Oscillating Pressure Gradient Research Articles

Turbulent oscillating channel flow subjected to a free-surface stress

The channel flow subjected to a wind stress at the free surface and an oscillating pressure gradient is investigated using large-eddy simulations. The orientation of the surface stress is parallel with the oscillating pressure gradient and a purely pulsating mean flow develops. The Reynolds number is typically Reω=106 and the Keulegan–Carpenter number—the ratio between the oscillation period and advection time scale—is KC=80. Results compare favorably to the data from direct numerical simulations obtained over a single period. A slowly pulsating mean flow occurs with the turbulent flow essentially being statistically steady. Logarithmic boundary layers are present at both the bottom wall and the free surface. Turbulent streaks are observed in the bottom and free-surface layer. The viscous sublayer below the free surface is, however, much thinner. This observation is verified by simulations we performed for a purely wind-driven channel flow. For the oscillating flow, additional low-speed splats (localized regions of upwelling) occur at the free surface when the mean velocity and stress are in the same direction.

Asymptotic analysis of blood flow in stented arteries: time dependency and direct simulations

This work aims to extend in two distinct directions results recently obtained in (10). In a rst step we focus on the possible extension of our results to the time dependent case. Whereas in the second part some preliminary numerical simulations aim to give orders of magnitudes in terms of numerical costs of direct 3D simulations. We consider, in the rst part, the time dependent rough problem for a simplied heat equation in a straight channel that mimics the axial velocity under an oscillating pressure gradient. We derive rst order approximations with respect to , the size of the roughness. In order to understand the problem and set up correct boundary layer approximations, we perform a time periodic fourier analysis and check that no frequency can interact with the roughness. We show rigorously on this toy problem that the boundary layers remain stationary in time (independent on the frequency number). Finally we perform numerical tests validating our theoretical approach. In the second part, we determine actual limits, when running three-dimensional blood ow simula- tions of the non-homogenized stented arteries. We solve the stationary Stokes equations for an artery containing a saccular aneurysm. Consecutive levels of uniform mesh renement, serve to relate spatial resolution, problem scale, and required computation time. Test computations are presented for femoral side aneurysm, where a simplied ten-wire stent model was placed across the aneurysm throat. We advocate the proposed stent homogenization model, by concluding that an actual computation power is not sucient to run accurate, direct simulations of a pulsatile ow in stented vessels.

Effects of Hall current on unsteady MHD flows of a second grade fluid

Abstract The aim of this present paper is to construct exact solutions corresponding to the motion of magnetohydrodynamic (MHD) fluid in the presence of Hall current, due to cosine and sine oscillations of a rigid plate as well as those induced by an oscillating pressure gradient. A uniform magnetic field is applied transversely to the flow. By using Fourier sine transform steady state and transient solutions are presented. These solutions satisfy the governing equations and all associated initial and boundary conditions. The results for a hydrodynamic second grade fluid can be obtained as a limiting case when B 0 → 0 and for a Newtonian fluid when α 1 → 0.

A note on longitudinal oscillations of a generalized Burgers fluid in cylindrical domains

The starting solutions for the oscillating motion of a generalized Burgers fluid due to longitudinal oscillations of an infinite circular cylinder, as well as those corresponding to an oscillating pressure gradient, are established as Fourier–Bessel series in terms of some suitable eigenfunctions. These solutions, presented as sum of steady-state and transient solutions, describe the motion of the fluid for some time after its initiation. After that time, when the transients disappear, the motion of the fluid is described by the steady-state solutions which are periodic in time and independent of the initial conditions. These solutions are also presented in simpler but equivalent forms in terms of modified Bessel functions of first and second kind. In both forms, the steady-state solutions can be specialized to give the similar solutions for Burgers, Oldroyd-B, Maxwell, second grade and Newtonian fluids performing the same motions. Finally, the required time to reach the steady-state for cosine and sine oscillations of the boundary is obtained by graphical illustrations.

