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1
Zhao, Wu, Quan Bin Zhang, Wei Tao Jia, and Zhan Qi Hu. "Influence on BTA Boring Bar Transverse Vibration Considering Inner Cutting Fluid Velocity and Axial Force." Advanced Materials Research 887-888 (February 2014): 1215–18. http://dx.doi.org/10.4028/www.scientific.net/amr.887-888.1215.
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A new simulation model on frequency is proposed, to analyze mutual relationship between intrinsic frequency and other factors in system. The study is mainly focused on the axial press effect, inner cutting fluid velocity and its Coriolis inertia effects acting on boring bar. The whole system is assumed to conform to the continuous equal span beam model synthesized with liquid-solid coupling vibration model inner the work and Timoshenko beam model outer the work. Simulations show that system vibration frequency is determined by mechanical properties, axial force, inner cutting fluid velocity and density. Three aspects influence BTA boring bar lateral vibration considering inner cutting fluid velocity and axial force, who are transverse inertial mass, inertia and self-excited vibration on the bar. Inner flowing of the cutting fluids also lead to instability on bar.
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Kim, Uihwan, Joo-Yong Kwon, Taehoon Kim, and Younghak Cho. "Particle Focusing in a Straight Microchannel with Non-Rectangular Cross-Section." Micromachines 13, no. 2 (January 20, 2022): 151. http://dx.doi.org/10.3390/mi13020151.
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Recently, studies on particle behavior under Newtonian and non-Newtonian fluids in microchannel have attracted considerable attention because particles and cells of interest can be manipulated and separated from biological samples without any external force. In this paper, two kinds of microchannels with non-rectangular cross-section were fabricated using basic MEMS processes (photolithography, reactive ion etching and anisotropy wet etching), plasma bonding and self-alignment between two PDMS structures. They were used to achieve the experiments for inertial and elasto-inertial particle focusing under Newtonian and non-Newtonian fluids. The particle behavior was compared and investigated for different flow rates and particle size in the microchannel with rhombic and equilateral hexagonal cross section. We also investigated the influence of Newtonian fluid and viscoelastic fluid on particle migration in both microchannels through the numerical simulation. The experimental results showed the multi-line particle focusing in Newtonian fluid over a wide range of flow rates, but the single-line particle focusing was formed in the centerline under non-Newtonian fluid. The tighter particle focusing appeared under non-Newtonian fluid in the microchannel with equilateral hexagonal cross-section than in the microchannel with rhombic cross section because of the effect of an obtuse angle. It revealed that particles suspended in the channel are likely to drift toward a channel center due to a negative net elasto-inertial force throughout the cross-sectional area. Simulation results support the present experimental observation that the viscoelastic fluid in the microchannel with rhombic and equilateral hexagonal cross-section significantly influences on the particle migration toward the channel center owing to coupled effect of inertia and elasticity.
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Kwon, Joo-Yong, Taehoon Kim, Jungwoo Kim, and Younghak Cho. "Particle Focusing under Newtonian and Viscoelastic Flow in a Straight Rhombic Microchannel." Micromachines 11, no. 11 (November 11, 2020): 998. http://dx.doi.org/10.3390/mi11110998.
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Particle behavior in viscoelastic fluids has attracted considerable attention in recent years. In viscoelastic fluids, as opposed to Newtonian fluids, particle focusing can be simply realized in a microchannel without any external forces or complex structures. In this study, a polydimethylsiloxane (PDMS) microchannel with a rhombic cross-sectional shape was fabricated to experimentally investigate the behavior of inertial and elasto-inertial particles. Particle migration and behavior in Newtonian and non-Newtonian fluids were compared with respect to the flow rate and particle size to investigate their effect on the particle focusing position and focusing width. The PDMS rhombic microchannel was fabricated using basic microelectromechanical systems (MEMS) processes. The experimental results showed that single-line particle focusing was formed along the centerline of the microchannel in the non-Newtonian fluid, unlike the double-line particle focusing in the Newtonian fluid over a wide range of flow rates. Numerical simulation using the same flow conditions as in the experiments revealed that the particles suspended in the channel tend to drift toward the center of the channel owing to the negative net force throughout the cross-sectional area. This supports the experimental observation that the viscoelastic fluid in the rhombic microchannel significantly influences particle migration toward the channel center without any external force owing to coupling between the inertia and elasticity.
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Li, Gaojin, Gareth H. McKinley, and Arezoo M. Ardekani. "Dynamics of particle migration in channel flow of viscoelastic fluids." Journal of Fluid Mechanics 785 (November 23, 2015): 486–505. http://dx.doi.org/10.1017/jfm.2015.619.
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The migration of a sphere in the pressure-driven channel flow of a viscoelastic fluid is studied numerically. The effects of inertia, elasticity, shear-thinning viscosity, secondary flows and the blockage ratio are considered by conducting fully resolved direct numerical simulations over a wide range of parameters. In a Newtonian fluid in the presence of inertial effects, the particle moves away from the channel centreline. The elastic effects, however, drive the particle towards the channel centreline. The equilibrium position depends on the interplay between the elastic and inertial effects. Particle focusing at the centreline occurs in flows with strong elasticity and weak inertia. Both shear-thinning effects and secondary flows tend to move the particle away from the channel centreline. The effect is more pronounced as inertia and elasticity effects increase. A scaling analysis is used to explain these different effects. Besides the particle migration, particle-induced fluid transport and particle migration during flow start-up are also considered. Inertial effects, shear-thinning behaviour, and secondary flows are all found to enhance the effective fluid transport normal to the flow direction. Due to the oscillation in fluid velocity and strong normal stress differences that develop during flow start-up, the particle has a larger transient migration velocity, which may be potentially used to accelerate the particle focusing.
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Mei, Renwei, and Ronald J. Adrian. "Effect of Reynolds Number on Isotropic Turbulent Dispersion." Journal of Fluids Engineering 117, no. 3 (September 1, 1995): 402–9. http://dx.doi.org/10.1115/1.2817276.
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The influence of the spatio-temporal structure of isotropic turbulence on the dispersion of fluid and particles with inertia is investigated. The spatial structure is represented by an extended von Ka´rma´n energy spectrum model which includes an inertial sub-range and allows evaluation of the effect of the turbulence Reynolds number, Reλ. Dispersion of fluid is analyzed using four different models for the Eulerian temporal auto-correlation function D(τ). The fluid diffusivity, normalized by the integral length scale L11 and the root-mean-square turbulent velocity u0, depends on Reλ. The parameter cE = T0u0/L11, in which T0 is the Eulerian integral time scale, has commonly been assumed to be constant. It is shown that cE strongly affects the value of the fluid diffusivity. The dispersion of a particle with finite inertia and finite settling velocity is analyzed for a large range of a particle inertia and settling velocity. Particle turbulence intensity and diffusivity are influenced strongly by turbulence structure.
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Jayaram, Rohith, Yucheng Jie, Lihao Zhao, and Helge I. Andersson. "Dynamics of inertial spheroids in a decaying Taylor–Green vortex flow." Physics of Fluids 35, no. 3 (March 2023): 033326. http://dx.doi.org/10.1063/5.0138125.
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Inertial spheroids, prolates and oblates, are studied in a decaying Taylor–Green vortex (TGV) flow, wherein the flow gradually evolves from laminar anisotropic large-scale structures to turbulence-like isotropic Kolmogorov-type vortices. Along with particle clustering and its mechanisms, preferential rotation and alignment of the spheroids with the local fluid vorticity are examined. Particle inertia is classified by a nominal Stokes number [Formula: see text] which to first-order aims to eliminate the shape effect. The clustering varies with time and peaks when the physically relevant flow and particle time scales are of the same order. Low inertial ([Formula: see text]) spheroids are subjected to the centrifuging mechanism, thereby residing in stronger strain-rate regions, while high inertial ([Formula: see text]) spheroids lag the flow evolution and modestly sample strain-rate regions. Contrary to the expectations, however, spheroids reside in high strain-rate regions when the particle and flow time scales are comparable due to the dynamic interactions between the particles and the evolving flow scales. Moderately inertial ([Formula: see text]) prolates preferentially spin and oblates tumble throughout the qualitatively different stages of the TGV flow. These preferential modes of rotation correlate with parallel and perpendicular alignments of prolate and oblate spheroids, respectively, with the local fluid vorticity. However, for high inertial spheroids preferential rotation and alignment are decorrelated due to a memory effect, i.e., inertial particles require longer time to adjust to the local fluid flow. This memory effect is not only due to high particle inertia, as in statistically steady turbulence, but also caused by the continuously evolving TGV flow scales.
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Salazar, Juan P. L. C., and Lance R. Collins. "Inertial particle relative velocity statistics in homogeneous isotropic turbulence." Journal of Fluid Mechanics 696 (March 5, 2012): 45–66. http://dx.doi.org/10.1017/jfm.2012.2.
