scholarly journals Numerical simulation of unsteady flow of a viscous incompressible liquid in flat channels of arbitrary shape of heat exchangers

2020 ◽  
Vol 34 ◽  
pp. 41-55
Author(s):  
Y. Chоvniuk ◽  
V. Kravchuk ◽  
A. Moskvitina ◽  
I. Pefteva
Keyword(s):  
Numerical Simulation ◽  
Fluid Flow ◽  
Unsteady Flow ◽  
Heat Exchangers ◽  
Arbitrary Shape ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Computational Domain ◽  
Two Dimensional ◽  
Navier Stokes Equations

Reasonable development and creation of any device in which there is an interaction between the fluid flow and the elements of the flow parts (for example, heat exchangers, transport and power machines, main pipelines), is impossible without detailed information about the characteristics of the flow, about the forces on the surfaces that are around, about vibroacoustic phenomena, etc. Among the various methods of obtaining information about the characteristics of the flow, about the forces on surfaces that are flown around, about vibroacoustic phenomena, an important role is played by theoretical methods that rely on the equation of hydrodynamics and numerous ways to solve them. In this case, the main efforts are aimed at solving the system of Navier-Stokes equations. In this paper, a general method is described for the numerical solution of the problem of unsteady flow of a viscous incompressible fluid in flat channels of an arbitrary shape of heat exchangers. An effective solution to the problem is achieved by using adaptive networks. The mathematical model of the flow is based on the two-dimensional Navier-Stokes equations in the variables "flow function - vortex" and the Poissonequation for pressure, which are solved on the basis of the finite-difference method. A numerical simulation of the fluid flow in a flat curvilinear elbow is carried out at the Reynolds number Re = 1000. This form reflects the most characteristic features of the flow paths of various hydraulic machines, heat exchangers, hydraulic and pipeline systems. The presentation of the numerical results was carried out on the basis of the VISSIM graphic processing package. One of the main problems (difficulties) in the numerical solution of problems of mathematical physics is the representation of boundary conditions for regions of arbitrary shape. The implementation of various artificial methods that are now used in the approximation of both the curvilinear boundaries themselves and the boundary conditions on them can lead to significant losses in the accuracy of the solution. This is especially evident in problems in which solutions in the boundary region have maximum gradients. An effective method for solving this problem is the use of adapted grids for the computational domain. The essence of this method lies in the fact that such a coordinate system, not necessarily orthogonal, is found in which the boundary lines (surfaces) of the region coincide with the coordinate lines (surfaces). In the flat case, the computational domain is transformed into a rectangular one, and the limit curve is displayed on the sides of the rectangle. In practice, the problem of constructing an adapted mesh is reduced to finding functions that describe the mappings of the canonical (rectangular) region onto the region for which the problem was originally formulated, that is, for the two-dimensional case, the functions x (ξ, η), y (ξ, η) are determined.

Numerical Simulation of Gas Flow Pattern in Cyclone Spray Scrubber

2011 ◽  
Vol 233-235 ◽  
pp. 701-706
Author(s):  
Bing Tao Zhao ◽  
Yi Xin Zhang ◽  
Kai Bin Xiong
Keyword(s):  
Numerical Simulation ◽  
Fluid Flow ◽  
Flow Pattern ◽  
Gas Flow ◽  
Stokes Equations ◽  
Tangential Velocity ◽  
Navier Stokes ◽  
Computational Domain ◽  
Spray Scrubber ◽  
Cfd Method

The numerical simulation of the fluid flow is presented by CFD technique to characterize the flow pattern of cyclone spray scrubber. In this process, the Reynolds-averaged Navier-Stokes equations with the Reynolds stress turbulence model (RSM) for fluid flow are solved by use of the finite volume method based on the SIMPLE pressure correction algorithm in the fluid computational domain. According to the computational results, the tangential velocity, axial velocity and turbulence intensity of the gas flow are addressed in the different flowrate. The results indicate that the CFD method can effectively reveal the mechanism of gas flow in the cyclone spray scrubber.

scholarly journals Unsteady flow around a two-dimensional section of a vertical axis turbine for tidal stream energy conversion

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Hyun Ju Jung ◽  
Ju Hyun Lee ◽  
Shin Hyung Rliee ◽  
Museok Song ◽  
Beom-Soo Hyun
Keyword(s):  
Unsteady Flow ◽  
Energy Conversion ◽  
Stokes Equations ◽  
Vertical Axis ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Tidal Stream ◽  
Tidal Stream Energy ◽  
Vertical Axis Turbine

