Transition Reynolds Number Research Articles

Numerical investigation of a pitching airfoil undergoing dynamic stall using Delayed Detached Eddy Simulations

This paper examines the detailed flow physics and predictive capabilities of Delayed Detached Eddy Simulations (DDES) related to the dynamic stall onset process during a pitching motion at a transitional Reynolds number of 200,000 and Mach number of 0.10. A comparison of the detailed flow physics of the onset of dynamic stall process between DDES and Large Eddy Simulations (LES) is first presented in this paper. State-of-the-art transition models will be tested in terms of their capabilities in capturing complex flow physics. The overall flow physics is captured in detail with a mesh composed of roughly 16 million grid points. A leading-edge separation region and formation of a dynamic stall vortex is examined in detail. The onset of lift stall was predicted slightly earlier using DDES with all turbulence transition models studied, and the peak lift coefficient was also slightly underpredicted compared to LES. However, DDES captures the important phenomena that are presented in LES including the formation and collapse of a Laminar Separation Bubble (LSB) and the subsequent formation of the Dynamic Stall Vortex (DSV). Coder’s SA Amplification Factor Transport (AFT) transition model is found to yield the most accurate results when compared with LES results and shows promising results for future use in more high-fidelity case studies. Langtry and Menter’s SST correlation-based transition model, its SA counterpart developed by Medida and Baeder, and a fully turbulent SA turbulent model are also investigated.

Experimental study on the effects of the cone nose-tip bluntness

In this Letter, hypersonic boundary-layer transition was investigated on a large-scale cone with a height of 3 m and a half-cone angle of 7° at a zero angle of attack in the JF-12 hypersonic flight duplicate shock tunnel. For the same freestream unit Reynolds number, with the increase in the bluntness Reynolds number, the transition Reynolds number has a trend of first increasing and then decreasing, showing a “transition reversal” phenomenon. As the bluntness increased, the high/low-frequency instability waves in the boundary-layer were modulated, which caused the boundary-layer transition to be delayed and then advanced.

Investigation on transition correlation of conical boundary layer in hypersonic wind tunnel experiments

The wind tunnel experiment is an important approach to studying boundary layer transition. In this study, the effects of bluntness, unit Reynolds number, and wall temperature ratio on hypersonic conical boundary layer transition were studied using numerical simulations and linear stability analyses based on the wind tunnel experimental data. Through the flow similarity principle, the treatment of the bluntness-varying problem was determined. Combining the experimental transition data and theoretical analysis results of sharp and blunt cones at home and abroad, the relation between the transition factor Ntr and the unit Reynolds number before ‘N factor reversal’, as well as the relation between the transition value Rtr and the unit Reynolds number from ‘N factor reversal’ to ‘transition reversal’ were determined too. Finally, according to the wind tunnel test data of China Aerodynamics Research and Development Center, the effect of wall temperature ratio on the receptivity of blunt-cone boundary layer was stated out, and the correlation of transition Reynolds number under different wall temperature ratios was determined. The influence law of parameters in this correlation was also determined.

High-blockage corrections for circular arcs at transitional Reynolds numbers

Model-scale testing might suffer from blockage effects due to the finite dimensions of the test section. Measurements must be corrected to predict the forces that would have been measured in unconfined conditions. Blockage corrections are well-established for streamlined and bluff bodies, while more data is needed to develop corrections for bodies that generate both high lift and large wakes. In this work, towing tank and water tunnel tests of two-dimensional circular arcs are employed to develop a correction for a blockage ratio, i.e. the ratio of the frontal area of the geometry to the cross-sectional area of the test section, up to 0.2477. Experiments are conducted at positive incidences between the ideal angle of attack and deep-stall at transitional Reynolds numbers from 53530 to 218000. The results show that a linear blockage correction can be devised for the whole range of tested blockage ratios. Furthermore, the critical angle of attack and Reynolds number at which the force crisis occurs is independent of the blockage ratio. These results may allow extending the range of model sizes that can be tested in water and wind tunnels and may contribute to the accurate accounting of blockage effects at transitional Reynolds number conditions.

