scholarly journals Comparison between the Lagrangian and Eulerian Approach in Simulation of Free Surface Air-Core Vortices

Water ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 726
Author(s):  
Maryam Azarpira ◽  
Amir Reza Zarrati ◽  
Pouya Farrokhzad
Keyword(s):  
Vortex Flow ◽  
Stokes Equations ◽  
Computational Cost ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Eulerian Approach ◽  
Advantages And Disadvantages ◽  
Air Core ◽  
Image Velocimetry ◽  
The Difference

The problematic consequences regarding formation of air-core vortices at the intakes and the drastic necessity of a thorough investigation into the phenomenon has resulted in particular attention being placed on Computational Fluid Dynamics (CFD) as an economically viable method. Two main approaches could be taken using CFD, namely the Eulerian and Lagrangian methods each of which is characterized by specific advantages and disadvantages. Whereas many researchers have used the Eulerian approach for vortex simulation, the Lagrangian approach has not been found in the literature. The present study dealt with the comparison of the Lagrangian and Eulerian approaches in the simulation of vortex flow. Simulations based on both approaches were carried out by solving the Navier–Stokes equations accompanied by the LES turbulence model. The results of the numerical model were evaluated in accordance with a physical model for steady vortex flow using particle image velocimetry (PIV), revealing that both approaches are sufficiently capable of simulating the vortex flow but with the difference that the Lagrangian method has greater computational cost with less accuracy.

scholarly journals Numerical Investigation on the Water Entry of Several Different Bow-Flared Sections

2020 ◽  
Vol 10 (22) ◽  
pp. 7952
Author(s):  
Qiang Wang ◽  
Boran Zhang ◽  
Pengyao Yu ◽  
Guangzhao Li ◽  
Zhijiang Yuan
Keyword(s):  
Stokes Equations ◽  
Water Entry ◽  
Navier Stokes ◽  
Hydrodynamic Characteristics ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Surface Evolution ◽  
Mesh Method ◽  
The Difference ◽  
Dynamics Method

The bow-flared section may be simplified in the prediction of slamming loads and whipping responses of ships. However, the difference of hydrodynamic characteristics between the water entry of the simplified sections and that of the original section has not been well documented. In this study, the water entry of several different bow-flared sections was numerically investigated using the computational fluid dynamics method based on Reynolds-averaged Navier–Stokes equations. The motion of the grid around the section was realized using the overset mesh method. Reasonable grid size and time step were determined through convergence studies. The application of the numerical method in the water entry of bow-flared sections was validated by comparing the present predictions with previous numerical and experimental results. Through a comparative study on the water entry of one original section and three simplified sections, the influences of simplification of the bow-flared section on hydrodynamic characteristics, free surface evolution, pressure field, and impact force were investigated and are discussed here.

Numerical Simulation of the Cooling Process of Cubic Shells

2011 ◽  
Author(s):  
Manabu Okura ◽  
Kiyoaki Ono
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Temperature Fields ◽  
Numerical Code ◽  
Navier Stokes ◽  
Cooling Process ◽  
Air Velocity ◽  
Navier Stokes Equations ◽  
The Difference ◽  
The Heat Transfer Coefficient

In order to keep the environment in an air-conditioned room comfortable, it is important to anticipate the air velocity and temperature fields precisely. The numerical code, solving simultaneously the Navier-Stokes equations governing flow field inside and outside the room and the heat conduction equation applying to walls, are developed. The assumption that the heat transfer coefficient between the fluid and the surface of solids is not used. This code is applied to investigate the cooling process of a cubic shell. The computational results agree with the experimental results. We also investigated the same process of the cubic shells whose walls are internally or externally insulated. The difference of the amount of heat transfer will be discussed.

Modeling of Particulate Pressure in the Frame of Mesoscopic Eulerian Formalism for Compressible Reactive Dispersed Two-Phase Flows

2006 ◽  
Author(s):  
M. Simoes ◽  
O. Simonin
Keyword(s):  
Stokes Equations ◽  
Flow Region ◽  
Navier Stokes ◽  
Two Phase Flows ◽  
Two Phase ◽  
Specific Flow ◽  
Navier Stokes Equations ◽  
Rocket Motors ◽  
Eulerian Approach ◽  
Liquid Rocket

In space propulsion, compressible reactive dispersed two-phase flows are investigated in order to predict the behavior of solid or liquid rocket motors. In the frame of full Eulerian approach, physical modeling of aerodynamic flows in such motors is performed resolving unsteady compressible Navier-Stokes equations for both phases. However, numerical simulations performed on a simple axisymmetric motor have pointed out a flaw of this basic Eulerian approach. Indeed, the variance of the particle velocity distribution is not accounted for, leading to unrealistic accumulations of particles in some specific flow region. To correct this shortcoming, we have developed an advanced Eulerian model based on a statistical approach in the framework of the Mesoscopic Eulerian Formalism (MEF).

