Numerical Simulation Of Channel Flow Research Articles

Spatially evolving cascades in wall turbulence with and without interface

Direct numerical simulations of channel flow and temporal boundary layer at a Reynolds number $Re_{\tau } = 1500$ are used to assess the scale-by-scale mechanisms of wall turbulence. From the peak of turbulence production embedded at the small scales of the near-wall region, spatially ascending reverse cascades are generated that move through self-similar eddies growing in size with the wall distance. These fluxes are followed by spatially ascending forward cascades through detached eddies thus reaching sufficiently small scales where eventually scale energy is dissipated. This phenomenology is shared by both boundary layer and channel flow and is recognized as a robust physical feature characterizing wall turbulence in general. Specific features related to the flow configuration are indeed identified in the outer region. In particular, the central region of channels is characterized by a generalized Richardson energy cascade where large scales are in equilibrium with small scales at different wall distances through a combined forward cascade and spatial flux. On the contrary, the interface region of boundary layers is characterized by an almost two-dimensional physics where spatially ascending reverse cascades sustain long and wide interface structures with a forward cascade that survives only in the wall-normal scales. The overall scenario consists in a variety of scale motions that while protruding from the turbulent core towards the external region, squeeze at the interface thus sustaining vertical shear in a thin layer. The observed multidimensional physics sheds light on the complex interactions between outer entrainment and near-wall self-sustaining mechanisms with possible repercussions for theories.

Direct numerical simulation of channel flow with real surface roughness using a ghost cell immersed boundary method

This paper investigates the impact of real surface roughness on channel flow using direct numerical simulation assisted by a ghost cell immersed boundary method (DNS-GCIBM). The principles and implementations of DNS-GCIBM are first introduced. Two test cases, including the two-dimensional flow around a cylinder and the three-dimensional flow in a sinusoidal roughness channel are employed to demonstrate the practicability and accuracy of the proposed approach, especially in numerical studies on the rough wall-bounded flow. Using DNS-GCIBM, channel flows under conditions of Ma = 0.3 and Reτ≈300, with both the real-world and regular roughness surfaces are studied. The results are statistically analyzed using the triple decomposition technique. The outer layer similarity in the streamwise mean velocity and Reynolds stress profiles indicate that the impact of roughness on the boundary layer primarily localizes within roughness sub-layer. In the streamwise mean velocity profile, both regular and real-world roughness surfaces induce obvious increase to the roughness function ΔU+ as roughness height Ra increases, while discrepancy of ΔU+ between the two types of roughness can be found. Furthermore, turbulence statistics are sensitive to the variations of Ra. As Ra increases, it becomes challenging to organize coherent structures near the wall, resulting in the reduction of streamwise Reynolds stress intensity. In addition, although the skin friction coefficient and ΔU+ are almost the same, the real-world roughness and the corresponding equivalent regular roughness manifest different flow structures near the wall. The real-world roughness contributes greater spatial inhomogeneity but lower turbulence intensity.

Phononic-subsurface flow stabilization by subwavelength locally resonant metamaterials

The interactions between a solid surface and a fluid flow underlie dynamical processes relevant to air, sea, and land vehicle performance and numerous other technologies. Key among these processes are unstable flow disturbances that contribute to fundamental transformations in the flow field. Precise control of these disturbances is possible by introducing a phononic subsurface (PSub). This comprises locally attaching a finite phononic structure nominally perpendicular to an elastic surface exposed to the flowing fluid. This structure experiences ongoing excitation by an unstable flow mode, or more than one mode, traveling in conjunction with the mean flow. The excitation generates small deformations at the surface that trigger elastic wave propagation within the structure, traveling away from the flow and reflecting at the end of the structure to return to the fluid-structure interface and back into the flow. By targeted tuning of the unit-cell and finite-structure characteristics of the PSub, the returning waves may be devised to resonate and reenter the flow out of phase, leading to significant destructive interference of the continuously incoming flow waves near the surface and subsequently to their attenuation over the spatial extent of the control region. This entire mechanism is passive, responsive, and engineered offline without needing coupled fluid-structure simulations; only the flow instability’s frequency, wavelength, and overall modal characteristics must be known. Disturbance stabilization in a wall-bounded transitional flow leads to delay in laminar-to-turbulent transition and reduction in skin-friction drag. Destabilization is also possible by alternatively designing the PSub to induce constructive interference, which is beneficial for delaying flow separation and enhancing chemical mixing and combustion. In this paper, we present a PSub in the form of a locally resonant elastic metamaterial, designed to operate in the elastic subwavelength regime and hence being significantly shorter in length compared to a phononic-crystal-based PSub. This is enabled by utilizing a sub-hybridization resonance. Using direct numerical simulations of channel flows, both types of PSubs are investigated, and their controlled spatial and energetic influence on the wall-bounded flow behavior is demonstrated and analyzed. We show that the PSub’s effect is spatially localized as intended, with a rapidly diminishing streamwise influence away from its location in the subsurface.