Exact solutions for some oscillating motions of a fractional Burgers’ fluid

This article presents some starting solutions corresponding to the oscillating flows of a Burgers’ fluid with fractional derivatives. The fractional calculus approach in the constitutive relationship model is introduced and a fractional Burgers’ model is built. The exact solutions for the oscillating motions of a fractional Burgers’ fluid due to cosine and sine oscillations of an infinite flat plate as well as those corresponding to an oscillating pressure gradient are established with the help of integral transforms (Fourier sine and Laplace transforms). In order to avoid lengthy calculations of residues and contour integrals, the discrete Laplace transform method has been used. The expressions for the velocity field and the resulting shear stress that have been obtained, presented under integral and series form in terms of the generalized G functions, satisfy all imposed initial and boundary conditions. Similar solutions for generalized Oldroyd-B, Maxwell and second grade fluids as well as those for ordinary Oldroyd-B, Maxwell, second grade and Newtonian fluids are obtained as limiting cases of our general solutions. Finally, the obtained solutions are graphically analyzed for variations of interesting flow parameters.

Inertial migration of a circular particle in nonoscillatory and oscillatory pressure-driven flows at moderately high Reynolds numbers

The inertial migration of a single neutrally buoyant circular particle in both nonoscillatory and oscillatory pressure-driven flows in a two-dimensional (2D) channel at moderately high Reynolds numbers has been numerically investigated by using the direct-forcing fictitious domain (DF/FD) method. In both nonoscillatory and oscillatory cases, there is only one equilibrium position for any Reynolds number, and the equilibrium positions first shift closer to the channel wall and then closer to the channel centerline as the Reynolds number increases, unlike the 3D nonoscillatory pipe case where there exist two branches of equilibrium positions. The equilibrium positions for a spherical particle in a 3D nonoscillatory channel flow are also computed and found to behave in the same way as the 2D case. The reason for the difference in the equilibrium positions between the channel and pipe flows is attributed to the effects of the outer boundary on the particle-induced flow structures. The oscillatory flow generally makes the equilibrium position closer to the channel centerline, and the equilibrium positions are more sensitive to the frequency than the amplitude of the oscillatory pressure gradient.

Pulsatile flow of viscous and viscoelastic fluids in constricted tubes

The unsteady flow of blood through stenosed artery, driven by an oscillatory pressure gradient, is studied. An appropriate shape of the time-dependent stenoses which are overlapped in the realm of the formation of arterial narrowing is constructed mathematically. A msathematical model is developed by treating blood as a non-Newtonian fluid characterized by the Oldroyd-B and Cross models. A numerical scheme has been used to solve the unsteady nonlinear Navier-stokes equations in cylindrical coordinate system governing flow, assuming axial symmetry under laminar flow condition so that the problem effectively becomes two-dimensional. Finite difference technique was used to investigate the effects of parameters such as pulsatility, non-Newtonian properties and the flow time on the velocity components, the rate of flow, and the wall shear stress through their graphical representations quantitatively at the end of the paper in order to validate the applicability of the present improved mathematical model under consideration.

Nonlinear Reduced-Order Analysis with Time-Varying Spatial Loading Distributions

Oscillating shocks acting in combination with high-intensity acoustic loadings present a challenge to the design of resilient hypersonic-flight vehicle structures. This paper addresses some features of this loading condition and certain aspects of a nonlinear reduced-order analysis with emphasis on system identification, leading to the formation of a robust modal basis. The nonlinear dynamic response of a composite structure subject to the simultaneous action of locally strong oscillating pressure gradients and high-intensity acoustic loadings is considered. The reduced-order analysis used in this work has been previously demonstrated to be both computationally efficient and accurate for time-invariant spatial loading distributions, provided that an appropriate modal basis is used. The challenge of the present study is to identify a suitable basis for loadings with time-varying spatial distributions. Using a proper orthogonal decomposition and modal expansion, it is shown that such a basis can be developed. The basis is made more robust by incrementally expanding it to account for changes in the location, frequency, and span of the oscillating pressure gradient.

On exact solutions for some oscillating motions of a generalized Oldroyd-B fluid

This paper deals with exact solutions for some oscillating motions of a generalized Oldroyd-B fluid. The fractional calculus approach is used in the constitutive relationship of fluid model. Analytical expressions for the velocity field and the corresponding shear stress for flows due to oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient are determined using Fourier sine and Laplace transforms. The obtained solutions are presented under integral and series forms in terms of the Mittag–Leffler functions. For α = β = 1, our solutions tend to the similar solutions for ordinary Oldroyd-B fluid. A comparison between generalized and ordinary Oldroyd-B fluids is shown by means of graphical illustrations.

