Large-scale Secondary Flow Research Articles

Effects of herringbone riblets on shock-wave/turbulent boundary-layer interactions

In the experiment reported in this paper, a spanwise array of herringbone riblets strips is applied upstream of the interaction region between an impinging shockwave and a turbulent boundary layer developing along a flat plate boundary layer at a freestream Mach number of 1.85. High-speed schlieren photography, surface oil flow visualization and PSP are used to examine the effect of herringbone riblets on the characteristics of the shockwave-boundary layer interactions. It shows that despite that the height of the riblets is less than 2 % of the local thickness of the undisturbed boundary layer, a profound modification to the shockwave-boundary layer interaction zone is observed, and the overall size of the separation bubble is decreased. The observed control effects are attributed to the large-scale secondary flow structures produced by the directional riblets. To the best knowledge of the author, this is the first study evaluating the control effect of herringbone riblets on shock wave and turbulent boundary layer interactions in supersonic flow using the experimental method.

A systematic investigation into the effect of roughness on self-propelled swimming plates

This study examines the effects of surface topography on the flow and performance of a self-propelled swimming (SPS) body. We consider a thin flat plate with an egg-carton roughness texture undergoing prescribed undulatory swimming kinematics at Strouhal number $0.3$ and tail amplitude to length ratio $0.1$ ; we use plate Reynolds numbers $Re=6$ , 12 and $24\times 10^3$ , and focus on $12\,000$ . As the roughness wavelength is decreased, we find that the undulation wave speed must be increased to overcome the additional drag from the roughness and maintain SPS. Correspondingly, the extra wave speed raises the power required to maintain SPS, making the swimmer less efficient. To decouple the roughness and the kinematics, we compare the rough plates to equivalent smooth cases by matching the kinematic conditions. We find that all but the longest roughness wavelengths reduce the required swimming power and the unsteady amplitude of the forces when compared to a smooth plate undergoing identical kinematics. Additionally, roughness can enhance flow enstrophy by up to 116 % compared to the smooth cases without a corresponding spike in forces; this suggests that the increased mixing is not due to increased vorticity production at the wall. Instead, the enstrophy is found to peak strongly when the roughness wavelength is approximately twice the boundary layer thickness over the $Re$ range, indicating the roughness induces large-scale secondary flow structures that extend to the edge of the boundary layer. This study reveals the nonlinear interaction between roughness and kinematics beyond a simple increase or decrease in drag, illustrating that roughness studies on static shapes do not transfer directly to unsteady swimmers.

Controlling secondary flows in Taylor–Couette flow using axially spaced superhydrophobic surfaces

Turbulent shear flows are abundant in geophysical and astrophysical systems and in engineering-technology applications. They are often riddled with large-scale secondary flows that drastically modify the characteristics of the primary stream, preventing or enhancing mixing, mass and heat transfer. Using experiments and numerical simulations, we study the possibility of modifying these secondary flows by using superhydrophobic surface treatments that reduce the local shear. We focus on the canonical problem of Taylor–Couette flow, the flow between two coaxial and independently rotating cylinders, which has robust secondary structures called Taylor rolls that persist even at significant levels of turbulence. We generate these structures by rotating only the inner cylinder of the system, and show that an axially spaced superhydrophobic treatment can weaken the rolls through a mismatching surface heterogeneity, as long as the roll size can be fixed. The minimum hydrophobicity of the treatment required for this flow control is rationalized, and its effectiveness beyond the Reynolds numbers studied here is also discussed.

The influence of roughness-element-spacing on turbulent entrainment over spanwise heterogeneous roughness

Spanwise heterogeneous surfaces have been found to modulate local turbulent entrainment by inducing large-scale secondary flows (SFs). This work aims to clarify the variations of the local and total entrainment fluxes with the intensity of SF. The SF intensity is controlled by the spanwise spacing between adjacent ridge-type roughness elements s. It is found that, for the two components of turbulent entrainment (nibbling and engulfment), their local fluxes grow rapidly with the SF intensity in the downwash regions; asymmetrically, both fluxes decline slowly and then become relatively stable in the upwash regions. In other words, the downwash flow is more effective in modulating the local entrainment flux than the upwash flow. Therefore, the largest total entrainment flux would be induced at s≈δ, where the SF intensity is the largest (δ is the boundary layer thickness). Moreover, the emergence of the tertiary flow when s≳2δ would lower the local entrainment flux, and reduce the total flux to the same level of the homogeneous roughness. Therefore, it is deduced that a heterogeneous surface with a large roughness-element spacing could not enhance the total entrainment flux.

