Laboratory-scale investigation of a periodically forced stratified basin with inclined endwalls

2021 ◽  
Vol 932 ◽  
Author(s):  
Sara Marković ◽  
Vincenzo Armenio
Keyword(s):  
Shear Stress ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Laboratory Scale ◽  
Navier Stokes ◽  
Fundamental Wave ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Vertical Mode

We present results of numerical simulations of a stratified reservoir with a three-layer stratification, subject to an oscillating surface shear stress. We investigate the effect of sloped endwalls on mixing and internal wave adjustment to forcing within the basin, for three different periods of forcing. The simulations are carried out at a laboratory scale, using large-eddy simulation. We solve the three-dimensional Navier–Stokes equations under the Boussinesq approximation using a second-order-accurate finite-volume solver. The model was validated by reproducing experimental results for the response of a reservoir to surface shear stress and resonant frequencies of internal waves. We find interesting combinations of wave modes and mixing under variation of the forcing frequencies and of the inclination of the endwalls. When the frequency of the forcing is close to the fundamental mode-one wave frequency, a resonant internal seiche occurs and the response is characterized by the first vertical mode. For forcing periods twice and three times the fundamental period, the dominant response is in terms of the second vertical mode. Adjustment to forcing via the second vertical mode is accompanied by the cancellation of the fundamental wave and energy transfer to higher-frequency waves. The study shows that the slope of the endwalls dramatically affects the location of mixing, which has a feedback on the wave field by promoting the generation of higher vertical modes.

Aerodynamic and Aeroacoustic Analyses of a Regenerative Blower

2015 ◽  
Author(s):  
Man-Woong Heo ◽  
Tae-Wan Seo ◽  
Chung-Suk Lee ◽  
Kwang-Yong Kim
Keyword(s):  
Shear Stress ◽  
Variational Formulation ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Side Channel ◽  
Leakage Flow ◽  
Navier Stokes Equations ◽  
Unsteady Flow Analysis

This paper presents a parametric study to investigate the aerodynamic and aeroacoustic characteristics of a side channel regenerative blower. Flow analysis in the side channel blower was carried out by solving three-dimensional steady and unsteady Reynolds-averaged Navier-Stokes equations with the shear stress transport turbulence closure. Aeroacoustic analysis was conducted by solving the variational formulation of Lighthill’s analogy on the basis of the aerodynamic sources extracted from the unsteady flow analysis. The height and width of the blade and the angle between inlet and outlet ports were selected as three geometric parameters, and their effects on the aerodynamic and aeroacoustic performances of the blower have been investigated. The results showed that the aerodynamic and aeroacoustic performances were enhanced by decreasing height and width of blade. It was found that angle between inlet and outlet ports significantly influences the aerodynamic and aeroacoustic performances of the blower due to the stripper leakage flow.

scholarly journals Influence of the Thermophysical Properties of a Liquid Coolant on Characteristics of the 3D Flows with Phase Transition

2019 ◽  
pp. 655-662
Author(s):  
Victoria B. Bekezhanova ◽  
Olga N. Goncharova
Keyword(s):  
Thermophysical Properties ◽  
Stokes Equations ◽  
Rectangular Cross Section ◽  
Numerical Technique ◽  
Invariant Solution ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Dynamical Structure ◽  
Longitudinal Temperature Gradient

