Pulsating Pressure Gradient Research Articles

Effects of diffusive Reynolds number on electro-osmotic pulsating nanofluid flow

We examine pulsating electro-osmotic nanofluid flow phenomena in a microchannel with porous walls. The combined effect of the injected nanofluid velocity and ion diffusion coefficients on the electrical potential formation is considered. A novel boundary condition is introduced so as to examine the effects of electro-osmosis and frictional forces on thermal profiles and nanoparticle volume fractions of nanofluids. Being motivated by the experimental works of Kong et al. [Phys. Chem. Chem. Phys. 19, 7678 (2017).], this paper aims to extend the study of ion diffusivity in terms of diffusive Reynolds number on nanofluid temperature in the pulsating pressure gradient setting. The semi-analytic differential transform method is used to solve the physical equations, represented as coupled ordinary differential equations, with a special emphasis on the convergence of solutions, which is presented in terms of tables and graphs. The study shows that the nanofluid velocity, temperature, and mass concentration are strongly influenced by the ion diffusion coefficient and the frequency of pulsating pressure gradient. The diffusive Reynolds number significantly influences the electric potential distribution. The velocity and temperature show an increasing trend in terms of diminishing sensitivity parameter. However, nanoparticle concentration increases with an enhancement of the sensitivity parameter. Finally, velocity and temperature increase with a diminution of the Womersley number.

RETRACTED: Construction and discrete processing of screw extruder based on three-dimensional spiral model

A method used to create products by forming an extruded shape or forcing material through a die or orifice that uses an extruder to produce a semi-finished or finished product. The Spiral 3D model of screw extruder causes unstable production in cable insulation. This productivity instability is caused by the pulsating pressure gradient of the molten polymer in the melding tool at the extruder. The frequency of the pressure pulsation of the molten polymer in the dosing zone is based on the boundaries of statistical processing and the screw speed. This system provides instant production stability between insulation applications, increases the regularity of insulation core diameter, and ensures the performance of the final manufactured cable's predefined service quality parameters.

Large eddy simulation of enhanced heat transfer in pulsatile turbulent channel flow

Heat transfer in pulsatile turbulent channel flow is investigated by means of Large Eddy Simulation. Incompressible flow within a periodic computational domain is driven by a pulsating axial pressure gradient at a turbulent Reynolds number of Reτ=350. A localized dynamic sub-grid scale approach is chosen to model unclosed stress terms. A layer-averaged sub-grid model determines turbulent Prandtl numbers that depend on wall distance. Compared to the existing literature, a much wider range of oscillation parameters is studied. In particular, forcing frequencies correspond to Womersley numbers from Wo=14 to 70, while forcing amplitudes reach values that result in strongly pronounced flow reversal, i.e. reverse flow velocities up to five times larger than the mean flow velocity.At moderate pulsation amplitudes, i.e. in the range of emerging flow reversal, strong deviations of instantaneous heat transfer rates from the temporal mean are observed. Particularly at times of flow reversal, an increase in heat transfer up to 60% above non-pulsatile values is observed. However, when averaging over a complete cycle, any enhancement in mean heat transfer is only minor.On the other hand, simulations at larger pulsations amplitudes that result in strongly pronounced flow reversal, show a enhancement of mean heat transfer in excess of 100%. Note that such significant enhancement of heat transfer has not been reported previously in Large Eddy Simulation of turbulent pulsatile flow. The paper offers a physical interpretation of the results and concludes that an overall increase in turbulent transport is responsible for the observed significant enhancement of convective heat transfer.

Numerical Research on the Influence of Deborah Number on Flow and Heat Transfer of Maxwell Fluid in a Tube with Laminar Pulsating Flow

The flow and heat transfer characteristics of Maxwell fluid in a pipe under pulsating pressure gradient were studied. The governing equations were made dimensionless. The Rubin boundary condition was adopted. The flow field was solved theoretically and the temperature field was obtained using finite volume method. A general model suitable for various fluctuating characteristics and physical parameters was established. The Deborah number (De) was used to characterize the fluidity of the fluid. The influence of De on flow and temperature fields was evaluated. The Nusselt number and start-up process of Maxwell fluid were studied. Results showed that the influence of De on flow field was greater than that on temperature field. The effect of De on Nusselt number was irregular and related to the oscillation parameters. The over-shooting amplitude and oscillation time of axis center velocity in start-up flow grow larger with De.

