Fluid Elastic Effects Research Articles

Numerical simulations of particle migration in rectangular channel flow of Giesekus viscoelastic fluids

In this paper, the lateral migration of a neutrally buoyant spherical particle in a pressure-driven rectangular-shaped channel flow of Giesekus viscoelastic fluids is numerically investigated with a fictitious domain method. The particle trajectories are shown for the channel aspect ratio 2, the ratio of the particle diameter to the channel height 0.15, the Reynolds number 1 and 50, and the Weissenberg number up to 2.5. When the fluid inertial effect is negligible, the particle migrates toward the channel centerline or the closest corner depending on its initial position, and the corner-attraction region is enlarged as the Weissenberg number increases. When both fluid inertial and elastic effects are important, most particles migrate toward the face centers of the shorter walls. The particle migration trajectories are significantly affected by the secondary flow.

Near-critical swirling flow of a viscoelastic fluid in a circular pipe

The interaction between flow inertia and elasticity in high-Reynolds-number, axisymmetric and near-critical swirling flows of an incompressible and viscoelastic fluid in an open finite-length straight circular pipe is studied at the limit of low elasticity. The stresses of the viscoelastic fluid are described by the generalized Giesekus constitutive model. This model helps to focus the analysis on low fluid elastic effects with shear thinning of the viscosity. The application of the Giesekus model to columnar streamwise vortices is first investigated. Then, a nonlinear small-disturbance analysis is developed from the governing equations of motion. It reveals the complicated interactions between flow inertia, swirl and fluid rheology. An effective Reynolds number that links between steady states of swirling flows of a viscoelastic fluid and those of a Newtonian fluid is revealed. The effects of the fluid viscosity, relaxation time, retardation time and mobility parameter on the flow development in the pipe and on the critical swirl for the appearance of vortex breakdown are explored. It is found that in vortex flows with either an axial jet or an axial wake profile, increasing the shear thinning by decreasing the ratio of the viscoelastic characteristic times from one (with fixed values of the Weissenberg number and the mobility parameter) increases the critical swirl ratio for breakdown. Increasing the fluid elasticity by increasing the Weissenberg number from zero (with a fixed ratio of the viscoelastic characteristic times and a fixed value of the mobility parameter) or increasing the fluid mobility parameter from zero (with fixed values of the Weissenberg number and the ratio of viscoelastic times) causes a similar effect. The results may explain the trend of changes in the appearance of breakdown zones as a function of swirl level that were observed in the experiments by Stokes et al. (J. Fluid Mech., vol. 429, 2001, pp. 67–115), where Boger fluids were used. This work extends for the first time the theory of vortex breakdown to include effects of non-Newtonian fluids.

Miniature Viscous Disk Pump: Performance Variations From Non-Newtonian Elastic Turbulence

Within the present investigation, a miniature viscous disk pump (VDP) is utilized to characterize and quantify non-Newtonian fluid elastic turbulence effects, relative to Newtonian flow behavior. Such deviations from Newtonian behavior are induced by adding polyacrylamide to purified water. The VDP consists of a 10.16 mm diameter disk that rotates above a C-shaped channel with inner and outer radii of 1.19 mm and 2.38 mm, respectively. A channel depth of 230 μm is employed. Fluid inlet and outlet ports are located at the ends of the C-shaped channel. Experimental data are given for rotational speeds of 126 1/s, 188 1/s, 262 1/s, and 366 1/s, pressure rises as high as 700 Pa, and flow rates up to approximately 0.00000005 m3/s. Reynolds number ranges from 2.9 to 6.5 for the non-Newtonian polyacrylamide solution flows and from 51.6 to 149.8 for the Newtonian pure water flows. To characterize deviations due to non-Newtonian elastic turbulence phenomena, two new parameters are introduced, PrR and HCR, where HCR is the ratio of head coefficient (HC) for the polyacrylamide solution and head coefficient for the water solution, and PrR is the ratio of pump power for the polyacrylamide solution and pump power for the water solution. Relative to Newtonian, pure water flows, the polyacrylamide solution flows give pump head coefficient data, dimensional pressure rise data, slip coefficients (SCs), specific speed (SS) values, and dimensional power data, which show significant variations and differences as they vary with flow coefficient (FC) or dimensional volumetric flow rate. Also important are different ranges of specific speed (SS) for the pure water and polyacrylamide solutions, and a lower range of SC or slip coefficient values for the polyacrylamide solution flows, compared to the pure water flows. These variations are due to increased elastic turbulence losses, which occur as viscosity magnitudes increase and the elastic polymers are excited by mechanical stress, which causes them to extend, deform, stretch, and intertwine.

