Transitional Channel Flow Research Articles

Spatiotemporal evolution of particle puffs in transitional channel flow

We study the shape evolution of puffs composed of tracers advected in a transitional channel flow. We perform a direct numerical simulation of a spatially evolving channel flow, where the inflow condition is given by a solution of the Orr–Sommerfeld equation and the flow evolves through all stages of transition up to fully developed turbulence. In this setting, we release spherical puffs of particles and track their evolution using measures derived from their approximation as ellipsoids. By varying the initial position of puffs, we characterize the spatial non-homogeneity of the flow, with respect to both the distance from the wall and, most importantly, the streamwise coordinate along which the flow evolves. Furthermore, we assess the influence of scale-dependent phenomena on puff shapes by varying the initial size of the clouds of particles. The present approach explores the interaction between flow features and advected Lagrangian structures. Additionally, it reveals the interplay between flow scales and how their balance changes during transition, where the intermittency causes large puffs to be much less elongated than smaller puffs independently of the distance from the walls.

Effect of transient inhalation on powder evacuation and dispersion in a typical dual air inlet dry powder inhaler

An optically accessible research dry powder inhaler (DPI) was used to investigate the impact of initial acceleration during inhalation on the powder evacuation and drug dispersion processes. The inhaler featured a swirling chamber connected with two inlets, closely resembling commercial devices such as the Aerolizer® and Osmohaler®. The dimensions of the inhaler were kept similar to the commercial devices, mimicking their flow situations. High-speed microscopic imaging and an in-house developed image processing technique were used to extract relevant statistics. The current literature on DPI flow dynamics provides valuable insights into the correlation between inspiratory flow rate, peak inspiratory pressure, and inhaler performance. However, it lacks data correlating powder evacuation characteristics and deagglomeration mechanisms for transient inhalation conditions inside the DPIs. This paper is an attempt to fill this gap by investigating the evacuation pattern and deagglomeration mechanism for three different initial accelerations qualitatively representing asthma severity and steady-state inhalation conditions representing laminar, transitional, and turbulent channel flow, using both pure drug and carrier particles. The study's key findings revealed that powder evacuation progressed in two stages. The first stage was slow, with a slope ranging from 0.25 to 0.27. Also, the evacuation rate was independent of the initial inhalation acceleration. The second stage was rapid, with a slope ranging from 0.87 to 1.23, which led to faster and complete powder evacuation. The slow stage consumed approximately ∼60 % of the total evacuation time to evacuate only ∼20% of the loaded drug, while the rapid stage evacuated ∼80% of the powder in the remaining time. The data collected from these experiments advances the understanding of the DPI flow dynamics and provides high-quality data for validating computational models used in the analysis of such inhaler systems.

Decomposition of skin-friction and wall heat flux of temporal transition in compressible channel flows with direct numerical and constrained large-eddy simulations

The twofold integral-based decompositions of skin-friction and wall heat flux coefficients are implemented in compressible temporal transitional channel flows with direct numerical simulation and constrained large eddy simulation (CLES) to explore (i) the generations of the skin-friction and wall heat flux coefficients and their overshoot during the transition and (ii) why CLES under-predicts the overshoot phenomenon. The Reynolds shear stress, the mean velocity gradient with respect to time, and the mean velocity convection are dominating terms during the transition process of skin friction coefficient Cf, and the effect of the mean velocity convection becomes stronger as the Mach number (Ma) increases. For the wall heat flux coefficient Bq, the turbulent heat transfer, the mean energy gradients in time, and the viscous stress are significant contributors. The effects of molecular heat transfer and the mean convection on transition are increasingly important to Bq as Ma increases. The overshoot of Cf and Bq at Ma = 1.5 is mainly caused by the significant changes of mean velocity profiles and mean energy profiles with respect to time respectively. At Ma = 3.0, the overshoot of Cf is due to the significant change of mean velocity profiles in time and the mean velocity convection, while the overshoot of Bq is due to the mean energy changes in time and mean energy convection. It is found that the underestimation of the overshoots of Cf and Bq in CLES is primarily caused by the variances of the mean velocity gradient and mean energy gradient, respectively.

