Oscillatory Pipe Flow Research Articles

Shear-induced particle migration in a cement slurry under oscillatory pipe flow

Shear-induced particle migration in a cement slurry under oscillatory pipe flow

Stokes layers in oscillatory flows of viscoelastic fluids

<h2>Abstract</h2> Oscillatory fluid flows play an important role in industrial problems such as pumping, drilling, and oil recovery, and in physiological processes such as mucous flow in respiration and blood pumping. A key concept in oscillatory flows is the Stokes layer, i.e. the region of fluid adjacent to a wall that is in motion as a result of the wall oscillatory motion along its own plane. In this talk we will discuss oscillatory flows of viscoelastic fluids from the perspective of Stokes viscoelastic layers. We will first revisit Stokes' second problem for a viscoelastic fluid modelled by a single-mode Maxwell constitutive equation, and the generation of viscoelastic shear waves. Next, we will turn the attention to wall-bounded zero-mean oscillatory flows, for which we will identify the governing dimensionless variables and discuss the presence of resonances in the one-dimensional base flow. Finally, we will present experimental evidence of the destabilization of the one-dimensional base flow for a wormlike micellar solution in a cylindrical pipe as the oscillatory forcing increases, and sketch a perturbative analysis based on the Giesekus constitutive equation that links the first instability of the base flow to the divergence of normal radial stresses. If there is enough time, we will also present recent experimental results of oscillatory pipe flow of shear-thinning non-elastic solutions.

Simplified Transition and Turbulence Modeling for Oscillatory Pipe Flows

One-dimensional unsteady Reynolds-averaged Navier–Stokes computations were performed for oscillatory transitional and turbulent pipe flows and the results were validated against existing experimental data for a wide variety of oscillatory Reynolds and Womersley numbers. An unsteady version of the Johnson–King model was implemented with optional near-wall modification to account for temporal pressure gradient variations, and the predictions were compared with those of the Spalart–Allmaras and k–ε turbulence models. Transition and relaminarization were based on empirical Womersley number correlations and assumed to occur instantaneously: in the former case, this assumption was valid, but in the latter case, deviations between data and predictions were observed. In flows where the oscillatory Reynolds numbers are substantially higher than the commonly accepted steady critical value (~2000), fully or continuously turbulent models produced the best correspondence with experimental data. Critically and conditionally turbulent models produced slightly inferior correspondence, and no significant benefit was observed when near-wall pressure gradient effects were implemented or when common one- and two-equation turbulence models were employed. The turbulent velocity profiles were mainly unaffected by the oscillations and this was explained by noting that the turbulent viscosity is significantly higher than its laminar counterpart. Thus, a turbulent Womersley number was proposed for the analysis and categorization of oscillatory pipe flows.

Non-modal transient growth of disturbances in pulsatile and oscillatory pipe flows

Abstract

Axial conduction and dissipation in oscillatory laminar pipe flow at low and high frequencies

The problem of fully developed laminar fluid flow in pipes, driven by an oscillatory pressure gradient, can be solved exactly for the time-dependent velocity field and related quantities such as flow rate and tidal displacement. When dissipation is neglected and the momentary axial variation of temperature is assumed to be linear, the corresponding thermal energy equation describing heat transfer along a pipe connecting two reservoirs at different temperatures can also be solved to yield exact solutions for the time-dependent temperature field, axial heat flux, and effective axial conductivity. In this paper, it is shown that these exact solutions for the unsteady temperature field are invalid at low Womersley numbers because the momentary axial variation of temperature is not linear. When the thermal energy equation is written in quasisteady form, approximate quasisteady analytical solutions can be found for the temperature field, which yield effective axial conductivities several orders of magnitude greater than those given by the low-Womersley-number, unsteady-flow solution. It is also shown that the conditions under which effects of dissipation on axial heat transfer become significant, at high Womersley numbers, can be determined by a simple criterion. When dissipation is significant, exact solutions for the unsteady temperature field are invalid at high Womersley numbers because the momentary axial variation of temperature is also nonlinear.

