Low Reynolds Number Case Research Articles

Experimental study of a separated shear layer transition under acoustic excitation

The paper discusses experimental results on the effect of broadband acoustic excitation on laminar-to-turbulent transition in a separated shear layer developing on a flat plate subjected to an adverse pressure gradient (APG) and freestream turbulence level equal to Tu ≅ 1 %. The study encompasses the influence of Reynolds number (Rex = 185 000 and 370 000) and sound pressure level (SPL). The inherent complexity of the problem is simplified by providing an acoustic excitation from a controlled source (loudspeaker), acting on the boundary layer developing on the flat plate with a given streamwise pressure gradient. Two types of instabilities were identified in the pre-transitional boundary layer in unexcited flows. One was related to the inviscid Kelvin-Helmholtz (K-H) instability, while the second one was associated with formation of streamwise-oriented Klebanoff streaks (so-called Klebanoff mode).In the low Reynolds number case (Rex = 185 000), the K-H was responsible for transition onset, while in the high Reynolds number flow (Rex = 370 000), the Klebanoff distortions dominated the turbulent breakdown with the minor effect of the K-H instability. In addition to the naturally developing boundary layer, the flow was exposed to a pink noise characterized by SPL = 125 dB and 135 dB. In the low Reynolds number case, the acoustic excitation enhanced the K-H instability. It resulted in an earlier laminar-to-turbulent transition in case with higher sound pressure level (135 dB). In the high Reynolds number flow, the acoustic excitation enhanced the mixed-type transition mechanism with dominant role of the Klebanoff streaks. Shrinking or complete suppression of the separation bubbles was observed, depending on the applied sound pressure level (125 and 135 dB).

LES of the T106 low-pressure turbine: Spectral proper orthogonal decomposition of the flow based on a fluctuating energy norm

This paper investigates the use of the spectral proper orthogonal decomposition (SPOD) on the flow around the T106 low-pressure turbine cascade. The chosen metric of the SPOD is based on the hydrodynamic flow disturbances for compressible flows and is used to characterize the flow structures holding large energy disturbances and synchronization processes with incoming wakes when considered. The input data for the SPOD is provided by large-eddy simulations of the T106 cascade. The Reynolds number and free-stream turbulence effects on the flow structures are studied using four operating points investigated in previous experiments and numerical simulations: Reynolds numbers of Re = 5.18 × 104 and Re = 1.48 × 105 without and with upstream wakes. The analysis of the SPOD indicates that the upstream wakes can amplify some modes of the suction side boundary layer (apparently a receptivity mechanism) and intensify the developing blade wake turbulent structures downstream of the trailing edge. This amplification happens over a reduced frequency bandwidth between Strouhal numbers equal to 7–10 for the low Reynolds number case and 20–24 for the high Reynolds number case.

A study on micro-step flow using a hybrid direct simulation Monte Carlo–Fokker–Planck approach

This study aimed to investigate the recirculation zone in a micro-step geometry using a hybrid molecular direct simulation Monte Carlo (DSMC) Fokker–Planck (FP) approach. As this hybrid approach benefits from the accuracy of the DSMC and reduced computational cost of FP, very low Knudsen number (Kn) and high Reynolds number (Re) cases were investigated for the first time. In particular, the role of Kn, specularity of walls, and Re was evaluated on the formation of concave and convex vortices. The Kn and Re ranges were from 0.0001 to 100 and from 0.04 to 5940, respectively. The latter considers a wide range of flow regimes from laminar to transitional flow. It is the first time that transitional flows have been treated in a micro-step using a rarefied flow solver. We demonstrated the formation of a vortex on the top wall of the micro-step geometry for low Kn conditions in the range of 0.0001 <Kn < 0.001. Extended positive pressure gradient in the geometry was found to be the cause of this secondary recirculation region. It was demonstrated that the recirculation zone lays on the vertical wall for Kn >1. It was shown that making the junction and bottom wall of the step specular did not eliminate the concave vortex but rather led to an increase in its strength. In addition, cold-to-hot transfer could be observed in all cases due to the competition between the higher-order term of the heat flux formula with the Fourier term.

Predictive Simulation of Two-dimensional Flat Plate Boundary Layer Transition

The laminar-turbulent transition is an old but still not a fully solved problem, which is mainly studied from the following aspects: (1) how the perturbation is generated and the receptivity problems (2) linear and nonlinear problems during the evolution of the perturbation (3) numerical simulation of the transition problem and the actual prediction. Considering that the power system of the vehicle is working in a low Reynolds number environment for a long time when flying at high altitudes. In this article, the research focuses on the turbulence model with the introduction of the AGS transition model is used to simulate the two-dimensional flat plate boundary layer transition in the low Reynolds number case, and to predict the transition location by combining the stability of different positions of the flow process, and to evaluate the accuracy of the transition model in comparison with other numerical simulation methods.

