scholarly journals Geometry of turbulent dissipation and the Navier–Stokes regularity problem

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Janet Rafner ◽  
Zoran Grujić ◽  
Christian Bach ◽  
Jakob Andreas Bærentzen ◽  
Bo Gervang ◽  
...  
Keyword(s):  
Fundamental Problem ◽  
Computational Simulation ◽  
Numerical Test ◽  
Navier Stokes ◽  
Mathematical Framework ◽  
Turbulent Dissipation ◽  
Regularity Problem ◽  
The 1960S ◽  
Regular Flow ◽  
Rule Out

AbstractThe question of whether a singularity can form in an initially regular flow, described by the 3D incompressible Navier–Stokes (NS) equations, is a fundamental problem in mathematical physics. The NS regularity problem is super-critical, i.e., there is a ‘scaling gap’ between what can be established by mathematical analysis and what is needed to rule out a singularity. A recently introduced mathematical framework—based on a suitably defined ‘scale of sparseness’ of the regions of intense vorticity—brought the first scaling reduction of the NS super-criticality since the 1960s. Here, we put this framework to the first numerical test using a spatially highly resolved computational simulation performed near a ‘burst’ of the vorticity magnitude. The results confirm that the scale is well suited to detect the onset of dissipation and provide numerical evidence that ongoing mathematical efforts may succeed in closing the scaling gap.

Stability of Horizontal Boundary Layers

2006 ◽  
Author(s):  
Jean-Yves Chemin ◽  
Benoit Desjardins ◽  
Isabelle Gallagher ◽  
Emmanuel Grenier
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
Mathematical Proof ◽  
Vertical Component ◽  
Ekman Layer ◽  
Numerical Results ◽  
Energy Estimates ◽  
Navier Stokes ◽  
The 1960S ◽  
The Stability

Let us now detail the stability properties of an Ekman layer introduced in Part I, page 11. First we will recall how to compute the critical Reynolds number. Then we will describe briefly what happens at larger Reynolds numbers. The first step in the study of the stability of the Ekman layer is to consider the linear stability of a pure Ekman spiral of the form where U∞ is the velocity away from the layer and ζ is the rescaled vertical component ζ = x3/√εν. The corresponding Reynolds number is Let us consider the Navier–Stokes–Coriolis equations, linearized around uE The problem is now to study the (linear) stability of the 0 solution of the system (LNSCε). If u=0 is stable we say that uE is linearly stable, if not we say that it is linearly unstable. Numerical results show that u=0 is stable if and only if Re<Rec where Rec can be evaluated numerically. Up to now there is no mathematical proof of this fact, and it is only possible to prove that 0 is linearly stable for Re<Re1 and unstable for Re>Re2 with Re1<Rec<Re2, Re1 being obtained by energy estimates and Re2 by a perturbative analysis of the case Re=∞. We would like to emphasize that the numerical results are very reliable and can be considered as definitive results, since as we will see below, the stability analysis can be reduced to the study of a system of ordinary differential equations posed on the half-space, with boundary conditions on both ends, a system which can be studied arbitrarily precisely, even on desktop computers (first computations were done in the 1960s by Lilly).

Experimental Measurements and Computational Solutions for Aerodynamic Forces on an Ahmed Body at Various Ground Clearances

2003 ◽  
Author(s):  
Ilhan Bayraktar ◽  
Drew Landman ◽  
Tuba Bayraktar
Keyword(s):  
Large Scale ◽  
Bluff Body ◽  
Ground Plane ◽  
Computational Simulation ◽  
Simulation Method ◽  
Full Scale ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Ground Clearance ◽  
Ahmed Body

Reliable computer solutions to external aerodynamic flow fields on road vehicles are extremely desirable to road vehicle designers. In a previous publication a study was performed to validate a Reynolds-averaged unsteady Navier-stokes solution for the aerodynamic characterization of a large-scale bluff body. In the present study, the external aerodynamics of this body as a function of ground clearance are explored. Experimental force measurements are obtained in a full-scale wind tunnel using an Ahmed body model and test conditions representative of full-scale operating conditions. A Reynolds averaged Navier-Stokes solver is employed for computational simulation of the external flowfield at the same conditions. Experimental and computational force coefficients versus vehicle ground clearance are presented for fixed ground, moving ground, and suction slot road simulations. Experimental results using boundary layer suction are compared to computational results with a moving ground plane in order to better understand the effect of a road simulation method.

Optimization of Propulsion Kinematics of a Flexible Foil Using Integrated CFD-CSD Simulations

2012 ◽  
Author(s):  
Jiho You ◽  
Jinmo Lee ◽  
Donghyun You
Keyword(s):  
Structural Dynamics ◽  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Computational Simulation ◽  
Moving Boundaries ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Navier Stokes Equations ◽  
Simulation Methodology ◽  
Computational Structural Dynamics

A computational simulation methodology, which combines a computational fluid dynamics technique and a computational structural dynamics technique, is employed to design a deformable foil of which kinematics is inspired by the propulsive motion of a fin or a tail of fish and cetacean. The unsteady incompressible Navier-Stokes equations are solved using a second-order accurate finite-difference method and an immersed-boundary method to effectively impose boundary conditions on complex moving boundaries. A finite-element-based structural dynamics solver is employed to compute the deformation of the foil due to interaction with fluid. A phase angle between pitching and heaving motions as well as the flexibility of the foil, which is represented by the Youngs modulus are varied to find out how these factors affect the propulsion efficiency.

scholarly journals PHASE TRANSITION IN QUANTUM GRAVITY?