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AbstractIn the present study, we investigate the scaling of relative velocity structure functions, of order two and higher, for inertial particles, both in the dissipation range and the inertial subrange using direct numerical simulations (DNS). Within the inertial subrange our findings show that contrary to the well-known attenuation in the tails of the one-point acceleration probability density function (p.d.f.) with increasing inertia (Bec et al., J. Fluid Mech., vol. 550, 2006, pp. 349–358), the opposite occurs with the velocity structure function at sufficiently large Stokes numbers. We observe reduced scaling exponents for the structure function when compared to those of the fluid, and correspondingly broader p.d.f.s, similar to what occurs with a passive scalar. DNS allows us to isolate the two effects of inertia, namely biased sampling of the velocity field, a result of preferential concentration, and filtering, i.e. the tendency for the inertial particle velocity to attenuate the velocity fluctuations in the fluid. By isolating these effects, we show that sampling is playing the dominant role for low-order moments of the structure function, whereas filtering accounts for most of the scaling behaviour observed with the higher-order structure functions in the inertial subrange. In the dissipation range, we see evidence of so-called ‘crossing trajectories’, the ‘sling effect’ or ‘caustics’, and find good agreement with the theory put forth by Wilkinson et al. (Phys. Rev. Lett., vol. 97, 2006, 048501) and Falkovich & Pumir (J. Atmos. Sci., vol. 64, 2007, 4497) for Stokes numbers greater than 0.5. We also look at the scaling exponents within the context of the model proposed by Bec et al. (J. Fluid Mech., vol. 646, 2010, pp. 527–536). Another interesting finding is that inertial particles at low Stokes numbers sample regions of higher kinetic energy than the fluid particle field, the converse occurring at high Stokes numbers. The trend at low Stokes numbers is predicted by the theory of Chun et al. (J. Fluid Mech., vol. 536, 2005, 219–251). This work is relevant to modelling the particle collision rate (Sundaram & Collins, J. Fluid Mech., vol. 335, 1997, pp. 75–109), and highlights the interesting array of phenomena induced by inertia.
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Meng, Fan-Ming, Sheng Yang, Zhi-Tao Cheng, Yong Zheng, and Bin Wang. "Effect of fluid inertia force on thermal elastohydrodynamic lubrication of elliptic contact." Mechanics & Industry 22 (2021): 13. http://dx.doi.org/10.1051/meca/2021010.
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A non-Newtonian thermal elastohydrodynamic lubrication (TEHL) model for the elliptic contact is established, into which the inertia forces of the lubricant is incorporated. In doing so, the film pressure and film temperature are solved using the associated equations. Meanwhile, the elastic deformation is calculated with the discrete convolution and fast Fourier transform (DC-FFT) method. A film thickness experiment is conducted to validate the TEHL model considering the inertia forces. Further, effects of the inertia forces on the TEHL performances are studied at different operation conditions. The results show that when the inertia forces are considered, the central and minimum film thicknesses increase and film temperature near the inlet increases obviously. Moreover, the inertial solution of the central film thickness is closer to the experimental result compared with its inertialess value.
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Блинков, Юрий Анатольевич, Лев Ильич Могилевич, Виктор Сергеевич Попов, and Елизавета Викторовна Попова. "Evolution of solitary hydroelastic strain waves in two coaxial cylindrical shells with the Schamel physical nonlinearity." Computational Continuum Mechanics 16, no. 4 (December 1, 2023): 430–44. http://dx.doi.org/10.7242/1999-6691/2023.16.4.36.
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The paper considers the formulation and solution of the hydroelasticity problem for studying wave processes in the system of two coaxial shells containing fluids in the annular gap between them and in the inner shell. We investigate the axisymmetric case for Kirchhoff–Lave type shells whose material obeys a physical law with a fractional exponent of the nonlinear term (Schamel nonlinearity). The dynamics of fluids in the shells is considered within the framework of the incompressible viscous Newtonian fluid model. The derivation of the Schamel nonlinear equations of shell dynamics makes it possible to develop a mathematical formulation of the problem, which includes the obtained equations, the dynamics equations of two shells, the fluid dynamics equations and the boundary conditions at the shell-fluid interfaces and at the flow symmetry axis. The asymptotic analysis of the problem is performed using perturbation techniques, and the system of two generalized Schamel equations is obtained. This system describes the evolution of nonlinear solitary hydroelastic strain waves in the coaxial shells filled with viscous fluids, taking into account the inertia of the fluid motion. In order to determine the fluid stress at the shell-fluid interfaces, we perform linearization of the fluid dynamics equations for fluids in the annular gap and in the inner shell. The linearized equations are solved by the iterative method. The inertial terms are excluded from the equations in the first iteration, while, in the second iteration, these are the values found in the first iteration. A numerical solution of the system of nonlinear evolution equations is obtained by applying a new difference scheme developed using the Gröbner basis technique. Computational experiments are performed to investigate the effect of fluid viscosity and the inertia of fluid motion in the shells on the wave process. In the absence of fluids in the inner shell, the results of calculations demonstrate that the strain waves in the shells during elastic interactions do not change their shape and amplitude, i.e., they are solitons. The presence of viscous fluid in the inner shell leads to attenuation of the wave process.
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Behera, Nalinikanta, Shubhadeep Mandal, and Suman Chakraborty. "Electrohydrodynamic settling of drop in uniform electric field: beyond Stokes flow regime." Journal of Fluid Mechanics 881 (October 24, 2019): 498–523. http://dx.doi.org/10.1017/jfm.2019.744.
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The electrohydrodynamics of a weakly conducting buoyant drop under the combined influence of gravity and a uniform electric field is studied computationally, focusing on the inertia-dominated regime. Numerical simulations are performed for both perfectly dielectric and leaky dielectric drops over a wide range of dimensionless parameters to explore the interplay of fluid inertia and electrical stress to govern the drop shape and charge convection. For perfectly dielectric drops, the fluid inertia alters the drop shape and the deformation behaviour of the drop follows a non-monotonic path. The drop shape at steady state exhibits the transition from oblate to prolate shape on increasing the electric field strength, in sharp contrast to the cases concerning the Stokes flow regime. Similar behaviour is also obtained for leaky dielectric drops for certain fluid properties. For leaky dielectric drops, the fluid inertia also affects the convective transport of charges at the drop surface and thereby alters the drop dynamics. Unlike the Stokes flow regime, where surface charge convection has little effect on the settling speed, the same modifies the drop settling speed quite significantly in the finite inertial regime depending on the combination of electrical conductivity ratio and permittivity ratio. For oblate drops at low capillary number, charge convection alters drop shape, while keeping the nature of deformation unaltered. However, for relatively large capillary number, the oblate drop transforms into a dimpled shape due to charge convection. For all cases, an interesting fact is noticed that under the combined action of electric and inertial forces, the resultant deformation is less than the summation of the deformations caused by individual effects, when inertial effects are strong. These results are likely to provide deep insights into the interplay of various nonlinearities towards altering electrohydrodynamic settling of drops and bubbles.
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Hazel, Andrew L., and Matthias Heil. "Finite-Reynolds-Number Effects in Steady, Three-Dimensional Airway Reopening." Journal of Biomechanical Engineering 128, no. 4 (February 2, 2006): 573–78. http://dx.doi.org/10.1115/1.2206203.
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Motivated by the physiological problem of pulmonary airway reopening, we study the steady propagation of an air finger into a buckled elastic tube, initially filled with viscous fluid. The system is modeled using geometrically non-linear, Kirchhoff-Love shell theory, coupled to the free-surface Navier-Stokes equations. The resulting three-dimensional, fluid-structure-interaction problem is solved numerically by a fully coupled finite element method. Our study focuses on the effects of fluid inertia, which has been neglected in most previous studies. The importance of inertial forces is characterized by the ratio of the Reynolds and capillary numbers, Re∕Ca, a material parameter. Fluid inertia has a significant effect on the system’s behavior, even at relatively small values of Re∕Ca. In particular, compared to the case of zero Reynolds number, fluid inertia causes a significant increase in the pressure required to drive the air finger at a given speed.
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Zandi Pour, Hamid Reza, and Michele Iovieno. "The Role of Particle Inertia and Thermal Inertia in Heat Transfer in a Non-Isothermal Particle-Laden Turbulent Flow." Fluids 9, no. 1 (January 19, 2024): 29. http://dx.doi.org/10.3390/fluids9010029.
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We present an analysis of the effect of particle inertia and thermal inertia on the heat transfer in a turbulent shearless flow, where an inhomogeneous passive temperature field is advected along with inertial point particles by a homogeneous isotropic velocity field. Eulerian–Lagrangian direct numerical simulations are carried out in both one- and two-way coupling regimes and analyzed through single-point statistics. The role of particle inertia and thermal inertia is discussed by introducing a new decomposition of particle second-order moments in terms of correlations involving Lagrangian acceleration and time derivative of particles. We present how particle relaxation times mediate the level of particle velocity–temperature correlation, which gives particle contribution to the overall heat transfer. For each thermal Stokes number, a critical Stokes number is individuated. The effect of particle feedback on the attenuation or enhancement of fluid temperature variance is presented. We show that particle feedback enhances fluid temperature variance for Stokes numbers less than one and damps is for larger than one Stokes number, regardless of the thermal Stokes number, even if this effect is amplified by an increasing thermal inertia.
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Ji, Bingyu, Yingfu He, Yongqiang Tang, and Shu Yang. "Inertial property of oscillatory flow for pulse injection in porous media." Energy Exploration & Exploitation 39, no. 4 (April 12, 2021): 1184–94. http://dx.doi.org/10.1177/0144598721999786.
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The low-frequency pulse wave makes the velocity of the fluid in the reservoir fluctuate dramatically, which results in a remarkable inertia force. The Darcy’s law was inapplicable to the pulse flow with strong effect of inertial force. In this paper, the non-Darcy flow equation and the calculation method of capillary number of pressure pulse displacement are established. The pressure pulse experiments of single-phase and two- phase flow are carried out. The results show that the periodic change of velocity can decrease the seepage resistance and enhance apparent permeability by generating the inertial force. The higher the pulse frequency improves the apparent permeability by enhancing influence of inertial force. The increase of apparent permeability of high permeability core is larger than that of low permeability core, which indicates that inertial force is more prominent in high permeability reservoir. For the water-oil two-phase flow, inertia force makes the relative permeability curve move towards right, and the equal permeability point becomes higher. In other words, with the increase of capillary number, part of residual oil is activated, and the displacement efficiency is improved.
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LAVEZZO, V., A. SOLDATI, S. GERASHCHENKO, Z. WARHAFT, and L. R. COLLINS. "On the role of gravity and shear on inertial particle accelerations in near-wall turbulence." Journal of Fluid Mechanics 658 (June 15, 2010): 229–46. http://dx.doi.org/10.1017/s0022112010001655.