Heat transfer enhancement in a rectangular channel with pillars

This paper numerically studied the heat transfer performance of water flowing in a rectangular channel with pillar structures. We systematically investigated the influence of the pitch, inclination angle, shape, and pillar arrangement on the flow and heat transfer characteristics. The results show that adopting spacing with S/d=2 can improve heat transfer performance sufficiently for a low Reynolds number case. Meanwhile, the noticeable enhancement can also be observed by making the pillar inclination direction consistent with the flow direction or staggered rhombic-shaped.

An adaptive plate at flapping wing’s trailing edge in promoting energy extraction performance

As is known, the maximum thickness position plays a key role in determining the energy extraction properties for flapping wing airfoils. Previous work demonstrated that the energy extraction efficiency might increase when we move the maximum thickness position towards the leading-edge direction. Inspired from this phenomenon, we propose in this work the addition of a flat plate at the tail of the flapping wings. Under two different Reynolds numbers (Re = 1100 and Re = 5×105), the effect of adding a rigid flat plate or a flexible flat plate to the trailing edge of the flapping wing on the flapping wing’s energy efficiency was investigated. The corresponding results were also compared with that of the original flapping wing. Results show that the addition of a rigid flat plate is sufficient for the amelioration of the flapping wing’s energy extraction efficiency in low Reynolds number cases. At high Reynolds number cases, the flapping wing with flexible flat plate trailing edge can maintain a relatively high energy extraction efficiency over a wide range of frequency, while the flapping wing with rigid flat plate trailing edge can only improve the energy extraction efficiency in the low frequency region. Therefore, we propose the application of flapping wings with flexible flat plate trailing edge for increasing the energy extraction efficiency under high Reynolds number conditions.

Jet noise analysis using an efficient LES/high-Order acoustic coupling method

The use of a CFD/CAA method, where fluctuations are extracted on a surface and propagated analytically to the far-field, is becoming a practical approach for industrial jet noise prediction. However, the placement of the surface can be problematic and a source of error, so here an efficient LES/APE coupling method that relies on volumetric sources is utilised. This allows the use of an existing, well validated and robust finite volume LES code to compute the unsteady flow, from which the volumetric sources are extracted, to then compute the propagation of the acoustic waves to the far-field using a high-order finite element APE code with a grid more appropriate for this task. Furthermore, this coupled methodology allows the studying of noise propagation in complex configurations in which the use of surface integral methods could be challenging.In this work, a coupling strategy is used in which all the necessary data is exchanged directly via the high-speed communication network using an open-source library. The efficiency of the parallel-coupling strategy is demonstrated by applying it to a 2D canonical case and comparing it with an existing file-based approach. For the acoustic propagation, the APE solver used is called AcousticSolver, part of the high-order spectral/hp finite element open-source code Nektar++. The present LES/APE framework is fist validated for 3D jet applications by studying the noise propagation of a low-Reynolds number case. Then the method is applied to a more realistic high Reynolds number jet obtaining encouraging results in terms of flow and acoustic predictions.

Stiffness effects on laminar separation flutter

This work explores self-sustained pitching oscillations of a NACA0012 airfoil operating at low-to-moderate Reynolds numbers in which the aerodynamic flow is in a transitional regime. One-degree of freedom (1-DOF) pitching oscillations are explored for chord-based Reynolds numbers of Rec=77,000 and 110,000, which fall on the lower end of the flutter regime, over a large range of torsional spring constants. Laminar separation flutter (LSF) is shown to persist over several orders of magnitude of structural rigidity. At the Reynolds numbers tested, the effect of changing structural rigidity at a fixed Reynolds number exhibits remarkable similarity to the effect of varying Reynolds number at a fixed stiffness. Although the two effects are not perfectly analogous, both parameters influence the timing of transition events relative to the limit-cycle. Raising stiffness values at either Reynolds number causes the structural response to outpace boundary layer transition which in turn yields an increasingly nonlinear aeroelastic response. Oscillations are no longer sustained when the structural frequency merges with the frequency of the aeroelastic response. At this point, the slow relaxation time of boundary layer transition fails to keep pace with the structural frequency and the processes that sustain LSF are inhibited. Oscillations terminate at a lower stiffness in the lower Reynolds number case—an apparent effect of slower boundary layer transition. Interestingly, hysteresis patterns and flow topologies coalesce into nearly identical topologies for both Reynolds numbers when stiffness is very low.

