On pulsatile flow of non-Newtonian liquids

Rheologica Acta - We consider the behaviour of non-Newtonian liquids as they are made to flow through straight pipes of circular cross section under the action of a pressure -gradient which...     

Autoregressive spectral estimation in transitional pulsatile flow

An autoregressive spectral estimation technique is applied to describe the frequency content of velocity disturbances created by pulsatile flow through a constricted tube. The Reynolds number and frequency parameter are such that transitional phenomena, including vortex formation and coherent disturbances, as well as turbulence, are created during various phases of the pulsatile cycle. Although under some circumstances Fourier methods of spectral estimation suffer from poor frequency resolution and large variance under these unsteady flow conditions, the autoregressive technique is shown to be capable of identifying essential flow disturbance features with good resolution and considerably smaller statistical variation. This method should be particularly useful in analyzing energy spectra of flow disturbance variables under unsteady mean flow conditions or when a limited amount of data is available.     

Effect of finite cavity width on flow oscillation in a low-Mach-number cavity flow

The current study is focused on examining the effect of the cavity width and side walls on the self-sustained oscillation in a low Mach number cavity flow with a turbulent boundary layer at separation. An axisymmetric cavity geometry is employed in order to provide a reference condition that is free from any side-wall influence, which is not possible to obtain with a rectangular cavity. The cavity could then be partially filled to form finite-width geometry. The unsteady surface pressure is measured using microphone arrays that are deployed on the cavity floor along the streamwise direction and on the downstream wall along the azimuthal direction. In addition, velocity measurements using two-component Laser Doppler Anemometer are performed simultaneously with the array measurements in different azimuthal planes. The compiled data sets are used to investigate the evolution of the coherent structures generating the pressure oscillation in the cavity using linear stochastic estimation of the velocity field based on the wall-pressure signature on the cavity end wall. The results lead to the discovery of pronounced harmonic pressure oscillations near the cavity’s side walls. These oscillations, which are absent in the axisymmetric cavity, are linked to the establishment of a secondary mean streamwise circulating flow pattern near the side walls and the interaction of this secondary flow with the shear layer above the cavity.     

Numerical solution of a pulsatile flow problem

Summary A numerical method, developed and used in previous work, is used to solve the Navier-Stokes equations for a two-dimensional incompressible flow in variable motion. A pulsatile flow through a pipe cross is studied to simulate blood flow in vascular aorto-renal junctions.

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Sommario In questo studio si è utilizzato uno schema numerico, già studiato e utilizzato in precedenti lavori, per risolvere le equazioni bidimensionali di Navier-Stokes per un fluido viscoso incomprimibile in un problema di moto vario. Nelle ipotesi di poter descrivere il moto fasico del sangue con il moto di un fluido viscoso newtoniano di opportuna viscosità, si è studiato il moto pulsante di questo fluido in due condotti raccordati per simulare il moto del sangue nel raccordo aorta-renale durante un ciclo temporale completo.

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Research carried out at Istituto di Idraulica del Politecnico di Milano, Milan, Italy.     

Investigation of the flow structure in a plane turbulent jet

Results of an experimental investigation of a plane, submerged air jet are elucidated. The distribution of the mean velocity, the longitudinal and transverse velocity component pulsations, the tangential friction stress, and the correlation coefficient in jet cross sections are presented. The results of measurements are compared with the data of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 176–179, July–August, 1970.     

An analysis model of pulsatile blood flow in arteries

IntroductionTheperiodicallypulsatilebloodflowinthearterycausesthecircumferentialandaxialmotionoftheelasticbloodvesselandinturntheoscillationofthevesselaffectsthatofthebloodflow .Womersley[1]resolvedsuccessfullythisfluid_solidcouplingproblembysolvingbothlinearNavier_Stokesequationsandthemotionequationsofthethin_walledelastictubeandgainedtheexpressionsofthebloodflowvelocitiesandthevasculardisplacements.Histheoryhasbeenthebasisforthequantitativeanalysisoftherelationshipofthearterialstructureandi…     