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Recent experiments in a turbulent boundary layer by Gerashchenko et al. (J. Fluid Mech., vol. 617, 2008, pp. 255–281) showed that the variance of inertial particle accelerations in the near-wall region increased with increasing particle inertia, contrary to the trend found in homogeneous and isotropic turbulence. This behaviour was attributed to the non-trivial interaction of the inertial particles with both the mean shear and gravity. To investigate this issue, we perform direct numerical simulations of channel flow with suspended inertial particles that are tracked in the Lagrangian frame of reference. Three simulations have been carried out considering (i) fluid particles, (ii) inertial particles with gravity and (iii) inertial particles without gravity. For each set of simulations, three particle response times were examined, corresponding to particle Stokes numbers (in wall units) of 0.9, 1.8 and 11.8. Mean and r.m.s. profiles of particle acceleration computed in the simulation are in qualitative (and in several cases quantitative) agreement with the experimental results, supporting the assumptions made in the simulations. Furthermore, by comparing results from simulations with and without gravity, we are able to isolate and quantify the significant effect of gravitational settling on the phenomenon.
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Marath, Navaneeth K., and Ganesh Subramanian. "The effect of inertia on the time period of rotation of an anisotropic particle in simple shear flow." Journal of Fluid Mechanics 830 (September 29, 2017): 165–210. http://dx.doi.org/10.1017/jfm.2017.534.
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We calculate the leading-order correction to the time period of rotation of a neutrally buoyant spheroid of arbitrary aspect ratio, in a simple shear flow ($\boldsymbol{u}^{\infty }=\dot{\unicode[STIX]{x1D6FE}}y\mathbf{1}_{1}$; $\mathbf{1}_{1}$ is the unit vector in the flow direction, $y$ being the coordinate along the gradient direction), in its long-time orbit set up by the weak fluid inertial drift at $O(Re)$. Here, $Re$ is the microscale Reynolds number, a dimensionless measure of the fluid inertial effects on the length scale of the spheroid, and is defined as $Re=\dot{\unicode[STIX]{x1D6FE}}L^{2}\unicode[STIX]{x1D70C}/\unicode[STIX]{x1D707}$, where $L$ is the semimajor axis of the spheroid, $\unicode[STIX]{x1D707}$ and $\unicode[STIX]{x1D70C}$ are respectively the viscosity and density of the fluid, and $\dot{\unicode[STIX]{x1D6FE}}$ is the shear rate. This long-time orbit is the tumbling orbit for prolate spheroids; for oblate spheroids, it is the spinning orbit for aspect ratios greater than $0.137$, and can be either the tumbling or the spinning orbit for oblate spheroids of aspect ratios less than $0.137$. We also calculate the leading-order correction to the time period of rotation of a neutrally buoyant triaxial ellipsoid in a simple shear flow, rotating with its intermediate principal axis aligned along the vorticity of the flow; the latter calculation is in light of recent evidence, by way of numerical simulations (Rosen, PhD dissertation, 2016, Stockholm), of the aforementioned rotation being stabilized by weak inertia. The correction to the time period for arbitrary $Re$ is expressed as a volume integral using a generalized reciprocal theorem formulation. For $Re\ll 1$, it is shown that the correction at $O(Re)$ is zero for spheroids (with aspect ratios of order unity) as well as triaxial ellipsoids in their long-time orbits. The first correction to the time period therefore occurs at $O(Re^{3/2})$, and has a singular origin, arising from fluid inertial effects in the outer region (distances from the spheroid or triaxial ellipsoid of the order of the inertial screening length of $O(LRe^{-1/2})$), where the leading-order Stokes approximation ceases to be valid. Since the correction comes from the effects of inertia in the far field, the rotating spheroid (triaxial ellipsoid) is approximated as a time-dependent point-force-dipole singularity, allowing for the reciprocal theorem integral to be evaluated in Fourier space. It is shown for all relevant cases that fluid inertia at $O(Re^{3/2})$ leads to an increase in the time period of rotation compared with that in the Stokes limit, consistent with the results of recent numerical simulations at finite $Re$. Finally, combination of the $O(Re^{3/2})$ correction derived here with the $O(Re)$ correction derived earlier by Dabade et al. (J. Fluid Mech., vol. 791, 2016, 631703) yields a uniformly valid description of the first effects of inertia for spheroids of all aspect ratios, including prediction of the arrest of rotation for extreme-aspect-ratio spheroids.
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Wang, Yueying, Jun Yao, and Zhaoqin Huang. "Parameter Effect Analysis of Non-Darcy Flow and a Method for Choosing a Fluid Flow Equation in Fractured Karstic Carbonate Reservoirs." Energies 15, no. 10 (May 15, 2022): 3623. http://dx.doi.org/10.3390/en15103623.
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Fractured karstic carbonate reservoirs have obvious multi-scale characteristics and severe heterogeneity due to the development of abundant karst caves and fractures with different scales. Darcy and non-Darcy flows coexist due to this property. Therefore, selecting the appropriate flow equations for different regions in the numerical simulation of fluid flows, particularly two-phase and multiphase flows, is a critical topic. This paper compares and analyses the displacement distance differences of waterfront travel using the Darcy, Forchheimer and Barree–Conway equations, as well as analyzes the influence of the Forchheimer constant, fluid viscosity, flow rate and absolute permeability on inertia action based on the Buckley–Leverett theory. The results show that the Forchheimer number/Reynolds number of water/oil two-phase flow is not a constant value and varies with water saturation, making it difficult to determine whether the inertial action should be considered solely based on these values; the influence of inertial action can be measured well by comparing the difference between the displacement distances of the waterflood front, and the quantitative standard is given for the selection of the flow equation of different regions by calculating the allowable error of the displacement distance of the waterflood front. The magnitude of the inertial effect is affected by the physical properties of the fluid and reservoir medium and the fluid velocity. The smaller the difference in the viscosity of the oil/water fluid, the smaller the inertial effect is. This technique was used a preliminary attempt to analyze the fractured karstic carbonate reservoirs at Tarim, and the results confirmed the validity of the method described in this article.
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Ren, Hong, Fan Chun Li, and Tian Yu Zhao. "Modal Analysis of Marine Propeller Submerged in Fluid." Advanced Materials Research 1030-1032 (September 2014): 1201–5. http://dx.doi.org/10.4028/www.scientific.net/amr.1030-1032.1201.
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The present work is aimed to free vibration characteristics of marine propeller in fluid, and analyze the influence of fluid inertial effect on propeller. The fully coupled three dimensional finite element method is applied, and the commercial finite element code, ANSYS WORKBENCH, has been used to perform modal analysis for both wet and dry configurations via fluid-structure interaction APDL commands for secondary development. On this basis, analyze a marine propeller in air and in fluid with finite element analysis, then the differences of natural vibration frequencies and vibration modes of the propeller for different boundary conditions are discussed. In addition, the natural frequencies curves are presented. Results show that the natural frequencies of propeller in fluid are significantly lower than those in air, the fluid inertia effect also has some influences on vibration mode.
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Singh, Udaya, Ram Gupta, and Vijay Kapur. "Effects of inertia in the steady state pressurised flow of a non-Newtonian fluid between two curvilinear surfaces of revolution: Rabinowitsch fluid model." Chemical and Process Engineering 32, no. 4 (December 1, 2011): 333–49. http://dx.doi.org/10.2478/v10176-011-0027-1.
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Effects of inertia in the steady state pressurised flow of a non-Newtonian fluid between two curvilinear surfaces of revolution: Rabinowitsch fluid modelIn many practical situations fluids are normally blended with additives (viscosity index improvers, viscosity thickeners, viscosity thinners) due to which they show pseudoplastic and dilatant nature which can be modelled as cubic stress model (Rabinowitsch model). The cubic stress model for pseudoplastic fluids is adopted because Wada and Hayashi have shown that the theoretical results with this model are in good agreement with the experimental results. The present theoretical analysis is to investigate the pseudoplastic effect along with the effect of rotational inertia on the pressure distribution, frictional torque and fluid flow rate of externally pressurised flow in narrow clearance between two curvilinear surfaces of revolution. The expression for pressure has been derived using energy integral approach. To analyse and discuss the effects of pseudoplasticity and fluid inertia on the pressure distribution, fluid flow rate and frictional torque, the examples of externally pressurised flow in the clearance between parallel disks and concentric spherical surfaces have been considered.
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Walicka, A., and J. Falicki. "Inertia Effects in the Flow of a Herschel-Bulkley ERF between Fixed Surfaces of Revolution." Smart Materials Research 2013 (July 24, 2013): 1–10. http://dx.doi.org/10.1155/2013/171456.
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Many electrorheological fluids (ERFs) as fluids with microstructure demonstrate viscoplastic behaviours. Rheometric measurements indicate that some flows of these fluids may be modelled as the flows of a Herschel-Bulkley fluid. In this paper, the flow of a Herschel-Bulkley ER fluid—with a fractional power-law exponent—in a narrow clearance between two fixed surfaces of revolution with common axis of symmetry is considered. The flow is externally pressurized, and it is considered with inertia effect. In order to solve this problem, the boundary layer equations are used. The influence of inertia forces on the pressure distribution is examined by using the method of averaged inertia terms of the momentum equation. Numerical examples of externally pressurized ERFs flows in the clearance between parallel disks and concentric spherical surfaces are presented.
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Walicka, A., and J. Falicki. "Reynolds Number Effects in the Flow of a Vočadlo Electrorheological Fluid in a Curved Gap." International Journal of Applied Mechanics and Engineering 22, no. 3 (August 1, 2017): 675–95. http://dx.doi.org/10.1515/ijame-2017-0043.
