scholarly journals Space–time dynamics of optimal wavepackets for streaks in a channel entrance flow

2018 ◽  
Vol 844 ◽  
pp. 669-706
Author(s):  
F. Alizard ◽  
A. Cadiou ◽  
L. Le Penven ◽  
B. Di Pierro ◽  
M. Buffat
Keyword(s):  
Turbulent Flows ◽  
Linear Optimization ◽  
Three Dimensional ◽  
Plane Channel ◽  
Base Flow ◽  
Channel Entrance ◽  
Target Time ◽  
Time Dynamics ◽  
Optimal Linear ◽  
Entrance Flow

The laminar–turbulent transition of a plane channel entrance flow is revisited using global linear optimization analyses and direct numerical simulations. The investigated case corresponds to uniform upstream velocity conditions and a moderate value of Reynolds number so that the two-dimensional developing flow is linearly stable under the parallel flow assumption. However, the boundary layers in the entry zone are capable of supporting the development of streaks, which may experience secondary instability and evolve to turbulence. In this study, global optimal linear perturbations are computed and studied in the nonlinear regime for different values of streak amplitude and optimization time. These optimal perturbations take the form of wavepackets having either varicose or sinuous symmetry. It is shown that, for short optimization times, varicose wavepackets grow through a combination of Orr and lift-up effects, whereas for longer target times, both sinuous and varicose wavepackets exhibit an instability mechanism driven by the presence of inflection points in the streaky flow. In addition, while the optimal varicose modes obtained for short optimization times are localized near the inlet, where the base flow is strongly three-dimensional, when the target time is increased, the sinuous and varicose optimal modes are displaced farther downstream, in the nearly parallel streaky flow. Finally, the optimal wavepackets are found to lead to turbulence for sufficiently high initial amplitudes. It is noticed that the resulting turbulent flows have the same wall-shear stress, whether the wavepackets have been obtained for short or for long time optimization.

Final stages of transition to turbulence in plane channel flow

1984 ◽  
Vol 148 ◽  
pp. 413-442 ◽  
Author(s):  
S. Biringen
Keyword(s):  
Flow Field ◽  
Turbulent Flows ◽  
Channel Flow ◽  
Stokes Equations ◽  
Flow Direction ◽  
Three Dimensional ◽  
Plane Channel ◽  
Turbulent Channel Flow ◽  
Transition To Turbulence ◽  
Plane Channel Flow

This paper involves a numerical simulation of the final stages of transition to turbulence in plane channel flow at a Reynolds number of 1500. Three-dimensional incompressible Navier–Stokes equations are numerically integrated to obtain the time evolution of two- and three-dimensional finite-amplitude disturbances. Computations are performed on the CYBER-203 vector processor for a 32 × 51 × 32 grid. Solutions indicate the existence of structures similar to those observed in the laboratory and characteristic of the various stages of transition that lead to final breakdown. In particular, evidence points to the formation of a A-shaped vortex and the subsequent system of horsehoe vortices inclined to the main flow direction as the primary elements of transition. Details of the resulting flow field after breakdown indicate the evolution of streaklike formations found in turbulent flows. Although the flow field does approach a steady state (turbulent channel flow), the introduction of subgrid-scale terms seems necessary to obtain fully developed turbulence statistics.

scholarly journals Optimal mixing in three-dimensional plane Poiseuille flow at high Péclet number

2018 ◽  
Vol 850 ◽  
pp. 875-923 ◽  
Author(s):  
L. Vermach ◽  
C. P. Caulfield
Keyword(s):  
Time Horizon ◽  
Initial Perturbation ◽  
Three Dimensional ◽  
Plane Channel ◽  
Concentration Field ◽  
Maximum Flow ◽  
Flow Speed ◽  
Transition To Turbulence ◽  
Target Time ◽  
Dimensional Plane

We consider a passive zero-mean scalar field organised into two layers of different concentrations in a three-dimensional plane channel flow subjected to a constant along-stream pressure gradient. We employ a nonlinear direct-adjoint-looping method to identify the optimal initial perturbation of the velocity field with given initial energy which yields ‘maximal’ mixing by a target time horizon, where maximal mixing is defined here as the minimisation of the spatially integrated variance of the concentration field. We verify in three-dimensional flows the conjecture by Foures et al. (J. Fluid Mech., vol. 748, 2014, pp. 241–277) that the initial perturbation which maximises the time-averaged energy gain of the flow leads to relatively weak mixing, and is qualitatively different from the optimal initial ‘mixing’ perturbation which exploits classical Taylor dispersion. We carry out the analysis for two different Reynolds numbers ($Re=U_{m}h/\unicode[STIX]{x1D708}=500$ and $Re=3000$, where $U_{m}$ is the maximum flow speed of the unperturbed flow, $h$ is the channel half-depth and $\unicode[STIX]{x1D708}$ is the kinematic viscosity of the fluid) demonstrating that this key finding is robust with respect to the transition to turbulence. We also identify the initial perturbations that minimise, at chosen target times, the ‘mix-norm’ of the concentration field, i.e. a Sobolev norm of negative index in the class introduced by Mathew et al. (Physica D, vol. 211, 2005, pp. 23–46). We show that the ‘true’ variance-based mixing strategy can be successfully and practicably approximated by the mix-norm minimisation since we find that the mix-norm-optimal initial perturbations are far less sensitive to changes in the target time horizon than their optimal variance-minimising counterparts.

