Mean Velocity Profiles Research Articles

Spatiotemporal Intermittency in Pulsatile Pipe Flow.

Despite its importance in cardiovascular diseases and engineering applications, turbulence in pulsatile pipe flow remains little comprehended. Important advances have been made in the recent years in understanding the transition to turbulence in such flows, but the question remains of how turbulence behaves once triggered. In this paper, we explore the spatiotemporal intermittency of turbulence in pulsatile pipe flows at fixed Reynolds and Womersley numbers (, ) and different pulsation amplitudes. Direct numerical simulations (DNS) were performed according to two strategies. First, we performed DNS starting from a statistically steady pipe flow. Second, we performed DNS starting from the laminar Sexl–Womersley flow and disturbed with the optimal helical perturbation according to a non-modal stability analysis. Our results show that the optimal perturbation is unable to sustain turbulence after the first pulsation period. Spatiotemporally intermittent turbulence only survives for multiple periods if puffs are triggered. We find that puffs in pulsatile pipe flow do not only take advantage of the self-sustaining lift-up mechanism, but also of the intermittent stability of the mean velocity profile.

Measurements of the static pressure near the surface in the atmospheric boundary layer

Measurements have been made of the three components of velocity and of the static pressure in the lowest 10 ​m of the atmospheric boundary layer. The measurements reported here were made on two occasions: the first with a single 10 ​m mast and the second with four 6 ​m masts. One-hour duration measurements at a sampling rate of 10 samples s−1 were processed for statistical properties including an assessment of the mean static pressure, and the time series processed for spectral properties. The mean velocity profile followed the expected boundary-layer log-region. An estimate of the mean static pressure compared to that above the boundary layer has been made and shows a dependency on the RMS (Root Mean Square) of dynamic pressure. The spectra of wind velocity and wind dynamic pressure follow the expected n−5/3 power-law decay rate in the inertial subrange, whereas static pressure spectra followed a decay rate close to n−4/3 - a result that was not predicted by published theory. Limited comparisons have been made with measurements from wind-tunnel boundary-layer flows, and with one other full-scale experiment. There is evidence from these comparisons that the static pressure spectra has a decay rate close to n−4/3 but there is also evidence of Reynolds-number sensitive. These measurements were made as part of a study of wind effects on buildings. The distinct spectral pattern of static pressure compared to that of dynamic pressure is a potential aid to identifying their separate contribution to wind loading and natural ventilation.

Shock-induced heating and transition to turbulence in a hypersonic boundary layer

Abstract

Breakup and coalescence of large and small bubbles in sudden expansions and contractions in vertical pipes

The present work studies the dynamics of large and small bubbles in sudden expansions and contractions in vertical pipes. The experimental apparatus was designed to permit changes in flow patterns through singularities provoked by an expansion followed by a contraction. The data were obtained through particle image velocimetry and the shadow sizer technique. Size and velocity distributions for small and long bubbles are presented for six vertical pipe positions and compared with existing theories for the motion of small and large confined bubbles. Results for the mean velocity profiles, local shear rate and turbulent kinetic energy of the continuous phase are also presented. Predictions on the permissible largest diameter of bubbles as a function of space coordinates and flow conditions based on phenomenological theories are compared with the experimental data. Results indicate that bubble breakup and coalescence are essentially ruled by the dynamic pressure forces of the turbulent motions, but shear induced breakup is also observed for the small and large bubbles. The formation of a gas pocket in the contraction is identified as an important promoter of bubble breakup.

