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.

On Direct Numerical Simulation of Turbulent Flows

2011 ◽  
Vol 64 (2) ◽  
Author(s):  
Giancarlo Alfonsi
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
High Performance Computing ◽  
Turbulent Flows ◽  
High Performance ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Navier Stokes Equations ◽  
Performance Computing

The direct numerical simulation of turbulence (DNS) has become a method of outmost importance for the investigation of turbulence physics, and its relevance is constantly growing due to the increasing popularity of high-performance-computing techniques. In the present work, the DNS approach is discussed mainly with regard to turbulent shear flows of incompressible fluids with constant properties. A body of literature is reviewed, dealing with the numerical integration of the Navier-Stokes equations, results obtained from the simulations, and appropriate use of the numerical databases for a better understanding of turbulence physics. Overall, it appears that high-performance computing is the only way to advance in turbulence research through the front of the direct numerical simulation.

scholarly journals Numerical stability analysis of a vortex ring with swirl

2019 ◽  
Vol 878 ◽  
pp. 5-36 ◽  
Author(s):  
Yuji Hattori ◽  
Francisco J. Blanco-Rodríguez ◽  
Stéphane Le Dizès
Keyword(s):  
Numerical Simulation ◽  
Growth Rate ◽  
Direct Numerical Simulation ◽  
Vortex Ring ◽  
Stokes Equations ◽  
Base Flow ◽  
Critical Layer ◽  
Navier Stokes ◽  
Instability Mode ◽  
Navier Stokes Equations

The linear instability of a vortex ring with swirl with Gaussian distributions of azimuthal vorticity and velocity in its core is studied by direct numerical simulation. The numerical study is carried out in two steps: first, an axisymmetric simulation of the Navier–Stokes equations is performed to obtain the quasi-steady state that forms a base flow; then, the equations are linearized around this base flow and integrated for a sufficiently long time to obtain the characteristics of the most unstable mode. It is shown that the vortex rings are subjected to curvature instability as predicted analytically by Blanco-Rodríguez & Le Dizès (J. Fluid Mech., vol. 814, 2017, pp. 397–415). Both the structure and the growth rate of the unstable modes obtained numerically are in good agreement with the analytical results. However, a small overestimation (e.g. 22 % for a curvature instability mode) by the theory of the numerical growth rate is found for some instability modes. This is most likely due to evaluation of the critical layer damping which is performed for the waves on axisymmetric line vortices in the analysis. The actual position of the critical layer is affected by deformation of the core due to the curvature effect; as a result, the damping rate changes since it is sensitive to the position of the critical layer. Competition between the curvature and elliptic instabilities is also investigated. Without swirl, only the elliptic instability is observed in agreement with previous numerical and experimental results. In the presence of swirl, sharp bands of both curvature and elliptic instabilities are obtained for $\unicode[STIX]{x1D700}=a/R=0.1$, where $a$ is the vortex core radius and $R$ the ring radius, while the elliptic instability dominates for $\unicode[STIX]{x1D700}=0.18$. New types of instability mode are also obtained: a special curvature mode composed of three waves is observed and spiral modes that do not seem to be related to any wave resonance. The curvature instability is also confirmed by direct numerical simulation of the full Navier–Stokes equations. Weakly nonlinear saturation and subsequent decay of the curvature instability are also observed.

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.

Direct Numerical Simulation of Effects of Small Angle of Incidence on Honji Instability

2011 ◽  
Author(s):  
Kun Yang ◽  
Liang Cheng ◽  
Hongwei An ◽  
Ming Zhao
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Angle Of Incidence ◽  
Navier Stokes Equations ◽  
Small Incidence ◽  
Inclination Angles

This paper concerns Honji instability generated around a circular cylinder in an oscillatory flow with a small oblique angle. In this study, direct numerical simulation has been conducted for an oscillatory flow past a stationary cylinder with small incidence angles (α) of 5° and 10° at KC number of 2 and β number of 200. The three-dimensional Navier-Stokes equations are solved using the Petrov-Galerkin finite element method. Flow structures around the cylinder are visualized through using streamlines, velocity vectors and vorticity contours. Honji instability has been captured at both chosen inclination angles. However Honji vortex pairs are asymmetric at α = 5° and 10° due to the inclination of the oscillation direction and can only be observed during the flow reversal. It is also found that the flow inclination appears to suppress the three-dimensional instability.

Direct numerical simulation of controlled transition in a flat-plate boundary layer

1995 ◽  
Vol 298 ◽  
pp. 211-248 ◽  
Author(s):  
U. Rist ◽  
H. Fasel
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Direct Numerical Simulation ◽  
Flat Plate ◽  
Stokes Equations ◽  
Plate Boundary ◽  
Numerical Data ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flat Plate Boundary Layer

The three-dimensional development of controlled transition in a flat-plate boundary layer is investigated by direct numerical simulation (DNS) using the complete Navier-Stokes equations. The numerical investigations are based on the so-called spatial model, thus allowing realistic simulations of spatially developing transition phenomena as observed in laboratory experiments. For solving the Navier-Stokes equations, an efficient and accurate numerical method was developed employing fourth-order finite differences in the downstream and wall-normal directions and treating the spanwise direction pseudo-spectrally. The present paper focuses on direct simulations of the wind-tunnel experiments by Kachanov et al. (1984, 1985) of fundamental breakdown in controlled transition. The numerical results agreed very well with the experimental measurements up to the second spike stage, in spite of relatively coarse spanwise resolution. Detailed analysis of the numerical data allowed identification of the essential breakdown mechanisms. In particular, from our numerical data, we could identify the dominant shear layers and vortical structures that are associated with this breakdown process.

scholarly journals Embedded direct numerical simulation for aeronautical CFD

2001 ◽  
Vol 105 (1046) ◽  
pp. 193-198 ◽  
Author(s):  
N. D. Sandham ◽  
M. Alam ◽  
S. Morin
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Euler Equations ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Modified Equations ◽  
Separation Bubbles

Abstract A method is proposed by which a direct numerical simulation of the compressible Navier-Stokes equations may be embedded within a more general aeronautical CFD code. The method may be applied to any code which solves the Euler equations or the Favre-averaged Navier-Stokes equations. A formal decomposition of the flowfield is used to derive modified equations for use with direct numerical simulation solvers. Some preliminary applications for model flows with transitional separation bubbles are given.

SMOOTHED PROFILE METHOD TO SIMULATE COLLOIDAL PARTICLES IN COMPLEX FLUIDS

2009 ◽  
Vol 20 (09) ◽  
pp. 1457-1465 ◽  
Author(s):  
RYOICHI YAMAMOTO ◽  
YASUYA NAKAYAMA ◽  
KANG KIM
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Colloidal Particles ◽  
Stokes Equations ◽  
Electrolyte Solutions ◽  
Rigid Body Dynamics ◽  
Spherical Particles ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Charged Colloids

A new direct numerical simulation scheme, called "Smoothed Profile (SP) method," is presented. The SP method, as a direct numerical simulation of particulate flow, provides a way to couple continuum fluid dynamics with rigid-body dynamics through smoothed profile of colloidal particle. Our formulation includes extensions to colloids in multicomponent solvents such as charged colloids in electrolyte solutions. This method enables us to compute the time evolutions of colloidal particles, ions, and host fluids simultaneously by solving Newton, advection-diffusion, and Navier–Stokes equations so that the electro-hydrodynamic couplings can be fully taken into account. The electrophoretic mobilities of charged spherical particles are calculated in several situations. The comparisons with approximation theories show quantitative agreements for dilute dispersions without any empirical parameters.

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