scholarly journals Numerical Study of Three-Dimensional Surface Jets Emerging from a Fishway Entrance Slot

Water ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1079
Author(s):  
Lena Mahl ◽  
Patrick Heneka ◽  
Martin Henning ◽  
Roman B. Weichert
Keyword(s):  
Boundary Conditions ◽  
Turbulent Flows ◽  
Numerical Study ◽  
Three Dimensional ◽  
Free Water ◽  
Lateral Wall ◽  
Lateral Spreading ◽  
Propagation Length ◽  
Vertical Slot ◽  
Surface Jets

The efficiency of a fishway is determined by the ability of immigrating fish to follow its attraction flow (i.e., its jet) to locate and enter the fishway entrance. The hydraulic characteristics of fishway entrance jets can be simplified using findings from widely investigated surface jets produced by shaped nozzles. However, the effect of the different boundary conditions of fishway entrance jets (characterized by vertical entrance slots) compared to nozzle jets must be considered. We investigate the downstream propagation of attraction jets from the vertical slot of a fishway entrance into a quiescent tailrace, considering the following boundary conditions not considered for nozzle jets: (1) slot geometry, (2) turbulence characteristics of the approach flow to the slot, and (3) presence of a lateral wall downstream of the slot. We quantify the effect of these boundary conditions using three-dimensional hydrodynamic-numeric flow simulations with DES and RANS turbulence models and a volume-of-fluid method (VoF) to simulate the free water surface. In addition, we compare jet propagation with existing analytical methods for describing jet propagations from nozzles. We show that a turbulent and inhomogeneous approach flow towards a vertical slot reduces the propagation length of the slot jet in the tailrace due to increased lateral spreading compared to that of a jet produced by a shaped nozzle. An additional lateral wall in the tailrace reduces lateral spreading and significantly increases the propagation length. For highly turbulent flows at fishway entrances, the RANS model tends to overestimate the jet propagation compared to the transient DES model.

Aspects of Shear Layer Unsteadiness in a Three-Dimensional Supersonic Wake

2005 ◽  
Vol 127 (6) ◽  
pp. 1085-1094 ◽  
Author(s):  
Alan L. Kastengren ◽  
J. Craig Dutton
Keyword(s):  
Shear Layer ◽  
Stream Flow ◽  
Free Stream ◽  
Angle Of Attack ◽  
Three Dimensional ◽  
Base Flow ◽  
Recirculation Region ◽  
Side View ◽  
Near Wake ◽  
Supersonic Wake

The near wake of a blunt-base cylinder at 10° angle-of-attack to a Mach 2.46 free-stream flow is visualized at several locations to study unsteady aspects of its structure. In both side-view and end-view images, the shear layer flapping grows monotonically as the shear layer develops, similar to the trends seen in a corresponding axisymmetric supersonic base flow. The interface convolution, a measure of the tortuousness of the shear layer, peaks for side-view and end-view images during recompression. The high convolution for a septum of fluid seen in the middle of the wake indicates that the septum actively entrains fluid from the recirculation region, which helps to explain the low base pressure for this wake compared to that for a corresponding axisymmetric wake.

scholarly journals Three dimensional flow around a circular cylinder confined in a plane channel

2011 ◽  
Vol 23 (6) ◽  
pp. 064106 ◽  
Author(s):  
Nicolas Kanaris ◽  
Dimokratis Grigoriadis ◽  
Stavros Kassinos
Keyword(s):  
Circular Cylinder ◽  
Three Dimensional ◽  
Plane Channel ◽  
Three Dimensional Flow ◽  
Dimensional Flow

Osborne Reynolds: Energy Methods in Transition and Loss Production: A Centennial Perspective