Regimes of the joint flows of the evaporating liquid and gas – vapor mixture induced by the action of a longitudinal temperature gradient in a three-dimensional channel of a rectangular cross-section in the terrestrial gravity field are studied in the present paper. The theoretical investigations are carried out on the basis of the partially invariant solution of rank 2 and defect 3 of the Boussinesq approximation of the Navier – Stokes equations. This solution allows one to correctly describe the two-layer flows with evapora- tion/condensation at the thermocapillary interface and to take into account the effects of thermodiffusion and diffusive thermal conductivity in the gas–vapor phase. The exact solution of governing equations are characterized by dependence of the velocity components on the transverse coordinates only. The functions of pressure, temperature and concentration of vapor linearly depend on the longitudinal coordinate and have the summands which are functions on transverse coordinates. The required functions satisfy the set of differential equations, boundary and interface conditions followed from the original three-dimensional problem statement and are found as a result of numerical technique. The presented solution of the evap- orative convection problem is very contensive. It permits to specify the 3D flow regimes with different topology, thermal and concentration characteristics observed in physical experiments. Differences of flows in the ethanol–nitrogen, HFE-7100 – nitrogen and FC-72 – nitrogen systems are studied. Impact of the thermophysical properties of the working liquids on the basic characteristics of the fluid motions (hydro- dynamical structure, temperature distribution, vapor content in the nitrogen, evaporative mass flow rate) is analyzed

Numerical Solution of the Three-Dimensional Navier-Stokes Equations With Applications to Channel Flows and a Buoyant Jet in a Cross Flow

1975 ◽  
Vol 42 (3) ◽  
pp. 575-579 ◽  
Author(s):  
J. C. Chien ◽  
J. A. Schetz
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Cross Flow ◽  
Boussinesq Approximation ◽  
Channel Flows ◽  
Navier Stokes ◽  
Buoyant Jet ◽  
Navier Stokes Equations ◽  
Eddy Viscosity Model ◽  
Good Agreement

The steady, three-dimensional, incompressible Navier-Stokes equations written in terms of velocity, vorticity, and temperature are solved numerically for channel flows and a jet in a cross flow. Upwind differencing of the convection term was used in the computation for convergence and simplicity. Comparisons were made with experimental results for laminar flow in the entrance region of a square channel, and good agreement was obtained. The method was also applied to a turbulent, buoyant jet in a cross-flow problem with the Boussinesq approximation and a constant Prandtl eddy viscosity model. Good agreement with experiment was obtained in this case also.

A Comprehensive Method to Predict Wear and to Define the Optimum Geometry of Fretting Surfaces

2006 ◽  
Vol 128 (3) ◽  
pp. 476-485 ◽  
Author(s):  
L. Gallego ◽  
D. Nélias ◽  
C. Jacq
Keyword(s):  
Shear Stress ◽  
Three Dimensional ◽  
Rolling Contact ◽  
Dissipated Energy ◽  
Surface Shear Stress ◽  
Surface Geometry ◽  
Surface Shear ◽  
Normal Loading ◽  
Slip Regime ◽  
The One

This paper presents a fast and robust three-dimensional contact computation tool taking into account the effect of cyclic wear induced from fretting solicitations under the gross slip regime. The wear prediction is established on a friction-dissipated energy criteria. The material response is assumed elastic. The contact solver is based on the half-space assumption and the algorithm core is similar to the one originally proposed by Kalker (1990, Three Dimensional Elastic Bodies in Rolling Contact, Kluwer, Dordrecht) for normal loading. In the numerical procedure the center of pressure may be imposed. The effect of surface shear stress is considered through a Coulomb friction coefficient. The conjugate gradient scheme presented by Polonsky and Keer (1999, Wear, 231, pp. 206–219) and an improved fast Fourier transform (FFT) acceleration technique similar to the one developed by Liu et al. (2000, Wear, 243, pp. 101–111) are used. Results for elementary geometries in the gross slip regime are presented. It is shown that the surface geometry influences the contact pressure and surface shear stress distributions found after each loading cycle. It is also shown that wear tends to be uniformly distributed. This process continuously modifies the micro- and macrogeometry of the rubbing surfaces, leading after a given number of cycles to (i) an optimum or ideal contact geometry and (ii) a prediction of wear.

