Dynamical mode decomposition of Gurney flap wake flow

The present work uses dynamic mode decomposition (DMD) to analyze wake flow of NACA0015 airfoil with Gurney flap. The physics of DMD is first introduced. Then the PIV-measured wake flow velocity field is decomposed into dynamical modes. The vortex shedding pattern behind the trailing edge and its high-order harmonics have been captured with abundant information such as frequency, wavelength and convection speed. It is observed that high-order dynamic modes convect faster than low-order modes; moreover the wavelength of the dynamic modes scales with the corresponding frequency in power law.     

Large-scale computer simulation of fully developed turbulent channel flow with heat transfer

Recently, with the advent of supercomputers, there has been considerable interest in the use of direct numerical simulation to obtain information about turbulent shear flow at low Reynolds number. This paper presents a pseudospectral technique to solve the full three-dimensional time-dependent Navier-Stokes and advection-diffusion equations without the use of subgrid-scale modelling. The technique has not been previously used for fully developed turbulent channel flow simulation and is based on methods applied in other contexts. The emphasis of this paper is to provide a reasonably detailed account of how the simulation is done rather than to present new calculations of turbulence. The details of an algorithm for turbulent channel flow simulation and the grid and time step sizes needed to integrate through transient behaviour to steady state turbulence have not been published before and are presented here. Results from a Cray-2 simulation of fully developed turbulent flow in a channel with heat transfer are presented along with a critical comparison between experiment and computation. The first- and second-order moments agree well with experimental measurements; the agreement is poor for higher-order moments such as the skewness and flatness near the walls of the channel. Detailed information given about the effects of spatial grid resolution on a computed results is important for estimating the size of the computation required to study various aspects of a turbulent flow.     

Large-eddy simulation of turbulent channel flow at transcritical states

We present well-resolved large-eddy simulations (LES) of a channel flow solving the fully compressible Navier–Stokes equations in conservative form. An adaptive look-up table method is used for thermodynamic and transport properties. A physically consistent subgrid-scale turbulence model is incorporated, that is based on the Adaptive Local Deconvolution Method (ALDM) for implicit LES. The wall temperatures are set to enclose the pseudo-boiling temperature at a supercritical pressure, leading to strong property variations within the channel geometry. The hot wall at the top and the cold wall at the bottom produce asymmetric mean velocity and temperature profiles which result in different momentum and thermal boundary layer thicknesses. Different turbulent Prandtl number formulations and their components are discussed in context of strong property variations.     

Interfacial instability in turbulent flow over a liquid film in a channel

We revisit the stability of a deformable interface that separates a fully-developed turbulent gas flow from a thin layer of laminar liquid. Although this problem has received considerable attention previously, a model that requires no fitting parameters and that uses a base-state profile that has been validated against experiments is, as yet, unavailable. Furthermore, the significance of wave-induced perturbations in turbulent stresses remains unclear. To address these outstanding issues, we investigate this problem and introduce a turbulent base-state velocity that requires specification of a flow rate or a pressure drop only; no adjustable parameters are necessary. This base state is validated extensively against available experimental data as well as the results of direct numerical simulations. In addition, the effect of perturbations in the turbulent stress distributions is investigated, and demonstrated to be small for cases wherein the liquid layer is thin. The detailed modelling of the liquid layer also elicits two unstable modes, ‘interfacial’ and ‘internal’, with the former being the more dominant of the two. We show that it is possible for interfacial roughness to reduce the growth rate of the interfacial mode in relation to that of the internal one, promoting the latter, to the status of most dangerous mode. Additionally, we introduce an approximate measure to distinguish between ‘slow’ and ‘fast’ waves, the latter being the case for ‘critical-layer’-induced instabilities; we demonstrate that for the parameter ranges studied, the large majority of the waves are ‘slow’. Finally, comparisons of our linear stability predictions are made with experimental data in terms of critical parameters for onset of wave-formation, wave speeds and wavelengths; these yield agreement within the bounds of experimental error.     

