Vorticity Transport Analysis of Turbulent Flows

1995 ◽  
Vol 117 (3) ◽  
pp. 410-416 ◽  
Author(s):  
J. J. Gorski ◽  
P. S. Bernard
Keyword(s):  
Turbulent Flows ◽  
Transport Theory ◽  
Stokes Equations ◽  
Transport Model ◽  
Plate Boundary ◽  
Separated Flow ◽  
Flow Region ◽  
Leeward Side ◽  
Mean Flow ◽  
Vorticity Transport

Turbulence closure for the Reynolds averaged Navier-Stokes equations based on vorticity transport theory is investigated. General expressions for the vorticity transport correlation terms in arbitrary two-dimensional mean flows are derived. Direct numerical simulation data for flow in a channel is used to evaluate the modeled terms and set unknown scales. Results are presented for a channel, flat plate boundary layer, and flow over a hill. The computed mean flow and kinetic energy compares well with numerical and physical experiments. The vorticity transport model appears to perform better than conventional Boussinesq eddy viscosity Reynolds stress models near the separated flow region on the leeward side of the hill.

scholarly journals Modification of Airflow Structure Due to Wave Breaking on a Submerged Topography

2021 ◽  
Author(s):  
Petter Vollestad ◽  
Atle Jensen
Keyword(s):  
Wind Wave ◽  
Separated Flow ◽  
Flow Region ◽  
Breaking Waves ◽  
Leeward Side ◽  
Geometrical Properties ◽  
Image Velocimetry ◽  
Wind Profiles ◽  
The Waves ◽  
Sheltered Area

AbstractExperimental results from a combined wind–wave tank are presented. Wind profiles and resulting wind–wave spectra are described, and an investigation of the airflow above breaking waves is presented. Monochromatic waves created by the wave maker are directed towards a submerged topography. This causes the waves to break at a predictable location, facilitating particle-image-velocimetry measurements of the airflow above steep breaking and non-breaking waves. We analyze how the breaking state modifies the airflow structure, and in particular the extent of the sheltered area on the leeward side of the waves. Results illustrate that while the geometrical properties of the waves greatly influence the airflow structure on the leeward side of the waves, the state of breaking (i.e., whether the waves are currently in a state of active breaking) is not observed to have a clear effect on the extent of the separated flow region, or on the velocity distribution within the sheltered region.

scholarly journals THE INFLUENCE OF THE TURBULENCE CLOSURE MODEL ON WAVE-CURRENT INTERACTION MODELING AT A LOCAL SCALE AT A LOCAL SCALE

2012 ◽  
Vol 1 (33) ◽  
pp. 64
Author(s):  
Maria João Teles ◽  
António Pires-Silva ◽  
Michel Benoit
Keyword(s):  
Numerical Simulations ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Local Scale ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Turbulence Effects ◽  
Interaction Modeling ◽  
Flow Components

An advanced CFD solver based on the RANS (Reynolds Averaged Navier-Stokes) equations is used to evaluate wave-current interactions through numerical simulations of combined wave-current free surface turbulent flows. The repercussions of various schemes for modeling turbulence effects is addressed with a special attention to the exchanges and fluxes of momentum and energy between the mean flow components and the wave (oscillatory) component. Numerical simulations are compared with experimental data from Klopman (1994).

scholarly journals Linear iterative method for closed-loop control of quasiperiodic flows

2019 ◽  
Vol 868 ◽  
pp. 26-65 ◽  
Author(s):  
Colin Leclercq ◽  
Fabrice Demourant ◽  
Charles Poussot-Vassal ◽  
Denis Sipp
Keyword(s):  
Turbulent Flows ◽  
Linear Models ◽  
Stokes Equations ◽  
Linear Time ◽  
Base Flow ◽  
Nonlinear Flow ◽  
Mean Flow ◽  
Loop Control ◽  
Linear Controller ◽  
The Mean

This work proposes a feedback-loop strategy to suppress intrinsic oscillations of resonating flows in the fully nonlinear regime. The frequency response of the flow is obtained from the resolvent operator about the mean flow, extending the framework initially introduced by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to study receptivity mechanisms in turbulent flows. Using this linear time-invariant model of the nonlinear flow, modern control methods such as structured ${\mathcal{H}}_{\infty }$-synthesis can be used to design a controller. The approach is successful in damping self-sustained oscillations associated with specific eigenmodes of the mean-flow spectrum. Despite excellent performance, the linear controller is however unable to completely suppress flow oscillations, and the controlled flow is effectively attracted towards a new dynamical equilibrium. This new attractor is characterized by a different mean flow, which can in turn be used to design a second controller. The method can then be iterated on subsequent mean flows, until the coupled system eventually converges to the base flow. An intuitive parallel can be drawn with Newton’s iteration: at each step, a linearized model of the flow response to a perturbation of the input is sought, and a new linear controller is designed, aiming at further reducing the fluctuations. The method is illustrated on the well-known case of two-dimensional incompressible open-cavity flow at Reynolds number $Re=7500$, where the fully developed flow is initially quasiperiodic (2-torus state). The base flow is reached after five iterations. The present work demonstrates that nonlinear control problems may be solved without resorting to nonlinear reduced-order models. It also shows that physically relevant linear models can be systematically derived for nonlinear flows, without resorting to black-box identification from input–output data; the key ingredient being frequency-domain models based on the linearized Navier–Stokes equations about the mean flow. Applicability to amplifier flows and turbulent dynamics has, however, yet to be investigated.