Capturing transition around low-Reynolds number hydrofoil with zero-equation transition model

Compared with the local correlation-based shear stress transport (SST) γ−Reθ transition model (where SST k−ω transport equations are coupled with intermittency γ and transitional momentum-thickness Reynolds number Reθ transport equations), relatively simple and convenient modifications are applied to the parent SST k−ω model for computing natural and separation-induced transitions over the hydrofoil at a low-Reynolds number (LRN). The curiosity toward hydrofoil performance at an LRN has been enhanced by increasing attention to autonomous marine systems, deserving numerical simulations for transitional flow using computational fluid dynamics. With the newly devised transitional SST (T-SST) model, the viscous sublayer blending function F2 is slightly modified, and a stress-intensity parameter as a function of eddy-to-laminar viscosity ratio RT is introduced; intended formulations are plausible and have significant impacts on the transition prediction. Owing to the inherent potential for predicting bypass transition, two anisotropic versions of the v¯2−f(V2F) turbulence model are selected to evaluate their competencies in capturing separation-induced and natural transitions. Results demonstrate that natural transition prediction is more challenging than separation-induced transition for the V2F model. Nonetheless, the T-SST model performs consistently well in replicating both transitional phenomena.

Flow over a confined mounted fence at low and moderate Reynolds number: A numerical study

Direct numerical simulations of a flow over a wall mounted fence confined by two parallel walls were conducted at low and transitional Reynolds number (50⩽ReD⩽2000) for blockage ratios ranging from 0.25 (low blockage) to 0.9 (high blockage). A primary recirculation bubble forms downstream of the fence and the length of this recirculation region increased with Reynolds numbers. A secondary recirculation bubble appeared on the opposite wall to the mounted fence for the laminar cases with higher blockage ratios at sufficiently large Reynolds number. The separation and reattachment locations were documented and compared with numerical and experimental data. The length of the primary recirculation bubble in current simulations are consistent with the literature while the comparison of the secondary recirculation bubble with experimental data had limited agreement. This secondary recirculation bubble disappeared for the cases at transitional Reynolds number. Instead, the strong primary recirculation bubble induced a corner eddy at the rear of the fence. ‘Packets’ of cross stream velocity fluctuations were observed as the initially 2D, steady, laminar shear layer breakdowns to a 3D turbulent flow. The space–time diagram also showed ripple-like fluctuations of the shear layer further downstream of the fence with a single distinct peak observed in the streamwise and cross flow velocity fluctuations spectra. This peak in the spectra can be predicted by linear stability analysis of a mixing layer (Yasuo et al., 1986). In the near wake, scale-like features were observed while patches of fluctuations of a longer timescale were noted in the recirculation region.

A Residual Thermodynamic Analysis of Turbulence – Part 2: Pipe Flow Computations and Further Development of Theory

Single-phase turbulent pipe flows are analysed utilizing a new theory presented in a parallel paper. Arguably this new theory implies improvements in matching modelling results with experimental observations: To illustrate, unique for these computations is that a 1st law balance agreement between simulations and corresponding experiments is achieved, while resolving the time-averaged fluid flow velocity (including the various inner turbulent zones) and accounting for the wall surface roughness. Testing this new approach, the computations of 20 cases of turbulent pipe flow arrives at a remarkably high amount of kinetic energy dissipation occurring at near-wall positions, where some 54-83% of the net kinetic energy dissipation occurs within the viscous sublayer-, and 17-39% within the buffer layer. Although turbulence incorporates time-varying phenomena, e.g. swirls, large eddies, and breakup of the latter, it is argued that simulating these would have practically no effect on the net kinetic energy dissipation – and the associated wall shear stress – for the present pipe flow cases. Another illustration of the improvements relate to transition computations: While a proposed nominal transition model arrives at fair values of transition Reynolds numbers, some improvements on this transition analysis can be made, e.g. allowing for the modelling of the turbulence onset/offset hysteresis behaviour. For scientists who wish to model time-varying phenomena, e.g. for the study of mixing, boundary layer thickness, or wall-pressure fluctuations, there should be possibilities to implement this new theory in computational flow solvers.

