Unsteady Hydrodynamics of the Maneuvering Submarine

L. Patrick Purtell*
Office of Naval Research
Arlington,
VA 22217

Abstract

The development of a fully unsteady Reynolds-averaged Navier-Stokes (UnRANS)
code for turbulent flow, together with the availability of fast parallel
computers able to execute extremely large problems, has for the first time
permitted addressing the prediction of maneuvering submarine hydrodynamics
without the use of extensive simplifying approximations. One such code, UNCLE,
is being utilized and modified to compute the complex flowfield around rotating
propulsors, around the hull and appendages, and finally around the complete
vehicle, predicting the forces and the resulting trajectory. This project
encompasses the prediction of unsteady, three-dimensional, turbulent flow at
high Reynolds number around complex shapes undergoing maneuvers and having
components in relative motion. The ultimate objective is the prediction of full
six-degree-of-freedom maneuvers and the time history of forces on various
components, incorporating operation of internal systems, such as ballasting, and
control histories for the propulsor and control surfaces. The present approach
obviates the previous extensive simplifications and approximations to the flow
physics and can in principle address high Reynolds number flows directly. The
flow solver uses an artificial compressibility formulation to solve the
three-dimensional time-dependent equations in multi-block transformed
coordinates. The overall code is being developed in two parts, a propulsor code
and a hull/appendage code, which will be integrated. A parallel version of the
propulsor code in rotating coordinates has been completed, validated against
data, and demonstrated on a very large computation of 11 million grid points and
time steps for five revolutions. Two-equation turbulence models, which are more
easily set up for complex problems, have been installed and tested. The number
of grid points accommodated by each processor has been increased by 40% by
improving the memory usage of the code. Both the propulsor and hull/appendage
versions of the parallel code are being validated against experimental data and
against previous serial code results. Computations on classified configurations
have also been run but not reported here.

Introduction: The Computational Problem

The development of high-speed parallel computers with large memory capacity
per node now permits addressing a variety of computational problems previously
inaccessible. Unsteady, turbulent, viscous flow at high Reynolds numbers around
moving bodies with parts in relative motion could not have been attempted
earlier but is now within reach of practical prediction. Such high Reynolds
number flow around complex shapes contains an enormous range of length scales
and requires high-resolution grids, accurate and stable numerics, turbulence
models, and efficient solution per time step. Over the past several years a code
has been under development to meet these demands for the important case of the
unsteady hydrodynamics of the maneuvering submarine (Davoudzadeh et al., 1997;
McDonald and Whitfield, 1996).

The prediction of the maneuvering of vehicles and weapons in general must
address the flow around components in relative motion, such as control surfaces,
as well as the unsteady nature of the flow around the overall body. Forces on
the hull, as opposed to lifting surfaces, dominate submarine dynamics, which
accentuates the requirement for accuracy in the prediction of three-dimensional
separation regions. Also, a large rotating propulsor is an essential component
of submarines whose performance must be captured accurately. The complex
geometry of the propulsor and its performance in unsteady, nonuniform inflow
conditions is a challenging problem in its own right, and the unsteady nature of
the flow through it in a body-fixed coordinate system is extremely demanding.

This computational project attempts to overcome the limitations of present
maneuvering prediction methods which depend on highly empirical approaches,
extensive approximations, and model-scale testing which must be scaled in a
somewhat ad hoc fashion to the extremely high Reynolds numbers of applications.
Of particular interest are severe maneuvers, which are the most challenging to
the present methods. The computational solution of the Reynolds-averaged
Navier-Stokes equations (RANS) in a fully unsteady (UnRANS) setting can in
principle address Reynolds numbers from model scale to full scale. However, to
achieve this objective requires efficient and accurate numerics, both in time
and space, spatial grids, which resolve the important flow features and which
accommodate relative motion of components, and turbulence models compatible with
the overall solution approach.