Effects of roughness on the turbulent Prandtl number, timescale ratio, and dissipation of a passive scalar

Turbulence models for scalar and momentum transport are often analogous to each other, but roughness breaks this similarity. The turbulent Prandtl number, the momentum and scalar time-scales, and the dissipation budget are among the central quantities in the modeling of scalar transport. This study examines how roughness affects them by analyzing the results of direct numerical simulations of channel flow with resolved roughness. The flow field below the crest of the elements, which is very difficult to access experimentally, provides answers to long-standing questions.

Perturbative model for the second-order velocity structure function tensor in turbulent shear flows

A model for the second order velocity structure function tensor, based on Kolmogorov's theory and valid for the inertial range, is proposed, incorporating the effect of anisotropy as a linear perturbation to the standard isotropic form. Structure functions measured from direct numerical simulations of channel flow and from experimental measurements in turbulent boundary layers are compared with predicted behavior and reasonable agreement is found.

Active control for drag reduction of turbulent channel flow based on convolutional neural networks

An active controller based on convolutional neural networks (CNNs) is designed for drag reduction of turbulent channel flow. CNNs are constructed to predict the normal velocities on the detection plane as wall blowing and suction using measurable quantities at the wall, i.e., spanwise or streamwise wall shear stress. The training data of CNNs are generated from the direct numerical simulation of channel flow. With different wall quantities, we design and train different CNNs for flow prediction. The purpose is to identify which wall quantity is associated with substantial drag reduction. A linear neural network based on the spanwise wall shear stress shows sufficient capability to predict the inflow field and obtain almost the same drag reduction rate as the opposite control, which does not perform well when using the streamwise wall shear stress as the input. Hence, a nonlinear CNN model with activation function and multiple convolutional layers is established to use the streamwise wall shear stress for flow prediction and drag reduction control. Applying the trained CNNs to a low Reynolds number turbulent channel flow at Reτ = 100, we obtain up to 19% and 10% drag reduction rates based on the spanwise and streamwise wall-shear stresses, respectively. These networks are also tested at different Reynolds numbers, i.e., Reτ = 180 and Reτ = 390, where substantial drag reduction rates are obtained as well. Effects of the controller on turbulent instantaneous flow field and statistics are presented.

Numerical simulation of channel flow over a skewed equilateral cavity

Numerical simulation of channel flow over a skewed equilateral cavity

Numerical investigation of the performance of interface conditions for fluid flow through a partially filled porous channel

Numerical simulations of channel flow with a partly filled porous medium made of cylinders were carried out using exact geometry of the porous medium. The results obtained from these simulations were compared with the analytical solutions obtained with the three hydrodynamic interface conditions used at the interface of a clear fluid and a porous medium. Three hydrodynamic interface conditions considered in this study were the slip condition, the stress continuity condition and the stress jump condition. These interface conditions were applied at various assumed locations and the performances of these conditions were evaluated by comparing with the results obtained from the numerical simulations. The numerical simulations were carried out by varying the geometry, the arrangement of the cylinders, and the porosity of the porous medium. The velocity profile in the clear fluid region is accurately modeled by all the three interface conditions. The velocity profile in the transition layer obtained using the stress jump condition at the interface is observed to be closer to the present numerical simulation results compared to the velocity profiles developed using the other two interface conditions for every configuration of the porous medium at every interface location.