New simple analytical method for flow enhancement predictions of pulsatile flow of a structured fluid

In this work, a new simplified method to find the fluidity enhancement of a non-Newtonian liquid under a pulsating (time-dependent) pressure gradient is analyzed. The fluidity enhancement is predicted by means of a Taylor series expansion of the flow rate in the vicinity of the applied wall stress. This expansion is shown to render the same results as several perturbation techniques used at length in the literature. Both new and the conventional perturbation methods are equivalent in their predictions of the fluidity enhancement. Even though the flow and rheology behavior are modeled using the Bautista-Manero-Puig constitutive equation, it is shown that the prediction of the fluidity enhancement does not depend on the constitutive model employed, but a condition of shear thinning behavior of the fluid is necessary for it. Flow enhancement is predicted using rheological data for blood since this fluid naturally flows under a pulsatile pressure gradient. The flow enhancement equation is found to have a similar form as the equation of the Rabinowitsch formalism in fully developed Poiseuille flow. This simplified technique will help in saving machine time for numerical predictions in computational blood flow simulations.

A new mechanism for buoyancy driven convection in pulsating viscous flows: A theoretical study

A new mechanism for the onset of thermal convection is proposed. This mechanism is the result of the interaction between a pulsating flow, viscous dissipation, and buoyancy within a channel. The study considers a Newtonian fluid moving inside an infinitely wide horizontal channel bounded by impermeable, rigid plates. The basic flow is characterized by a pulsating pressure gradient. Viscous dissipation acts as an internal heat source which produces a potentially unstable basic temperature gradient. The heat source has a vertical non uniform distribution inside the channel. This configuration is investigated with respect to the onset of buoyancy driven convection. The basic state fields are solved analytically by expanding them in series as functions of the pulsating frequency. In order to perform the linear stability analysis, an arbitrarily small perturbation is superimposed upon the basic state order zero solution. The normal mode method is employed and an ordinary differential eigenvalue problem is obtained. The perturbations were found to have zero angular frequency and thus the resonance phenomena between the basic flow and the perturbations can be neglected. The critical values of the governing parameter are obtained by solving the eigenvalue problem numerically. A growth rate analysis of the possibly unstable configurations relative to the most unstable mode is performed. The present study proves, theoretically, that a pulsating flow can undergo thermal convection. A future experimental study is suggested to validate the proposed instability mechanism.

On the pulsating flow behavior of a biological fluid: human blood

In this work, the rectilinear flow of a complex fluid (human blood) under a pulsating time-dependent pressure gradient is analyzed. A first approximation of the real case of blood flowing in a vein is described. The normalized pressure gradient simulates the pumping work of the heart while the flow geometry (circular tube) is assumed rigid, smooth, and cylindrical. The rheological behavior of blood with different cholesterol levels is modeled using the Bautista–Manero–Puig (BMP) constitutive equation. According to the analytical solution, a flow enhancement is predicted to first order which represents the optimum pumping work of the heart which governs the flow of blood in the entire body. This work is a contribution to the understanding of the complex rheology involved in the discontinuous pressure-driven flow of blood in the human body.

Nonlinear vibrations of plates in axial pulsating flow

A theoretical approach is presented to study nonlinear vibrations of thin infinitely long and wide rectangular plates subjected to pulsatile axial inviscid flow. The flow is set in motion by a pulsating pressure gradient. The case of plates in axial uniform flow under the action of constant transmural pressure is also addressed for different flow velocities. The plate is assumed to be periodically simply supported in both in-plane directions with immovable edges and the flow channel is bounded by a rigid wall. In this way the system under study is a finite rectangular plate with conditions on the fluid and the plate boundaries coming from the periodicity of the infinite system. The equations of motion are obtained based on the von Kárman nonlinear plate theory retaining in-plane inertia via Lagrangian approach. The fluid model is based on the potential flow theory. The resulting Lagrange equations of motion of the coupled system contain quadratic and cubic nonlinear terms and are studied by using a code based on the pseudo-arc-length continuation and collocation scheme. The effect of different system parameters such as flow velocity, pulsation amplitude, pulsation frequency and channel pressurization on the stability of the plate and its geometrically nonlinear response to pulsating flow are fully discussed. It has been found that the presence of positive transmural uniform pressure and small pulsation frequency would destroy the pitchfork bifurcation (divergence) that flat plates exhibit when subjected to uniform flow. Moreover, in case of zero uniform transmural pressure numerical results show a hardening type behavior for the entire flow velocity range when the pulsation frequency is spanned in the neighborhood of the plate׳s fundamental frequency. On the contrary, a softening type behavior is presented when a uniform transmural pressure is introduced.

Purely pulsating flow of a viscoelastic fluid in a pipe revisited: The limit of large Womersley number

The flow of a Maxwell fluid in a pipe generated by a pulsating pressure gradient is considered. The problem is governed by two non-dimensional parameters, the Womersley number α and a Deborah parameter γ. We obtain a simple approximate solution in the limit of large α (pipe diameter much larger than the viscous penetration depth) by solving the resulting boundary-layer problem through a two scales perturbation technique, which also helps to understand qualitatively the structure of the flow as γ increases. This limit is of interest, for instance, for the blood flow in arteries. The main qualitative differences between the Newtonian fluid flow (γ=0) and the highly elastic fluid with γ=O(1) or larger are easily discussed from the found solution in terms of just two algebraic functions of γ.