Investigation of incompressible flow within ½ circular cavity using lattice Boltzmann method

A wall‐driven incompressible viscous flow in a ½ circular cavity is simulated, based on the lattice Boltzmann method (LBM). The treatment of curved boundary with second‐order accuracy is used. The force evaluation is based on the momentum‐exchange method. The streamlines and vorticity contours and the velocity component along the central line of a semi‐circular cavity are obtained for different Reynolds numbers. The numerical results show that the LBM can capture the formation of primary, secondary and tertiary vortices exactly as the Reynolds number increases and has a great agreement with those of current literatures. Copyright © 2008 John Wiley & Sons, Ltd.     

Investigation of the structure of the flow in an axisymmetric dead-end

The results of an experimental investigation of the structure of the flow in an axisymmetrical dead-end, with central flow of the liquid, are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 2, pp. 16–23, March–April, 1977.     

Investigation of the flow in a circular cavity using stereo and tomographic particle image velocimetry

The turbulent flow over a circular cavity with an aspect ratio of D/H = 2 is investigated by multi-planar stereoscopic particle image velocimetry and with tomographic particle image velocimetry (PIV). The main aim of the study is the flow topology and the turbulent structure of the asymmetrical flow pattern that forms inside the cavity at these specific conditions. The flow field is measured in the vertical symmetry plane to describe the overall recirculation pattern in the cavity and the turbulent shear layer developing from the separation point. In this specific regime the shear layer fluctuations are recognized as those caused by instabilities together with the effect of the incoming boundary layer turbulence. Additional observations performed at several wall-parallel planes at different height inside the cavity allow to further evaluate the secondary flow circulation generated by this asymmetric regime. The observed flow pattern consists of a steady vortex, occupying the entire cavity volume and placed diagonally inside the cavity such to entrain the external flow from one side, capture it into a circulatory motion and eject it from the opposite side of the cavity. The spatial distribution of the turbulent fluctuations also reveals the same structure. The tomographic PIV measurement returns a visual inspection to the instantaneous three-dimensional structure of the turbulent fluctuations, which at the investigated height exhibit a low level of coherence with slightly elongated vortices in the recirculating flow inside the cavity.     

Investigation of bifurcation structure flow field for bipolar plates in PEMFC

Uniform flow field in fuel cells is important to the performance. Even distribution of reactant gases over the electrode surfaces is a key to the good performance of fuel cells since this enables them to operate as close as possible to maximum capability and electrochemical reactions. In this paper, the bifurcation principle can be used to design the flow field structure for bipolar plate in proton exchange membrane fuel cells (PEMFC). It is demonstrated by numerical simulation that branch flow field structure can provide substantially flow-field distribution, current density and heat transfer when compared to the traditional structure. Then a kind of excellent flow field structure for bipolar plate in PEMFC can be achieved.     

Localised dynamics of laminar pulsatile flow in a rectangular channel

The exploitation of flow pulsation in low-Reynolds number micro/minichannel flows is a potentially useful technique for enhancing cooling of high power photonics and electronics devices. Although the mechanical and thermal problems are inextricably linked, decoupling of the local instantaneous parameters provides insight into underlying mechanisms. The current study performs complementary experimental and analytical analyses to verify novel representations of the pulsating channel flow solutions, which conveniently decompose hydrodynamic parameters into amplitude and phase values relative to a prescribed flow rate, for sinusoidally-pulsating flows of Womersley numbers 1.4 ≤ Wo ≤ 7.0 and a fixed ratio of oscillating flow rate amplitude to steady flow rate equal to 0.9. To the best of the authors’ knowledge, the velocity measurements – taken using particle image velocimetry – constitute the first experimental verification of theory over two dimensions of a rectangular channel. Furthermore, the wall shear stress measurements add to the very limited number of studies that exist for any vessel geometry. The amplification of the modulation component of wall shear stress relative to a steady flow (with flow rate equal to the amplitude of the oscillating flow rate) is an important thermal indicator that may be coupled with future heat transfer measurements. The positive half-cycle time- and space-averaged value is found to increase with frequency owing to growing phase delays and higher amplitudes in the near-wall region of the velocity profiles. Furthermore, the local time-dependent amplification varies depending on the regime of unsteadiness: (i) For quasi-steady flows, the local values are similar during acceleration and deceleration though amplification is greater near the corners over the interval 0 – 0.5π. (ii) At intermediate frequencies, local behaviour begins to differ during accelerating and decelerating periods and the interval of greater wall shear stress near the corners lengthens. (iii) Plug-like flows experience universally high amplifications, with wall shear stress greater near the corners for the majority of the positive half-cycle. The overall fluid mechanical performance of pulsating flow, measured by the ratio of bulk mean wall shear stress and pressure gradient amplifications, is found to reduce from an initial value of 0.97 at Wo = 1.4 to 0.28 at Wo = 7.0, demonstrating the increasing work input required to overcome inertia.     