Energy dynamics in a turbulent channel flow using the Karhunen‐Loéve approach

The dynamical equations for the energy in a turbulent channel flow have been developed by using the Karhunen‐Loéve modes to represent the velocity field. The energy balance equations show that all the energy in the flow originates from the applied pressure gradient acting on the mean flow. Energy redistribution occurs through triad interactions, which is basic to understanding the dynamics. Each triad interaction determines the rate of energy transport between source and sink modes via a catalyst mode. The importance of the proposed method stems from the fact that it can be used to determine both the rate of energy transport between modes as well as the direction of energy flow. The effectiveness of the method in determining the mechanisms by which the turbulence sustains itself is demonstrated by performing a detailed analysis of triad interactions occurring during a turbulent burst in a minimal channel flow. The impact on flow modification is discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

The nature of near-wall convection velocity in turbulent channel flow

A novel notion of turbulent structure the local cascade structure-is introduced to study the convection phenomenon in a turbulent channel flow. A space-time cross-correlation method is used to calculate the convection velocity. It is found that there are two characteristic convection speeds near the wall, one associated with small-scale streaks of a lower speed and another with streamwise vortices and hairpin vortices of a higher speed. The new concept of turbulent structure is powerful to illustrate the dominant role of coherent structures in the near-wall convection, and to reveal also the nature of the convection-the propagation of patterns of velocity fluctuations-which is scale-dependent.     

A proper orthogonal decomposition of a simulated supersonic shear layer

The Karhunen–Loève procedure is applied to the analysis of an ensemble of snapshots obtained from a conditionally sampled localized shear layer simulation. The computed set of optimal basis functions is used to economically characterize sampled flow realizations. Pictorially it is seen that the essential features (and roughly 80% of the energy) of typical flows are captured by retaining roughly 10–20 parameters in the expansion. Smaller-scale features are resolved by retaining more terms in the series.     

Examination of wall damping for the k-ε turbulence model using direct simulations of turbulent channel flow

Handler, Hendricks and Leighton have recently reported results for the direct numerical simulation (DNS) of a turbulent channel flow at moderate Reynolds number. These data are used to evaluate the terms in the exact and modelled transport equations for the turbulence kinetic energy k and the isotropic dissipation function ε. Both modelled transport equations show significant imbalances in the high-shear region near the channel walls. The model for the eddy viscosity is found to yield distributions for the production terms which do not agree well with the distributions calculated from the DNS data. The source of the imbalance is attributed to the wall-damping function required in eddy viscosity models for turbulent flows near walls. Several models for the damping function are examined, and it is found that the models do not vary across the channel as does the damping when evaluated from the DNS data. The Lam-Bremhorst model and the standard van Driest model are found to give reasonable agreement with the DNS data. Modification of the van Driest model to include an effective origin yields very good agreement between the modelled production and the production calculated from the DNS data, and the imbalance in the modelled transport equations is significantly reduced.     

Numerical observations of turbulence structure modification in channel flow over 2D and 3D rough walls

The effects of wall roughness on turbulence structure modifications were explored by numerical experiments, carried out using Large Eddy Simulation techniques. The wall geometry was made using an archetypal artificial method, thus to achieve irregular two- and three-dimensional shapes. The proposed roughness shapes are highly irregular and are characterised by high and small peaks, thus it can be considered a practical realistic roughness. Their effects are analysed comparing the turbulence quantities over smooth, 2D and 3D rough walls of fully developed channel flow at relatively low friction Reynolds number ${\mathit{Re}}_{\tau }=395$. Both transitional and fully rough regimes have been investigated. The two rough surfaces were built in such a way that the same mean roughness height and averaged mean deviation is obtained. Despite of this, very different quantitative and qualitative results are generated. The analysis of the mean quantitative statistics and turbulence fluctuations shows that deviations are mainly concentrated in the inner layer. These results support the Townsend’s similarity hypothesis. Among the geometrical parameters, which characterise the wall geometries, roughness slope correlates well with the roughness function $\mathrm{\Delta }{U}^{+}$. Specifically, a logarithmic law is proposed to predict the downward shift of the velocity profile for the transitional regime. Instantaneous view of turbulent organised structures display differences in small-scale structures. The flow field over rough surfaces is populated with coherent structures shorter than those observed over flat planes. The comparative analysis of both streaks and wall-normal vortical structures shows that 2D and 3D irregularities have quite different effects. The results highlight that 3D rough wall are representative of a more realistic surface compared to idealised 2D roughness.     

Modelling a recirculating density-driven turbulent flow

A mathematical model of turbulent density-driven flows is presented and is solved numerically. A form of the k–? turbulence model is used to characterize the turbulent transport, and both this non-linear model and a sediment transport equation are coupled with the mean-flow fluid motion equations. A partitioned, Newton–Raphson-based solution scheme is used to effect a solution. The model is applied to the study of flow through a circular secondary sedimentation basin.     