A flow model for tip leakage flow in turbomachinery using a square duct with a longitudinal slit

A physical flow model to simulate the tip leakage flow (TLF) is proposed, in order to reproduce the jet flow/main flow shear mechanism of tip leakage vortex (TLV) roll-up in turbomachinery. The model is a main flow in a square duct with a jet flow from a longitudinal slit on the top, which could simplify the flow conditions for numerical simulations and experiments. The interaction of jet flow/main flow generates a streamwise vortex, resembling the TLV. The flow model is simulated using large-eddy simulation (LES) and compared with the measurements of a prototype rotor. The geometric parameters and boundary conditions are abstracted from the prototype rotor for verification. It is found that the flow model could generate similar flow field and turbulence structures to the prototype TLF, therefore it can be used to assess the turbulence models in practical flows. A RANS simulation under the same condition is also carried out, which shows the defect of current turbulence models. LES of a low-Reynolds number case indicates that the flow model could reproduce the TLF structures under various Reynolds number conditions, indicating that direct numerical simulation could also be applied to the investigation of the TLF model, thus the proposed model has the potential as a standard model for TLF research.

A two-dimensional-three-component model for spanwise rotating plane Poiseuille flow

Spanwise rotating plane Poiseuille flow (RPPF) is one of the canonical flow problems to study the effect of system rotation on wall-bounded shear flows and has been studied a lot in the past. In the present work, a two-dimensional-three-component (2D/3C) model for RPPF is introduced and it is shown that the present model is equivalent to a thermal convection problem with unit Prandtl number. For low Reynolds number cases, the model can be used to study the stability behaviour of the roll cells. It is found that the neutral stability curves, critical eigensolutions and critical streamfunctions of RPPF at different rotation numbers ($Ro$) almost collapse with the help of a rescaling with a newly defined Rayleigh number $Ra$ and channel height $H$. Analytic expressions for the critical Reynolds number and critical wavenumber at different $Ro$ can be obtained. For a turbulent state with high Reynolds number, the 2D/3C model for RPPF is self-sustained even without extra excitations. Simulation results also show that the profiles of mean streamwise velocity and Reynolds shear stress from the 2D/3C model share the same linear laws as the fully three-dimensional cases, although differences on the intercepts can be observed. The contours of streamwise velocity fluctuations behave like plumes in the linear law region. We also provide an explanation to the linear mean velocity profiles observed at high rotation numbers.

Performance and wake of a Savonius vertical‐axis wind turbine under different incoming conditions

AbstractIn this study, the performance, drag, and horizontal midplane wake characteristics of a vertical‐axis Savonius wind turbine are investigated experimentally. The turbine is drag driven and has a helical configuration, with the top rotated 180° relative to the bottom. Both performance and wake measurements were conducted in four different inflow conditions, using Reynolds numbers of ReD≈1.6×105 and ReD≈2.7×105 and turbulence intensities of 0.6% and 5.7%. The efficiency of the turbine was found to be highly dependent on the Reynolds number of the incoming flow. In the high Reynolds number flow case, the efficiency was shown to be considerably higher, compared with the lower Reynolds number case. Increasing the incoming turbulence intensity was found to mitigate the Reynolds number effects. The drag of the turbine was shown to be independent of the turbine's rotational speed over the range tested, and it was slightly lower when the inflow turbulence was increased. The wake was captured for the described inflow conditions in both optimal and suboptimal operating conditions by varying the rotational speed of the turbine. The wake was found to be asymmetrical and deflected to the side where the blade moves opposite to the wind. The largest region of high turbulent kinetic energy was on the side where the blade is moving in the same direction as the wind. Based on the findings from the wake measurements, some recommendations on where to place supplementary turbines are made.