Simulation study of the filamentation of counter-streaming beams of the electrons and positrons in plasmas

The filamentation instability (FI) driven by two spatially uniform and counter-streaming beams of charged particles in plasmas is modelled by a particle-in-cell simulation. Each beam consists of electrons and positrons. The four species are equally dense and have the same temperature. The one-dimensional simulation direction is orthogonal to the beam velocity vector. The magnetic field grows spontaneously and rearranges the particles in space, such that the distributions of the electrons of one beam and the positrons of the second beam match. The simulation demonstrates that as a result no electrostatic field is generated by the magnetic field through its magnetic pressure gradient prior to its saturation. This electrostatic field would be repulsive at the centres of the filaments and limit the maximum charge and current density. The filaments of electrons and positrons in this simulation reach higher charge and current densities than in one with no positrons. The oscillations of the magnetic field strength induced by the magnetically trapped particles result in an oscillatory magnetic pressure gradient force. The latter interplays with the statistical fluctuations in the particle density and it probably enforces a charge separation, by which electrostatic waves grow after the FI has saturated.

Drag force acting on a neuromast in the fish lateral line trunk canal. I. Numerical modelling of external-internal flow coupling.

Fishes use a complex, multi-branched, mechanoreceptive organ called the lateral line to detect the motion of water in their immediate surroundings. This study is concerned with a subset of that organ referred to as the lateral line trunk canal (LLTC). The LLTC consists of a long tube no more than a few millimetres in diameter embedded immediately under the skin of the fish on each side of its body. In most fishes, pore-like openings are regularly distributed along the LLTC, and a minute sensor enveloped in a gelatinous cupula, referred to as a neuromast, is located between each pair of pores. Drag forces resulting from fluid motions induced inside the LLTC by pressure fluctuations in the external flow stimulate the neuromasts. This study, Part I of a two-part sequence, investigates the motion-sensing characteristics of the LLTC and how it may be used by fishes to detect wakes. To this end, an idealized geometrical/dynamical situation is examined that retains the essential problem physics. A two-level numerical model is developed that couples the vortical flow outside the LLTC to the flow stimulating the neuromasts within it. First, using a Navier-Stokes solver, we calculate the unsteady flow past an elongated rectangular prism and a fish downstream of it, with both objects moving at the same speed. By construction, the prism generates a clean, periodic vortex street in its wake. Then, also using the Navier-Stokes solver, the pressure field associated with this external flow is used to calculate the unsteady flow inside the LLTC of the fish, which creates the drag forces acting on the neuromast cupula. Although idealized, this external-internal coupled flow model allows an investigation of the filtering properties and performance characteristics of the LLTC for a range of frequencies of biological interest. The results obtained here and in Part II show that the LLTC acts as a low-pass filter, preferentially damping high-frequency pressure gradient oscillations, and hence high-frequency accelerations, associated with the external flow.

Analytical solution for pulsatile viscous flow in a straight elliptic annulus and application to the motion of the cerebrospinal fluid

We present here the analytical solution of transient, laminar, viscous flow of an incompressible, Newtonian fluid driven by a harmonically oscillating pressure gradient in a straight elliptic annulus. The analytical formulation is based on the exact solution of the governing fluid flow equations known as Navier–Stokes equations. We validate the analytical solution using a finite-volume computational fluid dynamics approach. As the analytical solution includes Mathieu and modified Mathieu functions, we also present a stepwise procedure for their evaluation for large complex arguments typically associated with viscous flows. We further outline the procedure for evaluating the associated Fourier coefficients and their eigenvalues. We finally apply the analytical solution to investigate the cerebrospinal fluid flow in the human spinal cavity, which features a shape similar to an elliptic annulus.