Direct numerical simulations of turbulent flow over the converging and diverging riblets

Different from conventional streamwise-aligned riblets, converging and diverging (C–D) riblets are arranged obliquely along the main-flow direction, intending to induce a large-scale secondary flow that modulates or controls the existing large-scale vortical structures in wall turbulence. In this study, we perform direct numerical simulations of turbulent flow over the C–D riblets at a low Reynolds number and investigate the impacts of the C–D riblets on aerodynamic forces, turbulence statistics, and coherent structures. The results show that the C–D riblets can reduce the skin-friction drag, but at the expense of a significantly increased pressure drag in the diverging region, which leads to an increase in the total drag. We present detailed mean and statistical flow-fields to assess the flow characteristics in the presence of the C–D riblets, including modifications on the distributions of velocities, pressure, Reynolds stresses, and turbulence kinetic energy. Moreover, the re-arrangement of turbulence structures over the C–D riblets is examined in terms of instantaneous flow-fields and two-point correlations. The findings provide more insight into the physics of flow over C–D riblets and may contribute to the further development of this flow control strategy.

Turbulent secondary flows in low aspect ratio open-channels over heterogeneous surfaces: Anisotropy in forces

Studies of turbulent flows over heterogeneous surfaces revealed elevated turbulent kinetic energy and Reynolds shear stress in low-momentum-path regions. These regions induce large-scale multi-cellular secondary flows. The aim of the current study is to analyze the influence of these regions on drag, lift, and lateral forces acting on spherical particles at different exposure levels, thereby addressing the hitherto unknown contribution of the spanwise inhomogeneities. For this reason, numerical simulations of turbulent open-channel flow with varying aspect ratio (AR=1,3,5) over single-sized spherical particles with diameter D were studied. Ensemble-averaged cross-flow velocity vectors showed large-scale secondary flows to penetrate in-between the spherical particles, therefore stretching over the entire flow depth. Their magnitude above 0.8D was observed to range between 12.9%and14.9% of U. Strong tertiary vortices in the vicinity of the lateral walls were identified by analysis of swirl strength. Triple decomposition of streamwise velocity fluctuations showed strong backflow at the trailing edge of the spherical particles in high-momentum-path (HMP) regions. Furthermore, it was found that drag forces are higher in HMPs, which is attributed to the larger streamwise pressure gradient.

Direct numerical simulations of a turbulent channel flow developing over convergent–divergent riblets

Direct numerical simulations of a turbulent channel flow developing over convergent–divergent (C–D) riblets at a Reynolds number of Reb=2800 are presented. It is found that, with a fixed normalized riblet height of h+=5, as the ratio of the riblet spacing and the height, s/h, increases from 2 to 10, the strength of the large-scale secondary flow motion Γ generated by the C–D riblets peaks around s/h=4 when the C–D riblets behavior lies between d- and k-type roughness. Compared to the baseline case with smooth walls, the turbulent activities and energy level increase significantly and peak at s/h=4 when Γ is the highest. It is shown that while the intense local turbulent kinetic energy (TKE) production occurring in the diverging region is caused by the high local velocity gradient due to the downwelling of the secondary flow, the strong local TKE production occurring in the converging region is caused by the high turbulent shear stress associated with upwelling. Furthermore, the TKE transport characteristics are significantly altered by the secondary flow motion, especially over the converging and diverging regions. The secondary flow is not caused by the local imbalance between turbulent kinetic energy production and dissipation but by the yawed riblets. It is then more appropriate to classify this flow as a Prandtl’s secondary flow of the first kind, also known as the geometry-driven secondary flow. Finally, in comparison with the baseline case, the drag increases for all the riblet cases examined, and a direct correlation between the amount of drag and intensity of the secondary flow exists, both peaking at s/h=4.