Heat Transfer Enhancement by Sinusoidal Motion of a Water-Based Nanofluid

The oscillatory flows are often utilized in order to augment heat transfer rates in various industrial processes. It is also a well-known fact that nanofluids provide significant enhancement in heat transfer at certain conditions. In this research, heat transfer in an oscillatory pipe flow of both water and water–alumina nanofluid was studied experimentally under low frequency regime laminar flow conditions. The experimental apparatus consists of a capillary tube bundle connecting two reservoirs, which are placed at the top and the bottom ends of the capillary tube bundle. The upper reservoir is filled with the hot fluid while the lower reservoir and the capillary tube bundle are filled with the cold fluid. The oscillatory flow in the tube bundle is driven by the periodic vibrations of a surface mounted on the bottom end of the cold reservoir. The effects of the frequency and the maximum displacement amplitude of the vibrations on thermal convection were quantified based on the measured temperature and acceleration data. It is found that the instantaneous heat transfer rate between de-ionized (DI) water (or the nanofluid)-filled reservoirs is proportional to the exciter displacement. Significantly reduced maximum heat transfer rates and effective thermal diffusivities are obtained for larger capillary tubes. The nanofluid utilized oscillation control heat transport tubes achieve high heat transfer rates. However, heat transfer effectiveness of such systems is relatively lower compared to DI water filled tubes.

Assessment of the transition k-k-ω model application to transitional oscillatory pipe flows.

The flow transition from laminar to turbulent inside of typical thermoacoustic devices influences the heat-exchange capacities of these devices and dramatically impacts overall performances as well. A few measurements [Eckmann and Grotberg (1991), J. Fluid Mech. 222, 329-350; Hino, Sawamoto, and Takasu (1976). J. Fluid Mech. 75, 193-207] and direct simulations [Feldmann and Wagner (2012). J. Turbul. 13(32), 1-28; Feldmann and Wagner (2016a). New Results in Numerical and Experimental Fluid Mechanics X, pp. 113-122] were reported that describe the transitional oscillatory flows; however, almost no turbulence model has been developed that enables accurate detection and characterization of the reported intermittent turbulent fluctuations. The present work aims to assess the applicability of the k-kL-ω transition model to transitional oscillatory pipe flows. A sinusoidal pressure gradient is introduced into ANSYS finite-volume solver for flow field simulation at different acoustic frequencies, while a friction Reynolds number of 1440 is retained. The stationary turbulent and the laminar oscillatory pipe flows are first considered for validation and model calibration against published LDA measurements [Durst, Kikura, Lekakis, Jovanovic, and Ye (1996). Exp. Fluids 20, 417-428] and DNS results [Feldmann and Wagner (2012). J. Turbul. 13(32), 1-28] in addition to the Sexl's laminar-flow theory [Sexl (1930). Zeitschrift Phys. 61(5), 349-362]. Investigation of the total fluctuation kinetic energy of transitional oscillations reveals the appearance of intermittent fluctuations within the near-wall region at Wo = 13 during deceleration, while fully turbulent oscillations are predicted in the entire pipe domain at Wo = 5. Although the present results are qualitatively in good agreement with reported experimental [Eckmann and Grotberg (1991). J. Fluid Mech. 222, 329-350] and DNS findings [Feldmann and Wagner (2012). J. Turbul. 13(32), 1-28], the velocity profiles show poor agreement with corresponding DNS data during flow acceleration at Wo = 5.

Direct measurements of steady heat transfer maintained by oscillating pipe flow in thermoacoustic system

This study reports direct measurements of steady heat transfer in a heat exchanger pipe of a thermoacoustic heat pump driven by an oscillating helium gas flow. From simultaneous measurements of gas temperature, pressure, and velocity fluctuations, the steady heat transfer rate is determined from the radial profile of the temporal mean temperature and from the axial distribution of the enthalpy flux density. The heat transfer coefficient h is determined to be given by h=2k/r0 consistently in the range of 1.6≤r0/δα≤6.6, where k is the gas thermal conductivity, r0 is the tube radius, and δα=2α/ω is the characteristic transverse length given by using the thermal diffusivity and angular frequency.