Approach

The flow around a powered, maneuvering submarine is highly complex due to the
interactions among hull boundary layers, appendage boundary layers and wakes,
and the propulsor (Fig.1). Time-dependent trajectories, large angles of attack,
and relative motion of components result in a highly unsteady flow.
Consequently, the flow fields are represented by the UnRANS equations and solved
numerically using the code UNCLE as the primary flow solver both for the overall
flow and for the propulsor. This flow solver uses an artificial compressibility
formulation to solve the three-dimensional unsteady incompressible equations in
multi-block transformed coordinates (Sheng et al., 1997). The parallel
implementation uses domain decomposition to partition and map the data space
onto a set of processors. Static load balancing is done at the grid generation
stage based on a heuristic performance estimator that takes into account the
characteristics of the algorithm and the available system resources. The
unsteady finite-volume approximation of the governing equations is solved
iteratively at each time step using a parallel multigrid/relaxation iteration
scheme (Pankajakshan and Briley, 1995). This involves a point-to-point message
exchange at each subiteration level. The code uses MPI because of its extensive
portability and functionality.

The project has been divided into two parts for initial development:
propulsor flow and overall hull/appendage flow. The two will be conjoined during
the next year; serial code computations of the full maneuvering submarine,
incorporating a simple propulsor, fixed control surfaces, and other
simplifications, were completed previously indicating the feasibility of the
combined code. The combined propulsor and hull/appendage flow computational
routines will then be embedded in a six-degree-of-freedom (6DOF) dynamic shell
to determine at each time step the integrated forces and moments and the
resulting change in orientation and trajectory of the vehicle. Future
capabilities will include ballast effects, body-force propulsor models, and
other features such as flapped control surfaces and near-surface wave forces.
Thus the project is a team effort involving groups focused on algorithms and
gridding techniques, propulsor and hull components, and component integration
for the desired ultimate prediction capabilities. Classified configurations are
also being addressed but not reported here.

The computation of the propulsor flowfield, prior to the beginning of the
Challenge project, addressed only simple propellers or assumed multifold
symmetry for a reduced number of passages through turbomachine-like
configurations, such as the Syrenian concept from MIT (Kirwin et al., 1994).
However, the availability of sufficient computational resources permits
computing complete, complex configurations as will be required for a practical
code; asymmetries in the inflow will require computation of the entire
propulsor. The simplified versions are still useful, though, for comparison of
predictions with experiments in which the approximations are valid.

The computation of the flow around the hull and appendages, though relatively
straightforward overall, has some important complications: high Reynolds
numbers, flow separation at large angles of incidence, and moving control
surfaces. A further complication, strong interaction of the propulsor with the
stern and the stern appendages, will occur during a crashback maneuver (reversed
propulsor flow) under some conditions. A high Reynolds number increases demands
on the grids (e.g., more cells near surfaces) and may affect stability or
convergence rates. Preliminary tests indicate acceptable performance for the
UNCLE solver. Massive three-dimensional flow separation, which occurs at large
angles of incidence, may be more challenging, and its calculation is crucial to
the trajectory predictions in that it determines the pressure and friction on
the hull, the primary source of maneuvering forces. Previous steady calculations
indicated close agreement with experiments, but full unsteady calculations have
not yet been validated.

Progress

Prior to the initiation of the Challenge project, both serial and parallel
versions of the propulsor and hull/appendage codes were being developed with an
emphasis on the serial versions because of their reduced demands on
computational resources. With the approval of this Challenge project, however,
the plan was altered to discontinue the serial code developments and concentrate
on the parallel versions. Under this project parallel versions of the basic
codes for both propulsor and hull/appendage computations have been tested and
delivered. In addition, preliminary computations have been performed using the
codes, including comparison with experimental data for simple cases. Since the
parallel codes have not yet been integrated for full vehicle motion predictions
nor incorporated into the 6DOF shell, the existing serial code for the full
maneuvering submarine has continued to be used to establish flowfield prediction
requirements during various maneuvers.

Even the massive computational resources available on today's
high-performance computers are challenged by the requirements for advanced
propulsors or the complete maneuvering submarine. For instance, the memory
requirement per node had to be reduced on the T3E machine for a full,
nonsymmetric propulsor flow calculation involving 11 million grid points. A
reformulation of memory usage led to a 40% increase in the number of grid points
addressable by each processor, from 100K points to 140K points per 256MB of
memory. The propulsor for these demonstration calculations was the complicated
MIT Syrenian concept (fig. 2).

