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.

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.

scholarly journals A numerical geotechnical model for computing soil slides at banks of water reservoirs

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Nils Reidar B. Olsen ◽  
Stefan Haun
Keyword(s):  
Numerical Model ◽  
Water Level ◽  
Stokes Equations ◽  
Limit Equilibrium ◽  
Three Dimensional ◽  
Field Measurements ◽  
Navier Stokes ◽  
Adaptive Grids ◽  
Groundwater Levels ◽  
Before And After

AbstractSoil slides can occur when the water level in a lake or a reservoir is lowered. This may take place in situations when a reservoir is flushed to remove sediments. The current study describes a three-dimensional numerical model used for the simulation of reservoir flushing that includes the slide movements. The geotechnical failure algorithms start with modelling the groundwater levels at the banks of the reservoir. A limit equilibrium approach is further used to find the location of the slides. The actual movement of the sediments is computed by assuming the soil to be a viscous liquid and by solving the Navier–Stokes equations. The resulting bed elevation changes from the slides are computed in adaptive grids that change as a function of water level, bed erosion and slide movements. The numerical model is tested on the Bodendorf reservoir in Austria, where field measurements are available of the bank elevations before and after a flushing operation. The results from the numerical simulations are compared with these observations. A parameter test shows that the results are very sensitive to the cohesion and less sensitive to the E and G modules of the soil.

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.

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.

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.

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).

A Numerical Model for Casing Treatment Applications in Axial Flow Compressors

2013 ◽  
Author(s):  
Nina Wolfrum ◽  
Giovanni Brignole ◽  
Karl Engel
Keyword(s):  
Numerical Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Source Terms ◽  
Navier Stokes Equations ◽  
The Real ◽  
Casing Treatment ◽  
Unsteady Simulation ◽  
Casing Treatments

A numerical model has been developed to reproduce the effects of complex casing treatments (CT) in steady RANS simulations of multistage compressors. While some CTs, such as circumferential grooves, can be described by a rotation surface and can thus easily be included in conventional steady simulations, the CFD analysis of other casing treatments like axial slot or recessed vanes, currently requires a time-resolving analysis of the interaction between such structures and rotating parts. At present unsteady simulations are still too time consuming to be used in the early phase of a compressor design. In the presented study a numerical model was developed for casing treatment applications, to introduce the unsteady effects caused by such casing treatments into steady CFD-simulations. With the help of the model, non-axisymmetric elements can be eliminated from the geometry allowing a steady simulation to be used. The flow acceleration and redirection caused by these geometrical elements is replaced with adequate source terms introduced into the three-dimensional Navier-Stokes equations. These source terms, derived from a consecutive time- and circumferential averaging of the three-dimensional unsteady Reynolds-averaged Navier-Stokes-equations, arise from the momentum and energy equations. Using these additional terms, the CT-model simulates both the pressure forces that the walls of the real casing treatment exert on the flow, and the effects of the mean blockage induced by the omitted geometry. Furthermore, the deterministic stresses, caused by a circumferentially inhomogeneous flow within the CT-structure, are modeled. The source terms consist of geometrical data that can be derived directly from the real geometry of the casing treatment as well as physical quantities of the time-averaged flow in the real casing treatment. The latter terms can be obtained from a reference unsteady simulation. In the presented case one unsteady simulation was sufficient to set up the model for a complete speed line. The model was implemented into the three-dimensional Navier-Stokes-code TRACE [5][12]. By using steady instead of unsteady CFD simulations, the time required for a speedline computation was reduced by a factor of 10. At the same time, the numerical results of the CT-model showed good alignment with the reference data. The model was evaluated for several different styles of compressors. In this paper various results are presented, including speedlines as well as radial inflow- and outflow-profiles.

Solutions of the Three-Dimensional Navier-Stokes Equations in Non-Orthogonal Coordinates to Calculate the Flow in a Log Spiral Impeller

1982 ◽  
Author(s):  
B. W. Swanson
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Computational Procedure ◽  
Navier Stokes ◽  
Three Dimensional Flow ◽  
Elliptic Solution ◽  
Navier Stokes Equations ◽  
Orthogonal Grid ◽  
Good Agreement ◽  
Orthogonal Coordinates

A modification of Moore’s (12) method has been developed for solving the three-dimensional Navier Stokes equations to calculate the flow in a log spiral impeller. A complete mathematical development of this method is presented. The parabolic finite-difference marching code used to make the calculations is an extensive revision of a CATHY3 code obtained from D. B. Spalding. Calculations are made for Vr, Vθ and Vz on a non-orthogonal grid that is ideally suited for impellers with back-swept blades. An inviscid solution is in good agreement with the elliptic solution and validates the computational procedure. The method is applied to calculate the viscous three-dimensional flow in a log spiral impeller.

scholarly journals The curled wake model: A three-dimensional and extremely fast steady-state wake solver for wind plant flows

2020 ◽  
Author(s):  
Luis A. Martínez-Tossas ◽  
Jennifer King ◽  
Eliot Quon ◽  
Christopher J. Bay ◽  
Rafael Mudafort ◽  
...  
Keyword(s):  
Steady State ◽  
Wind Power ◽  
Power Plants ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Good Agreement

Abstract. This work focuses on minimizing the computational cost of steady-state wind power plant flow simulations that take into account wake steering physics. We present a simple wake solver with a computational cost on the order of seconds for large wind plants. The solver uses a simplified form of the Reynolds-averaged Navier-Stokes equations to obtain a parabolic equation for the wake deficit of a wind plant. We compare results from the model to supervisory control and data acquisition (SCADA) from the Lillgrund wind plant; good agreement is obtained. Results for the solver in complex terrain are also shown. Finally, the solver is demonstrated for a case with wake steering showing good agreement with power reported by large-eddy simulations. This new solver minimizes the time – and therefore the related cost – it takes to conduct a steady-state wind plant flow simulation to about a second on a personal laptop. This solver can be used for different applications including wake steering for wind power plants and layout optimization, and it will soon be available within the FLOw Redirection and Induction in Steady State (FLORIS) framework.

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