Solution For Channel Flow Research Articles

Analytical solution for channel flow of a Giesekus fluid with non-zero solvent viscosity

A semi analytical solution is obtained here for the fully developed plane Poiseuille flow of a Giesekus fluid with a Newtonian solvent. The fluid behaviour is described using the Deborah number, the mobility factor and an appropriate ratio of fluid viscosity to total viscosity as parameters. The given solution shows that the velocity increases significantly with rising the polymer concentration, confirming that dilution of the solution produces the same effect as an increase in resistance. The analysis demonstrates that there are limiting values of Deborah number related to the mobility parameter.

Numerical solution of MHD channel flow in a porous medium with uniform suction and injection in the presence of an inclined magnetic field

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

Performance evaluation of standard second-order finite volume method for DNS solution of turbulent channel flow

Performance evaluation of standard second-order finite volume method for DNS solution of turbulent channel flow

Temporal stability of multiple similarity solutions for porous channel flows with expanding or contracting walls

In this paper, the temporal stability of multiple similarity solutions (flow patterns) for the incompressible laminar fluid flow along a uniformly porous channel with expanding or contracting walls is analyzed. This work extends the recent results of similarity perturbations of Sun et al. [“Temporal stability analysis for multiple similarity solutions of viscous incompressible flows in porous channels with moving walls,” Appl. Math. Modell. 77, 738–755 (2020)] by examining the temporal stability with perturbations of general form (including similarity and nonsimilarity forms). Based on the linear stability theory, two-dimensional eigenvalue problems associated with the flow equations are formulated and numerically solved by a finite difference method on the staggered grids. The linear stability analysis reveals that the stability of the solutions is same with that under the perturbations of a similarity form within the range of the wall expansion ratio α. [−5≤α≤3 as in Sun et al., “Temporal stability analysis for multiple similarity solutions of viscous incompressible flows in porous channels with moving walls,” Appl. Math. Modell. 77, 738–755 (2020)]. Further, it is found that the expansion ratio α has a great influence on the stability of type I flows: in the case of wall contraction (α<0), the stability region of the cross-flow Reynolds number (R) increases as the contraction ratio (|α|) increases; in the case of wall expansion and 0<α≤1, the stability region increases as the expansion ratio (α) increases; in the case of 1≤α≤3, type I flows are stable for all R where they exist. The flows of other types (types II and III with −5≤α≤3 and type IV with α = 3) are always unstable. As a nonlinear stability analysis or a validation of the linear stability analysis, the original nonlinear two-dimensional time-dependent problem with an initial perturbation of general form over those flow patterns is solved directly. It is found that the stability with the nonlinear analysis is consistent with the linear stability analysis.

Caribbean plate tilted and actively dragged eastwards by low-viscosity asthenospheric flow

The importance of a low-viscosity asthenosphere underlying mobile plates has been highlighted since the earliest days of the plate tectonics revolution. However, absolute asthenospheric viscosities are still poorly constrained, with estimates spanning up to 3 orders of magnitude. Here we follow a new approach using analytic solutions for Poiseuille-Couette channel flow to compute asthenospheric viscosities under the Caribbean. We estimate Caribbean dynamic topography and the associated pressure gradient, which, combined with flow velocities estimated from geologic markers and tomographic structure, yield our best-estimate asthenospheric viscosity of (3.0 ± 1.5)*1018 Pa s. This value is consistent with independent estimates for non-cratonic and oceanic regions, and challenges the hypothesis that higher-viscosity asthenosphere inferred from postglacial rebound is globally-representative. The active flow driven by Galapagos plume overpressure shown here contradicts the traditional view that the asthenosphere is only a passive lubricating layer for Earth’s tectonic plates.

Superhydrophobic annular pipes: a theoretical study

Abstract

Exact Traveling Wave Solutions in Viscoelastic Channel Flow.

