Direct numerical simulations of a statistically stationary streamwise periodic boundary layer via the homogenized Navier-Stokes equations

Gravitationally driven motion arising from a sustained constant source of dense fluid in a horizontal channel is investigated theoretically using shallow-layer models and direct numerical simulations of the Navier–Stokes equations, coupled to an advection–diffusion model of the density field. The influxed dense fluid forms a flowing layer underneath the less dense fluid, which initially filled the channel, and in this study its speed of propagation is calculated; the outflux is at the end of the channel. The motion, under the assumption of hydrostatic balance, is modelled using a two-layer shallow-water model to account for the flow of both the dense and the overlying less dense fluids. When the relative density difference between the fluids is small (the Boussinesq regime), the governing shallow-layer equations are solved using analytical techniques. It is demonstrated that a variety of flow-field patterns are feasible, including those with constant height along the length of the current and those where the height varies continuously and discontinuously. The type of solution realised in any scenario is determined by the magnitude of the dimensionless flux issuing from the source and the source Froude number. Two important phenomena may occur: the flow may be choked, whereby the excess velocity due to the density difference is bounded and the height of the current may not exceed a determined maximum value, and it is also possible for the dense fluid to completely displace all of the less dense fluid originally in the channel in an expanding region close to the source. The onset and subsequent evolution of these types of motions are also calculated using analytical techniques. The same range of phenomena occurs for non-Boussinesq flows; in this scenario, the solutions of the model are calculated numerically. The results of direct numerical simulations of the Navier–Stokes equations are also reported for unsteady two-dimensional flows in which there is an inflow of dense fluid at one end of the channel and an outflow at the other end. These simulations reveal the detailed mechanics of the motion and the bulk properties are compared with the predictions of the shallow-layer model to demonstrate good agreement between the two modelling strategies.

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Partially Averaged Navier-Stokes Turbulence Modeling of Flow in 5x5 PWR Fuel Assembly With Spacer Grid

Volume 8: Computational Fluid Dynamics (CFD); Nuclear Education and Public Acceptance ◽

10.1115/icone26-82366 ◽

2018 ◽

Author(s):

Giacomo Busco ◽

Yassin A. Hassan

Keyword(s):

Large Eddy Simulation ◽

Numerical Simulations ◽

Stokes Equations ◽

Direct Numerical Simulations ◽

Navier Stokes ◽

Spacer Grid ◽

Navier Stokes Equations ◽

Eddy Simulation ◽

Large Eddy ◽

Reynolds Averaged Navier Stokes

The highly turbulent flow inside a pressurized water reactor makes unpractical the use of scale resolving simulations, due to the large number of space and time turbulent structures. The high computational cost associated with typical large eddies simulations or direct numerical simulations techniques is unsuitable due to the large spatiotemporal resolution required. Partially averaged Navier-Stokes turbulence model is presented as bridging model between Reynolds averaged Navier-Stokes equations and direct numerical simulations. As filtered representation of the Navier-Stokes equations, the model is able to continuously shift its energy-based filter, inside the turbulence spectrum, being able to resolve the turbulent scales of interest. The choice of energy based cut-off filters gives the chance to directly impose the degree of needed resolution, where the most important large scales unsteadiness are resolved at minimal computational expenses. The partially averaged Navier-Stokes modelling approach has been tested for a Reynolds number of 14,000, inside a 5 × 5 fuel bundle, with a single spacer grid and split-type mixing vanes. Four different filters have been tested, whose resolution ranged from Reynolds averaged Navier-Stokes and large eddy simulation. A comparison with large eddy simulation will be presented. The results show that the partially averaged Navier-Stokes modeling produces results comparable to those of large eddy simulation when the appropriate cut-off energy filter is chosen. The turbulence models results will be compared with the available particle image velocimetry experimental data.

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Computations of Boiling Flows

Volume 3 ◽

10.1115/ht-fed2004-56268 ◽

2004 ◽

Cited By ~ 1

Author(s):

Gre´tar Tryggvason ◽

Asghar Esmaeeli

Keyword(s):

Numerical Simulations ◽

Phase Boundary ◽

Energy Equation ◽

Stokes Equations ◽

Accurate Solution ◽

Direct Numerical Simulations ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Average Heat ◽

Long Time

Numerical simulations of boiling flows are discussed. The change of phase from liquid to vapor and vice-versa usually takes place in a highly unsteady manner where the phase boundary is very convoluted. Direct numerical simulations therefore require the accurate solution of the Navier-Stokes equations and the energy equation in each phase and the correct incorporation of the unsteady phase boundary. Such simulations, where the motion of an unsteady phase boundary is followed for a sufficiently long time to allow computation of average heat transfer are very recent. Here, we will describe one method that has been used successfully to simulate boiling flows and show a few examples of studies using the method.

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On reduction of turbulent wall friction through spanwise wall oscillations

Journal of Fluid Mechanics ◽

10.1017/s0022112098003784 ◽

1999 ◽

Vol 383 ◽

pp. 175-195 ◽

Cited By ~ 53

Author(s):

M. R. DHANAK ◽

C. SI

Keyword(s):

Boundary Layer ◽

Skin Friction ◽

Stokes Equations ◽

Direct Numerical Simulations ◽

Wall Friction ◽

Navier Stokes ◽

Spanwise Direction ◽

Streamwise Vortices ◽

Navier Stokes Equations ◽

Turbulent Wall

A model for turbulent skin friction, proposed by Orlandi & Jimenez, involving consideration of quasi-streamwise vortices in the cross-stream plane, is used to study the effect on the skin friction of oscillating the surface beneath the boundary layer in the spanwise direction. Using an exact solution of the Navier–Stokes equations, it is shown that the interaction between evolving, axially stretched, streamwise vortices and a modified Stokes layer on the oscillating surface beneath, leads to reduction in the skin friction, the Reynolds stress and the rate of production of kinetic energy, consistent with predictions based on experiments and direct numerical simulations.