A comparative study of alternating current and nanosecond plasma actuators in flow separation control

A combined numerical and experimental study is performed to elucidate the difference in flow separation control mechanisms between alternating current (ac) and nanosecond (ns) plasma actuators. The focus is on the visualization of detailed flow actuation process and establishment of relationship between flow control authority and characteristics of different actuators. Time-resolved particle image velocimetry (PIV) system is used to capture the transient separated flow over a stalled NACA 0015 airfoil at low Reynolds number (Re) of 6.3 × 104 and response of the flow to plasma actuation. Reynolds-averaged two-dimensional computation is performed for both low and high Reynolds number cases at Re = (0.063, 0.75) × 106 to complement experiment. Utilizing the elaborate Reynolds stress turbulence model in conjunction with an empirical body force model for surface ac plasma discharge and a sophisticated self-similar formulation for ns pulsed discharge, we have been able to numerically reproduce the experimentally observed intricate mechanisms, e.g. discretization of unstable shear layer into individual vortices, formation of large-scale spanwise vortex, strong entrainment effect of vortices and flow regularization procedure. Moreover, the information from simulation allows us to make a number of important observations which have no experimental counterparts. The detailed simulation shows that the convection of residual heat from ns discharge with cross flow makes ns plasma actuator more flexible in perturbing far downstream fluid in comparison with other actuators, and makes it superior to other devices in some high Re number flows. Also observed is the occurrence of strong flow resonance and frequency lock-in at a proper range of forcing frequency. In addition, the continuous ac plasma actuator appears to have complex control mechanisms, depending on flow conditions.

A Numerical Case Study: Effect of Heat Leakage on Thermodynamic Efficiency of Cylinders in Cross-Flow

Numerical and thermodynamic analyses have been undertaken in this study to examine energy and exergy efficiencies of in-line tube banks for unsteady cross-flow. Pitch ratio (PR) and the number of in-line tubes are varied for Reynolds numbers of 500 and 10,000, and artificial heat leakages are modeled as a source term. Numerical results are compared with published values, and good agreements are obtained regarding Nusselt number and pressure drop. Whereas the energy efficiency varied between 72% and 99%, the exergy efficiency ranged from 40% to 70%. It was found that while viscous dissipation has a low effect on energy and exergy efficiencies for the lower Reynolds number, it has a significant effect for the higher Reynolds number. On the other hand, heat leakage had a greater effect on exergy efficiency compared to energy efficiency, especially for the lower Reynolds number case. Overall, this study verified how heat leakage could play a vital role on efficiency for low-inlet temperature heat recovery systems.

Influence of Variable Viscosity on Peristaltic Motion of a Viscoelastic Fluid in a Tapered Microfluidic Vessel

The peristaltic flow of a viscoelastic fluid in the tapered microchannel with variable viscosity is investigated. This study is reinvigorated by discovering fluid dynamic in peristaltic motion as signified by biological flows, pharmacodynamics and gastro-intestinal motility enhancement. The microchannel non-uniform and asymmetry is developed by choosing a peristaltic wave train on the wall with different amplitudes and phases. The flow analysis has been arisen for low Reynolds number and long wavelength case. The solutions for stream function, axial velocity and pressure gradient are obtained. The effects of pertinent parameters on the average pressure rise per wavelength are investigated by means of numerical integration. The axial velocity and phenomena of trapping are further discussed.

Energy and Exergy Analyses of Tube Banks in Waste Heat Recovery Applications

In this study, energy and exergy analyses have been investigated numerically for unsteady cross-flow over heated circular cylinders. Numerous simulations were conducted varying the number of inline tubes, inlet velocity, dimensionless pitch ratios and Reynolds number. Heat leakage into the domain is modeled as a source term. Numerical results compare favorably to published data in terms of Nusselt number and pressure drop. It was found that the energy efficiency varies between 72% and 98% for all cases, and viscous dissipation has a very low effect on the energy efficiency for low Reynolds number cases. The exergy efficiency ranges from 40–64%, and the entropy generation due to heat transfer was found to have a significant effect on exergy efficiency. The results suggest that exergy efficiency can be maximized by choosing specific pitch ratios for various Reynolds numbers. The results could be useful in designing more efficient heat recovery systems, especially for low temperature applications.

Parameter influence on the evolution of low-aspect-ratio rectangular synthetic jets

The evolution of low-aspect-ratio rectangular synthetic jets is investigated with dye and laser-induced-fluorescence (LIF) flow visualization techniques. This paper analyzes the impacts of three key parameters on the evolution of vortical structures, respectively, including orifice aspect-ratio (AR), dimensionless stroke length, and Reynolds number. Compared with circular synthetic jet, all the rectangular synthetic jets display vortex ring axis switching, and may develop into two types of stream-wise vortices I and II. The evolution of the vortex ring and the generation of stream-wise vortices are influenced by three parameters. In particular, stream-wise vortices are not detected for a low AR, stroke length or Reynolds number case.