ABSTRACTThe two-dimensional unsteady flow around a vertical axis turbine for tidal stream energy' conversion was investigated using a computational fluid dynamics tool solving the Reynolds-Averaged Navier-Stokes equations. The geometry' of the turbine blade section was NACA653-01S airfoil. The computational analysis was done at several different angles of attack and the results were compared with the corresponding experimental data for validation and calibration. Simulations were then carried out for the two-dimensional cross section of a vertical axis turbine. The simulation results demonstrated the usefulness of the method for the typical unsteady flows around vertical axis turbines. The optimum turbine efficiency was achieved for carefully selected combinations of the number of blades and tip speed ratios.

scholarly journals A New Mass-Conservative, Two-Dimensional, Semi-Implicit Numerical Scheme for the Solution of the Navier-Stokes Equations in Gravel Bed Rivers with Erodible Fine Sediments

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 690
Author(s):  
Maurizio Tavelli ◽  
Sebastiano Piccolroaz ◽  
Giulia Stradiotti ◽  
Giuseppe Roberto Pisaturo ◽  
Maurizio Righetti
Keyword(s):  
Numerical Scheme ◽  
Stokes Equations ◽  
Transport Processes ◽  
Sediment Supply ◽  
Navier Stokes ◽  
Computational Domain ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Gravel Bed ◽  
Gravel Bed Rivers

The selective trapping and erosion of fine particles that occur in a gravel bed river have important consequences for its stream ecology, water quality, and overall sediment budgeting. This is particularly relevant in water bodies that experience periodic alternation between sediment supply-limited conditions and high sediment loads, such as downstream from a dam. While experimental efforts have been spent to investigate fine sediment erosion and transport in gravel bed rivers, a comprehensive overview of the leading processes is hampered by the difficulties in performing flow field measurements below the gravel crest level. In this work, a new two-dimensional, semi-implicit numerical scheme for the solution of the Navier-Stokes equations in the presence of deposited and erodible sediment is presented, and tested against analytical solutions and performing numerical tests. The scheme is mass-conservative, computationally efficient, and allows for a fine discretization of the computational domain. Overall, this makes the model suitable to appreciate small-scales phenomena such as inter-grain circulation cells, thus offering a valid alternative to evaluate the shear stress distribution, on which erosion and transport processes depend, compared to traditional experimental approaches. In this work, we present proof-of-concept of the proposed model, while future research will focus on its extension to a three-dimensional and parallelized version, and on its application to real case studies.

Numerical Simulation and Experiment Research on Pressure Fluctuation and Aerodynamic Noise Field of a Multi-Blade Centrifugal Fan

2012 ◽  
Vol 468-471 ◽  
pp. 2231-2234
Author(s):  
Feng Gao ◽  
Wei Yan Zhong
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Aerodynamic Noise ◽  
Navier Stokes ◽  
Computational Domain ◽  
Centrifugal Fan ◽  
Navier Stokes Equations ◽  
Simulation And Experiment

Numerical simulation of the three-dimensional steady and unsteady turbulent flow in the whole flow field of a multi-blade centrifugal fan is performed. Unstructured grids is used to discrete the computational domain. Pressure boundary conditions are specified to the inlet and the outlet. The SIMPLE algorithm in conjunction with the RNG k-ε turbulent model is used to solve the three-dimensional Navier-Stokes equations. The moving reference frame is adopted to transfer data between the interfaces of the rotating field and the stationary field. Based on the calculation of the inner-flow in the fan, the pressure pulsation of some important monitoring points and the aerodynamic noise distribution, banding together experiment data were farther analyzed The simulation results are of important significance to the optimal design and noise control of the fan.

Hydrodynamics of a Pump-Turbine at Off-Design Operating Conditions: Numerical Simulation

2011 ◽  
Author(s):  
Vlad Hasmatuchi ◽  
Steven Roth ◽  
Francisco Botero ◽  
Mohamed Farhat ◽  
Franc¸ois Avellan
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Operating Conditions ◽  
Scale Model ◽  
Navier Stokes ◽  
Computational Domain ◽  
Pump Turbine ◽  
Navier Stokes Equations ◽  
Guide Vanes ◽  
Radial Pump

