.
As shown in figure 36 the Florida Atlantic University’s system have their stinger or
pole attached to the underside of the UUV, which in turn interfaces with the recovery
system itself through a four-petal configuration that lets the vehicle approach from
any direction. The system is construction for ocean floor mounting and first and
foremost to be a recharging platform for the Florida Atlantic University’s Ocean
Explorer UUV.
The system from Woods Hole that is adapted successfully to their Odyssey AUV
(Singh, et al., 2001) has on the other hand a nose mounted scissor shaped latch body
that captures a vertical pole mounted between a buoy and a dead weight.
54
Figure 36 – Florida Atlantic University's Ocean Explorer stinger recovery system
6.3.3 Universal Launch and Recovery Module
This is a concept formulated by General Dynamics Electric Boat which are, at the
time of this investigation, updating the US Navy’s Ohio class submarines into modern
SSGNs, Ship Submersibles with Guided Missiles and Nuclear Powered, carrying
Tomahawk missiles. The Universal Launch and Recovery Module works as an air
lock allowing sailors to put a vehicle into the chamber flood it and eject the vehicle
out to sea. When retrieving the UUV the robotic arm would extend grab the vehicle
and pull it back on board. Electric Boat prime objective with the system is to let the
submarine deploy and recover vehicle that are too large to fit in a normal torpedo
tube. The Vertical Launch System is roughly 2.5 meters in diameter while a torpedo
tube restricts larger vehicles than 0.53 meter in diameter.
There is no information how the UUV homes in on the recovery system, most likely
USBL navigation though, nor how the vehicle actually attach itself to the system. A
theory, from the author, is that the vehicle could use something similar to the belly
mounted stinger, or a arrestor hook a fighter jet have attached to their empennage for
achieving the deceleration needed for landing on aircraft carriers.
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Figure 37 – Illustration of a missile tube recovery system
Image courtesy of Andrew Lightner, GE Electric Boat
6.3.4 Sea Owl SUBROV
The Sea Owl SUBROV is a recovery system intended to be used from a submarine
torpedo tube. Except for being able to recover an UUV the system can also be used
for inspection, underwater works, Mine Counter Measures and as a platform for
Communications/Surveillance.
The recovery works in that way that the SUBROV, which is controlled by a human
operator, moves and aligns itself with the incoming UUV. It then uses its gripping
tool to dock with the UUV and subsequently steers the vehicle into a torpedo tube for
recovery, se Figure 38.
The advantage with the system is that it can be incorporated onto any submarine
without prior modifications. The negative aspects is of course the system needs
human interaction and also that it, to the knowledge of the author, has yet to be tried
on a real submarine. SAAB Underwater Systems is presently using a mock up on the
bottom of Lake Vättern in Sweden to conduct their trials and demonstration of the
system.
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Figure 38 – Illustration of the SAAB Sea Owl SUBROV system
Copyright© SAAB Underwater Systems
6.3.5 Boeing Torpedo mounted retractable arm
The torpedo mounted retractable arm from Boeing Advanced Information Systems is
just as it sounds like an arm that takes hold of a UUV and pulls it into an
neighbouring torpedo tube. In figure 39 a drawing of the system is shown. The
recovery system is part of Boeings Long-term Mine Reconnaissance System (LMRS),
known as AN/BLQ-11, and is capable of launch and recoveries at speed from the US
Navy SSN 688 and NSSN class submarines.
The system was tested successfully in 2007 on the USS Hartford attack submarine but
not without difficulties. The UUV needs to line up directly with the torpedo tube so
that the robotic arm can reach out and grab it.
The advantage of the system is of course that it is works. Negatively, the system is
very expensive, heavy (2 000 kg) and that it use a torpedo tube. In addition, the
system could probably not be fitted on a Collins class submarine due to the different
positioning of the torpedo tubes compared to the US navy submarines8.
8
The Collins class have their torpedo tubes situated in the front on a horizontal row while the US Navy
submarines have their coming out on the side.
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Figure 39 – Schematic overview of a torpedo mounted arm recovery system9, where: 1 is the
Torpedo tube which the system is installed in, 2 is the torpedo tube which the UUV get recovered
to, 3 is the outer hull of the Submarine, 4 is an extendable cylindrical arm, 5 is the unfolding
gripping tool and 6 is the UUV.
Provided by PatentStorm, (PatentStorm).
6.3.6 Reverse Funnel Recovery – Authors suggestion
The author suggests a recovery system which offers a way around the control issues
with the torpedo shaped vehicle. In this case the LARS system looks similar to a
funnel but has its opening towards the front of the submarine. The UUV should in its
recovery mode position itself next to the submarine and in front of the funnel opening.
After which either the submarine could increase/or the UUV decrease its speed so that
the smaller vehicle would slide into the funnel with its aft first. By being in front of
the recovery system the UUV is not to experience any of the problems related to a
turbulent wake. To navigate the UUV to the designated position a triangulation with
i.e. USBL would be used.
9
This system was patented by Lockheed Martin and it is not known whether BOEING a similar or the
same system.
58
7 Conclusion
Position 1 would be at first glance a good choice for an engineer to conduct a
recovery with an UUV. There is no disturbance in terms of large trailing wakes after a
sail. There will probably be minor turbulence and wakes due to sonar arrays, openings
and irregularities in the hull. There are though other issues with recovering a UUV at
this position. There are and probably will be control surfaces around the sail and a few
antennas etc. that could get damaged if the recovery procedure of some reason would
fail.
The greatest force extracted from the simulations was from position 2 and is a spike
force in the order of roughly 75 Newton. Except from that case the forces at the rest of
the positions are in the size of 10-30 Newton, which shouldn’t create a problem for an
UUV. But as explained earlier these forces represents an average over an unknown
time which gives no knowledge how fast they are fluctuating or the size of the
magnitudes.
Problem could arise in this specific case with the REMUS 600 UUV which has its
rudders in front of its propeller thus a relatively long rudder response time. If the
turbulent fluid changes direction fast enough to push the UUV repeatedly out of its
trajectory it would have no way of counteract this with its limited control ability. The
same reasoning applies for all the torpedo shaped UUVs presented above.
Two of the Launch and Recovery System available on the market sounds promising.
Neither the Universal Launch and Recovery Module nore the Belly mounted Stinger
cause vorticity in the area of approach for the UUV.
Finally, even though a torpedo shaped UUV lacks in control the author believes that
its endurance abilities make it the best solution at this stage. However the recovery
system needs to be constructed and placed so that the UUV is minimally exposed of
turbulent fluid.
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8 Further work
Suggestively a person who continues this work should start with accessing more
detailed information about performance data for the different UUVs. If a supplier of
an “odd”-shaped UUV can present data showing that an “odd”-shaped UUV can
operate for 24 hours, and still have enough power to return to its mother vessel and
perform a safe recovery, then this type would have the advantage. Furthermore more
work on virtual tether systems and USBL triangulations should be conducted so it can
be determined whether a UUV is to have sufficient control and position accuracy to
manoeuvre itself close to its host.
In the CFD part more time should be spent on the grid around the UUVs control
surfaces, or omitting them completely, and successfully conducting a transient
simulation. Also providing that a new version of CD-Adapco Star CCM+ supports a
six degree of freedom simulation and or an overset grid approach such simulation
should be attempted.
However the easiest way of determine whether a UUV could be controlled in
turbulence would be to conduct real life experiments. A controlled way of doing so
could be obtained in a towing tank or in a cavitation tunnel.
60
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