scholarly journals On the over-production of turbulence beneath surface waves in Reynolds-averaged Navier–Stokes models

2018 ◽  
Vol 853 ◽  
pp. 419-460 ◽  
Author(s):  
Bjarke Eltard Larsen ◽  
David R. Fuhrman
Keyword(s):  
Kinetic Energy ◽  
Surface Waves ◽  
Turbulent Kinetic Energy ◽  
Exponential Growth ◽  
Potential Flow ◽  
Eddy Viscosity ◽  
Surf Zone ◽  
Breaking Waves ◽  
Navier Stokes ◽  
Closure Models

In previous computational fluid dynamics studies of breaking waves, there has been a marked tendency to severely over-estimate turbulence levels, both pre- and post-breaking. This problem is most likely related to the previously described (though not sufficiently well recognized) conditional instability of widely used turbulence models when used to close Reynolds-averaged Navier–Stokes (RANS) equations in regions of nearly potential flow with finite strain, resulting in exponential growth of the turbulent kinetic energy and eddy viscosity. While this problem has been known for nearly 20 years, a suitable and fundamentally sound solution has yet to be developed. In this work it is demonstrated that virtually all commonly used two-equation turbulence closure models are unconditionally, rather than conditionally, unstable in such regions. A new formulation of the $k$–$\unicode[STIX]{x1D714}$ closure is developed which elegantly stabilizes the model in nearly potential flow regions, with modifications remaining passive in sheared flow regions, thus solving this long-standing problem. Computed results involving non-breaking waves demonstrate that the new stabilized closure enables nearly constant form wave propagation over long durations, avoiding the exponential growth of the eddy viscosity and inevitable wave decay exhibited by standard closures. Additional applications on breaking waves demonstrate that the new stabilized model avoids the unphysical generation of pre-breaking turbulence which widely plagues existing closures. The new model is demonstrated to be capable of predicting accurate pre- and post-breaking surface elevations, as well as turbulence and undertow velocity profiles, especially during transition from pre-breaking to the outer surf zone. Results in the inner surf zone are similar to standard closures. Similar methods for formally stabilizing other widely used closure models ($k$–$\unicode[STIX]{x1D714}$ and $k$–$\unicode[STIX]{x1D700}$ variants) are likewise developed, and it is recommended that these be utilized in future RANS simulations of surface waves. (In the above $k$ is the turbulent kinetic energy density, $\unicode[STIX]{x1D714}$ is the specific dissipation rate, and $\unicode[STIX]{x1D700}$ is the dissipation.)

Calculation of Turbulent Kinetic Energy Budgets for Flow Through a Pebble Bed Using DNS

2016 ◽  
Author(s):  
Lambert H. Fick ◽  
Elia Merzari ◽  
Yassin A. Hassan
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Navier Stokes ◽  
Energy Budgets ◽  
High Fidelity ◽  
Face Centered Cubic ◽  
Pebble Bed ◽  
Data Set ◽  
Closure Models ◽  
Face Centered

Pebble bed high temperature reactors (PBR) are currently being investigated as a potential successor for light water reactor based designs in the future. Past analyses of flows through PBR cores using Reynolds averaged Navier-Stokes (RANS) approaches have had limited success. Due to a lack of available high fidelity experimental or computational data, optimization of RANS closure models for these geometries has not been extensively done. In the present study, direct numerical simulation (DNS) is employed to develop a high fidelity data set which may be used for the optimization of RANS closure models for pebble bed flows. Calculated parameters include turbulence statistics, as well as values for the turbulent kinetic energy (TKE) budget terms. A well documented, single face centered cubic domain with periodic boundaries was used. Flow was simulated at a Reynolds number of 9308. Tests were conducted to ensure sufficient spatial and temporal resolution for conforming to the requirements for DNS. A selection of the generated statistics and TKE budget terms is presented here.

A numerical study of breaking waves in the surf zone

1998 ◽  
Vol 359 ◽  
pp. 239-264 ◽  
Author(s):  
PENGZHI LIN ◽  
PHILIP L.-F. LIU
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Numerical Model ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Surf Zone ◽  
Breaking Waves ◽  
Numerical Results ◽  
Long Distance ◽  
The Mean