Drag decomposition of laminar channel flows developing over convergent–divergent riblets

Convergent–divergent (C–D) riblets are known to induce large-scale secondary flow motion in laminar flow that may point to their potential for flow separation control and heat transfer enhancement. In this paper, a fully-developed pressure-driven laminar channel flow with C–D riblets is studied numerically. The effects of Reynolds number, riblet wavelength and riblet cross-sectional shape on the secondary flow and drag characteristics are investigated. An exact expression for the drag coefficient of this flow is derived based on the balance of kinetic energy principle for a rough-wall channel. Furthermore, the triple decomposition technique is used to identify the contribution to drag production from the mean velocity field, the small- and large-scale dispersive flow field. Our results show that the normalized drag increment starts to rise when the secondary flow begins to alter the velocity field across the span as the Reynolds number based on the channel height (ReH) increases above 100, a behavior which is very different from that of a laminar channel flow developing over homogeneous roughness in which the normalized drag increment is found to remain constant up to a much greater Reynolds number due to an absence of secondary flow. It is found that the drag produced by C–D riblets is predominantly caused by the wall-normal gradient of streamwise velocity. In addition, while the drag increment is predominantly caused by the mean and small-scale dispersive velocity at ReH≤100, the contribution from the large-scale dispersive velocity field increases rapidly with the Reynolds number and becomes dominant as ReH exceeds 400. It is also observed that the secondary flow scales with the riblet wavelength Λ, and its swirling strength peaks around Λ=1.25H, which is accompanied by a drag maxima at ReH≥400. Finally, among the three C–D riblet cross-sectional shape (rectangular, triangular and sinusoidal) examined here, the triangular riblet pattern is found to produce a secondary motion with a similar strength to the other two shapes but with less drag penalty.

Direct numerical simulation of turbulent elliptical pipe flow under system rotation about the major axis

The effect of Coriolis forces on the turbulent flow in an elliptical pipe subjected to spanwise rotation has been studied using direct numerical simulations (DNS). In response to the system rotation, large-scale secondary flows appear in the cross-stream plane as a pair of counter-rotating vortices, which significantly impact the turbulence statistics and structures of the flow. The characteristics of the turbulence field is investigated in both physical and spectral spaces through analyses of the first- and second-order statistical moments, as well as the budget balance of the Reynolds stress transport equation and coherent flow structures.

Turbulent secondary flows in channels with no-slip and shear-free boundaries

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Dilatancy-driven secondary flows in dense granular materials

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Roughness-induced secondary flows in stably stratified turbulent boundary layers

Spanwise heterogeneous roughness, more specifically, spanwise-adjacent strips of relatively high and low roughness, is known to cause large-scale secondary flows in the vertical domain in neutral turbulent boundary layers. In this work, we study the response of secondary vortices to thermal stratification with focus on the stably stratified case. We systematically vary the Monin–Obukhov (MO) length scale from L/h = 0.3, which corresponds to relatively strong stratification, to ∞, which corresponds to the neutral condition. Here, L is the MO length and h is an outer length scale. The results show that stable stratification suppresses the vertical motions and reduces the vertical size and strength of the first off-wall secondary vortex. Moreover, the reduced vertical extent of the first off-wall vortex and the shear near its top together give rise to a second vortex, and the second to a third vortex. This leads to a stack of secondary vortices in a stably stratified boundary layer flow with decreasing strength when moving away from the wall.

Influence of viscoelasticity on mixing performance of primary and secondary circulation flows in stirred vessels

The aim of this study was to experimentally verify the mixing performance of primary and secondary circulation flows appearing in turbulence in stirred vessels of Newtonian and viscoelastic fluids. Impeller torque measurements, flow visualization, and particle image velocimetry and planar laser-induced fluorescence measurements were performed. In the case of the Newtonian fluid, a tornado-like flow that was a combination of primary and secondary circulation flows was observed with small-scale turbulent eddies. This flow required a moderate torque power and shortened the mixing time. Conversely, a large-scale primary circulation flow of a slow rigid vortex with no small-scale turbulent eddies was observed in the viscoelastic fluid. Although the discharge flow was enhanced or diminished dependently on the Reynolds number and surfactant concentration, it induced slow large-scale secondary circulation flows in the stirred vessel. As a result, the tornado-like flow disappeared, and these flows resulted in a long time constant of the mixing. Even with such flow characteristics, while the low-concentration case indicates that a low torque corresponding to the driving power is needed to drive the flow, the high-concentration case suggests that the high torque is due to the occurrence of additional viscoelastic stress.