Shear-induced migration and orientation of rigid fibers in an oscillatory pipe flow

Fibers in suspension migrate towards the center of the pipe where they are more aligned with the flow. The migration depends on the fraction of the volume of the suspension swept out by the rotating fibers.

Diffusive heat and mass transfer in oscillatory pipe flow

The enhancement of axial heat and mass transfer by laminar flow oscillation in pipes with axial gradients in temperature and concentration has been studied analytically for the cases of insulated and conducting walls. The axial diffusivity can exceed its molecular counterpart by many orders of magnitude, with a quadratic scaling on the pressure-gradient amplitude and the Prandtl or Schmidt number, and is a bimodal function of oscillatory frequency: quasi-steady behavior at low frequencies and a power-law decay at high frequencies. When the pipe wall is conductive and of sufficient thickness, and the flow oscillation is quasi-steady, the axial diffusivity may be enhanced by a further factor of about ten as a result of increased radial diffusion, for liquid and gas flows in pipes with walls with a wide range of thermal conductivities. Criteria for the wall thickness required to achieve this additional enhancement and for the limits placed on the validity of these solutions by viscous dissipation are also deduced. When the heat transfer per unit flow work achieved by oscillatory pipe flow is contrasted with that of a conventional parallel-flow heat exchanger, it is found to be of comparable size and the ratio of the two is shown to be a function only of the pipe geometry, heat-exchanger mean velocity, and fluid viscosity.

On the influence of computational domain length on turbulence in oscillatory pipe flow

We present results from direct numerical simulations (DNS) of oscillatory pipe flow at two different Womersley numbers (Wo ∈ {13, 26}) using a fully developed turbulent flow field as initial condition and different lengths of the computational pipe domain. By comparing high-frequency velocity signals and instantaneous flow fields for Wo=13, we found that the flow was conditionally turbulent for shorter pipe domains, while the flow completely laminarised in longer computational domains. This unforeseen observation is discussed in more detail by comparing spatial energy spectra, turbulence statistics and integral quantities calculated from the respective flow fields at different oscillation phases. We conclude that the critical maximum pipe length to maintain a conditionally turbulent flow lies within 3.54D < L < 5D for this special scenario characterised by Wo=13 and Re=11500. Interestingly, the occurring wall shear stress is slightly lower and the peak flow rate is slightly higher when the flow field is turbulent compared to the laminar scenario for the same set of control parameters. For Wo=26 we did not find such a critical domain length. The resulting flow field appears to be conditionally turbulent for L=1.25D and L=5D. Comparing two-point correlations for both Wo reveals a growing and shrinking behaviour of turbulent structures in the velocity field over the different phases of the oscillation cycle and how this mechanism is affected by the finite size of the periodic pipe domain. Further, this DNS study provides the important results that, first, the Floquet linear stability analysis of Thomas et al. (2012) is corroborated and second, that a minimum pipe length must be employed for DNS of oscillating pipe flow in the subcritical regime, otherwise there is questionable prediction of sustained turbulence.

Flow Separation and Turbulence in Jet Pumps for Thermoacoustic Applications

The effect of flow separation and turbulence on the performance of a jet pump in oscillatory flows is investigated. A jet pump is a static device whose shape induces asymmetric hydrodynamic end effects when placed in an oscillatory flow. This will result in a time-averaged pressure drop which can be used to suppress acoustic streaming in closed-loop thermoacoustic devices. An experimental setup is used to measure the time-averaged pressure drop as well as the acoustic power dissipation across two different jet pump geometries in a pure oscillatory flow. The results are compared against published numerical results where flow separation was found to have a negative effect on the jet pump performance in a laminar flow. Using hot-wire anemometry the onset of flow separation is determined experimentally and the applicability of a critical Reynolds number for oscillatory pipe flows is confirmed for jet pump applications. It is found that turbulence can lead to a reduction of flow separation and hence, to an improvement in jet pump performance compared to laminar oscillatory flows.

