Kyle A. Brucker

A comparative study of self-propelled and towed wakes in a stratified fluid

Direct numerical simulations (DNS) of axisymmetric wakes with canonical towed and self-propelled velocity profiles are performed at Re = 50 000 on a grid with approximately 2 billion grid points. The present study focuses on a comparison between towed and self-propelled wakes and on the elucidation of buoyancy effects. The development of the wake is characterized by the evolution of maxima, area integrals and spatial distributions of mean and turbulence statistics. Transport equations for mean and turbulent energies are utilized to help understand the observations. The mean velocity in the self-propelled wake decays more rapidly than the towed case due to higher shear and consequently a faster rate of energy transfer to turbulence. Buoyancy allows a wake to survive longer in a stratified fluid by reducing the 〈 u 1 ′ u 3 ′〉 correlation responsible for the mean-to-turbulence energy transfer in the vertical direction. This buoyancy effect is especially important in the self-propelled case because it allows regions of positive and negative momentum to become decoupled in the vertical direction and decay with different rates. The vertical wake thickness is found to be larger in self-propelled wakes. The role of internal waves in the energetics is determined and it is found that, later in the evolution, they can become a dominant term in the balance of turbulent kinetic energy. The non-equilibrium stage, known to exist for towed wakes, is also shown to exist for self-propelled wakes. Both the towed and self-propelled wakes, at Re = 50000, are found to exhibit a time span when, although the turbulence is strongly stratified as indicated by small Froude number, the turbulent dissipation rate decays according to inertial scaling.

Dynamics of a stratified shear layer above a region of uniform stratification

Direct numerical simulations (DNS) are performed to investigate the behaviour of a weakly stratified shear layer in the presence of a strongly stratified region beneath it. Both, coherent Kelvin―Helmholtz (KH) rollers and small-scale turbulence, are observed during the evolution of the shear layer. The deep stratification measured by the Richardson number J d is varied to study its effect on the dynamics. In all cases, a pycnocline is found to develop at the edges of the shear layer. The region of maximum shear shifts downward with increasing time. Internal waves are excited, initially by KH rollers, and later by small-scale turbulence. The wave field generated by the KH rollers is narrowband and of stronger amplitude than the broadband wave field generated by turbulence. Linear theory based on Doppler-shifted frequency of the KH mode is able to predict the angle of the internal wave phase lines during the direct generation of internal waves by KH rollers. Waves generated by turbulence are relatively weaker with a broader range of excitation angles which, in the deep region, tend towards a narrower band. The linear theory that works for the internal waves excited by KH rollers does not work for the turbulence generated waves. The momentum transported by the internal waves into the interior can be large, about 10 % of the initial momentum in the shear layer, when J d ≃ 0.25. Integration of the turbulent kinetic energy budget in time and over the shear layer thickness shows that the energy flux can be up to 17 % of the turbulent production, 33 % of the turbulent dissipation rate and 75 % of the buoyancy flux. These numbers quantify the dynamical importance of internal waves. In contrast to linear theory where the effect of deep stratification on the shear layer instabilities has been found to be weak, the present nonlinear simulations show that the evolution of the shear layer is significantly altered because of the significant momentum and energy carried away by the internal waves.

Evolution of an initially turbulent stratified shear layer

Direct numerical simulations of a stratified shear layer are performed for several different values of Reynolds, bulk Richardson, and Prandtl numbers. Unlike previous numerical studies, the initial perturbations are turbulent. These initial broadband perturbations do not allow the formation of distinct coherent structures such as Kelvin-Helmholtz rollers and streamwise vortices found in previous studies. In the absence of stratification, the shear layer thickness grows linearly and fully developed turbulence is achieved with mean velocities, turbulence intensities, and turbulent kinetic energy budgets that agree well with previous experimental and numerical data. When buoyancy is included, the shear layer grows to an asymptotic thickness, and the corresponding bulk Richardson number, Rib, is within the range, 0.32±0.06, found in previous studies. The apparent scatter in the evolution of Rib is shown to have a systematic dependence on Reynolds and Prandtl numbers. A detailed description of buoyancy effects...

Effect of the Prandtl number on a stratified turbulent wake

Direct numerical simulation is employed to study the effect of the Prandtl number, Pr=ν/α with ν the molecular viscosity and α the molecular diffusivity, on a turbulent wake in a stratified fluid. Simulations were conducted at a Reynolds number of 10 000, Re=UD/ν with U the velocity of the body and D the diameter of the body, for a range of Prandtl numbers: 0.2, 1, and 7. The simulations were run from x/D=6 to x/D=1200, a range that encompasses the near, intermediate, and far wake. Mean quantities such as wake dimensions and defect velocity were found to be weakly affected by Prandtl number, the same result was observed for vorticity as well. The Prandtl number has a strong effect on the density perturbation field and this results in a number of differences in quantities such as the total energy of the wake, wave flux, scalar and turbulent dissipation, mixing efficiency, spectral distribution of energy in the density and velocity fields, and the transfer of energy between kinetic and potential modes. The ...