1995 ◽  
Vol 117 (1) ◽  
pp. 142-153 ◽  
Author(s):  
J. Moore ◽  
J. G. Moore
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flows ◽  
Three Dimensional ◽  
Boundary Layer Transition ◽  
Turbulence Energy ◽  
Energy Methods ◽  
Layer Transition ◽  
Energy Balance Method ◽  
European Working ◽  
Transition Modeling

Osborne Reynolds’ developments of the concepts of Reynolds averaging, turbulence stresses, and equations for mean kinetic energy and turbulence energy are viewed in the light of 100 years of subsequent flow research. Attempts to use the Reynolds energy-balance method to calculate the lower critical Reynolds number for pipe and channel flows are reviewed. The modern use of turbulence-energy methods for boundary layer transition modeling is discussed, and a current European Working Group effort to evaluate and develop such methods is described. The possibility of applying these methods to calculate transition in pipe, channel, and sink flows is demonstrated using a one-equation, q-L, turbulence model. Recent work using the equation for the kinetic energy of mean motion to gain understanding of loss production mechanisms in three-dimensional turbulent flows is also discussed.

Numerical Simulation Study on the Asymmetric Structures of Oscillatory Flow Field in a Baffled Tube Reactor

2004 ◽  
Author(s):  
Yong-Wen Wu ◽  
Jia Wu
Keyword(s):  
Numerical Simulation ◽  
Turbulent Flows ◽  
Oscillatory Flow ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Structured Grid ◽  
Tube Reactor ◽  
Oscillating Boundary ◽  
The Asymmetry ◽  
Laminar And Turbulent Flows

The oscillatory flow in a baffled tube reactor provides a significant enhancement of radial transfer of momentum, heat and mass and a good control of axial back mixing at a wide range of net flow rate. But little has been known about reliable details of the three-dimensional structure of flow field in this kind of flow because most published studies in the area were based on the two-dimensional simulation techniques. This paper implemented a three-dimensional numerical simulation study on the asymmetry of flow pattern in the baffled tube reactor which was observed experimentally. A systematic study by numerical simulation was carried out which covered a range of oscillatory Reynolds number (Reo) from 100 to 5,000 and employed models respectively for laminar and turbulent flows. It was found in the simulation that under symmetric boundary conditions the transition from axially symmetric flow to asymmetric one depended on the numerical technique employed in simulation. With a structured grid frame the transition occurred at Reo much greater than that with an unstructured grid frame, for both laminar and turbulent flows. It is not rational that the onset of the transition changes with the accuracy of numerical technique. Based on the simulation results, it was postulated that the asymmetry appeared in simulations with symmetric boundary conditions might result from the accumulation of calculation errors but the asymmetry observed in experiments might result from the slight asymmetry of geometry which exists inevitably in any experiment apparatus. To explore the influence of the slight asymmetry of geometry, the effect of the eccentricity of baffles and the declination of oscillating boundary were studied by use of the finite volume method with a structured grid and adaptive time steps. The simulation result showed that both the eccentricity of baffles and the declination of oscillating boundary have obvious influence on the asymmetry of flow patterns for laminar and turbulent flow. More details were discussed in the paper.

Experimental and Numerical Investigation of Centrifugal Pump Performance When Handling Viscous Fluids

2005 ◽  
Author(s):  
M. H. Shojaee Fard ◽  
M. B. Ehghaghi ◽  
F. A. Boyaghchi
Keyword(s):  
Soviet Union ◽  
Centrifugal Pump ◽  
Turbulent Flows ◽  
Characteristic Curve ◽  
Three Dimensional ◽  
Operating Conditions ◽  
Viscous Fluids ◽  
Test Bed ◽  
Flow Process ◽  
Pump Performance

On the test bed of centrifugal pump, the centrifugal pump performance has been investigated using water and viscous oil as Newtonian fluids, whose kinematic viscosities are 1 × 10−6, 43 × 10−6 and 62 × 10−6 m2/s, respectively. Also, the finite volume method is used to model the three dimensional viscous fluids for different operating conditions. For these numerical simulations the SIMPLEC algorithm is used for solving governing equations of incompressible viscous/turbulent flows through the pump. The κ-ε turbulence model is adopted to describe the turbulent flow process. These simulations have been made with a steady calculation and using the multiple reference frame (MRF) technique to take into account the impeller-volute interaction. Numerical results are compared with the experimental characteristic curve for each viscous fluid. The data obtained allow the analysis of the main phenomena existent in this pump, such as: head, efficiency, power and pressure field changes for different operating conditions. Also, the correction factors for oils are obtained from the experimental for part loading (PL), best efficiency point (BEP) and over loading (OL) and the results are compared with proposed factors by American Hydraulic Institute (HIS) and Soviet Union (USSR). The comparisons between the numerical and experimental results show a good agreement.

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