Dynamics of shear-induced migration of spherical particles in oscillatory pipe flow

The large-amplitude oscillatory flow of a suspension of spherical particles in a pipe is studied at low Reynolds number. Particle volume fraction and velocity are examined through refractive index matching techniques. The particles migrate toward the centre of the pipe, i.e. toward regions of lower shear rate, for bulk volume fractions larger than 10 %. Steady results are in agreement with available experimental results and discrete-particle simulations for similar geometries. The dynamics of the shear-induced migration process are analysed and compared against the predictions of the suspension balance model using realistic rheological laws.

2F45 ピッチの異なる円周方向溝付管における間欠振動流中の可視化を通した流れの解析(GS8:生体流れ)

2F45 ピッチの異なる円周方向溝付管における間欠振動流中の可視化を通した流れの解析(GS8:生体流れ)

2F44 円周方向溝付管内振動流中での有効拡散係数に溝ピッチが及ぼす影響(GS8:生体流れ)

2F44 円周方向溝付管内振動流中での有効拡散係数に溝ピッチが及ぼす影響(GS8:生体流れ)

Longitudinal dispersion of turbulent oscillatory pipe flows

In the present study, we examine the longitudinal dispersion of oscillatory pipe flows in the turbulent range which is not well covered before. An analytical analysis was first performed using the homogenization approach (i.e. multiple scale perturbation analysis) to predict the magnitude of the longitudinal dispersion induced by a turbulent oscillatory flow forced by a sinusoidal pressure gradient inside a circular pipe. An axisymmetric co-axial eddy viscosity model was adopted to resolve the radial distribution of velocities and turbulent shear stresses. Based on the derived kinematic characteristics, the longitudinal dispersion coefficient for the turbulent oscillatory pipe flow was then quantified. The results demonstrated that a dimensionless parameter \(\alpha \), which is the ratio of the oscillatory velocity amplitude divided by the frequency and pipe radius, determines the flow structure as well as the magnitude of the induced longitudinal dispersion coefficient. Experiments were also conducted to quantify the longitudinal dispersion coefficient under different frequencies and oscillatory velocity magnitudes. The measurement approaches were based on the non-invasive laser imaging techniques of particle image velocimetry and planar laser induced fluorescence. The experimental conditions covered a relatively wide range of boundary Reynolds number \((\hbox {Re}_\delta )\) from 100 to 1,000, and included both laminar and turbulent flow regimes. The results showed that when the flow enters the conditional turbulence regime, i.e. \(\hbox {Re}_\delta \ge 500\), the longitudinal dispersion coefficient increases drastically. The analytical predictions based on the homogenization approach in the present study agree well with the measured longitudinal dispersion coefficients.

Vortex ring formation in oscillatory pipe flow of wormlike micellar solutions

The destabilization of rectilinear oscillatory pipe flow and the formation of vortex rings in a wormlike micellar solution, CPyCl/NaSal [100:60] mM, oscillated in a vertical cylinder of large aspect ratio, has been studied by means of time-resolved-particle image velocimetry measurements in a meridional plane of the cylinder. The flow was inertialess (Re<1) and dominated by fluid elasticity (De≫1). The oscillatory pipe flow of a Newtonian fluid under equivalent conditions would remain rectilinear and laminar. For the micellar solution, instead, the reversing character of the rectilinear flow induces vortex ring formation. The stability boundaries between rectilinear, axisymmetric-vortical, and non-axisymmetric-vortical flows in the middle region of the cylinder have been determined from the root-mean-square fluctuations of the measured vertical and radial velocity components. Measurements performed over the whole tube length reveal that the flow destabilization and the subsequent formation of vortex rings is favored at the bottom part of the cylinder, close to the driving piston. As the driving amplitude is increased, the vortical flow expands vertically upwards, giving rise to a number of coaxial toroidal vortices distributed over the vertical pipe. On short-time scales these axisymmetric vortex rings are periodic in time with the periodicity of the driving. On long time scales, much longer than the relaxation time of the fluid, we uncover an additional temporal evolution of the vortical flow which makes the spatiotemporal structure of the oscillatory flow more involved.