Direct Path from Turbulence to Time-Periodic Solutions.

Viscous flows through pipes and channels are steady and ordered until, with increasing velocity, the laminar motion catastrophically breaks down and gives way to turbulence. How this apparently discontinuous change from low- to high-dimensional motion can be rationalized within the framework of the Navier-Stokes equations is not well understood. Exploiting geometrical properties of transitional channel flow we trace turbulence to far lower Reynolds numbers (Re) than previously possible and identify the complete path that reversibly links fully turbulent motion to an invariant solution. This precursor of turbulence destabilizes rapidly with Re, and the accompanying explosive increase in attractor dimension effectively marks the transition between deterministic and de facto stochastic dynamics.

DNS of heat transfer in a plane channel flow with spatial transition

In the present work Direct Numerical Simulation of heat transfer in a spatial laminar-turbulent transitional channel flow is carried out to investigate the effects of the transitional phenomenon in the temperature field. The configuration is a spatially developing channel flow with two thermal boundary conditions: Uniform Wall Temperature (UWT) and Uniform Heat Flux (UHF). The set of simulations are carried out for Re=4200 and Pr=0.1,0.2,0.5,0.71 and 1. The spatial evolution of the Nusselt number (Nu) along the transition is computed to show five distinctive qualitative zones: a laminar development, the spike zone, where the quantities evolve to reach the peak transitional zone, the post-transitional zone and finally, the fully turbulent zone. This data is employed to develop a correlation that captures the space evolution of Nu along the transition. Moreover, the analysis of flow structures shows that near the wall and downstream the onset of the transition, streaks of velocity and temperature fluctuations have strong similarity. Different turbulent statistics are calculated along the transition and compared with fully turbulent reference data. It is shown that upstream the peak transitional zone, the existence of coherent hairpin vortices yields a high-intensity region for these quantities. Additionally, it is found that the thermal boundary condition exerts influence on the profile of the second-order parameters near the wall and in the logarithmic region all along the transition.

Slip boundary effect on the critical Reynolds number of subcritical transition in channel flow

In this letter, the effect of slip boundary on the origin of subcritical transition in two-dimensional channel flows is studied numerically and theoretically. It is shown that both the positive and the negative slip lengths will increase the critical Reynolds number of localized wave packet and hence postpone the transition. By applying a variable transformation and expanding the variables about a small slip length, it is illustrated that the slip boundary effect only exists in the second and higher order modulations of the no-slip solution, and hence explains the power law found in simulations, i.e. the relative increment of the critical Reynolds number due to the slip boundary is proportional to the square of the slip length.

Physics-informed dynamic mode decomposition

In this work, we demonstrate how physical principles—such as symmetries, invariances and conservation laws—can be integrated into thedynamic mode decomposition(DMD). DMD is a widely used data analysis technique that extracts low-rank modal structures and dynamics from high-dimensional measurements. However, DMD can produce models that are sensitive to noise, fail to generalize outside the training data and violate basic physical laws. Our physics-informed DMD (piDMD) optimization, which may be formulated as a Procrustes problem, restricts the family of admissible models to a matrix manifold that respects the physical structure of the system. We focus on five fundamental physical principles—conservation, self-adjointness, localization, causality and shift-equivariance—and derive several closed-form solutions and efficient algorithms for the corresponding piDMD optimizations. With fewer degrees of freedom, piDMD models are less prone to overfitting, require less training data, and are often less computationally expensive to build than standard DMD models. We demonstrate piDMD on a range of problems, including energy-preserving fluid flow, the Schrödinger equation, solute advection-diffusion and three-dimensional transitional channel flow. In each case, piDMD outperforms standard DMD algorithms in metrics such as spectral identification, state prediction and estimation of optimal forcings and responses.