Pulsatile Albumin Transport in Large Arteries: A Numerical Simulation Study

1996 ◽  
Vol 118 (4) ◽  
pp. 511-519 ◽  
Author(s):  
G. Rappitsch ◽  
K. Perktold
Keyword(s):  
Pulsatile Flow ◽  
Stokes Equations ◽  
Separated Flow ◽  
Flow Region ◽  
Navier Stokes ◽  
Permeability Model ◽  
Navier Stokes Equations ◽  
Area Reduction ◽  
Stenosed Artery ◽  
Percent Area

Albumin transport in a stenosed artery configuration is analyzed numerically under steady and pulsatile flow conditions. The flow dynamics is described applying the incompressible Navier-Stokes equations for Newtonian fluids, the mass transport is modelled using the convection diffusion equation. The boundary conditions describing the solute wall flux take into account the concept of endothelial resistance to albumin flux by means of a shear dependent permeability model based on experimental data. The study concentrates on the influence of steady and pulsatile flow patterns and of regional variations in vascular geometry on the solute wall flux and on the ratio of endothelial resistance to concentration boundary layer resistance. The numerical solution of the Navier-Stokes equations and of the transport equation applies the finite element method where stability of the convection dominated transport process is achieved by using an upwind procedure and a special subelement technique. Numerical simulations are carried out for albumin transport in a stenosed artery segment with 75 percent area reduction representing a late stage in the progression of an atherosclerotic disease. It is shown that albumin wall flux varies significantly along the arterial section, is strongly dependent upon the different flow regimes and varies considerably during a cardiac cycle. The comparison of steady results and pulsatile results shows differences up to 30 percent between time-averaged flux and steady flux in the separated flow region downstream the stenosis.

Direct numerical simulation of separated flow in a three-dimensional diffuser

2010 ◽  
Vol 650 ◽  
pp. 307-318 ◽  
Author(s):  
JOHAN OHLSSON ◽  
PHILIPP SCHLATTER ◽  
PAUL F. FISCHER ◽  
DAN S. HENNINGSON
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Turbulent Flows ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Separated Flow ◽  
Spectral Element ◽  
Mean Flow ◽  
Development Section ◽  
Inflow Condition

A direct numerical simulation (DNS) of turbulent flow in a three-dimensional diffuser at Re = 10000 (based on bulk velocity and inflow-duct height) was performed with a massively parallel high-order spectral element method running on up to 32768 processors. Accurate inflow condition is ensured through unsteady trip forcing and a long development section. Mean flow results are in good agreement with experimental data by Cherry et al. (Intl J. Heat Fluid Flow, vol. 29, 2008, pp. 803–811), in particular the separated region starting from one corner and gradually spreading to the top expanding diffuser wall. It is found that the corner vortices induced by the secondary flow in the duct persist into the diffuser, where they give rise to a dominant low-speed streak, due to a similar mechanism as the ‘lift-up effect’ in transitional shear flows, thus governing the separation behaviour. Well-resolved simulations of complex turbulent flows are thus possible even at realistic Reynolds numbers, providing accurate and detailed information about the flow physics. The available Reynolds stress budgets provide valuable references for future development of turbulence models.

Modeling the Transport of Fuel Mixture Perturbations and Entropy Waves in the Linearized Framework

2020 ◽  
Author(s):  
Thomas Ludwig Kaiser ◽  
Kilian Oberleithner
Keyword(s):  
Turbulent Flows ◽  
Channel Flow ◽  
Turbulent Mixing ◽  
Equivalence Ratio ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Computational Domain ◽  
Reynolds Stresses ◽  
Mean Flow