Oscillatory boundary layer close to a rough wall

The flow field, generated by an oscillating pressure gradient close to a rough wall, is investigated by means of direct numerical simulations of Navier–Stokes and continuity equations. The wall roughness consists of semi-spheres regularly placed on a plane wall. A comparison of the obtained results with the experimental measurements of Keiller and Sleath [D.C. Keiller, J.F.A. Sleath, Velocity measurements close to a rough plate oscillating in its own plane, J. Fluid Mech. 73 (1976) 673–691] supports the numerical findings. As in Keiller and Sleath [D.C. Keiller, J.F.A. Sleath, Velocity measurements close to a rough plate oscillating in its own plane, J. Fluid Mech. 73 (1976) 673–691], a secondary peak in the streamwise velocity component is observed close to flow reversal and the peak is shown to be generated by the coherent vortex structures which are shed by the roughness elements. The flow is found to be dominated by the shear layers which form at the top of the roughness elements during the accelerating phases of the cycle and by the horse-shoe vortices which form close to the base of the semi-spheres. The dynamics of the shear layers and of the horse-shoe vortices is found to have a relevant influence on the pressure distribution and on the force exerted by the fluid on the roughness elements. The obtained results shed light to the mechanism by which the sediment is picked-up from the bottom by the action of sea waves.

Exact solutions of starting flows for second grade fluid in a porous medium

This paper concentrates on the unsteady flows of a magnetohydrodynamic (MHD) second grade fluid filling a porous medium. The flow modeling involves modified Darcy's law. Three problems are considered. They are (i) starting flow due to an oscillating edge, (ii) starting flow in a duct of rectangular cross-section oscillating parallel to its length, and (iii) starting flow due to an oscillating pressure gradient. Analytical expressions of velocity field and corresponding tangential stresses are developed. These expressions are found to be significantly affected by the applied magnetic field, permeability of the porous medium and the material parameter of the fluid. Moreover, the influence of pertinent parameters on the flows is delineated and appropriate conclusions are drawn. Finally, a comparison is also made with the existing results in the literature.

A non-homogeneous constitutive model for human blood: Part III. Oscillatory flow

Numerous experiments have been performed to show that for oscillatory blood flow in a tube, sufficiently large volume flow rate amplitudes will break up blood aggregates leading to a loss of elasticity and to a response by the pressure gradient oscillations typical of those of a viscous fluid in inertial flow [G.B. Thurston, Elastic effects in pulsatile blood flow, Microvasc. Res. 9 (1975), 145–157]. In this paper we use the non-homogeneous blood model developed in Part I of this work [M. Moyers-Gonzalez, R.G. Owens, J. Fang, A non-homogeneous constitutive model for human blood. Part I. Model derivation and steady flow, submitted for publication] to simulate blood undergoing oscillatory flow and, in particular, to examine the behaviour of the components of the pressure gradient that are in phase and π / 2 out of phase with the volume flow rate, as the volume flow rate amplitude is varied. Excellent agreement is found with experimental data for a tube of radius 430 μ m . An improvement in the predictions compared to those of an earlier homogeneous model [J. Fang, R.G. Owens, Numerical simulations of pulsatile blood flow using a new constitutive model, Biorheology 43 (2006) 637–660] is evidenced. We also seek to relate the macroscopic blood behaviour in different size tubes and at two different angular frequencies to the aggregate properties such as the average aggregate size and the cell number density.

Unsteady flows in pipes with finite curvature

Motivated by the study of blood flow in a curved artery, we consider fluid flow through a curved pipe of uniform curvature, δ, driven by a prescribed oscillatory axial pressure gradient. The curved pipe has finite (as opposed to asymptotically small) curvature, and we determine the effects of both the centrifugal and Coriolis forces on the flow. In addition to δ, the flow is parameterized by the Dean number, D, the Womersley number, α, and a secondary streaming Reynolds number, Rs. Asymptotic solutions are developed for the case when δ≪1, α≪1 and the magnitude of the axial pressure gradient is small, using regular perturbation techniques. For intermediate values of the governing parameters, a pseudospectral code is used to obtain numerical solutions. For flows driven by a sinusoidal pressure gradient (D=0), we identify three distinct classes of stable solutions: 2π-periodic symmetric, 2π-periodic asymmetric, and asymmetric solutions that are either quasi-periodic, or periodic with period 2πk for k∈ $\mathbb{N}$. The transition between solutions is dependent on the value of δ; thus pipes with finite curvature may exhibit qualitatively different transitions between the solution classes as the governing parameters are varied from those of curved pipes with asymptotically small curvature. When α≫1, matched asymptotic expansions are used to simplify the system, and the resulting equations are solved analytically for Rs≪1, δ≪1 and numerically for larger parameter values. We then determine the effect of a non-zero steady component of the pressure gradient (D≠0), and show that, for certain parameter values, when D is above a critical value the periodic asymmetric solutions regain spatial symmetry. Finally, we show that the effects of finite curvature can lead to substantial quantitative differences in the wall shear stress distribution and discuss briefly the physiological implications of the results for blood flow in arteries.

