ON TURBULENCE MODELLING AND THE TRANSITION FROM LAMINAR TO TURBULENT FLOW

2014 ◽  
Vol 56 (1) ◽  
pp. 28-47 ◽  
Author(s):  
LAWRENCE K. FORBES
Keyword(s):  
Stokes Equations ◽  
Alternative Hypothesis ◽  
Turbulent Viscosity ◽  
Three Dimensional ◽  
Navier Stokes ◽  
General Description ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Satisfactory Account ◽  
Tollmien Schlichting

AbstractFluid turbulence is often modelled using equations derived from the Navier–Stokes equations, perhaps with some semi-heuristic closure model for the turbulent viscosity. This paper considers a possible alternative hypothesis. It is argued that regarding turbulence as a manifestation of non-Newtonian behaviour may be a viewpoint of at least comparable validity. For a general description of nonlinear viscosity in a Stokes fluid, it is shown that the flow patterns are indistinguishable from those predicted by the Navier–Stokes equation in one- or two-dimensional geometry, but that fully three-dimensional flows differ markedly. The stability of linearized plane Poiseuille flow to three-dimensional disturbances is then considered, in a Tollmien–Schlichting formulation. It is demonstrated that the flow may become unstable at significantly lower Reynolds numbers than those expected from Navier–Stokes theory. Although similar results are known in sections of the rheological literature, the present work attempts to advance the philosophical viewpoint that turbulence might always be regarded as a non-Newtonian effect, to a degree that is dependent only on the particular fluid in question. Such an approach could give a more satisfactory account of the underlying physics.

scholarly journals Doubly localized states in plane Couette flow

2014 ◽  
Vol 758 ◽  
pp. 1-4 ◽  
Author(s):  
Bruno Eckhardt
Keyword(s):  
Couette Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Linear Instability ◽  
Localized States ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Plane Couette Flow ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

AbstractMuch of our understanding of the transition to turbulence in flows without a linear instability came with the discovery and characterization of fully three-dimensional solutions to the Navier–Stokes equation. The first examples in plane Couette flow were periodic in both spanwise and streamwise directions, and could explain the transitions in small domains only. The presence of localized turbulent spots in larger domains, the spatiotemporal decoherence on larger scales and the ability to trigger turbulence with pointwise perturbations require solutions that are localized in both directions, like the one presented by Brand & Gibson (J. Fluid Mech., vol. 750, 2014, R3). They describe a steady solution of the Navier–Stokes equations and characterize in unprecedented detail, including an analytic computation of its localization properties. The study opens up new ways to describe localized turbulent patches.

scholarly journals About local fractional three-dimensional compressible Navier-Stokes equations in Cantor-type cylindrical co-ordinate system

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 847-851 ◽  
Author(s):  
Guo-Ping Gao ◽  
Carlo Cattani ◽  
Xiao-Jun Yang
Keyword(s):  
Fractional Derivative ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Local Fractional Derivative

In this article, we investigate the local fractional 3-D compressible Navier-Stokes equation via local fractional derivative. We use the Cantor-type cylindrical co-ordinate method to transfer 3-D compressible Navier-Stokes equation from the Cantorian co-ordinate system to the Cantor-type cylindrical co-ordinate system.

scholarly journals On three-dimensional incompressible Navier-Stokes fluid on cantor sets in spherical Cantor type co-ordinate system

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 853-858
Author(s):  
Zhi-Jun Meng ◽  
Yao-Ming Zhou ◽  
Dong-Mu Mei
Keyword(s):  
Heat Conduction ◽  
Stokes Equations ◽  
Heat Conduction Problem ◽  
Three Dimensional ◽  
Cantor Sets ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Stokes Fluid ◽  
Incompressible Navier Stokes Equation

This paper addresses the systems of the incompressible Navier-Stokes equations on Cantor sets without the external force involving the fractal heat-conduction problem vial local fractional derivative. The spherical Cantor type co-ordinate method is used to transfer the incompressible Navier-Stokes equation from the Cantorian co-ordinate system into the spherical Cantor type co-ordinate system.

scholarly journals On the existence and uniqueness of solutions to stochastic three-dimensional Lagrangian averaged Navier–Stokes equations