Elasto-inertial turbulence (EIT) is a new, two-dimensional chaotic flow state observed in polymer solutions with possible connections to inertialess elastic turbulence and drag-reduced Newtonian turbulence. In this Letter, we argue that the origins of EIT are fundamentally different from Newtonian turbulence by finding a dynamical connection between EIT and an elasto-inertial linear instability recently found at high Weissenberg numbers [Garg etal., Phys. Rev. Lett. 121, 024502 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.024502]. This link is established by isolating the first known exact coherent structures in viscoelastic parallel flows-nonlinear elasto-inertial traveling waves (TWs)-borne at the linear instability and tracking them down to substantially lower Weissenberg numbers where EIT exists. These TWs have a distinctive "arrowhead" structure in the polymer stretch field and can be clearly recognized albeit transiently in EIT as well as being attractors for EIT dynamics if the Weissenberg number is sufficiently large. Our findings suggest that the dynamical systems picture in which Newtonian turbulence is built around the coexistence of many (unstable) simple invariant solutions populating phase space carries over to EIT, though these solutions rely on elasticity to exist.

Linear feedback control of invariant solutions in channel flow

Abstract

On the importance of the drag coefficient modelling in the double averaged Navier-Stokes equations for prediction of the roughness effects

ABSTRACT The Discrete Element Method (DEM) for modelling of flow over rough walls is revised in the framework of the DANS (Double Averaged Navier-Stokes) equations, with a special focus on the drag term appearing in the mean momentum equation as a key to the robustness of the model. A set of 14 Direct Numerical Simulations (DNS) of channel flows with systematically varying roughness topographies is considered to assess the performances of different drag coefficient closures. While the standard model of Taylor et al. [J. Fluids Eng. 107 (1985), 251–257] is found not to be successful in reproducing the distribution of the drag force, a new model is derived. The new model along with the model recently proposed by Kuwata et al. [Int. J. Heat Fluid Flow 77 (2019), 186–201] are employed for the solution of channel flow along with a simple mixing length model. Both models are shown to be successful in prediction of roughness function as long as a constant in the latter model is readjusted. The velocity profiles are also well recovered and in particular the roughness sublayers are accurately reproduced.

Oblique stripe solutions of channel flow

With decreasing Reynolds number, Re, turbulence in channel flow becomes spatio-temporally intermittent and self-organises into solitary stripes oblique to the mean flow direction. We report here the existence of localised nonlinear travelling wave solutions of the Navier–Stokes equations possessing this obliqueness property. Such solutions are identified numerically using edge tracking coupled with arclength continuation. All solutions emerge in saddle-node bifurcations at values of Re lower than the non-localised solutions. Relative periodic orbit solutions bifurcating from branches of travelling waves have also been computed. A complete parametric study is performed, including their stability, the investigation of their large-scale flow, and the robustness to changes of the numerical domain.

H2 SU YÜZÜ PROFİLİNE SAHİP AÇIK KANAL AKIMININ SAYISAL MODELLEMESİ

In open channel flows, 12 different surface profiles are formed depending on the flow conditions.The occur of water surface profiles varies depending on the upstream and downstream waterdepths, bed slope and the geometric characteristics of the interacted structure. The relation of the measured water depth without any structure with the critical water depth, formed in situation ofcritical flow, are used in the classification of the flow profiles. Open channel flows with differentwater surface profiles have been investigated experimentally in detail by researchers. Because ofadvances in technology in recent years, it is possible to solve governing equations bycomputational fluid dynamics methods. Computational fluid dynamics methods, which are moreeconomical than experimental models, are frequently used in solving hydraulic problems. In thisstudy, numerical solutions of open channel flow with different water surface profiles arecalculated. The turbulence shear stress in numerical modeling is calculated by using the ReNormalization Group (RNG) model and the water-air intersection is determined by using theVolume of Fluids (VOF) method. Experimental measurements in the literature and numericalmodel results are compared. The numerical model is found to be successful in determining thewater surface, especially in the drop region where H2 profile is formed.

Solution of Ion Channel Flow Using Immersed Boundary-Lattice Boltzmann Methods.

Poisson-Nernst-Planck (PNP) model has been extensively used for the study of channel flow under the influence of electrochemical gradients. PNP theory is a continuum description of ion flow where ionic distributions are described in terms of concentrations. Nonionic interparticle interactions are not considered in this theory as in continuum framework, their impact on the solution is minimal. This theory holds true for dilute flows or flows where channel radius is significantly larger than ion radius. However, for ion channel flows, where channel dimensions and ionic radius are of similar magnitude, nonionic interactions, particularly related to the size of the ions (steric effect), play an important role in defining the selectivity of the channel, concentration distribution of ionic species, and current across the channel, etc. To account for the effect of size of ions, several modifications to PNP equations have been proposed. One such approach is the introduction of Lennard-Jones potential to the energy variational formulation of PNP system. This study focuses on understanding the role of steric effect on flow properties. To discretize the system, Lattice Boltzmann method has been used. The system is defined by modified PNP equations where the steric effect is described by Lennard-Jones potential. In addition, boundary conditions for the complex channel geometry have been treated using immersed boundary method.