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AbstractMany electrorheological fluids (ERFs) as fluids with micro-structure demonstrate a non-Newtonian behaviour. Rheometric measurements indicate that some flows of these fluids may by modelled as the flows of a Vočadlo ER fluid. In this paper, the flow of a Vočadlo fluid – with a fractional index of non-linearity – in a narrow gap between two fixed surfaces of revolution with a common axis of symmetry is considered. The flow is externally pressurized and it is considered with inertia effect. In order to solve this problem the boundary layer equations are used. The Reynolds number effects (the effects of inertia forces) on the pressure distribution are examined by using the method of averaged inertia terms of the momentum equation. Numerical examples of externally pressurized flows in the gap between parallel disks and concentric spherical surfaces are presented.
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Misbah, Chaouqi. "Soft suspensions: inertia cooperates with flexibility." Journal of Fluid Mechanics 760 (October 30, 2014): 1–4. http://dx.doi.org/10.1017/jfm.2014.443.
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AbstractCross-streamline migration of soft particles in suspensions is essential for cell and DNA sorting, blood flow, polymer processing and so on. Pioneering work by Poiseuille on blood flow in vivo revealed an erythrocyte-free layer close to blood vessel walls. The formation of this layer is related to a viscous lift force caused by cell deformation that pushes cells towards the centre of blood capillaries. This lift force has in this case a strong impact on blood flow. In contrast, rigid spherical particles migrate from the centre towards the periphery, owing to inertia (the Segré–Silberberg effect). An important open issue is to elucidate the interplay between particle deformation and inertia. By using a capsule suspension model, Krueger, Kaoui & Harting (J. Fluid Mech., 2014, vol. 751, pp. 725–745) discovered that capsule flexibility can suppress the Segré–Silberberg effect and inertia promotes overall flow efficiency thanks to a strong inertial flow focusing effect.
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Dabade, Vivekanand, Navaneeth K. Marath, and Ganesh Subramanian. "The effect of inertia on the orientation dynamics of anisotropic particles in simple shear flow." Journal of Fluid Mechanics 791 (February 24, 2016): 631–703. http://dx.doi.org/10.1017/jfm.2016.14.
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It is well known that, under inertialess conditions, the orientation vector of a torque-free neutrally buoyant spheroid in an ambient simple shear flow rotates along so-called Jeffery orbits, a one-parameter family of closed orbits on the unit sphere centred around the direction of the ambient vorticity (Jeffery, Proc. R. Soc. Lond. A, vol. 102, 1922, pp. 161–179). We characterize analytically the irreversible drift in the orientation of such torque-free spheroidal particles of an arbitrary aspect ratio, across Jeffery orbits, that arises due to weak inertial effects. The analysis is valid in the limit $Re,St\ll 1$, where $Re=(\dot{{\it\gamma}}L^{2}{\it\rho}_{f})/{\it\mu}$ and $St=(\dot{{\it\gamma}}L^{2}{\it\rho}_{p})/{\it\mu}$ are the Reynolds and Stokes numbers, which, respectively, measure the importance of fluid inertial forces and particle inertia in relation to viscous forces at the particle scale. Here, $L$ is the semimajor axis of the spheroid, ${\it\rho}_{p}$ and ${\it\rho}_{f}$ are the particle and fluid densities, $\dot{{\it\gamma}}$ is the ambient shear rate, and ${\it\mu}$ is the suspending fluid viscosity. A reciprocal theorem formulation is used to obtain the contributions to the drift due to particle and fluid inertia, the latter in terms of a volume integral over the entire fluid domain. The resulting drifts in orientation at $O(Re)$ and $O(St)$ are evaluated, as a function of the particle aspect ratio, for both prolate and oblate spheroids using a vector spheroidal harmonics formalism. It is found that particle inertia, at $O(St)$, causes a prolate spheroid to drift towards an eventual tumbling motion in the flow–gradient plane. Oblate spheroids, on account of the $O(St)$ drift, move in the opposite direction, approaching a steady spinning motion about the ambient vorticity axis. The period of rotation in the spinning mode must remain unaltered to all orders in $St$. For the tumbling mode, the period remains unaltered at $O(St)$. At $O(St^{2})$, however, particle inertia speeds up the rotation of prolate spheroids. The $O(Re)$ drift due to fluid inertia drives a prolate spheroid towards a tumbling motion in the flow–gradient plane for all initial orientations and for all aspect ratios. Interestingly, for oblate spheroids, there is a bifurcation in the orientation dynamics at a critical aspect ratio of approximately 0.14. Oblate spheroids with aspect ratios greater than this critical value drift in a direction opposite to that for prolate spheroids, and eventually approach a spinning motion about the ambient vorticity axis starting from any initial orientation. For smaller aspect ratios, a pair of non-trivial repelling orbits emerge from the flow–gradient plane, and divide the unit sphere into distinct basins of orientations that asymptote to the tumbling and spinning modes. With further decrease in the aspect ratio, these repellers move away from the flow–gradient plane, eventually coalescing onto an arc of the great circle in which the gradient–vorticity plane intersects the unit sphere, in the limit of a vanishing aspect ratio. Thus, sufficiently thin oblate spheroids, similar to prolate spheroids, drift towards an eventual tumbling motion irrespective of their initial orientation. The drifts at $O(St)$ and at $O(Re)$ are combined to obtain the drift for a neutrally buoyant spheroid. The particle inertia contribution remains much smaller than the fluid inertia contribution for most aspect ratios and density ratios of order unity. As a result, the critical aspect ratio for the bifurcation in the orientation dynamics of neutrally buoyant oblate spheroids changes only slightly from its value based only on fluid inertia. The existence of Jeffery orbits implies a rheological indeterminacy, and the dependence of the suspension shear viscosity on initial conditions. For prolate spheroids and oblate spheroids of aspect ratio greater than 0.14, inclusion of inertia resolves the indeterminacy. Remarkably, the existence of the above bifurcation implies that, for a dilute suspension of oblate spheroids with aspect ratios smaller than 0.14, weak stochastic fluctuations (residual Brownian motion being analysed here as an example) play a crucial role in obtaining a shear viscosity independent of the initial orientation distribution. The inclusion of Brownian motion leads to a new smaller critical aspect ratio of approximately 0.013. For sufficiently large $Re\,Pe_{r}$, the peak in the steady-state orientation distribution shifts rapidly from the spinning- to the tumbling-mode location as the spheroid aspect ratio decreases below this critical value; here, $Pe_{r}=\dot{{\it\gamma}}/D_{r}$, with $D_{r}$ being the Brownian rotary diffusivity, so that $Re\,Pe_{r}$ measures the relative importance of inertial drift and Brownian rotary diffusion. The shear viscosity, plotted as a function of $Re\,Pe_{r}$, exhibits a sharp transition from a shear-thickening to a shear-thinning behaviour, as the oblate spheroid aspect ratio decreases below 0.013. Our results are compared in detail to earlier analytical work for limiting cases involving either nearly spherical particles or slender fibres with weak inertia, and to the results of recent numerical simulations at larger values of $Re$ and $St$.
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Yuan, Chao, Hong-Na Zhang, Yu-Ke Li, Xiao-Bin Li, Jian Wu, and Feng-Chen Li. "Nonlinear effects of viscoelastic fluid flows and applications in microfluidics: A review." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 22 (May 7, 2020): 4390–414. http://dx.doi.org/10.1177/0954406220922863.
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Viscoelastic fluid naturally has both viscous and elastic properties. Therefore, there are two sources of nonlinear effects, namely inertial and elastic nonlinearities. The existence of elastic nonlinearity brings about various interesting flow phenomena in viscoelastic fluid flow, especially in microfluidics where the inertial nonlinearity can be negligible while the elastic nonlinearity can dominate the flow. Specifically, purely elasticity-induced instability and turbulence can occur in microchannels when the elastic nonlinearity is strong enough. Recently, those intriguing properties of viscoelastic fluid flow have motivated lots of researches on taking viscoelastic fluid as working fluid in different types of microfluidic devices, such as micro-mixers, micro heat exchangers, logic microfluidic circuits and particle manipulation. This paper aims to provide a state-of-the-art review of the nonlinear effect of viscoelastic fluids and its applications in the aforementioned microfluidic fields, which may provide a useful guidance for the researchers who are interested in this area.
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Chen, Xiaoming, Yuchuan Zhu, Travis Wiens, Doug Bitner, and Jie Ling. "Characteristic investigation of a flow-dependent inertia hydraulic converter driven by an equivalent fast switching valve." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 236, no. 7 (February 18, 2022): 3354–74. http://dx.doi.org/10.1177/09544062211038983.
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To acquire a linear load pressure with the potential of energy-saving compared with conventional throttling hydraulic systems, a switched hydraulic circuit (referred to as a flow-dependent inertia hydraulic converter) featuring a flow-dependent inertial effect was proposed. In this device, the flowing fluid modulated by an equivalent fast switching valve allows the fluid inertance at the connection pipe and rotation inertia incorporated in the flywheel to be combined. The theoretical and simulation models of the flow-dependent inertia hydraulic converter were established, and then the flow-dependent inertia was discussed and quantified. The predictions of the load pressure, flywheel speed and system efficiency were confirmed by experimental measurements. Results indicated that the theoretical and simulation predictions match well with the experiments for this configuration. The pressure wave propagation effect within the connection pipe is responsible for the variation in the transient load pressure and flywheel speed that is initially modulated by the rotation inertia theoretically, which seriously questions the predecessor's hypothesis of using a compressible volume to model the upstream connection pipe. The parabolic mean suction flow induced by the flow-dependent inertia draw our attention to the available supply flowrate and duty cycle. Finally, the throttling loss and system efficiency that varies with the desired characteristics is superior to that of conventional throttling hydraulic systems theoretically, and an acceptable system efficiency was obtained under the premise of ignoring friction experimentally.