Investigation of Heat Transfer in a Porous Annulus with Pulsating Pressure Gradient by Homotopy Analysis Method

The present research derives analytical expressions for the heat transfer in a porous annulus with pulsating pressure gradient imposed across the annulus. The governing partial and coupled equations are transformed to ordinary ones by utilizing the similarity variables and then solved analytically using Homotopy Analysis Method (HAM). The analytic solution is expressed in the form of series, and its convergence is analyzed. The resulting temperature distribution, Nusselt number and entropy generation profiles are shown graphically for the different values of the parameters of the problem. A numerical solution has also been obtained to verify the solution by HAM. Good agreement is observed between the two methods.

Role of streaming potential on pulsating mass flow rate control in combined electroosmotic and pressure‐driven microfluidic devices

In the present study, we investigate the implications of streaming potential on the mass flow rate control in a microfluidic device actuated by the combined application of a pulsating pressure gradient and a pulsating, externally applied, electric field. We demonstrate that the temporal dynamics due to streaming potential effects may lead to interesting non-trivial aspects of the resultant transport characteristics. Our results highlight the importance of an adequate accounting of the streaming potential effects for temporally tunable mass flow rate control strategies, which may act as a useful design artifice to augment mass flow rates in practical scenarios.

Finite Element Solutions for Non-Newtonian Pulsatile Flow in a Non-Darcian Porous Medium Conduit

The present analysis is motivated by the need to elucidate with more accuracy and sophistication the hydrodynamics of non-Newtonian flow via a channel containing a porous material under pulsating pressure gradient. A one-dimensional transient rheological model for pulsating flow through a Darcy-Forcheimmer porous channel is used. A modified Casson non-Newtonian constitutive model is employed for the transport fluid with a drag force formulation for the porous body force effects. The model is transformed and solved using a finite element numerical technique. Rheological effects are examined using a β parameter which vanishes in the limit (Newtonian flow). Velocity profiles are plotted for studying the influence of Reynolds number, Darcy number, Forchheimer number and the β (non-Newtonian) parameter. The channel considered is rigid with a pulsatile pressure applied via an appropriate pressure gradient term. The model finds applications in industrial filtration systems, pumping of polymeric fluids etc.

Pulsatile pipe flow of pseudoplastic fluids

This note is concerned with a laminar pipe flow of a non-Newtonian fluid under the action of a small pulsating pressure gradient superposed to a steady one. The constitutive law describing the rheological behaviour of the fluid is the so-called power law (Ostwald–de Waele). An approximated analytical solution is found for the velocity, as power series of the amplitude of the periodic disturbance. The analytic solution is compared with a direct numerical solution and the perfect accord of the values obtained is underscored.

Secondary flows of viscoelastic liquids in straight tubes

The unsteady flow of the Green–Rivlin fluids in straight tubes of arbitrary cross-section driven by a pulsating pressure gradient is investigated. The non-linear constitutive structure defined by a series of nested integrals over semi-infinite time domains is perturbed simultaneously with the boundary of the base flow through a novel approach to domain mapping. The dominant primary component of the flow, the longitudinal field, and the much weaker transversal field arise at the first and the second orders of the analysis, respectively. The secondary field is driven by first-order terms stemming from the linearly viscoelastic longitudinal flow at the first order. The domain mapping technique employed yields a continuous spectrum of unconventional closed cross-sectional shapes. We present longitudinal velocity profiles and transversal time-averaged, mean secondary flow streamline patterns for a specific fluid and for representative cross-sectional shapes in the spectrum the triangular, square and hexagonal shapes.

Numerical investigation of a laminar pulsating flow in a rectangular duct

A pulsating laminar flow of a viscous, incompressible liquid in a rectangular duct has been studied. The motion is induced under an imposed pulsating pressure difference. The problem is solved numerically. Different flow regimes are characterized by a non-dimensional parameter based on the frequency (ω) of the imposed pressure gradient oscillations and the width of the duct (h). This, in fact, is the Reynolds number of the problem at hand. The induced velocity has a phase lag (shift) with respect to the imposed pressure oscillations, which varies from zero at very slow oscillations, to 90° at fast oscillations. The influence of the aspect ratio of the rectangular duct and the pulsating pressure gradient frequency on the phase lag, the amplitude of the induced oscillating velocity, and the wall shear were analyzed

Nonsteady Flow of Viscous Fluid in a Tube of Triangular Cross-Section

By superposing of one-dimensional solutions an exact solution is obtained for the nonsteady two-dimensional problem of the motion of an incompressible viscous fluid in a rigid tube whose cross-section is a regular triangle. The fluid is driven by a time-dependent pressure gradient. The fluid particles may have a nonuniform initial velocity distribution over the tube cross-section. Solutions are obtained in the form of series for the cases in which the fluid is accelerated from rest by a varying pressure gradient and also in the stationary oscillating regime under the action of a periodically pulsating pressure gradient.