Numerical solution of the Giesekus model for incompressible free surface flows without solvent viscosity

We present a numerical method for solving the Giesekus model without solvent viscosity. This paper is concerned with incompressible two-dimensional free surface flows and employs the finite difference method to solve the governing equations. The methodology involves solving the momentum equation using the implicit Euler scheme and an implicit technique for computing the pressure condition on the free surface. The nonlinear Giesekus constitutive equation is computed by a second order Runge–Kutta method. A novel analytic solution for channel flow is developed and is used to verify the numerical technique presented herein. Mesh refinement studies establish the convergence of the method for complex free surface flows. To demonstrate that the technique can deal with complicated free surface flows, the time-dependent flow produced by a fluid jet flowing onto a rigid surface is simulated and the influence of the parameter α on the jet buckling phenomenon is investigated. In addition, the simulation of the extrudate swell of a Giesekus fluid was carried out and the effect of the parameter α on the flow was similarly examined.

Influence of magnetic fields on simultaneous stationary solutions of two-dimensional sudden expansion channel flow at low Rem

The influence of uniform magnetic fields on stationary simultaneous solutions in a channel with sudden expansion is studied in this work. Reynolds number (Re) values between 250 ≤ Re ≤ 550 and magnetic fields with Hartmann numbers (Ha) between 0 ≤ Ha ≤ 100 are considered. The global meshless method of approximate particular solutions (MAPS) is implemented to obtain the simultaneous stationary solutions that are presented in Re values above an approximate critical value of Rec ≈ 219. The base functions used in the MAPS to approximate velocity and pressure fields solve an auxiliary Stokes system. The four-sided lid-driven cavity (4SLDC) and backward facing step flows are considered as validation problems in order to show the ability of the method to study bifurcations and solve magnetohydrodynamic problems, respectively. The influence of transverse magnetic fields on the sudden expansion flow for low Ha contrasts with the few effects that a stream-wise field produces. The asymmetric flow is eliminated if a transverse magnetic field with Ha = 5 is imposed over the flow and recirculation zones almost disappear at Ha = 20 for Re values considered in this work.

Homotopy analysis method for predicting multiple solutions in the channel flow with stability analysis

The present theoretical investigation covers a study of finding the multiple solutions of a Jeffery–Hamel flow and heat transfer under the influence of magnetic field. An analytical technique (Homotopy Analysis Method) is applied to solve the cylindrical form of governing equations after getting non-dimensional system using suitable transformation. It is noticed that dual solutions exist only for convergent channel case. Critical values of channel angle (αc) are obtained which reveals the existence domain (αc < α < 0) for multiple solutions in convergent channel flow. Stability analysis is also performed by constructing eigenvalue problem to predict the physically stable solution. The minimum positive eigenvalue justifies the fact that the growth of disturbances given to the solution decays with time. The effect of various pertinent physical parameters is shown graphically on velocity, temperature, skin friction coefficient and Nusselt number.

Exact Solution for Asymmetric Turbulent Channel Flow with Applications in Ice-Covered Rivers

AbstractAsymmetric turbulent channel flow, such as ice-covered river flow, is a century-old problem but still unsolved in hydraulics and fluid mechanics. This study finds exact solutions for its ed...

Consistent lattice Boltzmann modeling of low-speed isothermal flows at finite Knudsen numbers in slip-flow regime: Application to plane boundaries.