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Huang, Shujuan, Diana-Andra Borca-Tasciuc, and John A. Tichy. "A simple expression for fluid inertia force acting on micro-plates undergoing squeeze film damping." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2126 (September 29, 2010): 522–36. http://dx.doi.org/10.1098/rspa.2010.0216.
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Squeeze film damping in systems employing micro-plates parallel to a substrate and undergoing small normal vibrations is theoretically investigated. In high-density fluids, inertia forces may play a significant role affecting the dynamic response of such systems. Previous models of squeeze film damping taking inertia into account do not clearly isolate this effect from viscous damping. Therefore, currently, there is no simple way to distinguish between these two hydrodynamic effects. This paper presents a simple solution for the hydrodynamic force acting on a plate vibrating in an incompressible fluid, with distinctive terms describing inertia and viscous damping. Similar to the damping constant describing viscous losses, an inertia constant, given by ρL 3 W / h (where ρ is fluid density, L and W are plate length and width, respectively, and h is separation distance), may be used to accurately calculate fluid inertia for small oscillation Reynolds numbers. In contrast with viscous forces that suppress the amplitude of the oscillation, it is found that fluid inertia acts as an added mass, shifting the natural frequency of the system to a lower range while having little effect on the amplitude. Dimensionless parameters describing the relative importance of viscous and inertia effects also emerge from the analysis.
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Annapurna T, K.S.R. Sridhar, and M Karuna Prasad. "Effect of Different Shapes of Nanoparticles on Mixed Convective Nanofluid Flow in a Darcy-Forchhiemer Porous Medium." CFD Letters 16, no. 12 (July 21, 2024): 38–58. http://dx.doi.org/10.37934/cfdl.16.12.3858.
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The nanofluid has diverse applications in industries, engineering, and medicine due to its greater thermal characteristics. However, various factors such as the shape and size of nanoparticles, the base fluid, the porous medium, the quadratic drag force, and the viscous dissipation have significant effects on the flow and heat transfer characteristics of nanofluids. Therefore, it is crucial to study the influence of these factors. In this paper, a theoretical investigation is conducted to analyze the mechanisms of thermal conductivities of different shapes of nanoparticles, such as platelet, cylinder, brick and blade on the mixed convective nanofluid flow in a vertical channel saturated with porous medium. Consider ethylene glycol and water as base fluids for the nanoparticles, including copper, aluminum oxide, titanium oxide, silver, and iron oxide. A thin, movable baffle plate of negligible thickness is inserted in the channel and made into double passages. To define the porous matrix, the Darcy-Brinkaman-Forchhiemer model is used, and to define the nanofluid, the Tiwari and Das model is used. Robin boundary conditions are considered for the channel flow. The differential transform method (DTM) is applied to solve non-linear governing equations with inertia, and the perturbation method is applied to solve the problem without inertia. Velocity and temperature cantors are shown graphically using MATLAB and MATHEMATICA. The obtained values by DTM and the perturbation method are well validated and shown graphically. The Nusselt number was evaluated and tabulated for all governing parameters. The objective of this article is to investigate the effect of nonspherical shapes of nanoparticles, the base fluid, the inertial forces of the porous medium, and the buoyancy force on the thermal characteristics of flow and heat transfer of nanofluids. The main findings of this problem are that the optimum velocity and temperature cantor are found for platelet-shaped water-based silver nanofluid.
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Hormozi, S., and I. A. Frigaard. "Dispersion of solids in fracturing flows of yield stress fluids." Journal of Fluid Mechanics 830 (September 29, 2017): 93–137. http://dx.doi.org/10.1017/jfm.2017.465.
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Solids dispersion is an important part of hydraulic fracturing, both in helping to understand phenomena such as tip screen-out and spreading of the pad, and in new process variations such as cyclic pumping of proppant. Whereas many frac fluids have low viscosity, e.g. slickwater, others transport proppant through increased viscosity. In this context, one method for influencing both dispersion and solids-carrying capacity is to use a yield stress fluid as the frac fluid. We propose a model framework for this scenario and analyse one of the simplifications. A key effect of including a yield stress is to focus high shear rates near the fracture walls. In typical fracturing flows this results in a large variation in shear rates across the fracture. In using shear-thinning viscous frac fluids, flows may vary significantly on the particle scale, from Stokesian behaviour to inertial behaviour across the width of the fracture. Equally, according to the flow rates, Hele-Shaw style models give way at higher Reynolds number to those in which inertia must be considered. We develop a model framework able to include this range of flows, while still representing a significant simplification over fully three-dimensional computations. In relatively straight fractures and for fluids of moderate rheology, this simplifies into a one-dimensional model that predicts the solids concentration along a streamline within the fracture. We use this model to make estimates of the streamwise dispersion in various relevant scenarios. This model framework also predicts the transverse distributions of the solid volume fraction and velocity profiles as well as their evolutions along the flow part.
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Ravichandran, S., and Rama Govindarajan. "Vortex-dipole collapse induced by droplet inertia and phase change." Journal of Fluid Mechanics 832 (October 26, 2017): 745–76. http://dx.doi.org/10.1017/jfm.2017.677.
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Droplet-laden flows with phase change are common. This study brings to light a mechanism by which droplet inertial dynamics and local phase change, taking place at sub-Kolmogorov scales, affect vortex dynamics in the inertial range of turbulence. To do this we consider vortices placed in a supersaturated ambient initially at constant temperature, homogeneous vapour concentration and uniformly distributed droplets. The droplets also act as sites of phase change. This allows the time scales associated with particle inertia and phase change, which could be significantly different from each other and from the time scale of the flow, to become coupled, and for their combined dynamics to govern the flow. The thermodynamics of condensation and evaporation have a characteristic time scale $\unicode[STIX]{x1D70F}_{s}$. The water droplets are treated as Stokesian inertial particles with a characteristic time scale $\unicode[STIX]{x1D70F}_{p}$, whose behaviour we approximate using an $O(\unicode[STIX]{x1D70F}_{p})$ truncation of the Maxey–Riley equation for heavy particles. This inertia leads the water droplets to vacate the vicinity of vortices, leaving no nuclei for the vapour to condense. The condensation process is thus spatially inhomogeneous, and leaves vortices in the flow colder than their surroundings. The combination of buoyancy and vorticity generates a lift force on the vortices perpendicular to their velocity relative to the fluid around them. In the case of a vortex dipole, this lift force can propel the vortices towards each other and undergo collapse, a phenomenon studied by Ravichandran et al. (Phys. Rev. Fluids, vol. 2, 2017, 034702). We find, spanning the space of the two time scales, $\unicode[STIX]{x1D70F}_{p}$ and $\unicode[STIX]{x1D70F}_{s}$, the region in which lift-induced dipole collapse can occur, and show numerically that the product of the time scales is the determining parameter. Our findings agree with our results from scaling arguments. We also study the influence of varying the initial supersaturation, and find that the strength of the lift-induced mechanism has a power-law dependence on the phase-change time scale $\unicode[STIX]{x1D70F}_{s}$. We then study systems of many vortices and show that the same coupling between the two time scales alters the dynamics of such systems, by energising the smaller scales. We show that this effect is significantly more pronounced at higher Reynolds numbers. Finally, we discuss how this effect could be relevant in conditions typical of clouds.
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San Andre´s, Luis. "Turbulent Hybrid Bearings With Fluid Inertia Effects." Journal of Tribology 112, no. 4 (October 1, 1990): 699–707. http://dx.doi.org/10.1115/1.2920318.
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High speed hybrid bearings for cryogenic applications demand large levels of external pressurization to provide substantial load capacity. These conditions give rise to large film Reynolds numbers, and thus, cause the fluid flow within the bearing film to be turbulent and dominated by fluid inertia effects both at the recess edges and at the thin film lands. The analysis includes the effect of recess fluid compressibility and a model for the pressure rise within the recess region. Flow turbulence is simulated by friction factors dependent on the local Reynolds numbers and surface conditions. A perturbation method is used to calculate the zeroth and first flow fields and determine the bearing steady-state and dynamic force response. Comparison of results with existing experimental data shows the accuracy of the present full inertial-turbulent analysis. A roughened bearing surface is shown to improve considerably the stability characteristics of hybrid bearings operating at high speeds.
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Patankar, N. A., and H. H. Hu. "A Numerical Investigation of the Detachment of the Trailing Particle From a Chain Sedimenting in Newtonian and Viscoelastic Fluids." Journal of Fluids Engineering 122, no. 3 (April 18, 2000): 517–21. http://dx.doi.org/10.1115/1.1287269.
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Particles sedimenting in a viscoelastic fluid form chains. It has been observed in experiments that, sometimes, the last particle in the chain gets detached. In this paper, we investigate this phenomenon. It is known that a long chain falls faster than a single particle in fluids. This long body effect tends to detach the last particle from the chain. The wake effect and the normal stress effect are the mechanisms that work against the long body effect. The last particle is not detached if the inertial wake effects are strong enough to cause substantial drag reduction on it. The detachment is also restricted by the elastic normal stress of the viscoelastic fluid. [S0098-2202(00)01003-8]
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Krüger, Timm, Badr Kaoui, and Jens Harting. "Interplay of inertia and deformability on rheological properties of a suspension of capsules." Journal of Fluid Mechanics 751 (June 27, 2014): 725–45. http://dx.doi.org/10.1017/jfm.2014.315.
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AbstractThe interplay of inertia and deformability has a substantial impact on the transport of soft particles suspended in a fluid. However, to date a thorough understanding of these systems is still missing, and only a limited number of experimental and theoretical studies are available. We combine the finite-element, immersed-boundary and lattice-Boltzmann methods to simulate three-dimensional suspensions of soft particles subjected to planar Poiseuille flow at finite Reynolds numbers. Our findings confirm that the particle deformation and inclination increase when inertia is present. We observe that the Segré–Silberberg effect is suppressed with respect to the particle deformability. Depending on the deformability and strength of inertial effects, inward or outward lateral migration of the particles takes place. In particular, for increasing Reynolds numbers and strongly deformable particles, a hitherto unreported distinct flow focusing effect emerges, which is accompanied by a non-monotonic behaviour of the apparent suspension viscosity and thickness of the particle-free layer close to the channel walls. This effect can be explained by the behaviour of a single particle and the change of the particle collision mechanism when both deformability and inertia effects are relevant.