Secondary flow in a laminar boundary layer developing over convergent-divergent riblets

Convergent-divergent (C-D) riblets are a type of bio-inspired surface pattern. They are known to induce secondary flow in a boundary layer that may point to their potential for surface friction drag reduction and flow separation control. In this paper, a systematic investigation of the effect of riblet height, wavelength and yaw angle on the secondary flow in a flat-plate laminar boundary layer developing over a C-D riblet section is undertaken. The large-scale secondary flow in the cross-stream plane belongs to Prandtl’s first kind, and is induced by the spanwise velocity generated by the yawed riblet passages. The exact structure of this secondary flow depends on the relative size of riblet height and wavelength to the local boundary layer thickness, and three different patterns are observed within the range of parameters examined. As the wavelength increases, the strength of the secondary flow increases firstly and then levels off at large wavelengths, whereas the average strength per unit area exhibits a peak around a ratio between wavelength and local boundary layer thickness of 1. As the yaw angle increases from 20o to 70o, the strength of the secondary flow exhibits a parabolic trend and achieves a maximum around a yaw angle of 45o. The findings from this work can be used to inform the choice of riblet geometry for maximizing the strength of the secondary flow in a given boundary layer flow.

Direct Numerical Simulation of Turbulent Flow in a Circular Pipe Subjected to Radial System Rotation

Direct numerical simulations have been performed with a high-order spectral element method computer code to investigate the Coriolis force effect on a fully-developed turbulent flow confined within a circular pipe subjected to radial system rotations. In order to study the radially rotating effects on the flow, a wide range of rotation numbers (Roτ) have been tested. In response to the system rotation imposed, large-scale secondary flows appear as streamwise counter-rotating vortices, which highly interact with the boundary layer and have a significant impact on the turbulent flow structures and dynamics. A quasi Taylor-Proudman region occurs at low rotation numbers, where the mean axial velocity is invariant along the rotating axis. As the rotation number increases, laminarization occurs near the bottom wall of the pipe, and the flow becomes fully laminarized when the rotation number approaches Roτ = 1.0. The characteristics of the flow field are investigated in both physical and spectral spaces, which include the analyses of the first- and second-order statistical moments, pre-multiplied spectra of velocity fluctuations, budget balance of the transport equation of Reynolds stresses, and coherent flow structures.

Secondary motion in turbulent pipe flow with three-dimensional roughness

The occurrence of secondary flows is investigated for three-dimensional sinusoidal roughness where the wavelength and height of the roughness elements are systematically altered. The flow spanned from the transitionally rough regime up to the fully rough regime and the solidity of the roughness ranged from a wavy, sparse roughness to a dense roughness. Analysing the time-averaged velocity, secondary flows are observed in all of the cases, reflected in the coherent stress profile which is dominant in the vicinity of the roughness elements. The roughness sublayer, defined as the region where the coherent stress is non-zero, scales with the roughness wavelength when the roughness is geometrically scaled (proportional increase in both roughness height and wavelength) and when the wavelength increases at fixed roughness height. Premultiplied energy spectra of the streamwise velocity turbulent fluctuations show that energy is reorganised from the largest streamwise wavelengths to the shorter streamwise wavelengths. The peaks in the premultiplied spectra at the streamwise and spanwise wavelengths are correlated with the roughness wavelength in the fully rough regime. Current simulations show that the spanwise scale of roughness determines the occurrence of large-scale secondary flows.

StreamVane Turbofan Inlet Swirl Distortion Generator: Mean Flow and Turbulence Structure

Engine/airframe integration in advanced aircraft concepts must account for nonuniform flows ingested by turbofan engines. In this work, flow details from a vane-based distortion generator were analyzed for turbulence structure and aerodynamic scaling of the mean flow. Experimental results were obtained using particle image velocimetry in a small-scale facility and a full-scale research turbofan engine for the same vane geometry. Tests were performed at nearly the same Mach number to isolate Reynolds number effects, but analysis and prior work indicate that the flow development downstream of the vanes is Mach number independent in the subsonic regime. As hypothesized from inviscid vortex dynamics, the secondary mean flow angles were consistent across scales, indicating Reynolds number independence of the large-scale secondary flow profile generated. Vane wakes produced a complex structure in the streamwise velocity component not seen in the streamwise vorticity, which resembles the distribution from the desired secondary flow profile. The most intense turbulence is concentrated in the outer radial regions of the duct and, as shown by contrast to vane wake-dominated regions, is dominated by shear flow turbulence and unsteadiness due to the distortion profile itself rather than vane wakes. Taken together, these results provide fundamental understanding of the aerodynamics of swirling flows needed for implementing complex turning vanes in the design of distortion generators.