1999 ◽  
Vol 14 (16) ◽  
pp. 1079-1082
Author(s):  
VIQAR HUSAIN ◽  
SEBASTIAN JAIMUNGAL
Keyword(s):  
Phase Transition ◽  
General Relativity ◽  
Quantum Gravity ◽  
Fundamental Problem ◽  
Critical Energy ◽  
Energy Scale ◽  
Classical Symmetry ◽  
Metric Functions ◽  
Theory Calculation ◽  
Rule Out

A fundamental problem with attempting to quantize general relativity is its perturbative non-renormalizability. However, this fact does not rule out the possibility that nonperturbative effects can be computed, at least in some approximation. We outline a quantum field theory calculation, based on general relativity as the classical theory, which implies a phase transition in quantum gravity. The order parameters are composite fields derived from space–time metric functions. These are massless below a critical energy scale and become massive above it. There is a corresponding breaking of classical symmetry.

Simulation on the Process of Cavity Wall Expansion of Cone at Constant Speed Water-Entry

2013 ◽  
Vol 419 ◽  
pp. 97-102
Author(s):  
Wei Cao ◽  
Chun Tao He ◽  
Cong Wang
Keyword(s):  
Computational Simulation ◽  
Water Entry ◽  
Constant Speed ◽  
Cavity Wall ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Half Angle ◽  
Expansion Dynamic ◽  
Different Depths ◽  
Volume Method

Computational simulation investigation which is based on the Navier-Stokes equation, finite-volume method, dynamic mesh method, and volume of fluid method, was carried out principally on the constant speed vertical water entry of the cone with 75 degree and a half angle. Based on this, the cavity generation and the process of cavity wall expansion of the cone with 75 degree and a half angle were analyzed. Through analyzing the expansion dynamic for the cavity wall in different depths, the velocity and acceleration with time in the process of cavity wall expansion were obtained, and the disturbances and splash feature laws of the free surface near the entrance of the cavity after cones water-entry were analyzed too.

The Effects of Hydrodynamics Characteristics on Mass Transfer During Droplet Formation Using Computational Approach

2006 ◽  
Author(s):  
A. Javadi ◽  
M. Taeibi-Rahni ◽  
D. Bastani ◽  
K. Javadi
Keyword(s):  
Mass Transfer ◽  
Stokes Equations ◽  
Computational Simulation ◽  
Mass Transfer Rate ◽  
Droplet Formation ◽  
Continuous Phase ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Two Phases ◽  
Expansion Model

For the reason that flow expansion model (developed in our previous work) for evaluating mass transfer during droplet formation involves with manifest hydrodynamic aspects, in this research computational simulation of this phenomenon was done for characterization of hydrodynamics effects on the mass transfer during droplet formation. For this purpose, an Eulerian volume tracking computational code based on volume of fluid (VOF) method was developed to solve the transient Navier-Stokes equations for the axisymmetric free-boundary problem of a Newtonian liquid that is dripping vertically and breaking as drops into another immiscible Newtonian fluid. The effects of hydrodynamics effects on the mass transfer during droplet formation have been discussed in the three features, including: 1- The intensity of the interaction between two phases 2-The strength and positions of the main vorticities on the nozzle tip 3-The effects of local interfacial vorticities (LIV). These features are considered to explain the complexities of drop formation mass transfer between Ethyl Acetoacetate (presaturated with water) as an organic dispersed phase and water as continuous phase for two big and small nozzle sizes (0.023 and 0.047 cm, ID) which have different level of mass transfer rate particularly in first stages of formation time.

scholarly journals About general solutions of Euler’s and Navier-Stokes equations

2019 ◽  
pp. 190-193
Author(s):  
V. I. Rozumniuk
Keyword(s):  
General Solution ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Fundamental Problem ◽  
Diffusion Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
General Solutions ◽  
And Diffusion

Constructing a general solution to the Navier-Stokes equation is a fundamental problem of current fluid mechanics and mathematics due to nonlinearity occurring when moving to Euler’s variables. A new transition procedure is proposed without appearing nonlinear terms in the equation, which makes it possible constructing a general solution to the Navier-Stokes equation as a combination of general solutions to Laplace’s and diffusion equations. Existence, uniqueness, and smoothness of the solutions to Euler's and Navier-Stokes equations are found out with investigating solutions to the Laplace and diffusion equations well-studied.

scholarly journals Numerical Study of a Turbulent Burner by Means of RANS and Detailed Chemistry

2019 ◽  
Vol 3 (2) ◽  
pp. 34
Author(s):  
Mohamed Hafid
Keyword(s):  
Schmidt Number ◽  
Numerical Study ◽  
Turbulent Flame ◽  
Navier Stokes ◽  
Turbulent Dissipation ◽  
Detailed Chemistry ◽  
Turbulent Schmidt Number ◽  
Complex Models ◽  
Pdf Model ◽  
Probability Density Function Pdf

The present paper shows a numerical study of the Co-flow turbulent flame configuration using the Reynolds Averaged Navier-Stokes (RANS) modelling with detailed chemistry. The presumed Probability Density Function (PDF) model combined with the k-Ɛ turbulence model is adopted. The GRI Mech-3.0 mechanism that involves 53 species and 325 reactions is used. The effect of the turbulent Schmidt number Sct and the C1ε constant in the turbulent dissipation transport equation is highlighted. Despite the simplicity of RANS approach compared to other complex models such as LES and DNS, the results show that this approach is still able to simulate the turbulent flame.

scholarly journals An Algebraic Reduction of the ‘Scaling Gap’ in the Navier–Stokes Regularity Problem

2018 ◽  
Vol 231 (3) ◽  
pp. 1983-2005
Author(s):  
Zachary Bradshaw ◽  
Aseel Farhat ◽  
Zoran Grujić
Keyword(s):  
Navier Stokes ◽  
Regularity Problem ◽  
Algebraic Reduction
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