Characteristic turbulent structure of a modified drag-reduced surfactant solution flow via dosing water from channel wall

The modification of the near-wall structure is very important for the control of wall turbulence. To ascertain the effect of near-wall modulation on the viscoelastic drag-reduced flow, the modified characteristics of a surfactant solution channel flow were investigated experimentally. The modulation was conducted on the boundary of the channel flow by injecting water from the whole surface of one side of the channel wall. The diffusion process of the injected water was observed by using the planar laser-induced fluorescence technique. The velocity statistics and characteristic structure including the spatial distributions of instantaneous streamwise velocity, swirling strength, and Reynolds shear stress were analyzed based on the velocity vectors acquired in the streamwise wall-normal plane by using the particle imaging velocimetry technique. The results indicated that the disturbance of the injected water was constricted within a finite range very near the dosing wall, and the Reynolds shear stress was increased in this region. However, the eventual drag reduction rate was found to be increased due to a relatively large decrement of viscoelastic shear stress in this near-wall region. Moreover, the flow structure under this modulation presented obvious regional characteristics. In the unstable disturbed region, the mixing of high-speed and low-speed fluids and the motions of ejection and sweep occurred actively. Many clockwise vortex cores were also found to be generated. This characteristic structure was similar to that in the ordinary turbulence of Newtonian fluid. Nevertheless, outside this disturbed region, the structure still maintained the characteristics of the drag-reduced flow with non-Newtonian viscoelastic additives. These results proved that the injected Newtonian fluid associated with the modified stress distribution creates a diverse characteristic structure and subsequent enhanced drag reduction. This investigation can provide the experimental basis for further study of turbulence control.     

Linear stability of channel entrance flow

The spatial stability of two dimensional, steady channel flow is investigated in the downstream entry zone for both exponentially and algebraically growing disturbances. A model based on previous work is presented for the base flow which represents a small deformation of plane Poiseuille flow. The base flow evolution towards the fully developed state comes from the experimental and theoretical study of M. Asai and J.M. Floryan [M. Asai, J.M. Floryan, Certain aspects of channel entrance flow, Phys. Fluids 16 (2004) 1160–1163]. This flow is found to be more stable than the parabolic Poiseuille flow. The most destabilizing base flow defect is then calculated using a variational method. The compromise between the destabilizing effect of the defect, which diffuses downstream, and the instability growth is found to be insufficient to provoke transition in the downstream laminar flow.     

Detached direct numerical simulations of turbulent two-phase bubbly channel flow

DNS simulations of two-phase turbulent bubbly channel flow at Re_τ = 180 (Reynolds number based on friction velocity and channel half-width) were performed using a stabilized finite element method (FEM) and a level set approach to track the air/water interfaces.     

Extensional behavior influence on viscoelastic turbulent channel flow

In this work we use in the simulation of a viscoelastic turbulent channel flow a modification of the finitely extensible of non-linear elastic dumbbells with the Peterlin approximation (FENE-P) constitutive model for dilute polymer solutions, applicable to high extensional deformations. The new feature introduced by this modification is that the free energy of the polymer (since it is assumed to be entirely entropically driven) remains always bounded (FENE-PB). The characteristics of the model under steady shear flow, pure elongational flow and transient extensional behavior are presented. It is found that the FENE-PB model is more shear thinning than FENE-P. Most importantly, it also shows a higher extensional viscosity than the FENE-P model. Although the steady-state Trouton ratio asymptotically reaches at high extensional rates the same limit as the FENE-P model, the transition from the Newtonian value is sharper and faster. We use the FENE-PB model in direct numerical simulations (DNS) of viscoelastic turbulent channel flow using spectral approximations. The results for various statistics of the flow and the polymer conformation, when compared against those obtained with the original FENE-P model and the same rheological parameters, show an enhanced polymer-induced drag reduction effect and enhanced deformation of the polymer molecules. This indicates that it is not only the asymptotic but also details from the extensional rheological behavior that matter in quantitatively specifying turbulent viscoelastic flow behavior.     