Turbulent Mixing Process of a Round Jet With Slot Lobes

Abstract Turbulent mixing in the near region of a round jet with three slot lobes is examined via mean velocity and turbulent statistics and structures at a Reynolds number of 15,000. The design utilizes separate flow motivations upstream of each geometric feature, deviating from conventional nozzles or orifice plates. Immediate outlet velocity profiles are heavily influenced by opposing pressure gradients between the neighboring round and slot streams. Spanwise mean velocity profiles reveal the majority of the convective exchange between a given slot and the round center occurs in the immediate near field, but has lasting effects on the axial centerline profiles downstream. This is also reflected by the velocity half-widths, exhibiting asymmetry across the entirety of available measurements. Centerline turbulence intensities exhibit strong and short-lived isotropy. The increasingly anisotropic intensities found downstream are lower than similar geometries from the literature, implying that mixing development is inhibited. Reynolds stresses at the round-slot interface are significantly smaller than the round-stagnant exchange, but achieve a symmetric condition at x/D ≅ 4. Two-point spatial correlations of the fluctuating streamwise velocity exhibit stronger dependence toward the axial centerline at the round-slot interface in comparison to the nominal round radius. In contrast, spanwise velocity fluctuations exhibit nearly identical, localized behaviors on each side of the jet. Corresponding differences in streamwise integral length scale peak in the range 1.0 ≤ x/D ≤ 1.5, and so too do the turbulent structures in this area, as a result of the collated jet geometry.

Study on the flow field of cluster-six nozzles injector in an entrained flow gasifier model

As one of the key equipment of a gasifier, the injector unit of a gasifier has significant impacts on its flow filed, and further, the performance of gasifier. With the growth demand for higher gasification efficiency, new gasifier injector designs were kept being invented. In this paper, a pilot cluster-six nozzles (CSN) injector was designed and implemented on a simplified non-ignited entrained flow gasifier model in order to exam its performance, the formulated flow fields were compared with traditional single nozzle injector, results showed that the mean velocity profile along radial direction for CSN injector was similar to a Gaussian curve. Several equations based on the assumption of free turbulence flow were proposed in order to analyze the characteristics of the flow field. Compared with single nozzle injector, the centerline mean velocity of CSN injector decay more serious, which could reduce the gasifier volume about 50%, and the flow features, for example: the flow rate and the half-thickness under the same experiment conditions and cross section are about twice as much as in the single nozzle injector, and energy dissipation rate were also became faster. Experiment results also showed a better particle dispersion effect from the CSN injector, that the solid particles ejected from CSN injector were occupying more gasifier space and kept a longer residue time in gasifier, which could cause larger overall rate for gasification reaction and carbon conversion rate. These results indicated that the CSN injector can effectively improve the gasification performance and also provide more information for new gasifier injector design.

Ratio-cut background removal method and its application in near-wall PTV measurement of a turbulent boundary layer

Optical contamination due to wall reflection creates limitations for near-wall velocity field measurement via either particle image velocimetry (PIV) or particle tracking velocimetry (PTV). In this paper, a simple image pre-processing method, i.e. the ratio cut method, is proposed to deal with this problem. It is based on the ratio between the grayscale intensities of tracer particles and those of the laser-illuminated background, on which a direct minimum cut is applied on the basis of a non-dimensional threshold for background removal. To evaluate its performance in near-wall measurement, this ratio cut method, along with two other typical pre-processing methods, i.e. the minimum removal method and the proper orthogonal decomposition (POD) filtering method, are applied to particle images in the near-wall region of turbulent boundary layers over an opaque roughness wall (ORW), whose characteristic roughness height is small enough to be regarded as hydraulically smooth, but still gives rise to severe wall reflection. Results for a case involving a transparent smooth wall, which suffers less from wall reflection issues, and direct numerical simulation (DNS) data at a similar Reynolds number are employed as reference baselines for performance evaluation. The examination of pre-processed particle images, as well as the probability density function (PDF) of grayscale intensities, indicates that the ratio cut method is capable of eliminating time-dependent flare, reducing noise level, and retaining low-intensity particles in the ORW case. These features are almost completely absent in both the minimum removal method and the POD filtering method. In addition, PTV-obtained velocity statistics for an ORW, pre-processed by the ratio cut method, including data relating to fluctuating intensity and the PDF distribution of fluctuating velocity, are shown to be more consistent with those relating to baseline cases than data obtained by either of the the other two methods used for comparison. Moreover, evidence is also provided regarding the superiority and robustness of this approach, in terms of estimating the mean skin friction from the near-all mean velocity profile.