Feedback Control for Transition Suppression in Direct Numerical Simulations of Channel Flow

For channel flow at subcritical Reynolds numbers ( R e < 5772 ), a laminar-to-turbulent transition can emerge due to a large transient amplification in the kinetic energy of small perturbations, resulting in an increase in drag at the walls. The objectives of the present study are three-fold: (1) to study the nonlinear effects on transient energy growth, (2) to design a feedback control strategy to prevent this subcritical transition, and (3) to examine the control mechanisms that enable transition suppression. We investigate transient energy growth of linear optimal disturbance in plane Poiseuille flow at a subcritical Reynolds number of R e = 3000 using linear analysis and nonlinear simulation. Consistent with previous studies, we observe that the amplification of the given initial perturbation is reduced when the nonlinear effect is substantial, with larger perturbations being less amplified in general. Moreover, we design linear quadratic optimal controllers to delay transition via wall-normal blowing and suction actuation at the channel walls. We demonstrate that these feedback controllers are capable of reducing transient energy growth in the linear setting. The performance of the same controllers is evaluated for nonlinear flows where a laminar-to-turbulent transition emerges without control. Nonlinear simulations reveal that the controllers can reduce transient energy growth and suppress transition. Further, we identify and characterize the underlying physical mechanisms that enable feedback control to suppress and delay laminar-to-turbulent transition.

Turbulent drag reduction by anisotropic permeable substrates – analysis and direct numerical simulations

We explore the ability of anisotropic permeable substrates to reduce turbulent skin friction, studying the influence that these substrates have on the overlying turbulence. For this, we perform direct numerical simulations of channel flows bounded by permeable substrates. The results confirm theoretical predictions, and the resulting drag curves are similar to those of riblets. For small permeabilities, the drag reduction is proportional to the difference between the streamwise and spanwise permeabilities. This linear regime breaks down for a critical value of the wall-normal permeability, beyond which the performance begins to degrade. We observe that the degradation is associated with the appearance of spanwise-coherent structures, attributed to a Kelvin–Helmholtz-like instability of the mean flow. This feature is common to a variety of obstructed flows, and linear stability analysis can be used to predict it. For large permeabilities, these structures become prevalent in the flow, outweighing the drag-reducing effect of slip and eventually leading to an increase of drag. For the substrate configurations considered, the largest drag reduction observed is ${\approx}$20–25 % at a friction Reynolds number $\unicode[STIX]{x1D6FF}^{+}=180$.

On the inherent bias of swirling strength in defining vortical structure

The traditional practice of using rotational motion as the principal attribute of coherent vortical structures in the buffer region of near-wall turbulent flow is shown to create a biased accounting of the role of vorticity within the structures. Vorticity associated with rotation is given a favored consideration against vorticity that is equally strong but not associated with rotation. Using data from a highly resolved direct numerical simulation of channel flow, it is shown that describing the structures based on the properties of the rotational field leads to a distorted view of the actual structures that are present. As a practical matter, this means that where hairpins are typically considered to be the flow structures, a more accurate description of the coherent events is that they are elongated mushroom-shaped vortical objects ejecting over low speed streaks. In this, hairpin-shaped rotational regions are embedded in the lobes of the mushrooms.

Exponential growth of lifetime of localized turbulence with its extent in channel flow

The transition to turbulence in wall-bounded flows, for example pipe flow, plane Couette flow and channel flow, initially occurs as localized clusters of turbulence. It is well known that these localized structures are transient and decay in a memoryless process. In this paper we investigate the relationship between the extent of a localized structure and its lifetime. By performing numerical simulations of channel flow with small spanwise periodicity we produce streamwise-localized but spanwise-extended turbulence, turbulent ‘puffs’ instead of spots. We vary the spanwise periodzation length as the parameter of its extent to show that the lifetime of turbulent ‘puffs’ increases double-exponentially as a function of the Reynolds number for any spanwise extent. It is also shown that the lifetime increases exponentially as a function of the spanwise size when it is not large.

Direct numerical simulation of channel flow with permeable walls

Direct numerical simulation of channel flow with permeable walls

Direct numerical simulation of turbulent flow above zigzag riblets

We investigate the drag-reducing performance of a zigzag riblet inspired by the “Miura fold” and its influence on the streamwise vortices above a wall-bounded turbulent flow through direct numerical simulations of channel flows. The employed channel wall geometries are a flat plate, straight riblet, and zigzag riblet. The drag-reducing performance of various zigzag riblets with adjusted configuration parameters is superior or at least comparable to that of the straight riblet. We assume an analogy between the drag reduction mechanisms of spatially periodic forcing and the zigzag riblet, because both methods induce similar sinusoidal velocity profiles. To investigate the characteristics of the zigzag riblets, we apply a conditional sampling technique to the near-wall streamwise vortices that is also applied to the wall-bounded flow under spatially periodic forcing. The flow toward the wall of the rotating motion of a vortex becomes relatively small, as the main flow levitates at the tips of the zigzag riblet. Thus, the ejection increases and the sweep decreases. In the phase where the direction of the induced spanwise velocity coincides with the vortical motion, the latter is weakened because the vortex tilts in the spanwise direction at the phase; then, vortex stretching is suppressed. The zigzag riblet can reduce the drag via a mechanism analogous to active control, such as periodic oscillation. However, the effect of the upward flow is dominant above the zigzag riblet, and the analogous mechanisms are less remarkable. The considered zigzag riblet has potential application as a kind of active feedback control.