The first nonequilibrium effect experienced by gaseous flows in contact with solid surfaces is the slip-flow regime. While the classical hydrodynamic description holds valid in bulk, at boundaries the fluid-wall interactions must consider slip. In comparison to the standard no-slip Dirichlet condition, the case of slip formulates as a Robin-type condition for the fluid tangential velocity. This makes its numerical modeling a challenging task, particularly in complex geometries. In this work, this issue is handled with the lattice Boltzmann method (LBM), motivated by the similarities between the closure relations of the reflection-type boundary schemes equipping the LBM equation and the slip velocity condition established by slip-flow theory. Based on this analogy, we derive, as central result, the structure of the LBM boundary closure relation that is consistent with the second-order slip velocity condition, applicable to planar walls. Subsequently, three tasks are performed. First, we clarify the limitations of existing slip velocity LBM schemes, based on discrete analogs of kinetic theory fluid-wall interaction models. Second, we present improved slip velocity LBM boundary schemes, constructed directly at discrete level, by extending the multireflection framework to the slip-flow regime. Here, two classes of slip velocity LBM boundary schemes are considered: (i) linear slip schemes, which are local but retain some calibration requirements and/or operation limitations, (ii) parabolic slip schemes, which use a two-point implementation but guarantee the consistent prescription of the intended slip velocity condition, at arbitrary plane wall discretizations, further dispensing any numerical calibration procedure. Third and final, we verify the improvements of our proposed slip velocity LBM boundary schemes against existing ones. The numerical tests evaluate the ability of the slip schemes to exactly accommodate the steady Poiseuille channel flow solution, over distinct wall slippage conditions, namely, no-slip, first-order slip, and second-order slip. The modeling of channel walls is discussed at both lattice-aligned and non-mesh-aligned configurations: the first case illustrates the numerical slip due to the incorrect modeling of slippage coefficients, whereas the second case adds the effect of spurious boundary layers created by the deficient accommodation of bulk solution. Finally, the slip-flow solutions predicted by LBM schemes are further evaluated for the Knudsen's paradox problem. As conclusion, this work establishes the parabolic accuracy of slip velocity schemes as the necessary condition for the consistent LBM modeling of the slip-flow regime.

The effects of lateral density gradients, slopes and buoyancy on channel flow: 1D analytical solutions and applications to the SE Canadian Cordillera

We present 1D analytical solutions for channel flow in orogens driven by various types of pressure gradients. Our calculations demonstrate that lateral density gradients in the upper crust, such as would occur across a suture zone separating arc rocks from pericratonic sediments provide a driving force for Poiseuille flow as large as topographic gradients observed in modern mountain belts. For cases for which the gradients are external (topographic and lateral density gradients) and internal (e.g. partial melting of channel material) to the channel, inclination decreases and increases the Poiseuille component of the average flow-velocity within the channel by the cosine and sine of the slope, respectively. The magnitude of the pressure gradient consequent upon the buoyancy generated by partial melting of metapelites in a channel with a 30° slope, such as would occur above an underthrusting basement ramp, is similar to that of topographic or lateral density gradients. Channel flow up a ramp could thus constitute an important exhumation mechanism in large hot orogens. Our calculations indicate that mid-crustal channel flow was a highly likely process in the Late Cretaceous-Paleocene setting of the southeastern Canadian Cordillera. The flow was first driven by the lateral density contrast between pericratonic sediments and the arc-related Intermontane terrane, then by combined effect of topographic gradient and melt-induced buoyancy of the Lower Selkirk Allochthon (part of the Shuswap Complex). Flow up the underthrusting basement ramp resulted in exhumation from mid- to upper-crustal levels. Channel flow then migrated downward to involve basement and overlying cover sequence rocks. Our results indicate that syn-convergent channel flow was a viable and very likely process in the southeastern Canadian Cordillera.

Localised dynamics of laminar pulsatile flow in a rectangular channel

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

Thermal-Flow Analysis of a Simple LTD (Low-Temperature-Differential) Heat Engine

A combined thermal and flow analysis was carried out to study the behavior and performance of a simple, commercial LTD (low-temperature-differential) heat engine. Laminar-flow solutions for annulus and channel flows were employed to estimate the viscous drags on the piston and the displacer, and the pressure difference across the displacer. Temperature correction factors were introduced in the thermal analysis to account for the departures from the ideal heat transfer processes. The flow analysis results indicate that the work required to overcome the viscous drags on engine moving parts is very small for engine speeds below 10 RPS (revolutions per second). The work required to move the displacer due to the pressure difference across the displacer is also one-to-two orders of magnitude smaller than the moving-boundary work of the piston for temperature differentials in the neighborhood of 20 °C and engine speeds below 10 RPS. A comparison with experimental data reveals large degradations from the ideal heat transfer processes inside the engine.