Abstract In this paper a new method is introduced to model the transport of entropy waves and equivalence ratio fluctuations in turbulent flows. The model is based on the Navier-Stokes equations and includes a transport equation for a passive scalar, which may stand for entropy or equivalence ratio fluctuations. The equations are linearized around the mean turbulent fields, which serve as the input to the model in addition to a turbulent eddy viscosity, which accounts for turbulent diffusion of the perturbations. Based on these inputs, the framework is able to predict the linear response of the flow velocity and passive scalar to harmonic perturbations that are imposed at the boundaries of the computational domain. These in this study are fluctuations in the passive scalar and/or velocities at the inlet of a channel flow. The code is first validated against analytic results, showing very good agreement. Then the method is applied to predict the convection, mean flow dispersion and turbulent mixing of passive scalar fluctuations in a turbulent channel flow, which has been studied in previous work with Direct Numerical Simulations (DNS). Results show that our code reproduces the dynamics of coherent passive scalar transport in the DNS with very high accuracy and low numerical costs, when the DNS mean flow and Reynolds stresses are provided. Furthermore, we demonstrate that turbulent mixing has a significant effect on the transport of the passive scalar fluctuations. Finally, we apply the method to explain experimental observations of transport of equivalence ratio fluctuations in the mixing duct of a model burner.

Flow Characteristics Inside Circular Injection Holes Normally Oriented to a Crossflow: Part I — Flow Visualizations and Flow Data in the Symmetry Plane

2000 ◽  
Vol 123 (2) ◽  
pp. 266-273 ◽  
Author(s):  
Sang Woo Lee ◽  
Sang Won Park ◽  
Joon Sik Lee
Keyword(s):  
Separation Bubble ◽  
Symmetry Plane ◽  
Flow Region ◽  
Windward Side ◽  
Leeward Side ◽  
Flow Data ◽  
Mean Flow ◽  
Injection Hole ◽  
Potential Core ◽  
Flow Visualizations

Experimental results are presented that describe flow behavior inside circular injection holes with a sharp square-edged inlet. Oil-film flow visualizations and mean flow data are obtained in the flow symmetry plane of injection holes that are normally oriented to a crossflow. Additional visualizations inside inclined holes are also performed for inclination angles of 30 and 60 deg. Data are presented for three different length-to-diameter ratios: L/D=0.5, 1.0, and 2.0. The blowing ratio is fixed at M=2.0 in the flow visualizations and takes the values M=0.5, 1.0, and 2.0 in the flow measurements. The normal-injection flow visualization in the case of L/D=2.0 clearly demonstrates the existence of four distinct near-wall flow regions: an inlet separation region, a reattachment region, a developing region, and a near-exit flow region. When L/D=1.0 and 2.0, an inlet separation bubble is apparent with a clear imprint of recirculating flow traces, especially on the windward side, even though it is not so well organized on the opposite side. For a short hole such as L/D=0.5, however, the separation bubble with flow recirculation seems to be suppressed by the crossflow. Due to the presence of the inlet separation bubble, actual flow passage is in the form of a converging–diverging channel, regardless of the L/D values. In general, the crossflow stabilizes the inside flow on the leeward side, meanwhile destabilizes it on the windward side. On the contrary, the inclination of the injection hole in the leeward direction of the crossflow stabilizes the flow near the windward wall but destabilizes it near the leeward wall. Relatively short holes such as L/D=0.5 and 1.0 do not allow the boundary-layer development on the wall. Particularly in the case of L/D=0.5, a direct interference is observed between the complicated inlet and exit flows. The inlet flow, however, seems to be isolated from the exit flow for a long hole such as L/D=2.0. It is also found that the potential-core inside the normal injection hole comprises a converging flow region, a diverging flow region, a developing flow region, and a flow region deflected by the crossflow.

Mean flow deformation in a laminar separation bubble: separation and stability characteristics

2010 ◽  
Vol 660 ◽  
pp. 37-54 ◽  
Author(s):  
OLAF MARXEN ◽  
ULRICH RIST
Keyword(s):  
Flat Plate ◽  
Stokes Equations ◽  
Separation Bubble ◽  
Plate Boundary ◽  
Base Flow ◽  
Laminar Separation Bubble ◽  
Mean Flow ◽  
Laminar Separation ◽  
The Mean ◽  
Flow Deformation

The mutual interaction of laminar–turbulent transition and mean flow evolution is studied in a pressure-induced laminar separation bubble on a flat plate. The flat-plate boundary layer is subjected to a sufficiently strong adverse pressure gradient that a separation bubble develops. Upstream of the bubble a small-amplitude disturbance is introduced which causes transition. Downstream of transition, the mean flow strongly changes and, due to viscous–inviscid interaction, the overall pressure distribution is changed as well. As a consequence, the mean flow also changes upstream of the transition location. The difference in the mean flow between the forced and the unforced flows is denoted the mean flow deformation. Two different effects are caused by the mean flow deformation in the upstream, laminar part: a reduction of the size of the separation region and a stabilization of the flow with respect to small, linear perturbations. By carrying out numerical simulations based on the original base flow and the time-averaged deformed base flow, we are able to distinguish between direct and indirect nonlinear effects. Direct effects are caused by the quadratic nonlinearity of the Navier–Stokes equations, are associated with the generation of higher harmonics and are predominantly local. In contrast, the stabilization of the flow is an indirect effect, because it is independent of the Reynolds stress terms in the laminar region and is solely governed by the non-local alteration of the mean flow via the pressure.

