scholarly journals New class of turbulence in active fluids

2015 ◽  
Vol 112 (49) ◽  
pp. 15048-15053 ◽  
Author(s):  
Vasil Bratanov ◽  
Frank Jenko ◽  
Erwin Frey
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Spatial Scales ◽  
Finite Size ◽  
Power Laws ◽  
Theoretical Work ◽  
Navier Stokes ◽  
Physical Parameters ◽  
New Class ◽  
General Terms

Turbulence is a fundamental and ubiquitous phenomenon in nature, occurring from astrophysical to biophysical scales. At the same time, it is widely recognized as one of the key unsolved problems in modern physics, representing a paradigmatic example of nonlinear dynamics far from thermodynamic equilibrium. Whereas in the past, most theoretical work in this area has been devoted to Navier–Stokes flows, there is now a growing awareness of the need to extend the research focus to systems with more general patterns of energy injection and dissipation. These include various types of complex fluids and plasmas, as well as active systems consisting of self-propelled particles, like dense bacterial suspensions. Recently, a continuum model has been proposed for such “living fluids” that is based on the Navier–Stokes equations, but extends them to include some of the most general terms admitted by the symmetry of the problem [Wensink HH, et al. (2012) Proc Natl Acad Sci USA 109:14308–14313]. This introduces a cubic nonlinearity, related to the Toner–Tu theory of flocking, which can interact with the quadratic Navier–Stokes nonlinearity. We show that as a result of the subtle interaction between these two terms, the energy spectra at large spatial scales exhibit power laws that are not universal, but depend on both finite-size effects and physical parameters. Our combined numerical and analytical analysis reveals the origin of this effect and even provides a way to understand it quantitatively. Turbulence in active fluids, characterized by this kind of nonlinear self-organization, defines a new class of turbulent flows.

Feedback Control of Turbulence

1994 ◽  
Vol 47 (6S) ◽  
pp. S3-S13 ◽  
Author(s):  
Parviz Moin ◽  
Thomas Bewley
Keyword(s):  
Feedback Control ◽  
Turbulent Flows ◽  
Systems Approach ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Flow Equations ◽  
Active Feedback ◽  
Active Feedback Control ◽  
Mathematical Techniques

A brief review of current approaches to active feedback control of the fluctuations arising in turbulent flows is presented, emphasizing the mathematical techniques involved. Active feedback control schemes are categorized and compared by examining the extent to which they are based on the governing flow equations. These schemes are broken down into the following categories: adaptive schemes, schemes based on heuristic physical arguments, schemes based on a dynamical systems approach, and schemes based on optimal control theory applied directly to the Navier-Stokes equations. Recent advances in methods of implementing small scale flow control ideas are also reviewed.

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.

Parameter Extension Simulation of Turbulent Flows in a Compressor Cascade With a High Reynolds Number

2020 ◽  
Author(s):  
Yan Jin
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Potential Method ◽  
Navier Stokes ◽  
Reference Solution ◽  
Compressor Cascade ◽  
High Reynolds

Abstract The turbulent flow in a compressor cascade is calculated by using a new simulation method, i.e., parameter extension simulation (PES). It is defined as the calculation of a turbulent flow with the help of a reference solution. A special large-eddy simulation (LES) method is developed to calculate the reference solution for PES. Then, the reference solution is extended to approximate the exact solution for the Navier-Stokes equations. The Richardson extrapolation is used to estimate the model error. The compressor cascade is made of NACA0065-009 airfoils. The Reynolds number 3.82 × 105 and the attack angles −2° to 7° are accounted for in the study. The effects of the end-walls, attack angle, and tripping bands on the flow are analyzed. The PES results are compared with the experimental data as well as the LES results using the Smagorinsky, k-equation and WALE subgrid models. The numerical results show that the PES requires a lower mesh resolution than the other LES methods. The details of the flow field including the laminar-turbulence transition can be directly captured from the PES results without introducing any additional model. These characteristics make the PES a potential method for simulating flows in turbomachinery with high Reynolds numbers.