A detailed assessment of numerical flow analysis (NFA) to predict the hydrodynamics of a deep-V planing hull

Over the past few years much progress has been made in Computational Fluid Dynamics (CFD) in its ability to accurately simulate the hydrodynamics associated with a deep-V monohull planing craft. This work has focused on not only predicting the hydrodynamic forces and moments, but also the complex multiphase free-surface flow field generated by a deep-V monohull planing boat at high Froude numbers. One of these state of the art CFD codes is Numerical Flow Analysis (NFA). NFA provides turnkey capabilities to model breaking waves around a ship, including both plunging and spilling breaking waves, the formation of spray and the entrainment of air. NFA uses a Cartesian-grid formulation with immersed body and volume-of-fluid methods. The focus of this paper is to describe and document a recent effort to assess NFA for the prediction of deep-V planing craft hydrodynamic forces and moments and evaluate how well it models the complex multiphase flows associated with high Froude number flows, specifically the formation of the spray sheet. This detailed validation effort was composed of three parts. The first part focused on assessing NFAs ability to predict pressures on the surface of a 10 degree deadrise wedge during impact with an undisturbed free surface. Detailed comparisons to pressure gauges are presented here for two different drop heights, 15.24 cm (6 in) and 25.4 cm (10 in). Results show NFA accurately predicted pressures during the slamming event. The second part examines NFAs ability to match sinkage, trim and resistance from Fridsmas experiments performed on constant deadrise planing hulls. Simulations were performed on two 20 degree deadrise hullforms of varying length to beam ratios (4 and 5) over a range of speed-length ratios (2, 3, 4, 5 and 6). Results show good agreement with experimentally measured values, as well as values calculated using Savitskys parametric equations. The final part of the validation study focused on assessing how well NFA was able to accurately model the complex multiphase flow associated with high Froude number flows, specifically the formation of the spray sheet. NFA simulations of a planing hull fixed at various angles of roll (0, 10, 20 and 30 degrees) were compared to experiments. Comparisons to underwater photographs illustrate NFAs ability to model the formation of the spray sheet and the free surface turbulence associated with planing boat hydrodynamics. Overall these three validation studies provide a detailed assessment on the current capabilities of NFA to predict the hydrodynamics of a deep-V planing hull.

A numerical simulation of a plunging breaking wave

ONR Program Manager: Dr. Patrick Purtell. ONR Contract Number: N00014-07-C-0184. Computer resources provided by the DoD High Performance Computing Modernization Program at the ERDC DoD Supercomputing Research Center, Vicksburg MS.

Computational Naval Ship Hydrodynamics

The primary purpose of our research efforts is to improve naval design and detection capabilities. Our current research efforts leverage high performance computing (HPC) resources to perform high-resolution numerical simulations with hundreds-of-millions to billions of unknowns to study wave breaking behind a transom stern, wave-impact loading, the generation of spray by high-speed planing craft, air entrainment by plunging breaking waves, forced-motion, and storm seas. This paper focuses on the air entrainment and free-surface turbulence in the flow behind a transom-stern and wave-impact loading on marine platforms. Two codes, Numerical Flow Analysis (NFA) and Boundary Data Immersion Method (BDIM), are used in this study. Both codes are Cartesian-based Large-Eddy Simulation (LES) formulations, and use either Volume-of-Fluid (VOF) (NFA) or conservative Volume-of-Fluid (cVOF) BDIM treatments to track the free-surface interface. The first project area discussed is the flow behind the transom stern. BDIM simulations are used to study the volume of entrained air behind the stern. The application of a Lagrangian bubble-extraction algorithm elucidates the location of air cavities in the wake and the bubble-size distribution for a flow that has over 10 percent void fraction. NFA simulations of the transom-stern flow are validated by comparing the numerical simulations to experiments performed at the Naval Surface Warfare Center, Carderock Division (NSWCCD), where good agreement between simulations and experiments is obtained for mean elevations and regions of white water in the wake. The second project area discussed is wave impact loading, a topic driven by recent structural failures of high-speed planing vessels and other advanced vehicles, as well as the devastation caused by Tsunamis impacting low-lying coastal areas. NFA simulations of wave breaking events are compared to the NSWCCD cube impact experiments and the Oregon State University, O.H. Hinsdale Wave Research Laboratories Tsunami experiments, and it is shown that NFA is able to accurately simulate the propagation of waves over long distances after which it also accurately predicts highly-energetic impact events.

Numerical Simulation of Short Duration Hydrodynamic Impact

Numerical simulations of wedge impact experiments, undertaken by the Naval Surface Warfare Center, Carderock Division, NSWCCD, and more recently by the United States Naval Academy, USNA, Hydromechanics Laboratory, were performed using the computational fluid dynamics code Numerical Flow Analysis, NFA, to assess its capabilities in simulating the short duration hydrodynamic loading associated with free-surface impact. NSWCCD performed experiments using drop heights of 15.24 cm (6 in) and 25.4 cm (10 in), while the Naval Academy used drop heights of: 7.94, 12.7, 15.88, 25.4, 31.75, 38.1, and 50.8 cm (3.125, 5.0, 6.25, 10.0, 12.5, 15.0, and 20.0 in), measured from the keel of the wedge to the calm water surface. Simulations and comparisons were made at heights of 15.24 cm (6 in) and 25.4 cm (10 in) with the NSWCCD data, and 12.5 inches for the USNA data providing for a detailed examination of NFA’s ability to simulate and predict short duration hydrodynamic impacts.Copyright