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Bound-state formation in interfacial turbulence: direct numerical simulations and theory

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.506 ◽

2013 ◽

Vol 716 ◽

Cited By ~ 10

Author(s):

M. Pradas ◽

S. Kalliadasis ◽

P.-K. Nguyen ◽

V. Bontozoglou

Keyword(s):

Numerical Simulations ◽

State Formation ◽

Stokes Equations ◽

Bound State ◽

Direct Numerical Simulations ◽

Navier Stokes ◽

Surface Boundary ◽

Navier Stokes Equations ◽

Oscillatory Dynamics ◽

Low Dimensional

AbstractWe examine pulse interaction and bound-state formation in interfacial turbulence using the problem of a falling liquid film as a model system. We perform direct numerical simulations (DNSs) of the full Navier–Stokes equations and associated wall and free-surface boundary conditions and we examine both analytically and numerically a low-dimensional (LD) model for the film. For a two-pulse system, DNSs reveal the existence of very rich and complex pulse interactions, characterized by either overdamped, underdamped or self-sustained oscillating behaviours, all of them found to be in excellent agreement with LD results. Having demonstrated the reliability of the LD model for two-pulse systems/smaller domains, we use it to investigate larger domains with many interacting pulses, where DNSs are computationally expensive. We demonstrate that such systems are likely to be dominated by a self-sustained oscillatory dynamics.

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A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽

10.3390/math9070756 ◽

2021 ◽

Vol 9 (7) ◽

pp. 756

Author(s):

Federico Lluesma-Rodríguez ◽

Francisco Álcantara-Ávila ◽

María Jezabel Pérez-Quiles ◽

Sergio Hoyas

Keyword(s):

Heat Transfer ◽

Stokes Equations ◽

Three Dimensional ◽

Turbulent Channel Flow ◽

Passive Scalar ◽

Direct Numerical Simulations ◽

Time Dependent ◽

Navier Stokes ◽

Thermal Flow ◽

Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

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Numerical Integration of the Navier-Stokes Equations for a Disk Rotating in a Housing

Zeitschrift für Naturforschung A ◽

10.1515/zna-1985-0802 ◽

1985 ◽

Vol 40 (8) ◽

pp. 789-799 ◽

Cited By ~ 1

Author(s):

A. F. Borghesani

Keyword(s):

Boundary Layer ◽

Cylindrical Cavity ◽

Boundary Layer Thickness ◽

Stokes Equations ◽

Fluid Motion ◽

Rotating Disk ◽

Infinite Medium ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Viscous Torque

The Navier-Stokes equations for the fluid motion induced by a disk rotating inside a cylindrical cavity have been integrated for several values of the boundary layer thickness d. The equivalence of such a device to a rotating disk immersed in an infinite medium has been shown in the limit as d → 0. From that solution and taking into account edge effect corrections an equation for the viscous torque acting on the disk has been derived, which depends only on d. Moreover, these results justify the use of a rotating disk to perform accurate viscosity measurements.

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Direct simulation of transition in an oscillatory boundary layer

Journal of Fluid Mechanics ◽

10.1017/s002211209800216x ◽

1998 ◽

Vol 371 ◽

pp. 207-232 ◽

Cited By ~ 92

Author(s):

G. VITTORI ◽

R. VERZICCO

Keyword(s):

Boundary Layer ◽

Pressure Gradient ◽

Stokes Equations ◽

Navier Stokes ◽

Turbulent Regime ◽

Two Dimensional ◽

Temporal Development ◽

Direct Simulation ◽

Navier Stokes Equations ◽

Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

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Nonlinear cellular instabilities of planar premixed flames: numerical simulations of the Reactive Navier–Stokes equations

Combustion Theory and Modelling ◽

10.1080/13647830500472354 ◽

2006 ◽

Vol 10 (3) ◽

pp. 483-514 ◽

Cited By ~ 18

Author(s):

G. J. Sharpe ◽

S. A. E. G. Falle

Keyword(s):

Numerical Simulations ◽

Stokes Equations ◽

Premixed Flames ◽

Navier Stokes ◽

Navier Stokes Equations

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Self-Excited Oscillation of Transonic Flow Around an Airfoil in Two-Dimensional Channel

Volume 1: Turbomachinery ◽

10.1115/89-gt-58 ◽

1989 ◽

Cited By ~ 5

Author(s):

Kazuomi Yamamoto ◽

Yoshimichi Tanida

Keyword(s):

Boundary Layer ◽

Shock Wave ◽

Transonic Flow ◽

Stokes Equations ◽

Flow Region ◽

Boundary Layer Separation ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Layer Separation ◽

Excited Oscillation

A self-excited oscillation of transonic flow in a simplified cascade model was investigated experimentally, theoretically and numerically. The measurements of the shock wave and wake motions, and unsteady static pressure field predict a closed loop mechanism, in which the pressure disturbance, that is generated by the oscillation of boundary layer separation, propagates upstream in the main flow and forces the shock wave to oscillate, and then the shock oscillation disturbs the boundary layer separation again. A one-dimensional analysis confirms that the self-excited oscillation occurs in the proposed mechanism. Finally, a numerical simulation of the Navier-Stokes equations reveals the unsteady flow structure of the reversed flow region around the trailing edge, which induces the large flow separation to bring about the anti-phase oscillation.

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