The law of the wall: A new perspective

The law of the wall, regarded as one of the very few pieces of turbulence hypothesis, predicts the mean-velocity profile (MVP) in a wall-bound flow. For about nine decades, the underlying physics of the law is deemed to be governed by an ad hoc mixing-length hypothesis. Here, we seek the origin of the law, for the first time, with the aid of a new hypothesis, which we call the mixing-instability hypothesis. The hypothesis unveils the previously unknown universal scaling behavior for the amplitude of turbulent ripples or waves (that cause spontaneous stretching and shrinking of turbulent eddies) within the overlap layer and accurately maps the experimental data of the MVPs for moderate to extremely large Reynolds numbers. This study offers a new mechanism of the momentum transfer in a turbulent wall-bound flow, calling for a revision of the conventional mixing-length hypothesis, which has persisted in standard textbooks on turbulence for many decades.

A review paper on heat transfer and flow dynamics in subsonic circular jets impinging on rotating disk

A review of the most important findings for jets impingement on rotating target is presented, the focus is on the heat transfer and flow dynamics in these jets. These jet configurations are encountered in many industrial applications. A significant number of research studies dealing with computational and experimental studies are reviewed. Different parameters are found to influence the flow and enhance mass and energy transfer in several heat configurations such as; Reynolds number (Re), nozzle geometry, spacing between jet exit and the impinging plate, jet impinging angle and the flow regime at the jet exit. There are a few studies that deal with heat transfer of a flow impinging on a rotating disk due to complexity of the flow structure and the challenges to conduct in-depth experimental investigation. Most studies present profiles of heat transfer coefficients, mean velocity and turbulence rates of the impinging flow. Many researches have reported that the LES can predict heat transfer and flow field data for different impinging angles to study the feedback mechanism between the nozzle and the plate.

On the wake structure of a micro-ramp vortex generator in hypersonic flow

In this paper, a direct numerical simulation is performed to study the wake structures of a micro-ramp vortex generator in the hypersonic flow. The whole evolution process of vortical structures of the wake flow has been carefully analyzed. First, the scaling laws for the profiles of mean velocities and fluctuations have been explored. The results show that the scaling laws based on the supersonic experiments can be directly applied in the hypersonic wake flow with a few discrepancies near the wall. Then, the detailed structures of arc-like vortices are examined, and the legs of vortices are found not being connected with each other. No full vortex ring is detected in the present simulation. At the downstream of the wake flow, the intensity of arc-like vortices has been augmented when passing the separation shock. The results reveal that a vortex train composed of arc-like vortices and shear layer is formed. With the help of the proper orthogonal decomposition, the impact of arc-like vortices on the heat flux has been revealed. The alternative positive and negative strips in the streamwise direction suggest the impinging process of arc-like vortices. The frequencies of the corresponding modes further prove that the strips are the footprint of arc-like vortices.

The O’KEYPS Equation and 60 Years Beyond

Some 60 years ago, six researchers obtained a semi-empirical equation that describes how the stability correction function for the mean velocity profile ( $$\phi _\mathrm{m}$$ ) in the atmospheric surface layer varies with the stability parameter—the famous O’KEYPS equation. Their derivations are essentially based on interpolation of the turbulent eddy viscosity between neutral and convective conditions. Comparing the O’KEYPS equation with new theoretical developments—such as phenomenological and cospectral budget models—suggests that Heisenberg’s eddy viscosity provides a unifying framework for interpreting the behaviour of $$\phi _\mathrm{m}$$ . The empirical coefficient in the O’KEYPS equation, which is on the order of 10 based on data fitting to observations, is found to be primarily linked to the increase of the size of turbulent eddies as instability increases. The ratio of the sizes of turbulent eddies under convective and neutral conditions is on the order of $$1{/}\kappa $$ , where $$\kappa $$ is the von Karman constant, and is modulated by the turbulent Prandtl number.

Pipe flow with large particles and their impact on the transition to turbulence

Large particles disturb a flow more than small particles. Using Magnetic Resonance Imaging (MRI) and pressure drop measurements we find that large spherical and cubic particles in pipe flow promote subcritical turbulent-like flow disturbances (as seen in the radial mean velocity and rms profiles at Re=700). These disturbances lead to significant changes in the laminar-turbulent transition at low particle concentrations ($l5$% per volume). We suggest these observations can be explained by the relative magnitude of (i) particle interactions, (ii) flow disturbances introduced by the particles and (iii) viscous dissipation in the system.