3E17 円周方向溝付管内における間欠振動流の可視化と流れ解析(GS8:呼吸器系のバイオメカニクス)

3E17 円周方向溝付管内における間欠振動流の可視化と流れ解析(GS8:呼吸器系のバイオメカニクス)

An Updated Portrait of Transition to Turbulence in Laminar Pipe Flows with Periodic Time Dependence (A Correlation Study)

Transition to turbulence in axially symmetrical laminar pipe flows with periodic time dependence classified as pure oscillating and pulsatile (pulsating) ones is the concern of the paper. The current state of art on the transitional characteristics of pulsatile and oscillating pipe flows is introduced with a particular attention to the utilized terminology and methodology. Transition from laminar to turbulent regime is usually described by the presence of the disturbed flow with small amplitude perturbations followed by the growth of turbulent bursts. The visual treatment of velocity waveforms is therefore a preferred inspection method. The observation of turbulent bursts first in the decelerating phase and covering the whole cycle of oscillation are used to define the critical states of the start and end of transition, respectively. A correlation study referring to the available experimental data of the literature particularly at the start of transition are presented in terms of the governing periodic flow parameters. In this respect critical oscillating and time averaged Reynolds numbers at the start of transition; Re os,crit and Re ta,crit are expressed as a major function of Womersley number, $\sqrt {\omega ^\prime } $ defined as dimensionless frequency of oscillation, f. The correlation study indicates that in oscillating flows, an increase in Re os,crit with increasing magnitudes of $\sqrt {\omega ^\prime } $ is observed in the covered range of $1<\sqrt {\omega ^\prime } <72$ . The proposed equation (Eq. 7), ${\rm{Re}}_{os,crit} ={\rm{Re}}_{os,crit} \left( {\sqrt {\omega ^\prime } } \right)$ , can be utilized to estimate the critical magnitude of $\sqrt {\omega ^\prime }$ at the start of transition with an accuracy of ±12 % in the range of $\sqrt {\omega ^\prime } <41$ . However in pulsatile flows, the influence of $\sqrt {\omega ^\prime }$ on Re ta,crit seems to be different in the ranges of $\sqrt {\omega ^\prime } <8$ and $\sqrt {\omega ^\prime } >8$ . Furthermore there is rather insufficient experimental data in pulsatile flows considering interactive influences of $\sqrt {\omega ^\prime } $ and velocity amplitude ratio, A 1. For the purpose, the measurements conducted at the start of transition of a laminar sinusoidal pulsatile pipe flow test case covering the range of 0.21< A 1 <0.95 with $\sqrt {\omega ^\prime } <8$ are evaluated. In conformity with the literature, the start of transition corresponds to the observation of first turbulent bursts in the decelerating phase of oscillation. The measured data indicate that increase in $\sqrt {\omega ^\prime } $ is associated with an increase in Re ta,crit up to $\sqrt {\omega ^\prime } =3.85$ while a decrease in Re ta,crit is observed with an increase in $\sqrt {\omega ^\prime } $ for $\sqrt {{\omega }'} >3.85$ . Eventually updated portrait is pointing out the need for further measurements on i) the end of transition both in oscillating and pulsatile flows with the ranges of $\sqrt {\omega ^\prime } <8$ and $\sqrt {\omega ^\prime } >8$ , and ii) the interactive influences of $\sqrt {\omega ^\prime } $ and A 1 on Re ta,crit in pulsatile flows with the range of $\sqrt {\omega ^\prime } >8$ .

ANALYSIS OF VELOCITY ANNULAR EFFECT OF OSCILLATORY FLOW INSIDE PARALLEL PLATE CHANNEL

This study focuses on the velocity-annular-effect (VAE) of compressible oscillatory flow inside parallel plate channel. By analyzing the mechanism of VAE, we conclude that VAE, which inevitably occurs in viscous oscillatory pipe flow, is most visible at the phase when the centerline velocity reaches zero. In order to quantitatively evaluate the VAE, coefficient of velocity annular effect (CVAE) was proposed as an index parameter, based on the slope of velocity profile when the centerline velocity reaches zero. Numerical computations with the index parameter CVAE were conducted to analyze the impacts of dimensionless parameters, i.e., Valensi number Va and maximum Reynolds number Remax, on the VAE of oscillatory flow inside parallel plate channel.