The femoral stem pump in cemented hip arthroplasty: An in vitro model

The presence of an intra-articular pump has been proposed as a central mechanism in the process of osteolysis and aseptic loosening of hip arthroplasty. It is not known if this pump exists and its mechanism remains uncharacterised. This study describes a new in vitro model of a cemented femoral stem in which cement/stem interface fluid pressures can be reliably measured under dynamic loads simulating stair climbing. A stem pump mechanism was found that generates both positive and negative clinically significant pressures (mean pressure ranges 5000–17,000 Pa). The timing of pressure peaks on the anterior and posterior aspects of the stem were in anti-phase, giving rise to oscillatory pressure gradients and potentially generating oscillatory fluid flows during the simulated physiological load cycle. The pump mechanism was shown to occur at the interface of a newly implanted polished double-tapered stem and emphasizes the importance of a complete mantle to protect the femoral bone from the raised fluid pressures.

Instabilities in the oscillatory flow of a complex fluid

The dynamics of a fluid in a vertical tube, subjected to an oscillatory pressure gradient, is studied experimentally for both a Newtonian and a viscoelastic shear-thinning fluid. Particle image velocimetry is used to determine the two-dimensional velocity fields in the vertical plane of the tube axis, in a range of driving amplitudes from 0.8 to 2.5 mm and of driving frequencies from 2.0 to 11.5 Hz. The Newtonian fluid exhibits a laminar flow regime, independent of the axial position, in the whole range of drivings. For the complex fluid, instead, the parallel shear flow regime exhibited at low amplitudes [Torralba, Phys. Rev. E 72, 016308 (2005)] becomes unstable at higher drivings against the formation of symmetric vortices, equally spaced along the tube. At even higher drivings the vortex structure itself becomes unstable, and complex nonsymmetric structures develop. Given that inertial effects remain negligible even at the hardest drivings (Re < 10(-1)), it is the complex rheology of the fluid that is responsible for the instabilities observed. The system studied represents an interesting example of the development of shear-induced instabilities in nonlinear complex fluids in purely parallel shear flow.

Steady streaming in a turbulent oscillating boundary layer

The turbulent flow generated by an oscillating pressure gradient close to an infinite plate is studied by means of numerical simulations of the Navier–Stokes equations to analyse the characteristics of the steady streaming generated within the boundary layer. When the pressure gradient that drives the flow is given by a single harmonic component, the time average over a cycle of the flow rate in the boundary layer takes both positive and negative values and the steady streaming computed by averaging the flow over n cycles tends to zero as n tends to infinity. On the other hand, when the pressure gradient is given by the sum of two harmonic components, with angular frequencies ω1 and ω2 = 2ω1, the time average over a cycle of the flow rate does not change sign. In this case steady streaming is generated within the boundary layer and it persists in the irrotational region. It is shown both theoretically and numerically that in spite of the presence of steady streaming, the time average over n cycles of the hydrodynamic force, acting per unit area of the plate, vanishes as n tends to infinity.

Colloid vibration potential in a suspension of soft particles

We develop a theory of the vibration potential produced in a dilute suspension of soft particles (i.e., hard particles covered with an ion-penetrable surface layer of polyelectrolytes) in an electrolyte solution when a sound wave (i.e., an oscillating pressure gradient field) is applied to the suspension. The total vibration potential (TVP) consists of two components. One is the colloid vibration potential (CVP) and the other is the ion vibration potential (IVP). The obtained CVP expression covers two extreme cases, that is, the CVP in a suspension of hard particles (in the absence of the polyelectrolyte layer) and that in a suspension of spherical polyelectrolytes (in the absence of the particle core). A simple analytic expression for CVP, which is proportional to the dynamic electrophoretic mobility of a soft particle, is given. It is shown that the CVP of a suspension of a soft particle depends on the density of the volume charge distributed in the polyelectrolyte layer, on the frictional coefficient characterizing the frictional forces exerted by the polymer segments on the liquid flow in the polyelectrolyte layer, on the particle size, on the thickness of the polyelectrolyte layer, and on the frequency of the applied oscillating pressure gradient field.