Effect of transverse magnetic fields on the flow and heat transfer characteristics of magnetogasdynamic flows in circular tubes

To address the issue of the thermal energy control of high-temperature conductive gases in circular tubes, a new method to regulate the flow and heat transfer by utilizing a transverse magnetic field (TMF) to act on magnetogasdynamic (MGD) flows is proposed. Considering the characteristics of the insufficient development of turbulence at the tube inlet, this study investigated the effects of magnetization range, magnetic transition gradients, Reynolds number (9612 ≤ Re ≤ 40050), and Hartmann number (0 ≤ Ha ≤ 740) on MGD flow in a circular tube under the action of a TMF by applying numerical simulations. The results demonstrated that the MGD flow and heat transfer in a circular tube are anisotropic under an applied TMF, and this behavior becomes increasingly evident with increasing Re and Ha. Moreover, the action of an applied TMF suppresses the overall heat transfer at the tube wall, but the effect exhibits saturation with increasing Ha. In addition, the above suppression effect increases with increasing Re, but the required value of Ha also increases with increasing Re. Finally, within regions that include a magnetic field gradient, symmetric high-speed zones appear near the Roberts boundary layer, and the heat transfer intersity is enhanced in these regions. This enhancement is positively correlated with the magnitude of the magnetic field gradient. The analysis presented herein provides a new and comprehensive means for utilizing magnetic fields to control the thermal energy of MGD flows in circular tubes.

Entrainment in dry and moist thermals

We study entrainment in dry thermals in neutrally and unstably stratified ambients, and moist thermals in dry-neutrally stratified ambients using direct numerical simulations (DNS). We find, in agreement with results of Lecoanet and Jeevanjee \tb{[J. Atmos. Sci. 76(12), 3785-3801, (2019)]} that turbulence plays a minor role in entrainment in dry thermals in a neutral ambient for Reynolds numbers $Re \lesssim 10^4$. We then show that the net entrainment rate increases when the buoyancy of the thermals increases, either by condensation heating or because of an unstably stratified ambient. This is in contrast with the findings of Morrison et al. [J. Atmos. Sci. 78(3), 797-816, (2021)]. We also show that the role of turbulence is greater in these cases than in dry thermals and, significantly, that the combined action of condensation heating and turbulence creates intense small scale vorticity, destroying the {coherent} vortex ring that is seen in dry and moist laminar thermals. These findings suggest that fully resolved simulations at Reynolds numbers significantly larger than the mixing transition Reynolds number $Re=10^4$ are necessary to understand the role of turbulence in the entrainment in growing cumulus clouds, which consist of a series of thermals rising and decaying in succession.

Dynamics of weakly evaporating and non-evaporating drops falling in air

The dynamics of evaporating and non-evaporating drops falling in air under the influence of gravity is experimentally and theoretically studied in this work. Water and drops with diameters 2.0 and 2.7 mm and acetone drops 1.8 and 2.0 in diameter were tracked for approximately 2 m, corresponding to a flight-time of almost one second; at the end of the observation region, in most cases, the drops reached velocities ∼80% terminal velocity. Vertical positions of falling drops as a function of time and horizontal positions at different heights were recorded. Initially, the motion of non-evaporating water drops was rectilinear with a remarkable reproducibility in all experimental runs, showing narrow standard deviations in their horizontal position. When the increasing Reynolds numbers reached approximately 700, trajectories of individual drops diverged from each other. This effect may be attributed to the laminar-turbulent transition of the drops wake. It was also observed that the spatial dispersion, along horizontal cuts along their fall, evolved from a narrow to a wider monomodal distribution to bimodal one as the traveled distance increases. The acetone drops evaporated as they fall and although their velocity increased, the diameter reduction prevented the drops from reaching the critical transition Reynolds number, maintaining the dispersion in the horizontal positions relatively narrow. A maximum volume loss due to evaporation of 13% is recorded at the lower end of the observation region. Simplified theories based on the drag coefficients of fixed spheres closely predict the drops vertical positions as a function of time, for both evaporating and non-evaporating drops. Calculations based on heat and mass transfer correlations for fixed spheres show a satisfactory agreement when compared with the experimental observations of the radii of evaporating drops as a function of time.