Modal Decomposition and Linear Modeling of Swirl Fluctuations in the Mixing Section of a Model Combustor Based on PIV Data

2021 ◽  
Author(s):  
Jens Satria Müller ◽  
Finn Lückoff ◽  
Thomas Ludwig Kaiser ◽  
Christian Oliver Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Acoustic Waves ◽  
Stokes Equations ◽  
Flow Instability ◽  
Theoretical Work ◽  
Navier Stokes ◽  
Inertial Waves ◽  
Linear Modeling ◽  
Swirl Combustor ◽  
Time Resolved ◽  
Flow Response

Abstract In order to determine the flame transfer function of a combustion system only based on isothermal flow field data, three governing mechanisms have been identified which need to be modeled: swirl fluctuations, equivalence fluctuations and velocity fluctuations excited by planar acoustic waves. This study focuses on the generation and propagation of swirl fluctuations downstream of a radial swirl combustor under isothermal conditions. Swirl fluctuations are generated experimentally by imposing acoustic perturbations. Time-resolved longitudinal and crosswise PIV measurements are conducted inside the mixing tube and combustion chamber to quantify the evolution of the swirl fluctuations. The measured flow response is decomposed using spectral proper orthogonal decomposition to unravel the contributions of different dynamical modes. In addition a resolvent analysis is conducted based on the linearized Navier-Stokes equations to reveal the intrinsically most amplified flow structures. Both, the data-driven and analytic approach, show that inertial waves are indeed present in the flow response and an inherent flow instability downstream of the swirler, which confirms the recent theoretical work of Albayrak et al. (Journal of Fluid Mechanics, 879). However, the contribution of these inertial waves to the total swirl fluctuations turns out to be very small. This is suggested to be due to the very structured forcing at the swirler and the amplification of shear-driven modes which are expected to be much more influential for this type of swirler. Overall, this work confirms the presence of inertial waves in highly turbulent swirl combustors and evaluates its relevance for industry-related configurations. It further outlines a methodology to analyze and predict their characteristics based on mean fields only, which is applicable for complex geometries of industrial relevance.

scholarly journals Development of a Three-Dimensional Geometry Optimization Method for Turbomachinery Applications

2004 ◽  
Vol 10 (5) ◽  
pp. 373-385
Author(s):  
Steffen Kämmerer ◽  
Jürgen F. Mayer ◽  
Heinz Stetter ◽  
Meinhard Paffrath ◽  
Utz Wever ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Optimization Techniques ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Flow Solver ◽  
Flow Simulations ◽  
Sensitivity Equations

This article describes the development of a method for optimization of the geometry of three-dimensional turbine blades within a stage configuration. The method is based on flow simulations and gradient-based optimization techniques. This approach uses the fully parameterized blade geometry as variables for the optimization problem. Physical parameters such as stagger angle, stacking line, and chord length are part of the model. Constraints guarantee the requirements for cooling, casting, and machining of the blades.The fluid physics of the turbomachine and hence the objective function of the optimization problem are calculated by means of a three-dimensional Navier-Stokes solver especially designed for turbomachinery applications. The gradients required for the optimization algorithm are computed by numerically solving the sensitivity equations. Therefore, the explicitly differentiated Navier-Stokes equations are incorporated into the numerical method of the flow solver, enabling the computation of the sensitivity equations with the same numerical scheme as used for the flow field solution.This article introduces the components of the fully automated optimization loop and their interactions. Furthermore, the sensitivity equation method is discussed and several aspects of the implementation into a flow solver are presented. Flow simulations and sensitivity calculations are presented for different test cases and parameters. The validation of the computed sensitivities is performed by means of finite differences.

Turbulent Flows Through a Disk-Type Prosthetic Heart Valve

1983 ◽  
Vol 105 (3) ◽  
pp. 263-267 ◽  
Author(s):  
W. J. Yang ◽  
J. H. Wang
Keyword(s):  
Turbulent Flows ◽  
Heart Valve ◽  
Stokes Equations ◽  
Turbulent Viscosity ◽  
Prosthetic Heart Valve ◽  
Equation Model ◽  
Velocity Shear ◽  
Navier Stokes ◽  
Normal Stresses

A numerical model is developed to predict the complex velocity, shear and pressure fields in steady turbulent flow through a disk-type prosthetic heart valve in a constant diameter chamber. The governing Navier-Stokes equations are reduced to a set of simultaneous algebraic finite-difference equations which are solved by a fast-converging line-iterations technique. A two-parameter, two-equation model is employed to determine the turbulent viscosity. Numerical results are obtained for stream function, vorticity, and shear and normal stresses. The regions of very high shear and normal stresses in the fluid and at the walls are identified. The maximum value of the shear stress occurring near the upstream corner of the disk may cause hemolysis. The technique can be used together with in-vitro physcial experiments to evaluate existing or future prosthetic heart valve designs.