Flow numerical simulations in a low specific speed radial pump-turbine scale model are performed to investigate off-design operating conditions in generating mode. The Best Efficiency Point (BEP) and the runaway operating conditions at 10° guide vanes opening are addressed. The computational domain includes the full reduced scale model water passage from the spiral casing inlet to the draft tube outlet. The numerical simulation is performed using the Ansys CFX code, solving the incompressible unsteady Reynolds-Averaged Navier-Stokes equations. Wall pressure measurements in the stator are used to validate the numerical results. Then, detailed analysis is focused on the onset of the flow instabilities when the machine is brought from BEP to runaway. In these severe operating conditions, one single stall cell is found to rotate with the impeller at subsynchronous speed in the vaneless gap between the impeller and the guide vanes. It is found to be the effect of flow separation developed at the inlet of several consecutive impeller channels which lead to their blockage.

Developing fluid flow in a curved duct of square cross-section and its fully developed dual solutions

1988 ◽  
Vol 188 ◽  
pp. 337-361 ◽  
Author(s):  
W. Y. Soh
Keyword(s):  
Fluid Flow ◽  
Cross Section ◽  
Stokes Equations ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Computational Domain ◽  
Central Difference ◽  
Navier Stokes Equations ◽  
Curved Duct ◽  
Inlet Conditions

Developing fluid flow in a curved duct of square cross-section is studied numerically by a factored ADI finite-difference method on a staggered grid. A central-difference scheme with primitive variables is used inside the computational domain to reduce numerical diffusion. Two Reynolds numbers, 574 and 790, based upon a bulk velocity and hydraulic diameter are chosen for curvature ratios of 1/6.45 and 1/2.3, respectively. It is found that the secondary flow is far more complicated than expected, with the appearance of at least two pairs of vortices. Main-flow separation is also observed for the higher curvature ratio. Furthermore, it is observed that the flow develops into two quite different states downstream, depending upon the inlet conditions.Solution of the fully developed Navier-Stokes equations is shown to be not unique beyond a certain critical Reynolds number. Developing flow seems to evolve into the fully developed state along a particular branch, into which the fully developed solution bifurcates.

scholarly journals Direct Numerical Simulation of Nano Channel Flows at Low Reynolds Number

2020 ◽  
Author(s):  
P. Srinivasa Rao
Keyword(s):  
Numerical Simulation ◽  
Fluid Flow ◽  
Direct Numerical Simulation ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Small Time ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Navier Stokes Equations ◽  
Nano Channel

The governing equations of viscous fluid flow are generally represented by Navier–Stokes (NS) equations. The output of Navier Stokes equations is in essence velocity vector from which rest of the flow parameters can be calculated. It is essentially a riotous task, sometimes it becomes so unmanageable that fluid flow over simplest topologies under low Reynold’s numbers also needs the most powerful supercomputing facility to solve, if needed to model the fluid and its behavior under the turbulent conditions the best way out is to solve the averaged NS equations. However in the process of averaging Reynolds introduced certain new terms such as Reynolds Stresses. Therefore it is required to close the system of equations by relating the unknown variables with known ones. Hence we have turbulence models. Direct Numerical Simulation (DNS) is a method of solving NS equations directly that is by forfeiting the need of turbulence models as the equations are not averaged. However originally direct numerical simulation procedure does not need of additional closure equations, it is essential to have very fine grid elements and should be estimated for exceptionally small time steps to achieve precise solutions. In the present chapter an interesting flow through nano-channel problem has been discussed using the indispensable mathematical technique of computational fluid dynamics (CFD) which is DNS.

scholarly journals Incompressible Fluid Flow Computation in an Arbitrary Two-dimensional Region on Nonstaggered Grids

2005 ◽  
Vol 5 (3) ◽  
pp. 242-258
Author(s):  
Mikhail Chuiko ◽  
Andrei Lapanik ◽  
Ricardo H. Nochetto
Keyword(s):  
Fluid Flow ◽  
Stokes Equations ◽  
Physical Region ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Flow Modeling ◽  
Incompressible Fluid Flow ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Fluid Flow Modeling

Abstract A numerical algorithm for solving the Navier-Stokes equations for incom- pressible viscous fluid in an arbitrary two-dimensional region on nonstaggered grids is presented. The idea of the transition to a general curvilinear coordinate system, trans- forming the physical region into a parametrical square is used. For the discrete solution an unconditional a priory estimate has been obtained. The results of the benchmark computations for a driven skewed cavity flow and the results of the fluid flow modeling in a cavity of an arbitrary shape are given.

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