Harmonic Analysis of a Cylinder Cluster in Square Confinement With Position-Dependent Fluid Damping

The vibration of cylinder clusters in axial flow is a classical engineering problem, with applications to nuclear fuel rods and steam generator tubes. The classical method of solution to this problem consists in development of modal analysis of the entire cluster including structural characteristics and fluid-elastic effects due to the presence of the dense medium in the space between cylinders, followed by a forced-vibration analysis. It is shown here that the out-of-phase fluid-elastic effects (added damping) are dependent on the position of cylinders within the bundle, not unlike the already proven in-phase effects (added mass). A two-dimensional arbitrary Lagrangian Eulerian (ALE) finite-element analysis is used to compute the hydrodynamic coupling effects in a 5×5 rod cluster subject to single-phase parallel flow. These motion-dependent effects are subsequently embedded into the equations of motion for scaled-down array of nuclear fuel rods, which are structurally modeled as variable-mass Euler–Bernoulli beams on elastic supports. The modal and harmonic analyses developed on the basis of these equations shows that the rod response is affected by the rod position within the cluster, relative to the confinement.

Methods for numerical study of tube bundle vibrations in cross-flows

In many industrial applications, mechanical structures like heat exchanger tube bundles are subjected to complex flows causing possible vibrations and damage. Part of fluid forces are coupled with tube motion and the so-called fluid-elastic forces can affect the structure dynamic behaviour generating possible instabilities and leading to possible short term failures through high amplitude vibrations. Most classical fluid force identification methods rely on structure response experimental measurements associated with convenient data processes. Owing to recent improvements in Computational Fluid Dynamics, numerical simulation of flow-induced vibrations is now practicable for industrial purposes. The present paper is devoted to the numerical identification of fluid-elastic effects affecting tube bundle motion in presence of fluid at rest and one-phase cross-flows. What is the numerical process? When fluid-elastic effects are not significant and are restricted to added mass effects, there is no strong coupling between structure and fluid motions. The structure displacement is not supposed to affect flow patterns. Thus it is possible to solve flow and structure problems separately by using a fixed nonmoving mesh for the fluid dynamic computation. Power spectral density and time record of lift and drag forces acting on tube bundles can be computed numerically by using an unsteady fluid computation involving for example a large Eddy simulation. Fluid force spectra or time record can then be introduced as inlet conditions into the structure code providing the tube dynamic response generated by flow. Such a computation is not possible in presence of strong flow structure coupling. When fluid-elastic effects cannot be neglected, in presence of tube bundles subjected to cross-flows for example, a coupling between flow and structure computations is required. Appropriate numerical methods are investigated in the present work. The purpose is to be able to provide a numerical estimate of the critical flow velocity for the threshold of fluid-elastic instability of tube bundle without experimental investigation. The methodology consists in simulating in the same time thermohydraulics and mechanics problems by using an arbitrary Lagrange Euler (ALE) formulation for the fluid computation. A fully coupled numerical approach is suggested and applied to the numerical prediction of the vibration frequency of a flexible tube belonging to a fixed tube bundle in fluid at rest or in flow. Numerical results turn out to be consistent with available experimental data obtained in the same configuration. This work is a first step in the definition of a computational process for the full numerical prediction of tube bundle vibrations induced by flows.

Self-excited oscillations of turbulent inflow along a perforated plate

The grazing flow of a fully turbulent boundary layer along a perforated plate, which is bounded by a closed cavity on its backside, can give rise to highly coherent, self-sustained oscillations of the shear flow, even in absence of acoustic resonant or fluid elastic effects. These oscillations are characterized in terms of unsteady pressure fluctuations and quantitative images of the instantaneous and averaged flow structure using a technique of high-image-density particle image velocimetry. This purely hydrodynamic instability, which rapidly emerges above the turbulent background, has a wavelength that is much longer than the hole diameter of the perforated plate. Variations of the effective length L of the perforated plate show nearly invariant values of dimensionless frequency fL/ U, in which f is the predominant frequency of oscillation and U is the freestream velocity. In fact, this relationship holds even when the diameter of the hole pattern is altered. Variation of the hole diameter D does, however, strongly influence the amplitude and degree of organization of the self-sustained oscillation. It is demonstrated that, as the hole diameter becomes larger relative to the inflow boundary layer thickness, the amplitude of the predominant spectral peak is substantially attenuated and, in a limiting case, undetectable. These features are interpreted in conjunction with instantaneous and averaged patterns of the flow structure, which include distributions of both Reynolds stress and amplitudes of spectral peaks. This type of instability is distinctively different from the classical instability associated with “singing” of perforated plates employed in attenuation liners in engineering systems, where the genesis of the instability is local vortex shedding within each hole of the perforation, in contrast to the long wavelength instability that is addressed herein.

Scaling of damping induced by bubbly flow across tubes

The damping of tubes subjected to two-phase air–water bubbly cross-flow is investigated with the use of an experimental database from several authors. A new definition of damping in stagnant flow is proposed using an extrapolation of the measured values at low dimensionless flow velocities. This approach yields values of damping substantially lower than those currently defined in the literature. They are found to vary continuously with void fraction, within the bubbly flow regime. These data are used to compare several models of the equivalent viscosity of a two-phase mixture. The effect of the flow velocity is then analysed up to fluidelastic instability. It is observed that, using scaling factors based on the characteristics of the liquid phase, fluidelastic effects of bubbly flows are closely related to those known in single-phase flows.