Effects of polymer addition on transition and length scales of flow structures in transitional channel flow

The effect of polymer addition on transition to turbulence in a two-dimensional water-flow channel was experimentally investigated by flow visualization using reflective flakes. The flow entering the channel test section maintains a high disturbance level by expanding laterally after reaching a high Reynolds number upstream the test section. In order to obtain the intermittency factor (turbulence fraction), the visualized images were classified into non-turbulent and turbulent regions, and the streamwise scale of the streaks appearing in the non-turbulent region was estimated from the autocorrelation coefficient computed by shifting the images in the streamwise direction. The visualization results show that similar to the pure water case, intermittent flow with a patch-like distribution of turbulent and non-turbulent areas clustered by streamwise streaks is observed. The Reynolds number at which the intermittency increases shifts toward higher Reynolds numbers with increasing polymer concentration, indicating a delay of transition. The streaks appearing in the non-turbulent region elongate with increasing polymer concentration. At high concentrations, straight elongated streaks penetrate through the turbulent regions, suggesting that the polymer addition affects the stability of the streaks. These changes of the streak behavior indicate that the polymer affects not only the transition Reynolds number but also the flow structure during the transition process.

Modal laminar–turbulent transition delay by means of topology optimization of superhydrophobic surfaces

When submerged under a liquid, the microstructure of a SuperHydrophobic Surface (SHS) traps a lubricating layer of gas pockets, which has been seen to reduce the skin friction of the overlying liquid flow in both laminar and turbulent regimes. More recently, spatially homogeneous SHS have also been shown to delay laminar–turbulent transition in channel flows, where transition is triggered by modal mechanisms. In this study, we investigate, by means of topology optimization, whether a spatially inhomogeneous SHS can be designed to further delay transition in channel flows. Unsteady direct numerical simulations are conducted using the spectral element method in a 3D periodic wall-bounded channel. The effect of the SHS is modelled using a partial slip length on the walls, forming a 2D periodic optimization domain. Following a density-based approach, the optimization procedure uses the adjoint-variable method to compute gradients and a checkpointing strategy to reduce storage requirements. This methodology is adapted to optimizing over an ensemble of initial perturbations.This study presents the first application of topology optimization to laminar–turbulent transition. We show that this method can design surfaces that delay transition significantly compared to a homogeneous counterpart, by inhibiting the growth of secondary instability modes. By optimizing over an ensemble of streamwise phase-shifted perturbations, designs have been found with comparable mean transition time and lower variance.

Size-dependent transient nature of localized turbulence in transitional channel flow

It has been reported that a fully localized turbulent band in channel flow becomes sustained when the Reynolds number is above a threshold. Here we show evidence that turbulent bands are of a transient nature instead. When the band length is controlled to be fixed, the lifetime of turbulent bands appears to be stochastic and exponentially distributed, a sign of a memoryless transient nature. Besides increasing with the Reynolds number, the mean lifetime also strongly increases with the band length. Given that the band length always changes over time in real channel flow, this size dependence may translate into a time dependence, which needs to be taken into account when clarifying the relationship between channel flow transition and the directed percolation universality class.

Data driven turbulence modeling in turbomachinery — An applicability study

The machine learning (ML) approaches have been introduced in Reynolds-Averaged Navier–Stokes (RANS) modeling in recent years. These ML-RANS models are usually trained from a training flow database, and are employed in the simulations of other flow cases. The training flows and real simulations can have different underlying physics. When the training flows have a typical physical constraint but real simulations do not have, the applicability of ML-RANS models should be evaluated. The present paper then aims at explaining the underlying physics and expansibility of a recent ML-RANS approach (Liu et al., 2021). A database of transitional channel flow is first used to estimate the flow states and data constraints, and to clarify the calculation methods for the input features. An industrial low pressure turbine (LPT) configuration is then calculated to test the applicability of the applied ML-RANS model. Analysis on the expansibility of constraints shows that the non-equilibrium turbulence and transitional flow cannot be correctly calculated by using a ML-RANS model learned from databases of equilibrium turbulence.

