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.

On the Flow Fields of Inertial Impactors

1974 ◽  
Vol 96 (4) ◽  
pp. 394-400 ◽  
Author(s):  
V. A. Marple ◽  
B. Y. H. Liu ◽  
K. T. Whitby
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Water Model ◽  
Navier Stokes ◽  
Visualization Technique ◽  
Navier Stokes Equations ◽  
Theoretical Results ◽  
Plate Distance ◽  
Good Agreement

The flow field in an inertial impactor was studied experimentally with a water model by means of a flow visualization technique. The influence of such parameters as Reynolds number and jet-to-plate distance on the flow field was determined. The Navier-Stokes equations describing the laminar flow field in the impactor were solved numerically by means of a finite difference relaxation method. The theoretical results were found to be in good agreement with the empirical observations made with the water model.

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.

scholarly journals Numerical and Analytical Study of Fluid Dynamic Forces in Seals and Bearings

1988 ◽  
Vol 110 (3) ◽  
pp. 315-325 ◽  
Author(s):  
L. T. Tam ◽  
A. J. Przekwas ◽  
A. Muszynska ◽  
R. C. Hendricks ◽  
M. J. Braun ◽  
...  
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Fluid Dynamic ◽  
Three Dimensional ◽  
Circumferential Velocity ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Lumped Model ◽  
Destabilizing Factors ◽  
Recirculation Zones

A numerical model based on a transformed, conservative form of the three-dimensional Navier-Stokes equations and an analytical model based on “lumped” fluid parameters are presented and compared with studies of modeled rotor/bearing/seal systems. The rotor destabilizing factors are related to the rotative character of the flow field. It is shown that these destabilizing factors can be reduced through a descrease in the fluid average circumferential velocity. However, the rotative character of the flow field is a complex three-dimensional system with bifurcated secondary flow patterns that significantly alter the fluid circumferential velocity. By transforming the Navier-Stokes equations to those for a rotating observer and using the numerical code PHOENICS-84 with a nonorthogonal body fitted grid, several numerical experiments were carried out to demonstrate the character of this complex flow field. In general, fluid injection and/or preswirl of the flow field opposing the shaft rotation significantly intensified these secondary recirculation zones and thus reduced the average circumferential velocity, while injection or preswirl in the direction of rotation significantly weakened these zones. A decrease in average circumferential velocity was related to an increase in the strength of the recirculation zones and thereby promoted stability. The influence of the axial flow was analyzed. The lumped model of fluid dynamic force based on the average circumferential velocity ratio (as opposed to the bearing/seal coefficient model) well described the obtained results for relatively large but limited ranges of parameters. This lumped model is extremely useful in rotor/bearing/seal system dynamic analysis and should be widely recommended. Fluid dynamic forces and leakage rates were calculated and compared with seal data where the working fluid was bromotrifluoromethane (CBrF3). The radial and tangential force predictions were in reasonable agreement with selected experimental data. Nonsynchronous perturbation provided meaningful information for system lumped parameter identification from numerical experiment data.

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.

Development of Numerical Code to Predict Three-Dimensional Sand Erosion Phenomena

2003 ◽  
Author(s):  
Kuki Junichi ◽  
Kazuyuki Toda ◽  
Makoto Yamamoto
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Suspended Particle ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Numerical Code ◽  
Particle Collision ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Sand Erosion

This paper presents a numerical procedure to predict a three-dimensional sand erosion phenomenon and the interaction between the flow field and the eroded surface. To simulate this phenomenon, the turbulent flow field, the particle trajectory and the amount of erosion on the eroded wall are calculated repeatedly. In computations of the flow field, compressible Navier-Stokes equations and low-Reynolds-number type k–ε turbulence model are adopted. Assuming that the concentration of suspended particle is dilute, particle-particle collision and the influence of particle motions on the flow field are neglected. The Neilson-Gilchrist erosion model is used to estimate the weight loss due to erosion. To verify the developed code, two types of 90-degree bends are computed. The results show that the present procedure can reasonably reproduce the sand erosion process and the temporal change of both the flow field and the wall surface qualitatively.

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.

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.

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.

Numerical Simulation of Three-Dimensional Cathode Flow Field of ECM for Inner-Wall Rectangle Weight-Reduction Blind Groove

2010 ◽  
Vol 102-104 ◽  
pp. 321-325 ◽  
Author(s):  
Jian Min Wu
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Electrochemical Machining ◽  
Navier Stokes ◽  
Three Dimensional Flow ◽  
Navier Stokes Equations ◽  
Workpiece Surface ◽  
Flow Passage

In order to design the flow field of the NC-Electrochemical Machining (NC-ECM), a three-dimensional physical model of the flow passage is constructed based on the characteristic of the fluid flow, and three-dimensional flow field simulation is conducted with the applications of the Reynolds time-averaged Navier-Stokes equations and standard k- turbulence numerical model, velocity vectors on workpiece surface are calculated respectively based upon the three cathode outlet slots under the steady electrochemical machining condition. The present analysis show that electrolyte insufficiency appeared on workpiece surface for initial cathode flow field, and the experiment results verified the correctness of numerical simulation.

Twin Inclined Circular Jets Evolution Through a Cool Crossflow

2007 ◽  
Author(s):  
Amina Radhouane ◽  
Nejla Mahjoub Sai¨d ◽  
Hatem Mhiri ◽  
George Lepalec ◽  
Philippe Bournot
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Vortical Structures ◽  
Circular Jets ◽  
Turbulent Closure ◽  
The Mean ◽  
Good Agreement

The aim of this paper is to examine experimentally as well as numerically the flowfield resulting from the interaction between a twin circular inclined hot jets emerging into a cooling crossflow. The resulting flowfield is quite complex due to the presence of different vortical structures including the kidney vortex, the horse-shoe vortex, etc... The evolution of the twin inclined jets through the crossflow could be depicted by tracking the mean-flow velocity field and its associated turbulence statistics by means of the PIV technique. This evolution can be influenced by many factors. Herein, we will deal with that resulted by the injection nozzles’ inclination and the jets’ spacing. Then, we performed a three dimensional sample of the studied configuration in order to simulate the evolution of the resulting flowfield. For that, the Navier Stokes equations were simulated with an RSM second order turbulent closure model. Then a non uniform meshing was applied. A good agreement was obtained between the experimental data and the numerical modeling. After validation we could represent in addition to the available results, the temperature distribution and the effects the variation of the injection inclination and that of the jets’ spacing bring on it (on its spatial evolution).

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