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.

Numerical Modelling of Circulation in Lake Sperillen, Norway

2000 ◽  
Vol 31 (1) ◽  
pp. 57-72 ◽  
Author(s):  
N. R. B. Olsen ◽  
D. K. Lysne
Keyword(s):  
Numerical Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Field Measurements ◽  
Navier Stokes ◽  
Water Current ◽  
Simple Method ◽  
Vertical Temperature Profile ◽  
Navier Stokes Equations ◽  
Good Agreement

A three-dimensional numerical model was used to model water circulation and spatial variation of temperature in Lake Sperillen in Norway. A winter situation was simulated, with thermal stratification and ice cover. The numerical model solved the Navier-Stokes equations on a 3D unstructured non-orthogonal grid with hexahedral cells. The SIMPLE method was used for the pressure coupling and the k-ε model was used to model turbulence, with a modification for density stratification due to the vertical temperature profile. The results were compared with field measurements of the temperature in the lake, indicating the location of the water current. Reasonably good agreement was found.

Numerical Simulation of a Pouring Flow From a Beverage Can

2019 ◽  
Author(s):  
Yu Nishio ◽  
Keiji Niwa ◽  
Takanobu Ogawa
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Angular Speed ◽  
Experimental Result ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Numerical Result ◽  
Liquid Flows ◽  
Good Agreement

Abstract Motion of liquid pouring from a beverage can is numerically studied. A liquid is poured from a can which is rotated at a prescribed angular speed. The flow is simulated by solving the unsteady three-dimensional Navier-Stokes equations. An experiment under the same condition is also carried out to validate the computational result. The result shows that, when the can is tipped, the liquid flows over the lid of the can and is once obstructed by the rim of the lid. The numerical result is in good agreement with the experimental result. The effect of condensation formed on a can surface is also considered. The effect of condensation is taken into account by adjusting a contact angle. The liquid pouring from a can trickles down along the can body. The computation reproduces these experimental observations.

scholarly journals Energy spectrum in the dissipation range of fluid turbulence

1997 ◽  
Vol 57 (1) ◽  
pp. 195-201 ◽  
Author(s):  
D. O. MARTÍNEZ ◽  
S. CHEN ◽  
G. D. DOOLEN ◽  
R. H. KRAICHNAN ◽  
L.-P. WANG ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fluid Turbulence ◽  
Theoretical Predictions ◽  
Dissipation Range ◽  
Good Agreement

High-resolution, direct numerical simulations of three-dimensional incompressible Navier–Stokes equations are carried out to study the energy spectrum in the dissipation range. An energy spectrum of the form A(k/kd)α exp[−βk/kd] is confirmed. The possible values of the parameters α and β, as well as their dependence on Reynolds numbers and length scales, are investigated, showing good agreement with recent theoretical predictions. A ‘bottleneck’-type effect is reported at k/kd≈4, exhibiting a possible transition from near-dissipation to far-dissipation.

scholarly journals ON NONISOTHERMAL TWO‐FLUID CHANNEL FLOWS

2007 ◽  
Vol 12 (1) ◽  
pp. 143-156
Author(s):  
Jajanek Sokolowsky
Keyword(s):  
Thermocapillary Convection ◽  
Stokes Equations ◽  
Boussinesq Approximation ◽  
Channel Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Free Boundary Value Problems ◽  
Fluid Channel ◽  
Stationary Problems ◽  
Two Fluid

Two‐fluid channel flows arise in different kinds of coating technologies. The corresponding mathematical models represent two‐dimensional free boundary value problems for the Navier‐Stokes equations or their modifications. In this paper we are concerned with the so‐called Boussinesq‐approximation of the coupled heat‐ and mass transfer. Thermocapillary convection is included. The solvability of two related stationary problems is discussed. The solution techniques of both problems are quite different. The obtained results generalize previous results for similar isothermal problems.

Calculations of Two and Three-Dimensional Transonic Cascade Flow Fields Using the Navier-Stokes Equations

1986 ◽  
Vol 108 (1) ◽  
pp. 93-102 ◽  
Author(s):  
B. C. Weinberg ◽  
R.-J. Yang ◽  
H. McDonald ◽  
S. J. Shamroth
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Solid Surfaces ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Cascade Calculation ◽  
Transonic Cascade ◽  
Good Agreement

The multidimensional, ensemble-averaged, compressible, time-dependent Navier-Stokes equations have been used to study the turbulent flow field in two and three-dimensional turbine cascades. The viscous regions of the flow were resolved and no-slip boundary conditions were utilized on solid surfaces. The calculations were performed in a constructive ‘O’-type grid which allows representation of the blade rounded trailing edge. Converged solutions were obtained in relatively few time steps (∼ 80–150) and comparisons for both surface pressure and heat transfer showed good agreement with data. The three-dimensional turbine cascade calculation showed many of the expected flow-field features.

A Three Dimensional Non-Hydrostatic Numerical Model for Free Surface Flow and Mass Transportation

2013 ◽  
Vol 353-356 ◽  
pp. 2496-2501
Author(s):  
Biao Lv
Keyword(s):  
Numerical Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Navier Stokes ◽  
Mass Transportation ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Good Agreement

A three dimensional non-hydrostatic numerical model is presented based on the incompressible Navier-Stokes equations and mass transport equations. An unstructured finite-volume technique is used to discretized the governing equations with good adaptable to complicated boundary. A conservative scalar transport algorithm is also applied in this model. An integral method of the top- layer pressure is applied to reduce the number of vertical layers. Three classical examples including periodic waves propagating over a submerged bar and non-hydrostatic lock exchange are used to demonstrate the capability and efficiency of the model. The simulation results are in good agreement with the analytical solution and experimental data.

Simulation of Three-Dimensional Shear Flow Around a Nozzle-Afterbody at High Speeds

1992 ◽  
Vol 114 (2) ◽  
pp. 178-185 ◽  
Author(s):  
Oktay Baysal ◽  
Wendy B. Hoffman
Keyword(s):  
Shear Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Surface Flow ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Duct Flow ◽  
Navier Stokes Equations ◽  
Eddy Viscosity Model ◽  
Pressure Distributions

Turbulent shear flows at supersonic and hypersonic speeds around a nozzle-afterbody are simulated. The three-dimensional, Reynolds-averaged Navier-Stokes equations are solved by a finite-volume and implicit method. The convective and the pressure terms are differenced by an upwind-biased algorithm. The effect of turbulence is incorporated by a modified Baldwin-Lomax eddy viscosity model. The success of the standard Baldwin-Lomax model for this flow type is shown by comparing it to a laminar case. These modifications made to the model are also shown to improve flow prediction when compared to the standard Baldwin-Lomax model. These modifications to the model reflect the effects of high compressibility, multiple walls, vortices near walls, and turbulent memory effects in the shear layer. This numerically simulated complex flowfield includes a supersonic duct flow, a hypersonic flow over an external double corner, a flow through a non-axisymmetric, internal-external nozzle, and a three-dimensional shear layer. The specific application is for the flow around the nozzle-afterbody of a generic hypersonic vehicle powered by a scramjet engine. The computed pressure distributions compared favorably with the experimentally obtained surface and off-surface flow surveys.

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