Use of Experimental Data for an Efficient Description of Turbulent Flows

1990 ◽  
Vol 43 (5S) ◽  
pp. S240-S245 ◽  
Author(s):  
N. Aubry
Keyword(s):  
Experimental Data ◽  
Turbulent Flows ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Original System ◽  
Navier Stokes ◽  
Lorenz Attractor ◽  
Wall Region ◽  
Lorenz Equations ◽  
Chaotic Solution

The proper orthogonal decomposition (POD), also called Karhunen-Loe`ve expansion, which extracts ‘coherent structures’ from experimental data, is a very efficient tool for analyzing and modeling turbulent flows. It has been shown that it converges faster than any other expansion in terms of kinetic energy (Lumley 1970). First, the POD is applied to the chaotic solution of the Lorenz equations. The dynamics of the Lorenz attractor is reconstructed by only the first three POD modes. In the second part of this paper, we show how the POD can be used in turbulence modeling. The particular case studied is the wall region of a turbulent boundary layer. In this flow, the velocity field is expanded into POD modes in the normal direction and Fourier modes in the streamwise and spanwise directions. Dynamical systems are obtained by Galerkin projections of the Navier Stokes equations onto the different modes. Aubry et al. (1988) applied the technique to derive and study a ten dimensional representation which reproduced qualitatively the bursting event experimentally observed. It is shown that streamwise modes, absent in Aubry et al.’s model, participate to the bursting events. This agrees remarkably well with experimental observations. In both examples, the dynamics of the original system is very well recovered from the contribution of only a few modes.

scholarly journals The emergence of localized vortex–wave interaction states in plane Couette flow

2013 ◽  
Vol 721 ◽  
pp. 58-85 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall ◽  
Andrew Walton
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Critical Layer ◽  
Navier Stokes ◽  
Turbulent Spots ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractThe recently understood relationship between high-Reynolds-number vortex–wave interaction theory and computationally generated self-sustaining processes provides a possible route to an understanding of some of the underlying structures of fully turbulent flows. Here vortex–wave interaction (VWI) theory is used in the long streamwise wavelength limit to continue the development found at order-one wavelengths by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). The asymptotic description given reduces the Navier–Stokes equations to the so-called boundary-region equations, for which we find equilibrium states describing the change in the VWI as the wavelength of the wave increases from $O(h)$ to $O(Rh)$, where $R$ is the Reynolds number and $2h$ is the depth of the channel. The reduced equations do not include the streamwise pressure gradient of the perturbation or the effect of streamwise diffusion of the wave–vortex states. The solutions we calculate have an asymptotic error proportional to ${R}^{- 2} $ when compared to the full Navier–Stokes equations. The results found correspond to the minimum drag configuration for VWI states and might therefore be of relevance to the control of turbulent flows. The key feature of the new states discussed here is the thickening of the critical layer structure associated with the wave part of the flow to completely fill the channel, so that the roll part of the flow is driven throughout the flow rather than as in Hall & Sherwin as a stress discontinuity across the critical layer. We identify a critical streamwise wavenumber scaling, which, when approached, causes the flow to localize and take on similarities with computationally generated or experimentally observed turbulent spots. In effect, the identification of this critical wavenumber for a given value of the assumed high Reynolds number fixes a minimum box length necessary for the emergence of localized structures. Whereas nonlinear equilibrium states of the Navier–Stokes equations are thought to form a backbone on which turbulent flows hang, our results suggest that the localized states found here might play a related role for turbulent spots.

Approximation of attractors, large eddy simulations and multiscale methods

1991 ◽  
Vol 434 (1890) ◽  
pp. 23-39 ◽  
Keyword(s):  
Turbulent Flows ◽  
Mathematical Theory ◽  
Stokes Equations ◽  
Multiscale Methods ◽  
Large Eddy Simulations ◽  
Navier Stokes ◽  
Theory Approach ◽  
Navier Stokes Equations ◽  
Approximate Inertial Manifolds ◽  
Large Eddy

Recent advances in the mathematical theory of the Navier-Stokes equations have produced new insight in the mathematical theory of turbulence. In particular, the study of the attractor for the Navier-Stokes equations produced the first connection between two approaches to turbulence that seemed far apart, namely the conventional approach of Kolmogorov and the dynamical systems theory approach. Similarly the study of the approximation of the attractor in connection with the newly introduced concept of approximate inertial manifolds has produced a new approach to large eddy simulations and the study of the interaction of small and large eddies in turbulent flows. Our aim in this article is to survey and describe some of the new results concerning the functional properties of the Navier-Stokes equations and to discuss their relevance to turbulence.

Sign in / Sign up

Export Citation Format

Share Document