A rotating-frame version of the propulsor code has been tested against
experimental data. It provides the option of more advanced turbulence models,
the k-e and q-w two-equation
models, compared to the previous simpler algebraic Baldwin-Lomax model. Ongoing
experimental measurements on an unclassified open propeller, designated P5168,
provide the opportunity to quantify the performance of the code. A calculation
on a grid of 4.5 million points, using 42 processors, was run for 18.8 hours or
1500 steps producing excellent agreement with the experimental data on thrust
coefficient (Kt) and torque coefficient (Kq) against advance coefficient (J,
ratio of forward velocity to rotational velocity) (Fig. 3). The results were so
impressive the code will be used during the redesign phase of the propeller
development. Calculations have also been completed for classified
configurations.

Prior to the beginning of the Challenge project, demonstration calculations
of a maneuvering submarine were performed using a serial code embedded in a full
6DOF shell including an operating propeller but without moving control surfaces.
The success of those preliminary tests prompted the formation of the plan for
the present project which set as an initial goal for the parallel hull/appendage
code the development of a technique to handle the deflection of the control
surfaces, the only important geometric feature remaining to be accommodated.
This has been accomplished in preliminary computations (fig. 4) and is now being
finalized for incorporation in the overall parallel maneuvering code. Because of
the extreme angles required for some rudders (up to 35 deg), grid
distortion/reconnection was found to be inadequate. A grid substitution method
was settled on instead which substitutes predefined blocks around the control
surface to match its new position whenever it is to be moved. Particular
attention was paid to the important gap region between the moving part of the
control surface and the hull or pedestal (fixed part attached to the hull) (fig.
5). Future gridding of control surfaces will also require handling flapped
configurations.

Summary

Significant advances have been achieved for both the propulsor and the
hull/appendage parts of the overall computational problem (Gorski et al., 1998).
In a test against experimental data, the propulsor code predicted exceptionally
accurate results for thrust and torque. The code has also been applied to a more
complex propulsor in an unusually large computation of 11 million grid points
for which improvements were required in the code to accommodate the resulting
memory demands per node. The only remaining important geometric feature of the
hull/appendage part of the code, moving control surfaces, has been captured
using a grid-substitution method. The process of integrating the parts of the
code, demonstrated previously in a serial version for simple components, is
underway. The next phase will then test the full code for mild maneuvers and
develop any required improvements or corrections. The final phase will address
emergency recoveries and other extreme maneuvers.

References

Davoudzadeh, F., Taylor, L.K., Zierke, W.C., Dreyer, J.J., McDonald, H., and
Whitfield, D.L., "Coupled Navier-Stokes and equations of motion simulation of
submarine maneuvers, including crashback", Proc. ASME Fluids Engineering
Division Summer Meeting, FEDSM97-3129, Vancouver, B.C., Canada, June 22-26,
1997.

Gorski, J.J., Briley, R.J., and Whitfield, D.L., Large-Scale Simulations for
Maneuvering Submarines and Propulsors", AIAA 29th Fl. Dyn. Conf.,
Paper No. 98-2930, 1998.

Kerwin, K.E., Keenan, D.P., Black, S.D., and Diggs, J.G., "A Coupled
Viscous/Potential Flow Design Method for Wake-Adapted, Multi-stage, Ducted
Propulsors," In Proceedings, Society of Naval Architects and Marine Engineers,
1994.

McDonald, H., and Whitfield, D.L., "Self propelled maneuvering underwater
vehicles", Proc. 21st Symp. Naval Hydrodynamics, National Academy
Press, Washington, D.C., 1996.

Pankajakshan, R. and Briley, W. R., "Parallel Solution of Viscous
Incompressible Flow on Multi-Block Structured Grids Using MPI". Parallel
Computational Fluid Dynamics: Implementations and Results Using Parallel
Computers, Edited by S. Taylor, A. Ecer, J. Periaux, and N. Satofuca, Elsevier
Science, B.V., Amsterdam, pp. 601-608, 1995.

Sheng, C., Chen, J.P., Taylor, L.K., Jiang, M.Y., and Whitfield, D.L.,
"Unsteady multigrid method for simulating 3-D incompressible Navier-Stokes flows
on dynamic relative motion grids", AIAA Paper 97-0446, 35th Aerospace
Sciences Meeting, January 6-10, 1997.

Figure 1. Conceptual submarine geometry.

Figure 2. Conceptual Syrenian propulsor.

Figure 3. Computed and measured thrust and torque coefficients for P5168
propeller.

Figure 4. Deflected control surface. Surface pressure shown in
shading.

Figure 5. Control surface with gridded gap.

last modifed June 10, 1998