Numerical Analysis of Three-Dimensional Bjo¨rk–Shiley Valvular Flow in an Aorta

1997 ◽  
Vol 119 (1) ◽  
pp. 45-51 ◽  
Author(s):  
E.-B. Shim ◽  
K.-S. Chang
Keyword(s):  
Shear Stress ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Leading Edge ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Jet Flows ◽  
Computational Results ◽  
Navier Stokes Equations ◽  
Disk Valve

Laminar vortical flow around a fully opened Bjo¨rk–Shiley valve in an aorta is obtained by solving the three-dimensional incompressible Navier–Stokes equations. Used is a noniterative implicit finite-element Navier–Stokes code developed by the authors, which makes use of the well-known finite difference algorithm PISO. The code utilizes segregated formulation and efficient iterative matrix solvers such as PCGS and ICCG. Computational results show that the three-dimensional vortical flow is recirculating with large shear in the sinus region of the valve chamber. Passing through the valve, the flow is split into major upper and lower jet flows. The spiral vortices generated by the disk are advected in the wake and attenuated rapidly downstream by diffusion. It is shown also that the shear stress becomes maximum near the leading edge of the disk valve.

Three-Dimensional CFD Rotordynamic Analysis of Gas Labyrinth Seals

2001 ◽  
Author(s):  
J. Jeffrey Moore
Keyword(s):  
Shear Stress ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Internal Flow ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Navier Stokes ◽  
Labyrinth Seals ◽  
Navier Stokes Equations ◽  
Rotordynamic Forces

Abstract Labyrinth seals are utilized inside turbomachinery to provide non-contacting control of internal leakage. These seals can also play an important role in determining the rotordynamic stability of the machine. Traditional labyrinth seal models are based on bulk-flow assumptions where the fluid is assumed to behave as a rigid body affected by shear stress at the interfaces. To model the labyrinth seal cavity, a single, driven vortex is assumed and relationships for the shear stress and divergence angle of the through flow jet are developed. These models, while efficient to compute, typically show poor prediction for seals with small clearances, high running speed, and high pressure (Childs, 1993). In an effort to improve the prediction of these components, this work utilizes three-dimensional computational fluid dynamics (CFD) to model the labyrinth seal flow path by solving the Reynolds Averaged Navier Stokes equations. Unlike bulk-flow techniques, CFD makes no fundamental assumptions on geometry, shear stress at the walls, as well as internal flow structure. The method allows modeling of any arbitrarily shaped domain including stepped and interlocking labyrinths with straight or angled teeth. When only leakage prediction is required, an axisymmetric model is created. To calculate rotordynamic forces, a full 3D, eccentric model is solved. The results demonstrate improved leakage and rotordynamic prediction over bulk-flow approaches compared to experimental measurements.

scholarly journals Unsteady Simulation of a Full-Scale CANDU-6 Moderator with OpenFOAM

Energies ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 330 ◽  
Author(s):  
Hyoung Kim ◽  
Se-Myong Chang ◽  
Young Son
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Boussinesq Approximation ◽  
Source Distribution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Geometry Model ◽  
Heavy Water Reactor ◽  
Heat Source Distribution

Three-dimensional moderator flow in the calandria tank of CANDU-6 pressurized heavy water reactor (PHWR) is computed with Open Field Operation and Manipulation (OpenFOAM), an open-source computational fluid dynamics (CFD) code. In this study, numerical analysis is performed on the real geometry model including 380 fuel rods in the calandria tank with the heat-source distribution to remove uncertainty of the previous analysis models simplified by the porous media approach. Realizable k-ε turbulence model is applied, and the buoyancy due to temperature variation is considered by Boussinesq approximation for the incompressible single-phase Navier-Stokes equations. The calculation results show that the flow is highly unsteady in the moderator. The computational flow visualization shows a circulation of flow driven by buoyancy and asymmetric oscillation at the pseudo-steady state. There is no region where the local temperature rises continuously due to slow circulating flow and its convection heat transfer.