Characteristics of flow past a slender, emergent cylinder in shallow open channels

The complex wake created by an emergent cylinder with a large aspect ratio in a shallow open channel flow is studied experimentally using particle image velocimetry. The unique characteristics of the bed-mounted slender cylinder wake are analysed. Velocity fields, turbulence parameters, and wake development in shallow open channel flow are studied at two different Reynolds numbers and subcritical Froude numbers by carrying out measurements in different horizontal and vertical planes. In the mid-depth plane, velocity and turbulence statistics are independent of Reynolds number, while higher turbulence intensities and Reynolds shear stresses were observed in the near-bed plane for the low Reynolds number case. The narrower wake is observed in the near-bed plane due to the effect of the bed. Combined with stronger vertical velocity and turbulence intensities noted near the bed in the vertical midplane, this suggests increased activity of the vortex structures in the low Reynolds number case. Under shallow conditions, stronger disturbances of the free surface are observed for the case of high Reynolds and Froude numbers. The study also revisits the definition of the wake stability parameter and proposes a new definition which incorporates not only the bed friction but also the drag experienced by the cylinder.

Dynamic structures of a submerged jet interacting with a free surface

The spatial structures of a submerged jet interacting with a free surface were examined experimentally. The time-resolved PIV technique was used for the quantitative measurements. Two Reynolds numbers (1920, 3480) were examined for a configuration, in which the depth of the jet beneath the free surface was fixed to H=2D. The dynamics of the flow structures were examined further using the space–time proper orthogonal decomposition (POD) analysis technique. Some common characteristics were found in both jet flows, which are believed to be the general features of the free-surface jet flows. On the other hand, the dynamic characteristics of the large-scale turbulent motions differed significantly with respect to the Reynolds number. In the low Reynolds number case, three dominant dynamic structures were found: flapping motion of the jet, very large scale vortical structure interacting with the free surface at the right side, and the transverse stretching of large scale structure due to the presence of free surface. The reconstructed fluctuating velocity fields and the swirling strength contours demonstrated that the very large scale structures began to move downward at about 10D downstream the initial interaction. In the high Reynolds number case, the first two dominant spatial modes showed the momentum exchange process between the jet flow and the free surface. The third mode displayed a vortex just below the free surface at the left side and the fourth mode showed the elongated vortex structures. The scale of vortical structures was much smaller in the high Reynolds number case than that in the low Reynolds case, and the downward motion of large scale structures was not found in the high Reynolds number case.

Extraction and recognization of large-scale structures in the turbulent near wake of a circular disc

Large-scale structures of the turbulent near wake behind a circular disc at Re = 2.2 × 104 were investigated using large eddy simulation (LES) and multi-plane snapshot proper orthogonal decomposition (POD). Instantaneous data of three cross-stream planes were extracted from LES computation domain (− 5 ⩽ x/D ⩽ 15, 0 ⩽ r/D ⩽ 10, 0 ⩽ θ ⩽ 2π) to form the snapshot for the POD. The application of POD with a vector form decomposed the spatiotemporal wake flow into M modes with different amounts of fluctuation energy and turbulent scales contained. For comparison, the same decomposition was also conducted for the low Reynolds number case, Re = 170, where the unsteady flow is featured by a plane of symmetry, significant shedding process and well visually resolved vortex structures. At high Reynolds number, it was found that modes 1 and 2 presented an anti-symmetric structure, which was associated with the first azimuthal mode, being most energetic at all considered locations. A 90° rotation emerged between the symmetry planes of the first two POD modes. This could be a hint of a double helix system. Quadrupole-like patterns were observed for modes 3 and 4, which were definitely related to higher azimuthal modes, especially m = ± 2. The double helix system was in accord with a three-dimensional POD reconstructed streamwise vorticity pattern.

Thin helical vortex dynamics in low-viscosity liquid

The problem of helical vortices description has the significant interest as from fundamental point of view as well for practice. In some sense this problem is close to the vortex ring one which attracted much more attention in last decades. The reviews on the vortex rings investigations can be found in recent papers (1, 2) or in book by Akhmetov (3). In particular, in series of papers by Kaplanskii with co-authors (4-6) there was considered the viscosity influence on the vortex ring evolution. Separate attention was paid to the low Reynolds number case and to high Reynolds number one, initial stage of viscous evolution and final one. This paper presents first attempt for research on the diffusion and dynamics of a viscous helical vortex. In this work the problem of thin helical dynamics in low-viscosity liquid is considered. Appearance of helical vortex in the flow assumes helical symmetry. It means, that all of flow characteristic will be constant along the helical lines. The flow of viscous incompressible fluid under condition of the helical symmetry is described in variables vorticity - stream function by the system of equations (7, 8) 2