Structure of wall-bounded flows at transcritical conditions

Direct numerical simulations of channel flow at transcritical conditions with density change in the flow field are conducted. We find a regime with useful semi-local scaling as well as streamwise velocity and energy spectrum scaling which support the attached eddy model at transcritical conditions.

Lattice Boltzmann simulations of turbulent channel flow and heat transport by incorporating the Vreman model

In this article, the Vreman model with a dynamic procedure is applied for subgrid scale modeling of turbulent channel flow and heat transport, under the Lattice Boltzmann framework. Numerical simulations of channel flow at Reτ=180 with a constant temperature difference at the upper and bottom boundaries are presented and verified via comparisons with existing data of direct numerical simulations and large eddy simulations with the dynamic Smagorinsky model. Additionally, in the same flow and thermal system, the effect of natural convection along the vertical direction is investigated both qualitatively and quantitatively. Results indicate that the bulk velocity is decreased whereas the heat transfer is substantially enhanced. Meanwhile, the vertical thermal convection also alters the profiles of first and second-order statistics, especially in that the temperature fluctuation is flattened in the central region of the channel. Overall, our work offers a useful extension of the current Lattice Boltzmann method in complex situations and will facilitate researches involving turbulent flow and heat transport.

A multifractal model for the momentum transfer process in wall-bounded flows

The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation , where l is the filtering length scale. According to the multifractal formalism, and in the log-region, where Re τ is the friction Reynolds number, p is a real number, L is an outer length scale and ζ p is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at Re τ = 4200.

Spectral analysis of near-wall turbulence in channel flow at Reτ=4200 with emphasis on the attached-eddy hypothesis

Results from a large direct numerical simulation of channel flow with a friction Reynolds number of 4200 are used to examine the structural and spectral properties of near-wall turbulence.

Effect of Reynolds Number on Turbulent Drag Reduction by Superhydrophobic Surface Textures

In turbulent flows over streamwise-aligned superhydrophobic surface (SHS) textures, the percent drag reduction is dependent on Reynolds number. This dependence is examined using direct numerical simulations of channel flow over SHS texture at three bulk Reynolds numbers, R e b = 2800, 6785 and 10975. Simulations of regular no-slip channel flows at the same bulk velocities are also performed for comparison. Changes in the flow due to the SHS texture are examined with particular focus on phase averaged statistics and coherent turbulent motions. As the Reynolds number is increased, the texture performance, or the percent drag reduction, is enhanced. In terms of turbulent motions, the weakened shear stresses are manifest as a decrease in the population of the small-scale vortical structures and a weakening of large-scale motions. The influence of stochastic fluctuations near the large-scale motions diminishes at higher Reynolds number. The enhanced performance is therefore due to a significant drop in the strength of small- and large-scale vortical structures. The weaker vortical motions yield a considerable reduction in the Reynolds shear stress and the transport of mean momentum. The SHS texture introduces a performance penalty in the form of a local increase in drag at the no-slip free-slip edge. This adverse effect is caused by the inhomogeneity of the near-wall flow field. However, the affected region narrows in width at higher Reynolds numbers. As a result, the percent drag reduction approaches the gas fraction of the texture.

On the role of pressure in elasto-inertial turbulence

The dynamics of elasto-inertial turbulence is investigated numerically from the perspective of the coupling between polymer dynamics and flow structures. In particular, direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 are used to study the formation and dynamics of elastic instabilities and their effects on the flow. Based on the splitting of the pressure into inertial and polymeric contributions, it is shown that the polymeric pressure is a non-negligible component of the total pressure fluctuations, although the rapid inertial part dominates. Unlike Newtonian flows, the slow inertial part is almost negligible in elasto-inertial turbulence. Statistics on the different terms of the Reynolds stress transport equation also illustrate the energy transfers between polymers and turbulence and the redistributive role of pressure. Finally, the trains of cylindrical structures around sheets of high polymer extension that are characteristics of elasto-inertial turbulence are shown to be correlated with the polymeric pressure fluctuations.