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Lott, François, Christophe Millet, and Jacques Vanneste. "Inertia–gravity waves in inertially stable and unstable shear flows." Journal of Fluid Mechanics 775 (June 19, 2015): 223–40. http://dx.doi.org/10.1017/jfm.2015.303.
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An inertia–gravity wave (IGW) propagating in a vertically sheared, rotating stratified fluid interacts with the pair of inertial levels that surround the critical level. An exact expression for the form of the IGW is derived here in the case of a linear shear and used to examine this interaction in detail. This expression recovers the classical values of the transmission and reflection coefficients $|T|=\text{e}^{-{\rm\pi}{\it\mu}}$ and $|R|=0$, where ${\it\mu}^{2}=J(1+{\it\nu}^{2})-1/4$, $J$ is the Richardson number and ${\it\nu}$ the ratio between the horizontal transverse and along-shear wavenumbers. For large $J$, a WKB analysis provides an interpretation of this result in term of tunnelling: an IGW incident on the lower inertial level becomes evanescent between the inertial levels, returning to an oscillatory behaviour above the upper inertial level. The amplitude of the transmitted wave is directly related to the decay of the evanescent solution between the inertial levels. In the immediate vicinity of the critical level, the evanescent IGW is well represented by the quasi-geostrophic approximation, so that the process can be interpreted as resulting from the coupling between balanced and unbalanced motion. The exact and WKB solutions describe the so-called valve effect, a dependence of the behaviour in the region between the inertial levels on the direction of wave propagation. For $J<1$ this is shown to lead to an amplification of the wave between the inertial levels. Since the flow is inertially unstable for $J<1$, this establishes a correspondence between the inertial-level interaction and the condition for inertial instability.
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Bhattacharya, Sukalyan, Dil K. Gurung, and Shahin Navardi. "Radial lift on a suspended finite-sized sphere due to fluid inertia for low-Reynolds-number flow through a cylinder." Journal of Fluid Mechanics 722 (March 28, 2013): 159–86. http://dx.doi.org/10.1017/jfm.2012.636.
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AbstractThis article describes the radial drift of a suspended sphere in a cylinder-bound Poiseuille flow where the Reynolds number is small but finite. Unlike past studies, it considers a circular narrow conduit whose cross-sectional diameter is only $1. 5$–$6$ times the particle diameter. Thus, the analysis quantifies the effect of fluid inertia on the radial motion of the particle in the channel when the flow field is significantly influenced by the presence of the suspended body. To this end, the hydrodynamic fields are expanded as a series in Reynolds number, and a set of hierarchical equations for different orders of the expansion is derived. Accordingly, the zeroth-order fields in Reynolds number satisfy the Stokes equation, which is accurately solved in the presence of the spherical particle and the cylindrical conduit. Then, recognizing that in narrow vessels Stokesian scattered fields from the sphere decrease exponentially in the axial direction, a simpler regular perturbation scheme is used to quantify the first-order inertial correction to hydrodynamic quantities. Consequently, it is possible to obtain two results. First, the sphere is assumed to follow the axial motion of a freely suspended sphere in a Stokesian condition, and the radial lift force on it due to the presence of fluid inertia is evaluated. Then, the approximate motion is determined for a freely suspended body on which net hydrodynamic force including first-order inertial lift is zero. The results agree well with the available experimental results. Thus, this study along with the measured data would precisely describe particle dynamics inside narrow tubes.
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Dai, Minglu, Chengxu Tu, Pengfei Du, Zhongke Kuang, Jiaming Shan, Xu Wang, and Fubing Bao. "Near-Wall Settling Behavior of a Particle in Stratified Fluids." Micromachines 13, no. 12 (November 25, 2022): 2070. http://dx.doi.org/10.3390/mi13122070.
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The phenomenon of near-wall particle settling in a stratified fluid is an emerging topic in the field of multiphase flow, and it is also widely found in nature and engineering applications. In stratified fluids, particle settling characteristics are affected by the physical and chemical properties of the upper and lower fluids, the particle size, the particle density, and the initial sedimentation conditions. In this study, the main objective is to determine the effect of liquid viscosity and particle density on the detaching process, and the trajectory and velocity of near-wall settling particles in stratified fluids. The inertia and velocity of the particle had a greater impact on the tail pinch-off model in low-viscosity lower fluids; that is, the lower the inertia and velocity, the more apparent the order between deep and shallow seal pinch-off. In comparison, in high-viscosity lower fluids, the tail pinch-off models of different inertia and velocity particles were similar. In terms of particle trajectory, the transverse motion of the particle in the low-viscosity lower fluid exhibited abrupt changes; that is, the particles moved away from the wall suddenly, whereas in the high-viscosity lower fluid, the transverse movement was gradual. Due to the existence of the wall, the transverse motion direction of the free settling particles in the stratified fluid, which is determined by the rotation direction of the particles, changed to a direction away from the wall regardless of the particle rotation direction. This transverse movement also caused the particle settling velocity to drop suddenly or its rising rate to decrease, this is because part of the energy was used for transverse motion and to increase the transverse velocity. In our study, the near-wall settling of particles in a stratified fluid mainly affected the particle trajectory; that is, forced movement away from the wall, thus changing the particle velocity. This characteristic provides a new approach to manipulate particles away from the wall.
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Miguel, Antonio F. "Experimental Study on Nanofluid Flow in a Porous Cylinder: Viscosity, Permeability and Inertial Factor." Defect and Diffusion Forum 362 (April 2015): 47–57. http://dx.doi.org/10.4028/www.scientific.net/ddf.362.47.
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Knowledge of fluid rheology and flow characteristics is important when studying nanofluid flow in porous media. In this study, an experimental investigation is presented to determine the nanofluid viscosity, the permeability and the inertial (non-Darcy) parameter of a porous cylinder made of several capillary tubes. The applicability of the Darcy-Forchheimer equation for power-law fluids to estimate pressure drop through the porous material is discussed. The occurrence of particle losses from the base fluid (deposition) is also verified.Experiments are completed in two steps. In the first step, physical properties of nanofluids consisting of deionized water and different volume concentrations of Al2O3nanoparticles is measured. In the second step, Al2O3-deionized water nanofluids are pumped through a porous cylinder (porosity 0.249) to evaluate hydraulic and intrinsic permeabilities, and the inertial parameter. The effect of Al2O3volume fraction on these flow properties is studied, and the void morphology changes within the porous cylinder via deposition of nanoparticles are analyzed.
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Tijjani Lawal Hassan, Abdul Rahman Mohd Kasim, and Mohd Haziezan Hassan. "A Comparative Analysis on Single and Two Phase Casson Fluid under Aligned Magnetic Field Effect and Newtonian Heating." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 110, no. 2 (December 15, 2023): 206–18. http://dx.doi.org/10.37934/arfmts.110.2.206218.
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This research investigates the impact of aligned magnetic fields and Newtonian heating on single and two-phase Casson fluid (a mixture of Casson fluid and dust particles), addressing a notable knowledge gap in comparing the two fluid models under the same effect. The problem of this study lies in the need to understand the similarities or differences in the reaction of these fluids to external forces. To achieve this, the governing equations for both fluids were formulated using a boundary layer approximation and numerical solutions were obtained utilizing the 'bvp4c' function within MATLAB software. The analysis revealed comparable trends in flow and thermal behaviour between the two fluids, it also showed that the magnetic field exerted a more pronounced influence on flow properties compared to forces such as buoyancy and inertia. Conversely, Newtonian heating conditions had a more significant impact on thermal properties compared to the magnetic field. Additionally, the single-phase Casson fluid showed higher velocity and temperature profiles than the two-phase Casson fluid phases. These findings suggest that the presence of dust particles reduces the velocity and temperature magnitudes of the Casson fluid.
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Liu, Benhua, Hao Zhan, Yiran Liu, Huan Qi, Linxian Huang, Zhengrun Wei, and Zhizheng Liu. "Effects of Slip Length and Inertia on the Permeability of Fracture with Slippery Boundary Condition." International Journal of Environmental Research and Public Health 17, no. 11 (May 28, 2020): 3817. http://dx.doi.org/10.3390/ijerph17113817.
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Although the slippery boundary condition (BC) has been validated to enhance fracture permeability (k), the coupling effects of heterogeneous slippery BC and inertia on k remain less understood. We used computational fluid dynamics to investigate the competing roles of slippery BC and inertial forces in controlling k evolution with increasing pressure gradient by designing six cases with different slip length scenarios for a two-dimensional natural fracture. Our results suggest that pronounced inertial effects were directly related to and demonstrated by the growth of recirculation zone (RZ); this caused flow regimes transitioning from Darcy to non-Darcy and significantly reduced k, with an identical tailing slope for six cases, regardless of the variability in slip lengths. Moreover, the slippery BC dominantly determine the magnitude of k with orders depending on the slip length. Lastly, our study reveals that the specific k evolution path for the case with a varying slip length was significantly different from other cases with a homogeneous one, thus encouraging more efforts in determining the slip length for natural fractures via experiments.
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Melkonyan, A., and M. Chuklin. "Calculation algorithm and software for pipeline vibrations with consideration of internal flow." Transactions of the Krylov State Research Centre S-I, no. 2 (December 28, 2020): 260–65. http://dx.doi.org/10.24937/2542-2324-2020-2-s-i-260-265.