Direct measurement of mixing quality in a pulsatile flow micromixer

Pulsatile action can be used to mix two streams entering a tube from two separate branches of a bifurcation at low Reynolds numbers. The pulsatile action is provided by two pinch valves, which deform flexible tubing immediately upstream of the connection. The pinch valve action is controlled using a master-slave pulse generator setup. The quality of mixing is evaluated directly by measuring the fluorescence that results from the chemical reaction of species transported in the two streams, one containing native biotin and the other, fluorescein biotin bound to streptavidin. The reaction kinetics are accounted for by normalization using fluorescence measurements on well mixed solutions at the same residence time. The results show that the pulsatile micromixer provides almost complete mixing. Furthermore, the present measurements match results obtained in a previous experiment where flow visualization and image analysis were used to measure mixing quality in a scaled-up model.     

Forcing frequency effects on turbulence dynamics in pulsatile pipe flow

The turbulence dynamics of pulsatile pipe flow are investigated using direct numerical simulation (DNS) at a mean friction Reynolds number of 180. Results are presented for a range of forcing frequencies at a fixed amplitude, which, based on existing classifications, corresponds to the current-dominated regime. This work directs attention towards the phase-variations of single and two-point turbulence statistics, with a particular emphasis on the response of the Reynolds shear stress to systematic changes in the applied forcing frequency. The study has yielded two key outcomes. (i) A new frequency classification procedure for pulsatile turbulent flows (at low-to-moderate friction Reynolds numbers), informed by the Reynolds shear stress frequency co-spectra and the value of the applied forcing frequency. (ii) A detailed account of single- and two-point Reynolds shear stress statistics, in response to high, very-high and ultra-high forcing frequencies in order to study turbulence dynamics in the physical and Fourier domains. Furthermore, the oscillatory velocity field obtained from the DNS data is compared against the laminar Womersley solution in order to assess the interaction (or lack thereof) between the oscillatory velocity field and phase-averaged Reynolds shear stress fluctuations. For the higher frequencies considered in this work, single- and two-point Reynolds shear statistics all enter the so-called “frozen” regime — which occurs as the forcing time-scale becomes smaller than that of the highest-frequency, energy-containing motions in the Reynolds shear stress co-spectra.     

A two-fluid model for pulsatile flow in catheterized blood vessels

The pulsatile flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the peripheral region of plasma as a Newtonian fluid. The resulting non-linear implicit system of partial differential equations is solved using perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio, amplitude, pulsatile Reynolds number ratio and peripheral layer thickness are discussed. It is observed that the velocity distribution and flow rate decrease, while, the wall shear, width of the plug flow region and longitudinal impedance increase when the yield stress increases. It is also found that the velocity increases, but, the longitudinal impedance decreases when the thickness of the peripheral layer increases. The wall shear stress decreases non-linearly, while, the longitudinal impedance increases non-linearly when the catheter radius ratio increases. The estimates of the increase in the longitudinal impedance are considerably lower for the present two-fluid model than those of the single-fluid model.     

