The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Fluid dynamic turbulence is one of the most challenging computational physics problems because of the extremely wide range of time and space scales involved, the strong nonlinearity of the governing equations, and the many practical and important applications. While most linear fluid instabilities are well understood, the nonlinear interactions among them makes even the relatively simple limit of homogeneous isotropic turbulence difficult to treat physically, mathematically, and computationally. Turbulence is modeled computationally by a two-stage bootstrap process. The first stage, direct numerical simulation, attempts to resolve the relevant physical time and space scales but its application is limited to diffusive flows with a relatively small Reynolds number (Re). Using direct numerical simulation to provide a database, in turn, allows calibration of phenomenological turbulence models for engineering applications. Large eddy simulation incorporates a form of turbulence modeling applicable when the large-scale flows of interest are intrinsically time dependent, thus throwing common statistical models into question. A promising approach to large eddy simulation involves the use of high-resolution monotone computational fluid dynamics algorithms such as flux-corrected transport or the piecewise parabolic method which have intrinsic subgrid turbulence models coupled naturally to the resolved scales in the computed flow. The physical considerations underlying and evidence supporting this monotone integrated large eddy simulation approach are discussed.

New insights into large eddy simulation

Western boundary currents (WBC) influence the global ocean circulation and climate, whereas it locally reaches out differently the continental margins relief. This study analyses the response of WBC over their interactions with the corn of South America Margin. Particularly, the North and East sectors of Rio Grande do Norte (RN) on northeastern Brazil are investigated based upon bathymetry, in situ currents measurements, and simulations of oceanic currents using the CROCO model. The RN margin provides a critical pathway to the WBC along the East and North sectors, which are narrow and retracted shelves (up to 40 km offshore) with steep upper continental slopes (1:11). These sectors are separated by the shallower topography of the Touros High which extends 80 km offshore. The results reveal that the interactions of the Northern Brazilian Undercurrent (NBUC) with the RN northern margin physiography produces a recirculating current region forced by current shear. Eddies and meanders are explicit in February and August, with meander predominance in the latter month because of the increasing of wind intensity eastward. The accelerated core position of NBUC (> 1.0 m.s1) corresponds to the upper slope region of Touros High on both months, and confirms the constrain effect of the margin on the NBUC. The change of margin direction from the N-S to E-W leads to the decreasing of current velocity (~0.1m.s1) near the northern continental slope. This contrast produces an abrupt variation in the shear velocities forming vortices and meanders. Thus, the physiography of the Touros High, the margin directions, and the intensity of the winds control these features development on a regional scale. These oceanic events near the shelf slope affect the sedimentary and ecological system on Brazilian Equatorial continental shelves.

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Dissertação de Mestrado

Large Eddy Simulation and theoretical investigations of the transient cavitating vortical flow structure around a NACA66 hydrofoil

Large-eddy simulation (LES) has proven to be a computationally tractable approach to simulate unsteady turbulent flows. However, prohibitive resolution requirements induced by near-wall eddies in high–Reynolds number boundary layers necessitate the use of wall models or approximate wall boundary conditions. We review recent investigations in wall-modeled LES, including the development of novel approximate boundary conditions and the application of wall models to complex flows (e.g., boundary-layer separation, shock/boundary-layer interactions, transition). We also assess the validity of underlying assumptions in wall-model derivations to elucidate the accuracy of these investigations, and offer suggestions for future studies.

Wall-Modeled Large-Eddy Simulation for Complex Turbulent Flows

We describe an approach to simulate dynamic cavitation behavior based on large eddy simulation of the governing flow, using an implicit approach for the subgrid terms together with a wall model and a single fluid, two-phase mixture description of the cavitation combined with a finite rate mass transfer model. The pressure-velocity coupling is handled using a PISO algorithm with a modified pressure equation for improved stability when the mass transfer terms are active. The computational model is first applied to a propeller flow in homogeneous inflow in both wetted and cavitating conditions and then tested in an artificial wake condition yielding a dynamic cavitation behavior. Although the predicted cavity extent shows discrepancy with the experimental data, the most important cavitation mechanisms are present in the simulation, including internal jets and leading edge desinence. Based on the ability of the model to predict these mechanisms, we believe that numerical assessment of the risk of cavitation nuisance, such as erosion or noise, is tangible in the near future.

Implicit LES Predictions of the Cavitating Flow on a Propeller

A reformulation of the large eddy simulation (LES) equations is presented, based on an alternative decomposition of the subgrid stress tensor leading to modified Leonard, cross, and Reynolds terms, which are all individually frame indifferent. The new Leonard tensor, identical to the scale similarity model proposed by Bardina et al(J. Bardina, J. H. Ferziger and W. C. Reynolds, 1980, AIAA Paper 80-1357), is computable and thus becomes an integral part of the LES equations, so this formulation clearly emphasizes the difference between Reynolds averaged Navier–Stokes (RANS) and LES. The remaining modified cross and Reynolds terms can be regrouped further into a reconstructable part and a true subgrid component, where we here use an approximate deconvolution model and a subgrid viscosity model for the respective parts. This structure justifies the use of a dissipative model term in mixed models based on, e.g., the scale similarity model. The reformulated LES model is tested on two basic flows, the Taylor Gre...

On the justification and extension of mixed models in LES

Improvement of cavitation mass transfer modeling based on local flow properties

The flow around an axisymmetric hull, with and without appendages, is investigated using large eddy simulation (LES), detached eddy simulation (DES), and Reynolds averaged Navier Stokes (RANS) models. The main objectives of the study is to investigate the effect of the different simulation methods and to demonstrate the feasibility of using DES and LES on relatively coarse grids for submarine flows, but also to discuss some generic features of submarine hydrodynamics. For this purpose the DARPA Suboff configurations AFF1 (bare hull) and AFF8 (fully appended model) are used. The AFF1 case is interesting because it is highly demanding, in particular for LES and DES, due to the long midship section on which the boundary layer is developed. The AFF8 case represents the complex flow around a fully appended submarine with sail and aft rudders. An actuator disc model is used to emulate some of the effects of the propulsor for one of the AFF8 cases studied. Results for the AFF8 model are thus presented for both “towed” and “self-propelled” conditions, whereas for the bare hull, only a “towed” condition is considered. For the AFF1 and the “towed” AFF8 cases experimental data are available for comparison, and the results from both configurations show that all methods give good results for first-order statistical moments although LES gives a better representation of structures and second-order statistical moments in the complex flow in the AFF8 case.

Rickard Bensow

Papers

Implicit LES Predictions of the Cavitating Flow on a Propeller

On the justification and extension of mixed models in LES

Improvement of cavitation mass transfer modeling based on local flow properties

Current Capabilities of DES and LES for Submarines at Straight Course

Numerical and experimental investigation of shedding mechanisms from leading-edge cavitation