A Quasi-Generalized-Coordinate Approach for Numerical Simulation of Complex Flows

2006 ◽  
Vol 128 (6) ◽  
pp. 1394-1399 ◽  
Author(s):  
Donghyun You ◽  
Meng Wang ◽  
Rajat Mittal ◽  
Parviz Moin
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Effective ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Generalized Coordinate

A novel structured grid approach which provides an efficient way of treating a class of complex geometries is proposed. The incompressible Navier-Stokes equations are formulated in a two-dimensional, generalized curvilinear coordinate system complemented by a third quasi-curvilinear coordinate. By keeping all two-dimensional planes defined by constant third coordinate values parallel to one another, the proposed approach significantly reduces the memory requirement in fully three-dimensional geometries, and makes the computation more cost effective. The formulation can be easily adapted to an existing flow solver based on a two-dimensional generalized coordinate system coupled with a Cartesian third direction, with only a small increase in computational cost. The feasibility and efficiency of the present method have been assessed in a simulation of flow over a tapered cylinder.

Development of a Pressure-Based Coupled CFD Solver for Turbulent and Compressible Flows in Turbomachinery Applications

2014 ◽  
Author(s):  
Luca Mangani ◽  
Marwan Darwish ◽  
Fadl Moukalled
Keyword(s):  
Compressible Flows ◽  
Stokes Equations ◽  
Computational Cost ◽  
Simple Algorithm ◽  
Numerical Data ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Analysis And Design ◽  
Flow Problems ◽  
Matrix Coefficients

In this paper we present a fully coupled algorithm for the resolution of compressible flows at all speed. The pressure-velocity coupling at the heart of the Navier Stokes equations is accomplished by deriving a pressure equation in similar fashion to what is done in the segregated SIMPLE algorithm except that the influence of the velocity fields is treated implicitly. In a similar way, the assembly of the momentum equations is modified to treat the pressure gradient implicitly. The resulting extended system of equations, now formed of matrix coefficients that couples the momentum and pressure equations, is solved using an algebraic multigrid solver. The performance of the coupled approach and the improved efficiency of the novel developed code was validated comparing results with experimental and numerical data available from reference literature test cases as well as with segregated solver as exemplified by the SIMPLE algorithm. Moreover the reference geometries considered in the validation process cover the typical aerodynamics applications in gas turbine analysis and design, considering Euler to turbulent flow problems and clearly indicating the substantial improvements in terms of computational cost and robustness.

Non-parallel stability of a flat-plate boundary layer using the complete Navier-Stokes equations

1990 ◽  
Vol 221 ◽  
pp. 311-347 ◽  
Author(s):  
H. Fasel ◽  
U. Konzelmann
Keyword(s):  
Boundary Layer ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Plate Boundary ◽  
Detailed Comparison ◽  
Problem Formulation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Difference ◽  
Direct Numerical Integration

Non-parallel effects which are due to the growing boundary layer are investigated by direct numerical integration of the complete Navier-Stokes equations for incompressible flows. The problem formulation is spatial, i.e. disturbances may grow or decay in the downstream direction as in the physical experiments. In the past various non-parallel theories were published that differ considerably from each other in both approach and interpretation of the results. In this paper a detailed comparison of the Navier-Stokes calculation with the various non-parallel theories is provided. It is shown, that the good agreement of some of the theories with experiments is fortuitous and that the difference between experiments and theories concerning the branch I neutral location cannot be explained by non-parallel effects.

Strongly Coupled Fluid-Structure Interactions via a New Navier-Stokes Method for Prediction of Vortex-Induced Vibrations

2005 ◽  
Author(s):  
Yannis Kallinderis ◽  
Hyung Taek Ahn
Keyword(s):  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Design Tool ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibrations ◽  
Offshore Industry

Numerical prediction of vortex-induced vibrations requires employment of the unsteady Navier-Stokes equations. Current Navier-Stokes solvers are quite expensive for three-dimensional flow-structure applications. Acceptance of Computational Fluid Dynamics as a design tool for the offshore industry requires improvements to current CFD methods in order to address the following important issues: (i) stability and computation cost of the numerical simulation process, (ii) restriction on the size of the allowable time-step due to the coupling of the flow and structure solution processes, (iii) excessive number of computational elements for 3-D applications, and (iv) accuracy and computational cost of turbulence models used for high Reynolds number flow. The above four problems are addressed via a new numerical method which employs strong coupling between the flow and the structure solutions. Special coupling is also employed between the Reynolds-averaged Navier-Stokes equations and the Spalart-Allmaras turbulence model. An element-type independent spatial discretization scheme is also presented which can handle general hybrid meshes consisting of hexahedra, prisms, pyramids, and tetrahedral.

scholarly journals Dynamics of laminar flows with coaxial oppositely-rotating layers

Vestnik MGSU ◽  
2019 ◽  
pp. 332-346
Author(s):  
Andrey L. Zuikov
Keyword(s):  
Reynolds Number ◽  
Active Zone ◽  
Vortex Flow ◽  
Stokes Equations ◽  
Laminar Flows ◽  
Radial Velocities ◽  
Navier Stokes ◽  
Recirculation Region ◽  
Vortex Flows ◽  
Navier Stokes Equations