Numerical study on the laminar pulsatile flow of slurries

The laminar pulsatile flow of slurries is studied numerically. A slurry is usually described as a Bingham plastic fluid, but since the apparent viscosity coefficient of a Bingham plastic fluid diverges if the velocity gradient becomes zero, a modified Bingham model (bi-viscosity model) is used in this calculation.As one of the characteristics of the pulsatile flow of non-Newtonian fluids is the flow enhancement (the increase in the mean flow rate due to pulsation), the calculated flow enhancement rates are compared with the experimental results of Kajiuchi and Saito and good agreements are obtained. Finally, the extra power required to pulsate the flow and the characteristics of the calculated velocity distribution and the shear stress at the wall are investigated.     

Mass transfer characteristics in an axisymmetric wavy-walled tube for pulsatile flow with backward flow

Under the pulsatile flow with backward flow (PFBF) conditions, flow mixing and mass transfer characteristics are experimentally investigated in an axisymmetric wavy-walled tube at a net flow Reynolds number from 50 to 1,000. An electrochemical technique is employed to measure the mass transfer rate. An optimal Strouhal number corresponding to the peak value of the mass transfer enhancement factor is observed, which is independent of the oscillatory fraction of the flow rate, but decreases with the increasing net flow Reynolds number. It was found that the mass transfer enhancement under PFBF has the similar characters of resonant enhancement in two-dimensional (2-D) channels, but there also exists an essential difference since no self-sustained oscillation occurs in the wavy-walled tube.     

Boundary layer development of pulsatile blood flow in a tapered vessel

Assuming that the tapered angle is small,the problems of developing flow under unsteady oscillatory condition are studied in this paper.The formula of velocity distribution is obtained.The analyses for the results show that the blood flow in a converging tapered vessel remains a developing flow throughout the length,and the effects of tapered angle on the developing flow are increased with the increment of the tapered angle.     

Numerical simulation of pulsatile non-Newtonian flow in the carotid artery bifurcation

Both clinical and post mortem studies indicate that, in humans, the carotid sinus of the carotid artery bifurcation is one of the favored sites for the genesis and development of atherosclerotic lesions. Hemodynamic factors have been suggested to be important in atherogenesis. To understand the correlation between atherogenesis and fluid dynamics in the carotid sinus, the blood flow in artery was simulated numerically. In those studies, the property of blood was treated as an incompressible, Newtonian fluid. In fact, however, the blood is a complicated non-Newtonian fluid with shear thinning and viscoelastic properties, especially when the shear rate is low. A variety of non-Newtonian models have been applied in the numerical studies. Among them, the Casson equation was widely used. However, the Casson equation agrees well only when the shear rate is less than 10 s-1. The flow field of the carotid bifurcation usually covers a wide range of shear rate. We therefore believe that it may not be sufficient to describe the property of blood only using the Casson equation in the whole flow field of the carotid bifurcation. In the present study, three different blood constitutive models, namely, the Newtonian, the Casson and the hybrid fluid constitutive models were used in the flow simulation of the human carotid bifurcation. The results were compared among the three models. The results showed that the Newtonian model and the hybrid model had verysimilar distributions of the axial velocity, secondary flow and wall shear stress, but the Casson model resulted in significant differences in these distributions from the other two models. This study suggests that it is not appropriate to only use the Casson equation to simulate the whole flow field of the carotid bifurcation, and on the other hand, Newtonian fluid is a good approximation to blood for flow simulations in the carotid artery bifurcation.     

Investigation of unsteady flow structure during discharge of a shock-heated gas

This paper examines the structure of the near-gasdynamic section of a jet discharging into a rarefied volume. The experimental part of the article deals with unsteady discharge of a high-temperature gas. Discharge from a slot and from a circular aperture is investigated for air, nitrogen, CO₂, and argon with nonuniformities from 20–200. Approximate relations are obtained to describe the motion of the front of a discharging substance in dimensionless coordinates and the associated perturbation along the flow axis. It is established that the time for a steady geometric structure to form in the gasdynamic section of the jet is greater than the values obtained from data available in the literature.Translated from Zhurnal Prikladnoi Mekhaniki i Teoreticheskoi Fiziki, No. 5, pp. 34–40, September–October, 1973.