Transition induced by wall-normal vibration in flow around a flat plate with roughness

The effects of wall-normal vibration on bypass transition in a boundary-layer flow over a flat plate with roughness elements in the form of circular cylinders are investigated using direct numerical simulations (DNS), linear Floquet analyses and dynamic mode decompositions (DMD). The vibration of the plate strengthens the streamwise vorticity, consequently enhancing the velocity streaks and reducing the critical Reynolds number for transition. A map is constructed to identify the coupling effect of the vibration amplitude and Reynolds number on transition. Among all investigated combinations of height and diameter of roughness, the critical Reynolds numbers at different vibration amplitude $A$ can be unified by a scaling function of $(1-10A)$ . Two instability modes are identified in the vibration-induced transition process: a wake mode immediately downstream of the roughness, related to the inviscid Kelvin–Helmholtz instability of the wall-normal shear in the wake; and a streak mode, in response to the spanwise shear of the streaky flow, occurring further downstream. The first one results in the generation of central hairpin vortices which then feed the second one. Further development of the streak instability leads to two arrays of hairpin vortices. Results from linear Floquet analyses and DMD further confirm the two modes of instability observed in DNS. A quantitative study suggests that the amplification of vibration-induced disturbance by the base shear dominates the production of streamwise vorticity and subsequently the hairpin vortices.

A numerical study of the side-wall effects on turbulent bands in channel flow at transitional Reynolds numbers

We investigated the side-wall effects on turbulent bands in channel flow at transitional Reynolds numbers by direct numerical simulations using the open source spectral-element code Nektar++. The width-to-height aspect ratio of 50:1 is considered for this study. Our study shows that turbulent bands can survive the collision with the side wall above bulk Reynolds number of Re≃1000 but decay below Re≃975, i.e. the critical Reynolds number should be approximately between the two Reynolds numbers. We also discussed about the underlying mechanism for the decay of the band at low Reynolds numbers and potential effects of larger spanwise channel widths than that considered in our study. The results are informative for experimental studies of channel flow turbulence at transitional Reynolds numbers.

Analysis of the onset and evolution of a dynamic stall vortex on a periodic plunging aerofoil

The onset and evolution of the dynamic stall vortex (DSV) are analysed by means of large eddy simulations of an SD7003 aerofoil undergoing periodic plunging motion in a transitional Reynolds number flow ($Re =6\times 10^{4}$). Interactions between upstream propagating Kelvin–Helmholtz instabilities and a shear layer formed at the leading edge trigger flow separation. The former appear to be related to acoustic waves scattered at the trailing edge due to initial vortex shedding. Two freestream Mach numbers ($M_{\infty }=0.1$and$0.4$) are employed to examine the flow differences due to compressibility variations. The existence of a common timing for the acoustic perturbations in both flows suggests a possible Mach number invariance for the birth of the Kelvin–Helmholtz instability. Increasing compressibility, however, induces earlier spanwise fluctuations, higher flow three-dimensionality and a weaker and more diffuse DSV, which is formed further downstream of the leading edge and has lower residency time. In order to better characterize the onset of the DSV, two empirical criteria are assessed: the leading edge suction parameter and the chord-normal shear layer height. Results demonstrate a higher robustness of the latter with respect to Mach number variations. Modal decomposition, performed with both the classical dynamic mode decomposition (DMD) and its multi-resolution variant (mrDMD), highlights key trends and demonstrates the capacity of the mrDMD to extract physically meaningful flow structures related to the stall onset. Such detailed characterization of the shear layer can be used for a systematic exploration of flow control strategies for unsteady aerofoils.

Enhanced settling and dispersion of inertial particles in surface waves

Particulate matter in the environment, such as sediment, marine debris and plankton, is transported by surface waves. The transport of these inertial particles is different from that of fluid parcels described by Stokes drift. In this study, we consider the transport of negatively buoyant particles that settle in flow induced by surface waves as described by linear wave theory in arbitrary depth. We consider particles that fall under both a linear drag regime in the low Reynolds number limit and in a nonlinear drag regime in the transitional Reynolds number range. Based on an analysis of typical applications, we find that the nonlinear regime is the most widely applicable. From an expansion in the particle Stokes number, we find kinematic expressions for inertial particle motion in waves, and from a multiscale expansion in the dimensionless wave amplitude, we find expressions for the wave-averaged drift velocities. These drift velocities are analogous to Stokes drift and can be used in large-scale models that do not resolve surface waves. We find that the horizontal drift velocity is reduced relative to the Stokes drift of fluid parcels and that the vertical drift velocity is enhanced relative to the particle terminal settling velocity. We also demonstrate that a cloud of settling particles released simultaneously will disperse in the horizontal direction. Finally, we discuss the accuracy of our expressions by comparing against numerical simulations, which show excellent agreement, and against experimental data, which show the same trends.