Long-wave peristaltic transport of a compressible viscous fluid in a finite pipe subject to a time-dependent pressure drop

Axisymmetric viscous flow in a long pipe, driven by the pulsating pressure gradient and the wall deformation, is investigated. This kind of a flow is relevant to the peristaltic transport of blood due to the heart pumping along with the synchronic expansion/constriction of the vessel. Following the spirit of the lubrication theory, a reduced system of equations is derived. An obtained explicit solution demonstrates crucial role of peristalsis on the total fluid flux through the pipe. In order to account for the inertia effect, a model based on an averaging of the momentum equation using an a priori parabolic flow pattern across the pipe, is also derived.

Unsteady axial viscoelastic pipe flows

The main objective of this work is to examine in detail basic unsteady pipe flows and to investigate any new physical phenomena. We take the viscoelastic upper-convected Maxwell fluid as our non-Newtonian model and consider the flow of such a fluid in pipes of uniform circular cross-section in the following three cases: 1. (a) when the pressure gradient varies exponentially with time; 2. (b) when the pressure gradient is pulsating; 3. (c) a starting flow under a constant pressure gradient. In the first problem we looked separately at the pressure gradient rising exponentially with time and falling exponentially with time, i.e. the pressure gradient is proportional to e ± α 2 τ . The behaviour of the flow field depends to a large extent on β where β 2 = α 2(1 ± Hα 2) with H being the quotient of the Weissenberg and Reynolds numbers. In both cases for small | βη|, η being the radial distance from the axis, the velocity profiles are seen to be parabolic. However, for large | βη| the flows are vastly different. In the case of increasing pressure gradient the flow depicts boundary-layer characteristics while for decreasing pressure gradient the velocity depends on the wall distance. The case of a pulsating pressure gradient is investigated in the second problem. Here the pressure gradient is proportional to cos nτ. Again the flow depends to a large extent on a parameter β ( β 2 = i n − n 2 H). For small values of | βη| the velocity profile is parabolic. However, it is found that, unlike Newtonian fluids, the velocity distribution for the upper-convected Maxwell fluid is not in phase with the exciting pressure distribution. In the case of large | βη| the solution displays a boundary-layer characteristic and the phase of the motion far from the wall is shifted by half a period. The final problem examines a flow that is initially at rest and then set in motion by a constant pressure gradient. A closed form solution has been obtained with the aid of a Fourier-Bessel series. The variation of the velocity across the pipe has been sketched and comparison made with the classical solution.

Numerical simulation of fully developed flow and heat transfer characteristics in a curved tube with pulsating pressure gradient

Characteristics of fluid flow and convective heat transfer of a pulsating flow in a curved tube have been investigated numerically. The tube wall is assumed to be maintained at a uniform temperature peripherally in a fully developed pulsating flow region. The temperature and flow distributions over a cross-section of a curved tube with the associated velocity field need to be studied in detail. This problem is of particular interest in the design of Stirling engine heat exchangers and in understanding the blood flow in the aorta. The time-dependent, elliptic governing equations are solved, employing finite volume technique. The periodic steady state results are obtained for various governing dimensionless parameters, such as Womersley number, pulsation amplitude ration, curvature ratio and Reynolds number. The numerical results indicate that the phase difference between the pressure gradient and averaged axial velocity increases gradually up to π/2 as Womersley number increases. However, this phase difference is almost independent of the amplitude ratio of pulsation. It is also found that the secondary flow patterns are strongly affected by the curvature ratio and Reynolds number. These, in turn, give a strong influence on the convective heat transfer from the pipe wall to the pulsating flow. The results obtained lead to a better understanding of the underlying physical process and also provide input that may be used to design the relevant system. The numerical approach is discussed in detail, and the aspects that must be included for an accurate simulation are discussed.

Energy Considerations in the Flow Enhancement of Viscoelastic Liquids

Flow enhancement effects due to different waveforms in the tube flow of rheologically complex fluids driven by a pulsating pressure gradient are investigated. It is found that the squarer the waveform the larger the enhancement. In each case the enhancement is strongly dependent on the viscosity function, but the elastic properties also play an important role. We determine that considerable energy savings may be obtained in the transport of viscoelastic liquids if an oscillatory gradient is superposed on a mean gradient. The closer the oscillation to the square wave the larger the energy savings.