The thermocapillary migration of gas bubbles in a viscoelastic fluid

The steady thermocapillary flow of a spherical bubble in a linear temperature field is analyzed by considering that the continuous phase is a weak viscoelastic fluid. Convective heat and momentum transfers are neglected but the action of gravity is taken into account. The problem is formulated for non shear thinning elastic fluids which may be described by the Olroyd-B constitutive equation. The analysis is restricted to weak elastic fluids, an assumption that in dimensionless terms is equivalent to assuming that the Weissenberg number Wi=λ/tc where λ is the relaxation time of the fluid and tc the scale time of the flow, is small compared to unity. Thus, the corresponding boundary value problem is solved following a perturbation procedure by regular expansions of the kinematic and stress variables in powers of Wi (retarded motion expansion). Velocity fields as well as the force exerted by the fluid upon the bubble are determined at second order in Wi. It is shown that when the motion is driven by buoyancy in the presence of surface tension forces of a comparable order of magnitude, the velocity fields are strongly affected. Unlike the newtonian case where the recirculation region generated is symmetrical, in a non-newtonian fluid elastic effects produce a breaking of symmetry, so that this region is enhanced and shifted in the downstream direction. The analysis also provides the second order correction to both the terminal velocity and the temperature gradient needed to hold the bubble at rest.

OSCILLATIONS OF A TURBULENT JET INCIDENT UPON AN EDGE

For the case of a jet originating from a fully turbulent channel flow and impinging upon a sharp edge, the possible onset and nature of coherent oscillations has remained unexplored. In this investigation, high-image-density particle image velocimetry and surface pressure measurements are employed to determine the instantaneous, whole-field characteristics of the turbulent jet–edge interaction in relation to the loading of the edge. It is demonstrated that even in the absence of acoustic resonant or fluid–elastic effects, highly coherent, self-sustained oscillations rapidly emerge above the turbulent background. Two clearly identifiable modes of instability are evident. These modes involve large-scale vortices that are phase-locked to the gross undulations of the jet and its interaction with the edge, and small-scale vortices, which are not phase-locked. Time-resolved imaging of instantaneous vorticity and velocity reveals the form, orientation, and strength of the large-scale concentrations of vorticity approaching the edge in relation to rapid agglomeration of small-scale vorticity concentrations. Such vorticity field–edge interactions exhibit rich complexity, relative to the simplified pattern of vortex–edge interaction traditionally employed for the quasi-laminar edgetone. Furthermore, these interactions yield highly nonlinear surface pressure signatures. The origin of this nonlinearity, involving the coexistence of multiple frequency components, is interpreted in terms of large- and small-scale vortices embedded in distributed vorticity layers at the edge. Eruption of the surface boundary layer on the edge due to passage of the large-scale vortex does not occur; rather apparent secondary vorticity concentrations are simply due to distension of the oppositely signed vorticity layer at the tip of the edge. The ensemble-averaged turbulent statistics of the jet quickly take on an identity that is distinct from the statistics of the turbulent boundary layer in the channel. Large increases in Reynolds stress occur due to onset of the small-scale concentrations of vorticity immediately downstream of separation; substantial increases at locations further downstream arise from development of the large-scale vorticity concentrations.

Measurement of Critical Velocities for Fluidelastic Instability Using Vibration Control

Fluidelastic effects may be responsible for instabilities of heat exchanger tubes when the fluid flow reaches the critical velocity. The fluidelastic phenomenon is usually studied on experimental mock-ups, which may display only one critical velocity. In this paper, a method based on active vibration control is proposed in order to derive several critical velocities for fluidelastic instability corresponding to several different values of damping, which is artificially varied on the same mock-up. Experimental tests are performed on a flexible tube equipped with piezoelectric actuators in a rigid array under air-water cross-flow. It is shown that the reduced critical velocities thus obtained fit well in a classical stability map. [S0739-3717(00)01603-2]

The Measurement of Fluidelastic Effects at Low Reduced Velocities Using Piezoelectric Actuators

Fluidelastic effects which are responsible for fluidelastic instabilities may be indirectly measured through the analysis of the vibrating motion of a system under flow. In this paper, piezoelectric actuators are used to increase the vibratory level when buffeting forces which excite tube vibration are low, and to improve the measurement of fluidelastic forces. The proposed method based on an added excitation allows the study of the added mass and provides a better accuracy on the measurement of the vibrating characteristics and, thereby, of the fluidelastic forces. This added excitation method is compared with a standard indirect approach on a tube underwater crossflow. The influence of the level of piezoelectric excitation forces is discussed, as well as the range of application of this technique.