On the Underlying Drag-Reduction Mechanisms of Flow-Control Strategies in a Transitional Channel Flow: Temporal Approach

The underlying mechanisms of three different flow-control strategies on drag reduction in a channel flow are investigated by direct numerical simulations at friction Reynolds numbers ranging from 65 to 85. These strategies include the addition of long-chain polymers, the incorporation of slip surfaces, and the application of an external body force. While it has been believed that such methods lead to a skin-friction reduction by controlling near-wall flow structures, the underlying mechanisms at play are still not as clear. In this study, a temporal analysis is employed to elucidate underlying drag-reduction mechanisms among these methods. The analysis is based on the lifetime of intermittent phases represented by the active and hibernating phases of a minimal turbulent channel flow (Xi and Graham, Phys Rev Lett 2010). At a similar amount of drag reduction, the polymer and slip methods show a similar mechanism, while the body force method is different. The polymers and slip surfaces cause hibernating phases to happen more frequently, while the duration of active phases is decreased. However, the body forces cause hibernating phases to happen less frequently but prolong its duration to achieve a comparable amount of drag reduction. A possible mechanism behind the body force method is associated with its unique roller-like vortical structures formed near the wall. These structures appear to prevent interactions between inner and outer regions by which hibernating phases are prolonged. It should motivate adaptive flow-control strategies to exploit the distinct underlying mechanisms for robust control of turbulent drag at low Reynolds numbers.

Structured input–output analysis of transitional wall-bounded flows

Input–output analysis of transitional channel flows has proven to be a valuable analytical tool for identifying important flow structures and energetic motions. The traditional approach abstracts the nonlinear terms as forcing that is unstructured, in the sense that this forcing is not directly tied to the underlying nonlinearity in the dynamics. This paper instead employs a structured-singular-value-based approach that preserves certain input–output properties of the nonlinear forcing function in an effort to recover the larger range of key flow features identified through nonlinear analysis, experiments and direct numerical simulation (DNS) of transitional channel flows. Application of this method to transitional plane Couette and plane Poiseuille flows leads to not only the identification of the streamwise coherent structures predicted through traditional input–output approaches, but also the characterization of the oblique flow structures as those requiring the least energy to induce transition, in agreement with DNS studies, and nonlinear optimal perturbation analysis. The proposed approach also captures the recently observed oblique turbulent bands that have been linked to transition in experiments and DNS with very large channel size. The ability to identify the larger amplification of the streamwise varying structures predicted from DNS and nonlinear analysis in both flow regimes suggests that the structured approach allows one to maintain the nonlinear effects associated with weakening of the lift-up mechanism, which is known to dominate the linear operator. Capturing this key nonlinear effect enables the prediction of a wider range of known transitional flow structures within the analytical input–output modelling paradigm.

Large eddy simulation of transitional channel flow using a machine learning classifier to distinguish laminar and turbulent regions

Breakdown to turbulence in wall-bounded flows takes place through sporadic bursts of turbulent spots. Wall-modelled large-eddy simulations (LES) of transition to turbulence must dynamically identify the nascent turbulent regions, track their evolution, and apply the appropriate wall stress within and outside the turbulent/non-turbulent (T-NT) interface. Self-organized maps (SOM), a machine learning classifier, objectively and efficiently captures the T-NT interface. Wall-modeled LES with SOM interface identification predicts both orderly and bypass transition.

Data-driven resolvent analysis

Abstract

Flow visualization and skin friction determination in transitional channel flow

The present study experimentally determines the transitional Reynolds number range for plane channel flow and characterizes its transitional state. The pressure along the channel is measured to determine the skin friction coefficient as function of Reynolds number from the laminar state, through the transitional region into the fully turbulent state. The flow structure was studied through flow visualisation which shows that as the Reynolds number increases from the laminar state the transitional region starts showing randomly occurring turbulent spots. With increasing Reynolds number the spots shift into oblique patches and bands of small scale turbulence that form across the channel width, together with large-scale streaky structures found in areas between the turbulent regions. An image analysing technique was used to determine the intermittency factor, i.e. the turbulence fraction in the flow, as function of Reynolds number. It is found that the skin friction coefficient reaches its turbulent value before the flow is fully turbulent (the intermittency factor is still below one). This suggests that the observed streaky structures in non-turbulent regions contribute to the enhancement of the wall-normal transfer of momentum. Also above the Reynolds numbers where the turbulent skin friction coefficient has been established large-scale features consisting of irregular streaky structures are found. They have an oblique shape similar to the non-turbulent and turbulent patches in the transitional flow indicating that the transition process is not fully complete even above the Reynolds number where the skin friction reaches its turbulent level.Graphic abstractProcessing of flow visualization images to determine the turbulenceintermittency in the transitional region. Flow is from left to right, (a)unprocessed, (b) filtered (c) standard deviation of (b), (d) binary picture

Intermittency, Moments, and Friction Coefficient during the Subcritical Transition of Channel Flow.