This paper describes the development of a numerical model for studying the evolution of a wave train, shoaling and breaking in the surf zone. The model solves the Reynolds equations for the mean (ensemble average) flow field and the k–ε equations for the turbulent kinetic energy, k, and the turbulence dissipation rate, ε. A nonlinear Reynolds stress model (Shih, Zhu & Lumley 1996) is employed to relate the Reynolds stresses and the strain rates of the mean flow. To track free-surface movements, the volume of fluid (VOF) method is employed. To ensure the accuracy of each component of the numerical model, several steps have been taken to verify numerical solutions with either analytical solutions or experimental data. For non-breaking waves, very accurate results are obtained for a solitary wave propagating over a long distance in a constant depth. Good agreement between numerical results and experimental data has also been observed for shoaling and breaking cnoidal waves on a sloping beach in terms of free-surface profiles, mean velocities, and turbulent kinetic energy. Based on the numerical results, turbulence transport mechanisms under breaking waves are discussed.

scholarly journals Experimental Observations of Turbulent Events in the Surfzone

2019 ◽  
Vol 7 (10) ◽  
pp. 332 ◽  
Author(s):  
De Serio ◽  
Mossa
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Large Scale ◽  
Surf Zone ◽  
Breaking Waves ◽  
Gas Transfer ◽  
Principal Characteristics ◽  
Sea Bottom ◽  
Elevation Data ◽  
Water Gas

In coastal dynamics, large-scale eddies transport and spread smaller turbulent vortices both towards the sea surface, thus contributing to the processes of air-water gas transfer, and towards the sea bottom, inducing sediment pick-up and resuspension. The mechanical role of the breaking-induced vortices to the redistribution of turbulence and turbulent kinetic energy is still unclear and needs a more thorough study, possibly supported by more measurements in this field. Based on this, the present paper aims to investigate the effects of experimental breaking waves in the surf zone. Two regular breaking waves, a spiller and a plunger, which propagate on a fixed slope, were generated in a laboratory channel and were examined shoreward to the breaker line. The measurements of their velocities in the cross-shore plane were assessed by means of a 2D Laser Doppler Anemometer. At the same time and location, elevation data were also acquired using a resistive wave gauge. Here, the principal characteristics are addressed in terms of turbulent intensities, turbulent kinetic energy, length scales and coherent motions. Our results could thus contribute to better define conceptual models used in typical engineering applications in coastal areas.

scholarly journals Development and Validation of Quasi-Eulerian Mean Three-Dimensional Equations of Motion Using the Generalized Lagrangian Mean Method

2021 ◽  
Vol 9 (1) ◽  
pp. 76
Author(s):  
Duoc Nguyen ◽  
Niels Jacobsen ◽  
Dano Roelvink
Keyword(s):  
Surface Waves ◽  
Deep Water ◽  
Surf Zone ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Breaking Waves ◽  
Successful Implementation ◽  
Random Waves ◽  
Mean Motion ◽  
Generalized Lagrangian

This study aims at developing a new set of equations of mean motion in the presence of surface waves, which is practically applicable from deep water to the coastal zone, estuaries, and outflow areas. The generalized Lagrangian mean (GLM) method is employed to derive a set of quasi-Eulerian mean three-dimensional equations of motion, where effects of the waves are included through source terms. The obtained equations are expressed to the second-order of wave amplitude. Whereas the classical Eulerian-mean equations of motion are only applicable below the wave trough, the new equations are valid until the mean water surface even in the presence of finite-amplitude surface waves. A two-dimensional numerical model (2DV model) is developed to validate the new set of equations of motion. The 2DV model passes the test of steady monochromatic waves propagating over a slope without dissipation (adiabatic condition). This is a primary test for equations of mean motion with a known analytical solution. In addition to this, experimental data for the interaction between random waves and a mean current in both non-breaking and breaking waves are employed to validate the 2DV model. As shown by this successful implementation and validation, the implementation of these equations in any 3D model code is straightforward and may be expected to provide consistent results from deep water to the surf zone, under both weak and strong ambient currents.

scholarly journals AUTOMATIC INSERTION OF A TURBULENCE MODEL IN THE FINITE ELEMENT DISCRETIZATION OF THE NAVIER–STOKES EQUATIONS

2009 ◽  
Vol 19 (07) ◽  
pp. 1139-1183 ◽  
Author(s):  
CHRISTINE BERNARDI ◽  
TOMÁS CHACÓN REBOLLO ◽  
FRÉDÉRIC HECHT ◽  
ROGER LEWANDOWSKI
Keyword(s):  
Finite Element ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Stokes Equations ◽  
A Posteriori Error Estimates ◽  
Navier Stokes ◽  
Mesh Adaptivity ◽  
Finite Element Discretization ◽  
Navier Stokes Equations ◽  
Element Discretization

We consider the finite element discretization of the Navier–Stokes equations locally coupled with the equation for the turbulent kinetic energy through an eddy viscosity. We prove a posteriori error estimates which allow to automatically determine the zone where the turbulent kinetic energy must be inserted in the Navier–Stokes equations and also to perform mesh adaptivity in order to optimize the discretization of these equations. Numerical results confirm the interest of such an approach.