Steady and Unsteady Computations of Turbulent Flows Induced by a 4/45° Pitched-Blade Impeller

1999 ◽  
Vol 121 (2) ◽  
pp. 318-329 ◽  
Author(s):  
K. Wechsler ◽  
M. Breuer ◽  
F. Durst
Keyword(s):  
Steady State ◽  
Turbulent Flows ◽  
Turbulence Model ◽  
High Performance ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Computational Effort ◽  
Stirred Tank ◽  
Mean Flow ◽  
Stirred Vessel

The present paper summarizes steady and unsteady computations of turbulent flow induced by a pitched-blade turbine (four blades, 45° inclined) in a baffled stirred tank. Mean flow and turbulence characteristics were determined by solving the Reynolds averaged Navier-Stokes equations together with a standard k-ε turbulence model. The round vessel had a diameter of T = 152 mm. The turbine of diameter T/3 was located at a clearance of T/3. The Reynolds number (Re) of the experimental investigation was 7280, and computations were performed at Re = 7280 and Re = 29,000. Techniques of high-performance computing were applied to permit grid sensitivity studies in order to isolate errors resulting from deficiencies of the turbulence model and those resulting from insufficient grid resolution. Both steady and unsteady computations were performed and compared with respect to quality and computational effort. Unsteady computations considered the time-dependent geometry which is caused by the rotation of the impeller within the baffled stirred tank reactor. Steady-state computations also considered neglect the relative motion of impeller and baffles. By solving the governing equations of motion in a rotating frame of reference for the region attached to the impeller, the steady-state approach is able to capture trailing vortices. It is shown that this steady-state computational approach yields numerical results which are in excellent agreement with fully unsteady computations at a fraction of the time and expense for the stirred vessel configuration under consideration.

Direct numerical simulation of turbulent slope flows up to Grashof number

2017 ◽  
Vol 829 ◽  
pp. 589-620 ◽  
Author(s):  
M. G. Giometto ◽  
G. G. Katul ◽  
J. Fang ◽  
M. B. Parlange
Keyword(s):  
Turbulent Flows ◽  
Outer Layer ◽  
Turbulent Transport ◽  
Vertical Wall ◽  
Flow Region ◽  
Return Flow ◽  
Mean Flow ◽  
Outer Flow ◽  
Pressure Transport ◽  
Surface Buoyancy

Stably stratified turbulent flows over an unbounded, smooth, planar sloping surface at high Grashof numbers are examined using direct numerical simulations (DNS). Four sloping angles ($\unicode[STIX]{x1D6FC}=15^{\circ },30^{\circ },60^{\circ }$ and $90^{\circ }$) and three Grashof numbers ($\mathit{Gr}=5\times 10^{10},1\times 10^{11}$ and $2.1\times 10^{11}$) are considered. Variations in mean flow, second-order statistics and budgets of mean- (MKE) and turbulent-kinetic energy (TKE) are evaluated as a function of $\unicode[STIX]{x1D6FC}$ and $Gr$ at fixed molecular Prandtl number $(Pr=1)$. Dynamic and energy identities are highlighted, which diagnose the convergence of the averaging operation applied to the DNS results. Turbulent anabatic (upward moving warm fluid along the slope) and katabatic (downward moving cold fluid along the slope) regimes are identical for the vertical wall set-up (up to the sign of the along-slope velocity), but undergo a different transition in the mechanisms sustaining turbulence as the sloping angle decreases, resulting in stark differences at low $\unicode[STIX]{x1D6FC}$. In addition, budget equations show how MKE is fed into the system through the imposed surface buoyancy, and turbulent fluctuations redistribute it from the low-level jet (LLJ) nose towards the boundary and outer flow regions. Analysis of the TKE budget equation suggests a subdivision of the boundary layer of anabatic and katabatic flows into four distinct thermodynamical regions: (i) an outer layer, corresponding approximately to the return flow region, where turbulent transport is the main source of TKE and balances dissipation; (ii) an intermediate layer, bounded below by the LLJ and capped above by the outer layer, where the sum of shear and buoyant production overcomes dissipation, and where turbulent and pressure transport terms are a sink of TKE; (iii) a buffer layer, located at $5\lessapprox z^{+}\lessapprox 30$, where TKE is provided by turbulent and pressure transport terms, to balance viscous diffusion and dissipation; and (iv) a laminar sublayer, corresponding to $z^{+}\lessapprox 5$, where the influence of viscosity is significant. $(\cdot )^{+}$ denotes a quantity rescaled in inner units. Interestingly, a zone of global backscatter (energy transfer from the turbulent eddies to the mean flow) is consistently found in a thin layer below the LLJ in both anabatic and katabatic regimes.

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