Three-Dimensional Steady Flow Through A Bifurcation

1990 ◽  
Vol 112 (2) ◽  
pp. 189-197 ◽  
Author(s):  
Chain-Nan Yung ◽  
Kenneth J. De Witt ◽  
Theo G. Keith
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Steady Flow ◽  
Stokes Equations ◽  
Control Volume ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Simple Algorithm ◽  
Outer Wall ◽  
Navier Stokes

Steady flow of an incompressible, Newtonian fluid through a symmetric bifurcated rigid channel was numerically analyzed by solving the three-dimensional Navier-Stokes equations. The upstream Reynolds number ranged from 100 to 1500. The bifurcation was symmetrical with a branch angle of 60 deg and the area ratio of the daughter to the mother vessel was 2.0. The numerical procedure utilized a coordinate transformation and a control volume approach to discretize the equations to finite difference form and incorporated the SIMPLE algorithm in performing the calculation. The predicted velocity pattern was in qualitative agreement with experimental measurements available in the literature. The results also showed the effect of secondary flow which can not be predicted using previous two-dimensional simulations. A region of reversed flow was observed near the outer wall of the branch except for the case of the lowest Reynolds number. Particle trajectory was examined and it was found that no fluid particles remained within the recirculation zone. The shear stress was calculated on both the inner and the outer wall of the branch. The largest wall shear stress, located in the vicinity of the apex of the branch, was of the same order of magnitude as the level that can cause damage to the vessel wall as reported in a recent study.

On the front velocity of gravity currents

2007 ◽  
Vol 586 ◽  
pp. 1-39 ◽  
Author(s):  
MARIANO I. CANTERO ◽  
J. R. LEE ◽  
S. BALACHANDAR ◽  
MARCELO H. GARCIA
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Gravity Currents ◽  
Front Velocity ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Small Density ◽  
Flow Transitions

Highly resolved three-dimensional and two-dimensional simulations of gravity currents in planar and cylindrical configurations are presented. The volume of release of the heavy fluid is varied and the different phases of spreading, namely acceleration, slumping, inertial and viscous phases, are studied. The incompressible Navier–Stokes equations are solved assuming that the Boussinesq approximation is valid for small density difference. The simulations are performed for three different Reynolds numbers (Re): 895, 3450 and 8950 (this particular choice corresponds to values of Grashof number: 105, 1.5 × 106 and 107, respectively). Following their sudden release, the gravity currents are observed to go through an acceleration phase in which the maximum front velocity is reached. As the interface of the current rolls up, the front velocity slightly decreases from the maximum and levels off to a nearly constant value. At higher Re, three-dimensional disturbances grow rapidly and the currents become strongly turbulent. In contrast, in two-dimensional simulations, the rolled-up vortices remain coherent and very strong. Depending on the initial Re of the flow and on the size of the release, the current may transition from the slumping to the inertial phase, or directly to the viscous phase without an inertial phase. New criteria for the critical Re are introduced for the development of the inertial phase. Once the flow transitions to the inertial or viscous phase, it becomes fully three-dimensional. During these phases of spreading, two-dimensional approximations underpredict the front location and velocity. The enhanced vortex coherence of the two-dimensional simulations leads to strong vortex interaction and results in spurious strong time variations of the front velocity. The structure and dynamics of the three-dimensional currents are in good agreement with previously reported numerical and experimental observations.

Miniature Pressure Probe for Measuring the Surface-Shear-Stress Vector in Turbulent Flow

1981 ◽  
Vol 32 (1) ◽  
pp. 43-47 ◽  
Author(s):  
N. Pontikos ◽  
P. Bradshaw
Keyword(s):  
Shear Stress ◽  
Pressure Difference ◽  
Three Dimensional ◽  
Pressure Probe ◽  
Surface Shear Stress ◽  
Pressure Gradients ◽  
Stress Vector ◽  
Three Dimensional Flow ◽  
Surface Shear ◽  
Plan View

SummaryIf two small fences are arranged approximately at right angles in plan view, the magnitude and direction of surface shear stress can be deduced from measurements of the pressure difference across each fence. Fence heights as small as 0.05 mm are easily achieved. The device is simpler to use than null-seeking arrangements, and is accurate even in the presence of strong pressure gradients, which are shown to have large effects on other types of surface obstacle in three-dimensional flow.

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