Introduction. The work relates to the scientific foundations of hydraulic and energy construction and is devoted to the study of laminar flows with coaxial oppositely-rotating layers. In the literature, such flows are called counter-vortex. In the turbulent range, counter-vortex flows are characterized by intensive mixing of the medium, which is widely used in the technologies of mixing non-natural and multi-phase media in thermal and atomic energy, in systems of mass- and heat transfer, in chemistry and microbiology, ecology, engine and rocket production. The aim of the theoretical study is to study the physical laws of the hydrodynamics of counter-vortex flows. Research methods. The theoretical Navier-Stokes equations and continuity equation are the basis of the theoretical model of the laminar counter-vortex flow. Results. Assuming the radial velocities are much less than the azimuthal and axial velocities and taking the Oseen approximation, the solution of the Navier - Stokes equations is obtained as Fourier - Bessel series or products of Fourier - Bessel series. In particular, the following were obtained: formulas for calculating the radial-longitudinal distributions of the normalized azimuthal, axial and radial velocities in the flow under study, the velocities are presented graphically in the form of radial profiles; equations for the calculation of current lines and viscous vortex fields, which are also presented in the form of graphs, were obtained. The two-layer and four-layer counter-vortex flows are considered. The analysis of the obtained theoretical results is performed. Conclusions. On the axis at the beginning of the active zone, the formation of a return flow with significant negative velocities is characteristic. This leads to the formation of a recirculation region, the mass exchange between which and the external flow is absent. Cascades of concentric vortexes of such high intensity that are not found in streams of a different nature are generated in the active zone. Calculation formulas include exp (-λ2x/Re) exponent multiplied by Reynolds number in degree b = 0 or b = -1, therefore increasing Reynolds number when b = 0 leads to proportional transfer of arbitrary characteristic counter-vortex flow down the pipe; and at b = -1, the bias of characteristic is accompanied by a proportional decrease in its scale.

scholarly journals A Note on Stokes Approximations to Leray Solutions of the Incompressible Navier–Stokes Equations in ℝn

Fluids ◽  
2021 ◽  
Vol 6 (10) ◽  
pp. 340
Author(s):  
Joyce Rigelo ◽  
Janaína Zingano ◽  
Paulo Zingano
Keyword(s):  
Decay Rate ◽  
Stokes Flow ◽  
Stokes Equations ◽  
Energy Decay ◽  
Energy Norm ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Energy Decay Rate ◽  
The Difference

In the early 1980s it was well established that Leray solutions of the unforced Navier–Stokes equations in Rn decay in energy norm for large t. With the works of T. Miyakawa, M. Schonbek and others it is now known that the energy decay rate cannot in general be any faster than t−(n+2)/4 and is typically much slower. In contrast, we show in this note that, given an arbitrary Leray solution u(·,t), the difference of any two Stokes approximations to the Navier–Stokes flow u(·,t) will always decay at least as fast as t−(n+2)/4, no matter how slow the decay of ∥u(·,t)∥L2(Rn) might be.

Asymptotic Model of the 3D Flow in a Progressing-Cavity Pump

SPE Journal ◽  
2011 ◽  
Vol 16 (02) ◽  
pp. 451-462 ◽  
Author(s):  
S.F.A.. F.A. Andrade ◽  
J.V.. V. Valério ◽  
M.S.. S. Carvalho
Keyword(s):  
Stokes Equations ◽  
Computing Time ◽  
Petroleum Industry ◽  
Lubrication Theory ◽  
Moving Boundaries ◽  
Navier Stokes ◽  
Channel Height ◽  
Asymptotic Model ◽  
Navier Stokes Equations ◽  
The Difference

Summary Fundamental understanding of the flow inside progressing-cavity pumps (PCPs) represents an important step in the optimization of the efficiency of these pumps, which are largely used in artificial-lift processes in the petroleum industry. The computation of the flow inside a PCP is extremely complex because of the transient character of the flow, the moving boundaries, and the difference in length scale of the channel height between the stator and rotor. This complexity makes the use of computational fluid dynamics (CFD) as an engineering tool almost impossible. This work presents an asymptotic model to describe the single-phase flow inside PCPs using lubrication theory. The model was developed for Newtonian fluid, and lubrication theory was used to reduce the 3D Navier-Stokes equations in cylindrical coordinates to a 2D Poisson's equation for the pressure field at each timestep, which is solved numerically by a second-order finite-difference method. The predictions are close to the experimental data and the results obtained by solving the complete 3D, transient Navier-Stokes equations with moving boundaries, available in the literature. Although the accuracy is similar to the complete 3D model, the computing time of the presented model is orders of magnitude smaller. The model was used to study the effect of geometry, fluid properties, and operating parameters in the pump-performance curves and can be used in the design of new pumping processes.

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