Interaction between a spatially growing turbulent boundary layer and embedded streamwise vortices

1996 ◽  
Vol 326 ◽  
pp. 151-179 ◽  
Author(s):  
Junhui Liu ◽  
Ugo Piomelli ◽  
Philippe R. Spalart
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Turbulent Kinetic Energy ◽  
Vortex Core ◽  
Eddy Viscosity ◽  
Shear Stresses ◽  
Streamwise Vortices ◽  
Mean Velocity ◽  
Production Term

The interaction between a zero-pressure-gradient turbulent boundary layer and a pair of strong, common-flow-down, streamwise vortices with a sizeable velocity deficit is studied by large-eddy simulation. The subgrid-scale stresses are modelled by a localized dynamic eddy-viscosity model. The results agree well with experimental data. The vortices drastically distort the boundary layer, and produce large spanwise variations of the skin friction. The Reynolds stresses are highly three-dimensional. High levels of kinetic energy are found both in the upwash region and in the vortex core. The two secondary shear stresses are significant in the vortex region, with magnitudes comparable to the primary one. Turbulent transport from the immediate upwash region is partly responsible for the high levels of turbulent kinetic energy in the vortex core; its effect on the primary stress 〈u′v′〉 is less significant. The mean velocity gradients play an important role in the generation of 〈u′v′〉 in all regions, while they are negligible in the generation of turbulent kinetic energy in the vortex core. The pressure-strain correlations are generally of opposite sign to the production terms except in the vortex core, where they have the same sign as the production term in the budget of 〈u′v′〉. The results highlight the limitations of the eddy-viscosity assumption (in a Reynolds-averaged context) for flows of this type, as well as the excessive diffusion predicted by typical turbulence models.

The Application of Eddy-Viscosity Stress Limiters for Modeling Cross-Flow Separation

2010 ◽  
Vol 132 (9) ◽  
Author(s):  
P. A. Gregory ◽  
P. N. Joubert ◽  
M. S. Chong ◽  
A. Ooi
Keyword(s):  
Kinetic Energy ◽  
Skin Friction ◽  
Turbulent Kinetic Energy ◽  
Flow Separation ◽  
Eddy Viscosity ◽  
Cross Flow ◽  
The Body ◽  
Mean Flow ◽  
Viscosity Models ◽  
Experimental Apparatus

The ability of eddy-viscosity models to simulate the turbulent wake produced by cross-flow separation over a curved body of revolution is assessed. The results obtained using the standard k−ω model show excessive levels of turbulent kinetic energy k in the vicinity of the stagnation point at the nose of the body. Additionally, high levels of k are observed throughout the wake. Enforcing laminar flow upstream of the nose (which replicates the experimental apparatus more accurately) gives more accurate estimates of k throughout the flowfield. A stress limiter in the form of Durbin’s T-limit modification for eddy-viscosity models is implemented for the k−ω model, and its effect on the computed surface pressures, skin friction, and surface flow features is assessed. Additionally, the effect of the T-limit modification on both the mean flow and the turbulent flow quantities within the wake is also examined. The use of the T-limit modification gives significant improvements in predicted levels of turbulent kinetic energy and Reynolds stresses within the wake. However, predicted values of skin friction in regions of attached flow become up to 50% greater than the experimental values when the T-limit is used. This is due to higher values of near-wall turbulence being created with the T-limit.

Grid Requirements for Multiscale Resolution in Separated Unsteady High Speed Turbulent Flows

2006 ◽  
Author(s):  
D. Basu ◽  
A. Hamed ◽  
K. Das
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Sound Pressure Level ◽  
High Speed ◽  
Sound Pressure ◽  
Pressure Fluctuations ◽  
Pressure Level ◽  
Navier Stokes ◽  
Detached Eddy Simulation

This study deals with the computational grid requirements in multiscale simulations of separated turbulent flows at high Reynolds number. The two-equation k-ε based DES (Detached Eddy Simulation) model is implemented in a full 3-D Navier-Stokes solver and numerical results are presented for transonic flow solution over an open cavity. Results for the vorticity, pressure fluctuations, SPL (Sound Pressure level) spectra and for modeled and resolved TKE (Turbulent Kinetic Energy) are presented and compared with available experimental data and with LES results. The results indicate that grid resolution significantly influences the resolved scales and the peak amplitude of the unsteady sound pressure level (SPL) and turbulent kinetic energy spectra.

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