Transport of Turbulence Across Permeable Interface in a Turbulent Channel Flow: Interface-Resolved Direct Numerical Simulation

Turbulence transportation across permeable interfaces is investigated using direct numerical simulation, and the connection between the turbulent surface flow and the pore flow is explored. The porous media domain is constructed with an in-line arranged circular cylinder array. The effects of Reynolds number and porosity are also investigated by comparing cases with two Reynolds numbers (Reapprox 3000,6000) and two porosities (varphi =0.5,0.8). It was found that the change of porosity leads to the variation of flow motions near the interface region, which further affect turbulence transportation below the interface. The turbulent kinetic energy (TKE) budget shows that turbulent diffusion and pressure transportation work as energy sink and source alternatively, which suggests a possible route for turbulence transferring into porous region. Further analysis on the spectral TKE budget reveals the role of modes of different wavelengths. A major finding is that mean convection not only affects the distribution of TKE in spatial space, but also in scale space. The permeability of the wall also have an major impact on the occurrence ratio between blow and suction events as well as their corresponding flow structures, which can be related to the change of the Kármán constant of the mean velocity profile.

Evaluation of the momentum integral method to determine the wall skin friction in separated flows

The momentum integral-based method developed by Mehdi and White (Exp Fluids 50(1):43–51. https://doi.org/10.1007/s00348-010-0893-1 , 2011) for determining wall skin friction in turbulent wall-bounded flow is evaluated in separated flows in which independent estimates of wall skin friction are known. Owing to flow complexities, a direct measurement of the wall skin friction in separated flow is experimentally challenging. In this pursuit, the momentum integral-based method is particularly attractive as the method is mathematically exact and determination of the wall skin friction only requires measurement of the wall-normal profile of mean velocity and Reynolds shear stress. The present analysis uses existing experimental particle image velocimetry and direct numerical simulation data of flow over a backward-facing step as well as DNS over a smooth hump to demonstrate that the method is viable. The method is also shown to be viable in estimating the wall skin friction in flows over non-flat geometries.

Rough-wall turbulence in minimal flow units with rod-roughened walls

Numerical simulation of minimal flow units (MFUs) can obtain “healthy turbulence” below a certain wall-normal height by limiting the effects of large-scale motions in the outer region. By “health,” it is meant that the mean velocity profile is consistent with the full-sized flow. In the present study, MFUs with rod-roughened walls at friction Reynolds numbers of 1000, 2000, and 4000 are studied by direct numerical simulation. For all the minimal channels, the domain size in streamwise and spanwise directions and the geometric parameters of roughness elements remain unchanged under the normalization of viscous units. The spurious spanwise uniform motions (SUM), induced by the narrow width of MFU, have significant contribution to turbulent fluctuations, especially to pressure. The spurious SUM are proved to be structures traveling downstream, holding strong relationship with the domain width. A new decomposition method is proposed to eliminate the spurious SUM. The results of MFU show that the roughness functions at different Reynolds numbers agree well with each other, implying that the effect of roughness on the main flow is independent of Reynolds numbers. In the context of the same wall roughness, the turbulent fluctuations and the roughness-induced fluctuations exhibit good Reynolds number independence. Additionally, the results of premultiplied spectra of the three velocity components suggest that the MFU could represent the near-wall small-scale motions within the full-sized domain. The universal signals extracted from the full-sized channel agree well with the near-wall velocity fluctuations in the MFU for all three velocity components.

Wave-Current Flow and Vorticity Close to a Fixed Rippled Bed

An experimental study of wave and current interaction over ripples is presented in this paper. The campaign was carried out at the shallow water tank at the Danish Hydraulic Institute (DHI, Denmark), in the framework of the TA WINGS (Waves plus currents INteracting at a right anGle over rough bedS), funded by the European Union (EU) through the Hydralab+ program. Mean velocity profiles, measured with acoustic Doppler velocimeters for different flow conditions including current only, wave only and wave plus current were recorded and allowed to recover flow and vorticity fields. Recirculating cells in both wave only and wave plus current conditions form but they flatten when the current superposes over the wave. It was found that the superposition of current reduces the undertow present in the case of only waves and leads to an increase of vorticity outside the boundary layer. Instead, inside the boundary layer, the vorticity is dumped by the effect of current.

