Twenty-Fourth Symposium on Naval Hydrodynamics (2003) / Chapter Skim
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Numerical Simulation of Wakes in a Weakly Stratified Fluid
Numerical Simulation of Wakes in a Weakly Stratified Fluid
Pages 517-533
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From page 517... ...
ABSTRACT This paper describes some preliminary numerical studies using large eddy simulation of full-scale submarine wakes. Submarine wakes are a combination of the wake generated by a smooth slender body and a number of superimposed vortex pairs generated by various control surfaces and other body appendages.
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From page 518... ...
Since the entire wake is too long to compute as a whole, we make the approximation that the flow can be computed within a rectangular box, with axial dimensions much smaller than the total length of the wake, that moves with the mean flow speed U Within this box the flow is computed by solving numerically the governing equations for an incompressible Boussinesq fluid using large eddy simulation (LES)
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From page 519... ...
The fluctuating velocity field is constructed from a realization of fully-developed homogeneous turbulence that is pro jected onto the rms velocity distribution, as is described in more detail in Dommermuth, et al.~1997~. The rms fluctuations are initially uncorrelated and the turbulent shear stresses are zero.
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From page 520... ...
We believe that once the effects of stratification disrupt the turbulent production mechanism, the wake persists significantly longer than it would in a non-stratified fluid. This effect is more significant for momentumless wakes than it is for drag 4 0.01 ant= 0.001 _ 0.0001 _ ....
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From page 521... ...
The flow is initialized with an approximation to a measured mean velocity field of a rolled up aircraft wing vortex, and a superimposed homogeneous turbulent velocity field in an unstratified background. A relaxation procedure is introduced, as described in the previous section, to allow the turbulence field to establish a balance between production and dissipation before the calculation is begun.
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From page 523... ...
Initialization The initial flow field consists of the combination of a homogeneous turbulent velocity field and the velocity field associated with a vortex pair. The vorticity distribution within each vortex is an empirical fit to that measured in large-scale airplane wing vortices.
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From page 524... ...
12 laniinar unstratified - - turbulent unstratified turbulent stratified ~ M'' / J 0 2 -''1 4 6 10 12 Figure 7: The trajectory of the vortex pair for laminar unstratified conditions, turbulent unstratified and turbulent stratified. Vortex ascent rate The time series for the ascent of the vortex pair is shown in Figure 7.
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From page 525... ...
Conclusions We have presented some preliminary results from using large eddy simulation to compute the late wake of a selfpropelled body moving at constant speed through a nonstratified and a uniformly stratified fluid at Re = 105 as well as the motion of a pair of counter-rotating vortices in both non-stratified and stably stratified fluids. An important aspect of the simulations is the use of a relaxation procedure to adjust the initial turbulence fields so that turbulent production and dissipation are in balance.
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From page 526... ...
contour plots of axially-averaged turbulent kinetic energy at (from left to right and top to bottom)
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From page 527... ...
o -1 1 -1 -2 0 2 0.4 10.2 Jo -2 0 -21 ~0.4 1 0' 0.2 o 0.2 910.4 10.2 Jo Figure 11: Transverse plane (y, z) contour plots of axially-averaged turbulent kinetic energy at (from left to right and top to bottom)
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From page 528... ...
The distribution of turbulent kinetic energy in the vortex pair was studied and found to be quite different in the intermediate and late times of the simulations. The non-stratified simulation shows the turbulent kinetic energy mainly decaying everywhere except in the vortex cores.
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From page 529... ...
density stratified fluids," Nonlinear Properties of Internal Waves, American Institute of Physics, 1981, pp.
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From page 530... ...
, but also as a significant step forward in resolving some of the conundrums in coherent structure formation from disordered initial conditions, a process that seems quite characteristic of flows in stably-stratified fluids. The paper by Rottman et al.
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From page 531... ...
The second possible effect of averaging is in the comparison of the kinetic energy distributions of rising vortex pairs in homogeneous and stratified ambients (Figs 10 & 11) , while looking across the vertical axis.
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From page 532... ...
Pancake eddy formation from initially turbulent wakes Prof. Spedding's observations and questions about the differences between the wakes in nonstratified and stratified fluids are the main issue.
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From page 533... ...
We have no knowledge of such full-scale field tests that are available in the open literature. He then asks about comparisons of our vortex pair simulations with laboratory data and with data from full-scale aircraft generated vortex pairs.
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