2005 ◽  
Vol 462 (2066) ◽  
pp. 459-479 ◽  
Author(s):  
Tomás Caraballo ◽  
José Real ◽  
Takeshi Taniguchi
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Stochastic Version ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

We prove the existence and uniqueness of solutions for a stochastic version of the three-dimensional Lagrangian averaged Navier–Stokes equation in a bounded domain. To this end, we previously prove some existence and uniqueness results for an abstract stochastic equation and justify that our model falls within this framework.

scholarly journals The Modelling of Flow in the Volute and Vanes of a High Pressure Radial Inflow Turbine

1993 ◽  
Author(s):  
M. Lobo ◽  
R. L. Elder
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
General Description ◽  
Navier Stokes Equations ◽  
Flow Modelling ◽  
Comparison With Experiment ◽  
Flow Features ◽  
Radial Inflow Turbine

The flow in a vaned volute of a radial inflow turbine is analysed using PHOENICS, a very general three-dimensional viscous CFD code based on finite-volume pressure-correction techniques for solving the Navier-Stokes equations. The study involves two physically complementary but mathematically very different problems — flow modelling in the vaneless section of the volute and flow modelling in the vanes. Each of these problems is considered in turn — and each presents characteristic hurdles. Particular attention is paid to grid-generation and the process is carried out alongside the flow computation, the grids being modified in such a way so as to facilitate convergence and accuracy. Numerical results are presented in the form of vector plots for purposes of general description and tables for comparison with experiment. Agreement with experiment is good. However experimental results, for comparison are available only in the vanes. In the vaneless section of the volute, the converged solution depicts some interesting secondary flow features — in regions inaccesible to the current experimental measurements.

scholarly journals Exact coherent structures at extreme Reynolds number

2016 ◽  
Vol 794 ◽  
pp. 1-4 ◽  
Author(s):  
G. P. Chini
Keyword(s):  
Reynolds Number ◽  
Coherent Structures ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Navier Stokes Equations ◽  
Wall Flows ◽  
Tollmien Schlichting ◽  
Turbulent Wall

Exact coherent structures (ECS), unstable three-dimensional solutions of the Navier–Stokes equations, play a fundamental role in transitional and turbulent wall flows. Dempsey et al. (J. Fluid Mech., vol. 791, 2016, pp. 97–121) demonstrate that at large Reynolds number reduced equations can be derived that simplify the computation and facilitate mechanistic understanding of these solutions. Their analysis shows that ECS in plane Poiseuille flow can be sustained by a novel inner–outer interaction between oblique near-wall Tollmien–Schlichting waves and interior streamwise vortices.

Numerical investigation of the interaction of the Klebanoff-mode with a Tollmien–Schlichting wave

2002 ◽  
Vol 450 ◽  
pp. 1-33 ◽  
Author(s):  
HERMANN F. FASEL
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Low Frequency ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Free Stream Turbulence ◽  
Turbulent Transition ◽  
Tollmien Schlichting

Direct numerical simulations (DNS) of the Navier–Stokes equations are used to investigate the role of the Klebanoff-mode in laminar–turbulent transition in a flatplate boundary layer. To model the effects of free-stream turbulence, volume forces are used to generate low-frequency streamwise vortices outside the boundary layer. A suction/blowing slot at the wall is used to generate a two-dimensional Tollmien–Schlichting (TS) wave inside the boundary layer. The characteristics of the fluctuations inside the boundary layer agree very well with those measured in experiments. It is shown how the interaction of the Klebanoff-mode with the two-dimensional TS-wave leads to the formation of three-dimensional TS-wavepackets. When the disturbance amplitudes reach a critical level, a fundamental resonance-type secondary instability causes the breakdown of the TS-wavepackets into turbulent spots.

scholarly journals On the Convergence of Solutions of Globally Modified Navier-Stokes Equations with Delays to Solutions of Navier-Stokes Equations with Delays

2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Pedro Marín-Rubio ◽  
José Real ◽  
Antonio M. Márquez-Durán
Keyword(s):  
Weak Solution ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Additional Case ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Convergence Of Solutions

AbstractWe prove that under suitable assumptions, from a sequence of solutions of Globally Modified Navier-Stokes equations with delays we can extract a subsequence which converges in an adequate sense to a weak solution of a three-dimensional Navier-Stokes equation with delays. An additional case with a family of different delays involved in the approximating problems is also discussed.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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