Rapid mixing by turbulent-like electrokinetic microflow

Rapid mixing has been achieved in a pressure-driven microflow which is forced under AC electric field. In our previous investigations, the mixing on large scale at the centerline of microchannel has been studied. Here, we show that the evaluation on mixing effect by flow visualization could be misleading, if its temporal resolution is not sufficiently high. By using single-point laser induced fluorescence (LIF) method, the mixing on both large and small scales can be investigated with high spatiotemporal resolution. It is found fast mixing is not only achieved at the centerline, but also in the majority of cross-sectional area, even near the bottom wall region. This is resulted from the large scale secondary flow due to unbalanced AC electroosmotic flow near the bottom wall. The temporal −5/3 spectrum of concentration measured with LIF in our previous investigations is also supported by the spatial spectrum of concentration. The physical process of mixing on small scales is further investigated by the flatness of concentration gradients.

Pollutant Dispersion in Boundary Layers Exposed to Rural-to-Urban Transitions: Varying the Spanwise Length Scale of the Roughness

Both large-eddy simulations (LES) and water-tunnel experiments, using simultaneous stereoscopic particle image velocimetry and laser-induced fluorescence, have been used to investigate pollutant dispersion mechanisms in regions where the surface changes from rural to urban roughness. The urban roughness was characterized by an array of rectangular obstacles in an in-line arrangement. The streamwise length scale of the roughness was kept constant, while the spanwise length scale was varied by varying the obstacle aspect ratio l / h between 1 and 8, where l is the spanwise dimension of the obstacles and h is the height of the obstacles. Additionally, the case of two-dimensional roughness (riblets) was considered in LES. A smooth-wall turbulent boundary layer of depth 10h was used as the approaching flow, and a line source of passive tracer was placed 2h upstream of the urban canopy. The experimental and numerical results show good agreement, while minor discrepancies are readily explained. It is found that for l/h=2 the drag induced by the urban canopy is largest of all considered cases, and is caused by a large-scale secondary flow. In addition, due to the roughness transition the vertical advective pollutant flux is the main ventilation mechanism in the first three streets. Furthermore, by means of linear stochastic estimation the mean flow structure is identified that is responsible for street-canyon ventilation for the sixth street and onwards. Moreover, it is shown that the vertical length scale of this structure increases with increasing aspect ratio of the obstacles in the canopy, while the streamwise length scale does not show a similar trend.

Non-Newtonian perspectives on pulsatile blood-analog flows in a 180° curved artery model

Complex, unsteady fluid flow phenomena in the arteries arise due to the pulsations of the heart that intermittently pumps the blood to the extremities of the body. The many different flow waveform variations observed throughout the arterial network are a result of this process and a function of the vessel properties. Large scale secondary flow structures are generated throughout the aortic arch and larger branches of the arteries. An experimental 180° curved artery test section with physiological inflow conditions was used to validate the computational methods implemented in this study. Good agreement of the secondary flow structures is obtained between experimental and numerical studies of a Newtonian blood-analog fluid under steady-state and pulsatile, carotid artery flow rate waveforms. Multiple vortical structures, some of opposite rotational sense to Dean vortices, similar to Lyne-type vortices, were observed to form during the systolic portion of the pulse. Computational tools were used to assess the effect of blood-analog fluid rheology (i.e., Newtonian versus non-Newtonian). It is demonstrated that non-Newtonian, blood-analog fluid rheology results in shear layer instabilities that alter the formation of vortical structures during the systolic deceleration and onwards during diastole. Additional vortices not observed in the Newtonian cases appear at the inside and outside of the bend at various times during the pulsation. The influence of blood-analog shear-thinning viscosity decreases mean pressure losses in contrast to the Newtonian blood analog fluid.