The intermittent distribution of localized turbulent structures is a key feature of the subcritical transitions in channel flows, which are studied in this paper with a wind channel and theoretical modeling. Entrance disturbances are introduced by small beads, and localized turbulent patches can be triggered at low Reynolds numbers (Re). High turbulence intensity represents strong ability of perturbation spread, and a maximum turbulence intensity is found for every test case as Re ≥ 950, where the turbulence fraction increases abruptly with Re. Skewness can reflect the velocity defects of localized turbulent patches and is revealed to become negative when Re is as low as about 660. It is shown that the third-order moments of the midplane streamwise velocities have minima, while the corresponding forth-order moments have maxima during the transition. These kinematic extremes and different variation scenarios of the friction coefficient during the transition are explained with an intermittent structure model, where the robust localized turbulent structure is simplified as a turbulence unit, a structure whose statistical properties are only weak functions of the Reynolds number.

Transitional Channel Flow: A Minimal Stochastic Model.

In line with Pomeau’s conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes observed in channel flow before its return to laminar flow. Numerical simulations show that a regime with bands obliquely drifting in two stream-wise symmetrical directions bifurcates into an asymmetrical regime, before ultimately decaying to laminar flow. The model is expressed in terms of a probabilistic cellular automaton of evolving von Neumann neighborhoods with probabilities educed from a close examination of simulation results. It implements band propagation and the two main local processes: longitudinal splitting involving bands with the same orientation, and transversal splitting giving birth to a daughter band with an orientation opposite to that of its mother. The ultimate decay stage observed to display one-dimensional DP properties in a two-dimensional geometry is interpreted as resulting from the irrelevance of lateral spreading in the single-orientation regime. The model also reproduces the bifurcation restoring the symmetry upon variation of the probability attached to transversal splitting, which opens the way to a study of the critical properties of that bifurcation, in analogy with thermodynamic phase transitions.

Trigger turbulent bands directly at low Reynolds numbers in channel flow using a moving-force technique

Abstract

Analysis of flow characteristics downstream delta-winglet vortex generator using stereoscopic particle image velocimetry for laminar, transitional, and turbulent channel flow regimes

The evolution of flow structures downstream a single pair of delta-winglet vortex generators (VGs) is investigated experimentally using stereoscopic particle image velocimetry. In addition, the laser Doppler anemometer technique is performed to characterize the upstream flow. Experiments are conducted in a bounded channel flow (height H) for the Reynolds numbers (ReDH, based on the hydraulic diameter height) ranging from 400 to 12 000. The purpose of this study is to provide detail insight into the generation and the dissipation of longitudinal vortices over a wide flow regime range including the laminar–turbulent transition. With a focus on transverse sections, the flow field is detailed. For all flow regimes, the main flow topology shows that the two main counter-rotating vortices are generated at a certain streamwise distance downstream the VG and then are advected gradually toward the channel lateral-walls. A secondary vortex pair is induced closer to the wall. Our results show that close to the VGs, local regions (1 > z/H > −1) are strongly defined as the inception of the turbulence production. The intensity of this latter is shown to vanish beyond a certain distance far from the origin of the perturbation (when x/H is greater than 3). The instantaneous flow structure describes the mechanism of vortex generation, relying on the intermittence of the flow organization and the sweep and ejection event balance. Detailed analysis on the turbulence properties and wall shear stress has been assessed and revealed that the flow transition induced by the perturbation of the VG is achieved at a Reynolds number no greater than 1500.