Leading-edge pressure gradient effect on boundary layer receptivity to free-stream turbulence

Free-stream turbulence (FST) induced boundary layer transition is an intricate physical process that starts already at the leading edge (LE) with the LE receptivity process dictating how the broad spectrum of FST scales is received by the boundary layer. The importance of the FST integral length scale, apart from the turbulence intensity, has recently been recognized in transition prediction but a systematic variational study of the LE pressure gradient has still not been undertaken. Here, the LE pressure gradient is systematically varied in order to quantify its effect on the transition location. To this purpose, we present a measurement technique for accurate determination of flat-plate boundary layer transition location. The technique is based on electret condenser microphones which are distributed in the streamwise direction with high spatial resolution. All time signals are acquired simultaneously and post-processed giving the full intermittency distribution of the flow over the plate in a few minutes. The technique is validated against a similar procedure using hot-wire anemometry measurements. Our data clearly shows that the LE pressure gradient plays a decisive role in the receptivity process for small integral length scales, at moderate turbulence intensities, leading to variations in the transitional Reynolds number close to 40 %. To our knowledge, this high sensitivity of LE pressure gradient to transition has so far not been reported and our experiments were therefore partly repeated using another LE to ensure set-up independence and result repeatability.

Turbulent flow around circular arcs

The flow around a circular arc is governed by the effect of the sharp leading edge and the arc's curvature. There is a range of incidences where a leading-edge separation bubble (LESB) is formed on the convex side of the arc, and the reattached boundary layer separates further downstream. Akin to foils and cylinders, for increasing values of the Reynolds number, the boundary layer turns from laminar to turbulent resulting in a step change in the forces, here termed force crisis. This phenomenon is characterized experimentally for an arc with a camber-to-chord ratio of 0.22 and for a range of the Reynolds number from 53 530 to 218 000. Forces are measured both in a towing tank and in a water tunnel, and particle image velocimetry is undertaken in the water tunnel. In stark contrast to cylinders, where the force crisis is associated with the laminar-to-turbulent transition of the boundary layer, here, it is found to be associated with the suppressed relaminarization of the boundary layer. In fact, the LESB is always turbulent at the tested conditions, and relaminarization occurs up to a combination of critical angles of attack and critical Reynolds numbers. The critical angle of attack varies linearly with the Reynolds number. These results may contribute to the design of thin cambered wings, sails, and blades at a transitional Reynolds number such as the wings of micro aerial vehicles, swept wings in subsonic flight, turbomachinery blades, and the sails of autonomous sailing vessels.

On Directional Sensitivity of Thermo-Anemometer Split-Fiber Probes

Hot-wire thermo-anemometer probes are extremely fragile and they are used mostly in clean flows with neither debris nor small particles to prevent sensor destruction. Consequently, application of hot-wire probes is limited mostly to clean laboratory environments, their employment in semi-industrial research is extremely rare, and not always successful. Film probes with deposited thin metallic sensors on cylindrical fibers are more rugged and can be successfully employed for research tasks in semi-industrial environment. Surprisingly the potentials of these probes are not yet fully utilized. Detailed investigation of direction characteristics of a split-fiber probe was carried out during the course of this work. Several interesting outcomes resulted from this study. First, it has been shown that the split-fiber probe direction sensitivity rises with the increasing velocity contrary to the decrease of the velocity sensitivity, which is a common hindrance to application of single-sensor thermo-probes to high-speed and transonic flows. Second, the analysis of the acquired data revealed a sudden shift in the effective zero angle offset. It can be speculated that such a shift can related to the transition of the laminar vortex street into the turbulent one. However, the observed shift occurred at Reynolds number values between 900 and 1000, which is markedly higher than the usually reported transitional Reynolds number range between 150 and 300. Finally, the resilience of split-fiber probes to impairment by in-flow debris has been demonstrated proving the probe ability for effective use of these probes in semi-industrial or even industrial research tasks.

