Numerical Simulation of Turbulent Flows Using Navier Stokes Equations

1987 ◽  
pp. 473-497
Author(s):  
Wolfgang Schmidt
Keyword(s):  
Numerical Simulation ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

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 Controlling the onset of turbulence by streamwise travelling waves. Part 2. Direct numerical simulation

2010 ◽  
Vol 663 ◽  
pp. 100-119 ◽  
Author(s):  
BINH K. LIEU ◽  
RASHAD MOARREF ◽  
MIHAILO R. JOVANOVIĆ
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Travelling Waves ◽  
Base Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Equations ◽  
Onset Of Turbulence

This study builds on and confirms the theoretical findings of Part 1 of this paper (Moarref & Jovanović, J. Fluid Mech., 2010, doi:10.1017/S0022112010003393). We use direct numerical simulation of the Navier–Stokes equations to assess the efficacy of blowing and suction in the form of streamwise travelling waves for controlling the onset of turbulence in a channel flow. We highlight the effects of the modified base flow on the dynamics of velocity fluctuations and net power balance. Our simulations verify the theoretical predictions of Part 1 that the upstream travelling waves promote turbulence even when the uncontrolled flow stays laminar. On the other hand, the downstream travelling waves with parameters selected in Part 1 are capable of reducing the fluctuations' kinetic energy, thereby maintaining the laminar flow. In flows driven by a fixed pressure gradient, a positive net efficiency as large as 25 % relative to the uncontrolled turbulent flow can be achieved with downstream waves. Furthermore, we show that these waves can also relaminarize fully developed turbulent flows at low Reynolds numbers. We conclude that the theory developed in Part 1 for the linearized flow equations with uncertainty has considerable ability to predict full-scale phenomena.

scholarly journals Finite-scale equations for compressible fluid flow

2009 ◽  
Vol 367 (1899) ◽  
pp. 2861-2871 ◽  
Author(s):  
L.G. Margolin
Keyword(s):  
Numerical Simulation ◽  
Turbulent Flows ◽  
Compressible Fluid ◽  
High Speed ◽  
Energy Transport ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Scale Models

Finite-scale equations (FSE) describe the evolution of finite volumes of fluid over time. We discuss the FSE for a one-dimensional compressible fluid, whose every point is governed by the Navier–Stokes equations. The FSE contain new momentum and internal energy transport terms. These are similar to terms added in numerical simulation for high-speed flows (e.g. artificial viscosity) and for turbulent flows (e.g. subgrid scale models). These similarities suggest that the FSE may provide new insight as a basis for computational fluid dynamics. Our analysis of the FS continuity equation leads to a physical interpretation of the new transport terms, and indicates the need to carefully distinguish between volume-averaged and mass-averaged velocities in numerical simulation. We make preliminary connections to the other recent work reformulating Navier–Stokes equations.

Numerical Simulation of Cavities Flow

2010 ◽  
Author(s):  
Jing Hu ◽  
Zhiguo Zhang ◽  
Dakui Feng
Keyword(s):  
Numerical Simulation ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Simple Algorithm ◽  
Navier Stokes ◽  
Complex Flow ◽  
Navier Stokes Equations ◽  
Simple Geometry ◽  
Flow Phenomena ◽  
The Mathematical Model

Flow across the cavity represents a simple geometry complex flow phenomena for many industry field. This paper presents a series of simulation results of both laminar and turbulent flows over cavities. Several important results and conclusions are reported. The mathematical model corresponds to the incompressible, Reynolds-averaged, Navier-Stokes equations plus a turbulence model, and the numerical simulation is performed using the SIMPLE algorithm.

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.

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