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This paper discusses the development of calculation complex (model, algorithm and software) needed to investigate vibration parameters (amplitudes of displacements, internal forces and support responses) of a constant cross-section pipeline with a perfect incompressible fluid flowing inside it. This paper presents a pipeline model as quasi-monomeric finite-element system. Presently, the study discusses vibration of a straight constant cross-section pipeline resting on two elastic supports. Calculation algorithm is based on the discrete variant of partial-response method. The effect of fluid flow is taken into account as an additional inertial load incorporated, in its turn, by means of corrections and modifications of inertia & stiffness parameters of pipeline model. The study gives calculation expressions for partial responses and partial parameters, needed to implement the algorithm suggested by the authors. The problem formulated in this paper was solved as per specially developed mathematical model taking into account the forces due to the flow in the pipe. The paper also suggests calculation algorithm for vibration parameters of the adopted model. These vibration parameters were obtained in specially developed Koriolis software. The study also investigated the effect of additional inertial load components upon vibration parameters and natural frequencies of the structure at question. All these activities made it possible to accomplish the task of the whole study, i.e. to develop the calculation complex for determination of pipeline vibration parameters.
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Ma, Xuezhong. "Combined Effect of Fluid Cavitation and Inertia on the Pressure Buildup of Parallel Textured Surfaces." Lubricants 11, no. 7 (June 21, 2023): 270. http://dx.doi.org/10.3390/lubricants11070270.
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A mathematical model is developed to investigate the combined effect of fluid cavitation and inertia on the fluid pressure buildup of parallel textured surfaces. The fluid cavitation is analyzed using the Rayleigh–Plesset model, and the fluid inertia is analyzed with an averaged method. The finite element method and Newton-downhill method are employed to solve the governing equations. The numerical model is validated by comparing the experimental and numerical results, and the combined effect of fluid cavitation and inertia on the fluid pressure buildup is analyzed and discussed. The research indicates that the cavitation weakens the fluid inertia effect on the pressure distribution at the inlet area of textures. The fluid inertia greatly enhances the hydrodynamic effect and effectively limits the excessive extension of the low-pressure zone caused by cavitation. The fluid cavitation and inertia, especially their interaction, significantly affect the fluid pressure buildup and generate a net load-carrying capacity (LCC). The numerical model with the fluid inertia and cavitation is more time saving than the commercial CFD tools in solutions, which gives a novel and optional HD foundation for developing a more efficient and accurate THD or TEHD model by numerical programming.
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MAGNAUDET, JACQUES, SHU TAKAGI, and DOMINIQUE LEGENDRE. "Drag, deformation and lateral migration of a buoyant drop moving near a wall." Journal of Fluid Mechanics 476 (February 10, 2003): 115–57. http://dx.doi.org/10.1017/s0022112002002902.
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The problem of a drop of arbitrary density and viscosity moving close to a vertical wall under the effect of buoyancy is analysed theoretically. The case where the suspending fluid is at rest far from the drop and that of a linear shear flow are both considered. Effects of inertia and deformation are assumed to be small but of comparable magnitude, so that both of them contribute to the lateral migration of the drop. Expressions for the drag, deformation and migration valid down to separation distances from the wall of a few drop radii are established and discussed. Inertial and deformation-induced corrections to the drag force and slip velocity of a buoyant drop moving in a linear shear flow near a horizontal wall are also derived.
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Banerjee, I., M. E. Rosti, T. Kumar, L. Brandt, and A. Russom. "Analogue tuning of particle focusing in elasto-inertial flow." Meccanica 56, no. 7 (March 23, 2021): 1739–49. http://dx.doi.org/10.1007/s11012-021-01329-z.
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AbstractWe report a unique tuneable analogue trend in particle focusing in the laminar and weak viscoelastic regime of elasto-inertial flows. We observe experimentally that particles in circular cross-section microchannels can be tuned to any focusing bandwidths that lie between the “Segre-Silberberg annulus” and the centre of a circular microcapillary. We use direct numerical simulations to investigate this phenomenon and to understand how minute amounts of elasticity affect the focussing of particles at increasing flow rates. An Immersed Boundary Method is used to account for the presence of the particles and a FENE-P model is used to simulate the presence of polymers in a Non-Newtonian fluid. The numerical simulations study the dynamics and stability of finite size particles and are further used to analyse the particle behaviour at Reynolds numbers higher than what is allowed by the experimental setup. In particular, we are able to report the entire migration trajectories of the particles as they reach their final focussing positions and extend our predictions to other geometries such as the square cross section. We believe complex effects originate due to a combination of inertia and elasticity in the weakly viscoelastic regime, where neither inertia nor elasticity are able to mask each other’s effect completely, leading to a number of intermediate focusing positions. The present study provides a fundamental new understanding of particle focusing in weakly elastic and strongly inertial flows, whose findings can be exploited for potentially multiple microfluidics-based biological sorting applications.
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Siddiqui, Abdul Majeed, Khadija Maqbool, Afifa Ahmed, and Amer Bilal Mann. "Inertial and Linear Re-Absorption Effects on a Synovial Fluid Flow Through a Lubricated Knee Joint." Lubricants 13, no. 5 (April 27, 2025): 196. https://doi.org/10.3390/lubricants13050196.
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This study examines the flow dynamics of synovial fluid within a lubricated knee joint during movement, incorporating the effect of inertia and linear re-absorption at the synovial membrane. The fluid behavior is modeled using a couple-stress fluid framework, which accounts for mechanical phenomena and employs a lubricated membrane. synovial membrane plays a crucial role in reducing drag and enhancing joint lubrication for the formation of a uniform lubrication layer over the cartilage surfaces. The mathematical model of synovial fluid flow through the knee joint presents a set of non-linear partial differential equations solved by a recursive approach and inverse method through the software Mathematica 11. The results indicate that synovial fluid flow generates high pressure and shear stress away from the entry point due to the combined effects of inertial forces, linear re-absorption, and micro-rotation within the couple-stress fluid. Axial flow intensifies at the center of the knee joint during activity in the presence of linear re-absorption and molecular rotation, while transverse flow increases away from the center and near to synovium due to its permeability. These findings provide critical insights for biomedical engineers to quantify pressure and stress distributions in synovial fluid to design artificial joints.
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Jafargholinejad, Shapour, and Mohammad Najafi. "Inertia flows of Bingham fluids through a planar channel: Hydroelastic instability analysis." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 13 (May 29, 2017): 2394–403. http://dx.doi.org/10.1177/0954406217711470.
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In this paper, the effect of inertial terms on hydroelastic stability of a pressure-driven flow of a viscoplastic fluid flowing through a channel lined with a highly compliant polymeric gel is investigated. It is assumed that the fluid obeys the Bingham constuitive equation and the polymeric gel follows a two-constant Mooney–Rivlin material, which is used for modeling a nonviscous hyperelastic polymeric coating. A base-state solution is obtained for the fluid motion and solid deformation, simultaneously. Next, some infinitesimally small two-dimensional disturbances are imposed on the base-state solution. Dropping out all nonlinear perturbation terms, the modal linear stability analysis of the channel flow is conducted. The effects of the Bingham number and material constants are then examined on the critical Reynolds number. It is found that the yield stress has a stabilizing effect while the Mooney–Rivlin parameters have destabilizing effects on the pressure-driven flow of Bingham fluids.
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Dalwadi, Mohit P., S. Jonathan Chapman, James M. Oliver, and Sarah L. Waters. "The effect of weak inertia in rotating high-aspect-ratio vessel bioreactors." Journal of Fluid Mechanics 835 (November 27, 2017): 674–720. http://dx.doi.org/10.1017/jfm.2017.760.
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One method to grow artificial body tissue is to place a porous scaffold seeded with cells, known as a tissue construct, into a rotating bioreactor filled with a nutrient-rich fluid. The flow within the bioreactor is affected by the movement of the construct relative to the bioreactor which, in turn, is affected by the hydrodynamical and gravitational forces the construct experiences. The construct motion is thus coupled to the flow within the bioreactor. Over the time scale of a few hours, the construct appears to move in a periodic orbit but, over tens of hours, the construct drifts from periodicity. In the biological literature, this effect is often attributed to the change in density of the construct that occurs via tissue growth. In this paper, we show that weak inertia can cause the construct to drift from its periodic orbit over the same time scale as tissue growth. We consider the coupled flow and construct motion problem within a rotating high-aspect-ratio vessel bioreactor. Using an asymptotic analysis, we investigate the case where the Reynolds number is large but the geometry of the bioreactor yields a small reduced Reynolds number, resulting in a weak inertial effect. In particular, to accurately couple the bioreactor and porous flow regions, we extend the nested boundary layer analysis of Dalwadi et al. (J. Fluid Mech., vol. 798, 2016, pp. 88–139) to include moving walls and the thin region between the porous construct and the bioreactor wall. This allows us to derive a closed system of nonlinear ordinary differential equations for the construct trajectory, from which we show that neglecting inertia results in periodic orbits; we solve the inertia-free problem analytically, calculating the periodic orbits in terms of the system parameters. Using a multiple-scale analysis, we then systematically derive a simpler system of nonlinear ordinary differential equations that describe the long-time drift of the construct due to the effect of weak inertia. We investigate the bifurcations of the construct trajectory behaviour, and the limit cycles that appear when the construct is less dense than the surrounding fluid and the rotation rate is large enough. Thus, we are able to predict when the tissue construct will drift towards a stable limit cycle within the bioreactor and when it will drift out until it hits the bioreactor edge.
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RAY, BAIDURJA, and LANCE R. COLLINS. "Preferential concentration and relative velocity statistics of inertial particles in Navier–Stokes turbulence with and without filtering." Journal of Fluid Mechanics 680 (June 6, 2011): 488–510. http://dx.doi.org/10.1017/jfm.2011.174.