Hierarchical structures in a turbulent pipe flow

A hierarchical structure (HS) analysis (β-test and γ-test) is applied to a fully developed turbulent pipe flow. Velocity signals are measured at two cross sections in the pipe and at a series of radial locations from the pipe wall. Particular attention is paid to the variation of turbulent statistics at wall units 10<y⁺<3000. It is shown that at all locations the velocity fluctuations satisfy the She–Leveque hierarchical symmetry (Phys. Rev. Lett. 72 (1994) 336). The measured HS parameters, β and γ, are interpreted in terms of the variation of fluid structures. Intense anisotropic fluid structures generated near the wall appear to be more singular than the most intermittent structures in isotropic turbulence and appear to be more outstanding compared to the background fluctuations; this yields a more intermittent velocity signal with smaller γ and β. As turbulence migrates into the logarithmic region, small-scale motions are generated by an energy cascade and large-scale organized structures emerge which are also less singular than the most intermittent structures of isotropic turbulence. At the center, turbulence is nearly isotropic, and β and γ are close to the 1994 She–Leveque predictions. A transition is observed from the logarithmic region to the center in which γ drops and the large-scale organized structures break down. We speculate that it is due to the growing eddy viscosity effects of widely spread turbulent fluctuations in a similar way as in the breakdown of the Taylor vortices in a turbulent Couette–Taylor flow at high Reynolds numbers.     

Temporal large-eddy simulation of unstratified and stably stratified turbulent channel flows

Recently, Pruett et al. [Pruett, C.D., Gatski, T.B., Grosch, C.E., Thacker, W.D., 2003. The temporally filtered Navier–Stokes equations: properties of the residual stress. Phys. Fluids 15, 2127–2140] proposed an approach to large-eddy simulation (LES) based on time-domain filtering; their approach was termed temporal large-eddy simulation or TLES. In a continuation of their work, Pruett and collaborators tested their methodology by successfully performing TLES of unstratified turbulent channel flow up to Reynolds number of 590 (based on channel half-height and friction velocity) [Pruett, C.D., Thomas, B.C., Grosch, C.E., Gatski, T.B., 2006. A temporal approximate deconvolution model for LES. Phys. Fluids 18, 028104, 4p]. Here, we carefully analyze the TLES methodology in order to understand the role of its key components and in the process compare TLES to more traditional approaches of spatial LES. Furthermore, we extend the methodology to stably stratified turbulent channel flow.     

Influence of gravity and lift on particle velocity statistics and transfer rates in turbulent vertical channel flow

The present study reports detailed statistics for velocity and transfer rates of heavy particles dispersed in turbulent boundary layers. Statistics have been extracted from a homogeneous source of data covering a large target parameter space and are used here to analyze the effects of gravity and lift on particle dispersion and deposition in a systematic way. Datasets were obtained performing Direct Numerical Simulation (DNS) of particle-laden turbulent upward/downward flow in a vertical channel. Six values for the particle timescale (the particle Stokes number, St) ranging three orders of magnitude were considered to analyze the deposition process as the controlling mechanism was shifting from turbulent diffusion to inertia-moderated crossing trajectories. For the particle timescales examined, gravity and lift do not influence the qualitative behavior of particles even though velocity profiles and deposition coefficients are modified in a non-monotonic fashion, reaching an optimum for St ? 15. Physical mechanisms for the different behavior are discussed. Raw data and statistics obtained from the present DNS are made available at http://cfd.cineca.it (mirror site: http://158.110.32.35/download/database) and can be used to test simple models and closure equations for multiphase RANS and Large Eddy simulations.     

Effects of blowing through a porous strip in a turbulent channel flow

An experimental investigation is performed on a fully developed turbulent channel flow with local injection through a porous strip. The Reynolds number based on the channel half-width was set to 5000. In addition to the no blowing case, measurements are made for three different blowing rates σ = 0.22, 0.36 and 0.58 (where σ is the ratio of momentum flux gain due to the blowing and momentum flux of the incoming channel flow). Measurements carried out with hot-wire anemometry reveal that injection strongly affects both the velocity profiles and the turbulence characteristics. The injection decreases the skin friction coefficient and increases all the Reynolds stresses downstream the blowing strip. The turbulence structure and the bursting phenomena were examined using space-time correlations measurements and conditional analysis. It is found that the injection increases the frequency of occurrence of the bursts.     

Flow structure of microbubble-laden turbulent channel flow measured by PIV combined with the shadow image technique

The turbulence structure of a horizontal channel flow with microbubbles is experimentally investigated using combined particle image velocimetry (PIV) in order to clarify the mechanism of drag reduction caused by microbubbles. A new system which simultaneously measures the liquid phase and the dispersed bubbles is proposed, based on a combination of particle tracking velocimetry (PTV), laser-induced fluorescence (LIF) and the shadow image technique (SIT). To accurately obtain the velocity of the liquid phase, tracer particles which overlap with the bubble shadow images are almost entirely eliminated in the post-processing. Finally, the turbulence characteristics of the flow field are presented, including measurements for both phases, and the bubble effect on the turbulence is quantified.