Experimental assessment of scale-effects on the aerodynamic characterization of a transitionally-operating airfoil working under clean flow conditions

Wind tunnel tests are carried out upon a NACA0021 airfoil subjected to transitional Reynolds numbers. Transitionally-operating airfoils show a high sensitivity to external conditions and pose relevant measurement issues for capturing the physical processes adequately. On the global side, the employed set of techniques measures lift forces directly and uses the momentum-deficit method for drag coefficients. Locally, the development of transitional structures is acknowledged via surface pressure measurements carried out by pressure taps together with oil-flow visualizations. The coupling of such techniques with a well-founded uncertainty analysis shows two relevant aspects of the measurement protocolization: on the one hand, the limitations of either the global or local methods for completely accounting for all transitional phenomena. On the other hand, the fact that combining the proposed set of different measurement techniques with a systematic protocol is a mandatory requirement for achieving a holistic characterization of transitionally-operating airfoils.

Multi-scale study of the transitional shock-wave boundary layer interaction in hypersonic flow

A high-fidelity simulation of the massively separated shock/transitional boundary layer interaction caused by a 15-degrees axisymmetrical compression ramp is performed at a free stream Mach number of 6 and a transitional Reynolds number. The chosen configuration yields a strongly multiscale dynamics of the flow as the separated region oscillates at low-frequency, and high-frequency transitional instabilities are triggered by the injection of a generic noise at the inlet of the simulation. The simulation is post-processed using Proper Orthogonal Decomposition to extract the large scale low-frequency dynamics of the recirculation region. The bubble dynamics from the simulation is then compared to the results of a global linear stability analysis about the mean flow. A critical interpretation of the eigenspectrum of the linearized Navier–Stokes operator is presented. The recirculation region dynamics is found to be dominated by two coexisting modes, a quasi-steady one that expresses itself mainly in the reattachment region and that is caused by the interaction of two self-sustained instabilities, and an unsteady one linked with the separation shock-wave and the mixing layer. The unsteady mode is driven by a feedback loop in the recirculation region, which may also be relevant for other unsteady shock-motion already documented for shock-wave/turbulent boundary layer interaction. The impact of the large-scale dynamics on the transitional one is then assessed through the numerical filtering of those low wavenumber modes; they are found to have no impact on the transitional dynamics.

Numerical simulations of MHD flows around a 180-degree sharp bend under a strong transverse magnetic field

The quasi-two-dimensional flow of a liquid metal subjected to a strong transverse magnetic field around a 180-degree sharp bend is investigated by means of parametric numerical simulations where the Reynolds number Re, Hartmann number Ha and the gap ratio β (defined as the ratio of the gap thickness to the inlet width) vary in the respective ranges [100–50 000], [100–2000] and [0.04–1]. Both steady-state flow solutions and the evolution of unsteady flow regimes can be captured within this parameter space. The critical Reynolds number for transition from steady to unsteady flow increases as Ha increases for all β. It is shown, for 0.04 ⩽ β ⩽ 0.25, the critical Reynolds number remains almost linear relationship with the parameter Re/Ha0.9, whereas for β = 1, the key parameter is dominated by Re/Ha0.6. The present simulations aim to investigate the physical mechanism of this phenomenon and characterizing the position where the vortices are shed from the free shear layer. We discover that the vortices shedding is originated in the outlet region for 0.04 ⩽ β ⩽ 0.25 other than the turning part in bend region for β = 1. Additionally, the free shear layer separates the recirculation bubble from mainstream and its instability is proposed to interpret the transition, commonly known as Kelvin–Helmholtz instability. The effect of a strong transverse magnetic field on flow characteristics is considered such as the length of recirculation bubbles and the pressure drop between inlet and outlet. A further frequency analysis reveals that at the end of vortices shedding, the oblique waves resonance exists, or a new vortex street consisting of the vortices detached from the boundary layer and upstream fluctuations appears. Finally, according to the influence of β on the transition, we present a modified map of fluid regimes for prediction, which provides useful information for improved mixing and heat transport.