Direct numerical simulation of turbulent bubbly down flow using an efficient CLSVOF method

We use direct numerical simulations (DNS) to investigate the turbulent modulation due to the presence of bubbles in vertical channels flowing downward. The Reynolds number for single-phase flow based on half channel height h* and friction velocity is Reτ= 180. A density and viscosity ratio of ρd*/ρc*=0.01 and μd*/μc*=0.018 is chosen for two void fractions of ϵ=1.2% and ϵ=2.4%. For each void fraction three different bubble sizes are simulated: D/h=0.2130, 0.2684 and 0.3382, where D denotes the diameter of the bubbles. Numerical simulations are based on multiple markers Coupled Level-Set/Volume-of-Fluid (CLSVOF) method. To improve the efficiency of this method, a fast pressure-correction method is used in order to enable the simulation to exploit a constant coefficient Poisson equation which can be solved with FFT-based technique. Extensive verification and validation were performed and perfect accuracy and agreement are obtained. In all the simulations performed in this work, the new Poisson solver showed a minimum speedup of 22 times.Accumulation of bubbles in the core region of the channel for all cases is observed, which forms a bubble-free layer in the near-wall region. The presence of bubbles resulted in considerable modification in the mean velocity profile compared to single-phase flow. Another common observation is that all the components of velocity fluctuations in the near-wall region decrease with increasing void fraction and decreasing wall layer thickness. The opposite happens in the core region, where the presence of bubbles favours turbulence. With respect to the bubble size, the wall-normal and spanwise velocity fluctuations decrease in the near-wall region for smaller bubbles, however, the streamwise velocity fluctuations remained almost unaffected. The investigation of turbulent kinetic budgets shows that, unlike single-phase flow, the dissipation terms rises to large values in the core region of the channel. This behaviour is referred to the presence of bubbles and hence enhancement of turbulent kinetic energy in the core region.

A review of drag reduction by additives in curved pipes for single‐phase liquid and two‐phase flows

AbstractThe effect of drag‐reducing agents (DRAs) on fluid flows in straight pipes has been well documented. Key among these is the effect of DRAs on turbulence statistics (Reynolds shear stress, turbulence intensity, streamwise and wall‐normal velocity fluctuation among others). These primary effects result in secondary effects such as modification of mean velocity profile and reduction in frictional losses (drag reduction, DR). Interestingly, in curved pipe flows, the characteristic of flow is more complex due to secondary flow, wake effects and under‐developed flow characteristics. Therefore, a review of investigations on the effect of DRAs in curved pipe flows is presented in this paper. The paper highlights the difference between DR in straight and curved conduits as well as the interaction between DRAs and flow characteristics of curved pipe flows. Proposed mechanisms of DR, and factors that influence their effectiveness also received attention. It was shown that significant DR can be achieved in curved pipes. A review of various experimental results revealed that DR by additives in curved pipes is generally lower than in straight pipes but with certain similarities. It decreases with increase in curvature ratio and is more pronounced in the transition and turbulent flow regimes. Maximum DR asymptote differed between straight and curved pipes and between polymer and surfactant. Due to the limited studies in the area of DR for gas‐liquid flow in curved pipes, no definite conclusion could be drawn on the effect of DRAs on such flows. A number of questions remain such as physical interaction between molecules of DRA and flow features such as secondary flow streamlines and wakes. Hence, some research gaps have been identified with recommendations for areas of future researches.

Calculation of the mean velocity profile for strongly turbulent Taylor–Couette flow at arbitrary radius ratios

Abstract

Relaminarized and recovered turbulence under nonuniform body forces

We show that wall-bounded turbulence can be relaminarized and reorganized by adding nonuniform streamwise body forces. A nonuniform body force can distort the parabolic mean velocity profile, thus altering turbulence production due to mean shear. In the quasi-laminar state, all Reynolds stress tensor components are fairly weak except for streamwise fluctuations far from the wall, indicating a collapse of the near-wall turbulence self-sustaining cycle. In the recovered turbulence regime, the Reynolds shear stress has a negative range in the bulk connected with a positive range near the wall corresponding to the M-shaped velocity profile.