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The radial distribution function (RDF, a statistical measure of preferential concentration), and the relative velocity measured along the line-of-centres of two particles are the key statistical inputs to the collision kernel for finite-inertia particles suspended in a turbulent flow Sundaram & Collins (J. Fluid Mech., vol. 335, 1997, p. 75). In this paper, we investigate the behaviour of these two-particle statistics using direct numerical simulation (DNS) of homogeneous isotropic turbulence. While it is known that the RDF for particles of any Stokes number (St) decreases with separation distance Sundaram & Collins (J. Fluid Mech., vol. 335, 1997, p. 75), Reade & Collins (Phys. Fluids, vol. 12, 2000, p. 2530), Salazar et al. (J. Fluid Mech., vol. 600, 2008, p. 245), we observe that the peak in the RDF versus St curve shifts to higher St as we increase the separation distance. Here, St is defined as the ratio of the particle's viscous relaxation time to the Kolmogorov time-scale of the flow. Furthermore, as found in a previous study Wang, Wexler, & Zhou (J. Fluid Mech., vol. 415, 2000, p. 117), the variance of the radial relative velocity (wr) is found to increase monotonically with increasing separation distance and increasing Stokes number; however, we show for the first time that the parameteric variation of the skewness of wr with St and r/η is qualitatively similar to that of the RDF, and points to a connection between the two. We then apply low-pass filters (using three different filter scales) on the DNS velocity field in wavenumber space in order to produce ‘perfect’ large-eddy simulation (LES) velocity fields without any errors associated with subgrid-scale modelling. We present visual evidence of the effect of sharp-spectral filtering on the flow structure and the particle field. We calculate the particle statistics in the filtered velocity field and find that the RDF decreases with filtering at low St and increases with filtering at high St, similar to Fede & Simonin (Phys. Fluids, vol. 18, 2006, p. 045103). We also find that the variation of the RDF with St shifts towards higher St with filtering at all separation distances. The variance of wr is found to decrease with filtering for all St and separation distances, but the skewness of wr shows a non-monotonic response to filtering that is qualitatively similar to the RDF. We consider the variation of the RDF and moments of wr with filter scale and find that they are approximately linear in the inertial range. We demonstrate that a simple model consisting of a redefinition of the St based on the time-scale of the filtered velocity field cannot recover the unfiltered statistics. Our findings provide insight on the effect of subgrid-scale eddies on the RDF and wr, and establish the requirements of a LES model for inertial particles that can correctly predict clustering and collisional behaviour.
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Lardigue, A., and S. Bennis. "Pulsatile Laminar Flow in a Viscoelastic System." Journal of Fluids Engineering 118, no. 4 (December 1, 1996): 829–32. http://dx.doi.org/10.1115/1.2835516.
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This work involves the study of Newtonian transitory and permanent flow regimes in a rigid tube that has been extended to include a viscoelastic enclosure. Variable pressures are applied at the free end of the tube. The problem is solved analytically by direct integration of the Navier-Stokes equations. In addition to the nondimensional parameter γ1 introduced previously by other authors, we found a new nondimensional parameter γ2 which also governs the fluid flow. This parameter may be interpreted as the ratio of the and the membrane viscosity force to the fluid friction force. The effects of small values of the membrane viscosity only attenuate the oscillating effect when inertia dominates on fluid friction force. When the membrane viscosity is important, however, it may cancel out the inertial effect resulting in a damped aperiodic flow. When the fluid friction force predominates, the membrane viscosity slows down an already damped aperiodic flow. All these types of flow are well characterized by well defined intervalls of variation of γ1, and γ2. In addition to the transitory flow regime, we also consider permanent pulsatile flow. An experimental device makes it possible to validate the theoretical assertions in the particular case of a pulsed pressure.
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Maeyama, Kohei, Shunichi Ishida, and Yohsuke Imai. "Peristaltic transport of a power-law fluid induced by a single wave: A numerical analysis using the cumulant lattice Boltzmann method." Physics of Fluids 34, no. 11 (November 2022): 111911. http://dx.doi.org/10.1063/5.0122182.
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Peristaltic pumping is the primary mechanism of food transport in the human intestine. Intestinal contents are often modeled as power-law fluids with low-behavior indices ( n < 1). Peristaltic flows were studied for periodic contraction waves ([Formula: see text]) with infinitely long wavelengths ([Formula: see text]) in the Stokes flow regime ([Formula: see text]). However, the peristaltic flow generated by an isolated contraction wave with a short wavelength at nonzero Reynolds numbers is more relevant to physiological conditions. In this study, we investigated the peristaltic transport of a power-law fluid with a low behavior index of n = 0.21 at nonzero Reynolds numbers up to Re = 10, generated by a single short contraction wave. First, we investigated the analytical solution for the peristaltic transport of the power-law fluid for [Formula: see text] and [Formula: see text]. The analytical solution shows that the discharge flow rate of a power-law fluid generated by a single contraction wave is much smaller than that of a Newtonian fluid ( n = 1). Next, we investigated the peristaltic transport for [Formula: see text] 10 using the cumulant lattice Boltzmann method. The numerical results demonstrate that the discharge flow rate for the power-law fluid sharply increased owing to the inertia effect. The power-law fluid induces an asymmetric flow field with respect to the contraction wave at smaller Reynolds numbers than Newtonian fluids. The inertia effect was increased by the sharpness of the contraction wave. These results suggest that intestinal contents can be transported more quickly by an isolated contraction wave with a shorter wavelength when the contents have low consistency indices or when the contraction wave has a large propagation velocity.
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BHATTI, M. M., and A. ZEESHAN. "HEAT AND MASS TRANSFER ANALYSIS ON PERISTALTIC FLOW OF PARTICLE–FLUID SUSPENSION WITH SLIP EFFECTS." Journal of Mechanics in Medicine and Biology 17, no. 02 (March 2017): 1750028. http://dx.doi.org/10.1142/s0219519417500282.
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In this paper, the effect of heat and mass transfer on particle–fluid suspension due to peristaltic motion is examined with of slip effects. The governing equations of fluid phase and particulate phase for Casson fluid model with embedded particles are interpreted under the approximation of long wavelength and neglecting the inertial forces. The obtained coupled resulting partial differential equations are solved analytically and an exact form of solutions are conferred. The impact of various sundry parameters are plotted and discussed for velocity, temperature and concentration distribution for both fluid and particle phase. Numerical solution is evaluated for pressure rise along the whole channel. The present analysis reveals various interesting behavior that warrant further analysis on various Newtonian and non-Newtonian fluids. In the present flow problem, the influence of slip represents opposite attitude on the walls of the channel whereas due to the impact of particle volume fractions, the velocity of the fluid diminishes along the whole length of the channel.
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Meng, Meng, Stefan Z. Miska, Mengjiao Yu, and Evren M. Ozbayoglu. "Fully Coupled Modeling of Dynamic Loading of the Wellbore." SPE Journal 25, no. 03 (November 14, 2019): 1462–88. http://dx.doi.org/10.2118/198914-pa.
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Summary Loadings acting on a wellbore are more realistically regarded as dynamic rather than static, and the wellbore response under dynamic loading can be different from that under static loading. Under dynamic loading, the inertia term should be considered and the changing rate of loading could induce a change in the mechanical properties of the wellbore, which might compromise wellbore stability and integrity. In this paper, a fully coupled poroelastodynamic model is proposed to study wellbore behavior. This model not only considers fully coupled deformation/diffusion effects, but also includes both solid and fluid inertia terms. The implicit finite-difference method was applied to solve the governing equations, which allows this model to handle all kinds of dynamic loading conditions. After modifying the existing code only slightly, our numerical solution can neglect inertia terms. The numerical results were validated by comparing them to the analytical solution with a simulated sinusoidal boundary condition. To understand this model better, a sensitivity analysis was performed, and the influence of inertia terms was investigated. After that, the model was applied to analyze wellbore stability under tripping operations. The results show that the inertial effect is insignificant for tripping and a fully coupled, quasistatic model is recommended for wellbore stability under tripping operations. The fully coupled poroelastodynamic model should be used for rapid dynamic loading conditions, such as earthquakes and perforations.
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Moruzzi, Rodrigo Braga, Joice Gonçalves, Lais Galileu Speranza, and André Luiz de Oliveira. "Influência da ação combinada do transporte inercial e da sedimentação diferencial nos agregados após cessada a floculação mecanizada." Engenharia Sanitaria e Ambiental 27, no. 4 (August 2022): 723–29. http://dx.doi.org/10.1590/s1413-415220200291.
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RESUMO Durante a floculação mecanizada, o gradiente médio de velocidade (Gf) pode ser controlado de modo a formar agregados compatíveis com as unidades de separação sólido/líquido nas estações de tratamento de água, conferindo flexibilidade operacional ao sistema. Os ensaios de bancada auxiliam na definição da melhor condição de coagulação e floculação, permitindo até mesmo o controle da agitação (floculação ortocinética) e do tempo de detenção hidráulica. Todavia, não são conhecidos todos os efeitos secundários da formação dos agregados decorrentes do transporte inercial nem da sedimentação diferencial, após cessada a agitação mecânica na floculação. O presente trabalho buscou monitorar a influência combinada desses dois efeitos na formação dos agregados, por meio de técnica não intrusiva de captura de imagem associada à técnica particle image velocimetry. Foi possível verificar que o transporte dos agregados formados após a etapa de floculação decorre da ação do movimento inercial do fluido e da sedimentação diferencial, em proporção que varia no tempo. O movimento inercial apresenta predominância na influência da formação dos agregados do momento em que é cessada a agitação mecânica (Gf de 20 s-1) até 5,5 ± 0,5 minutos, quando os agregados passam a ser modificados predominantemente pela sedimentação diferencial. Por meio da análise dos agregados, foram observados dois momentos de crescimento no comprimento deles. O primeiro ocorreu entre os dois primeiros minutos, e o segundo, durante os minutos 4 e 6 de sedimentação, quando se deu a provável transição entre os mecanismos investigados.