Couette Poiseuille Research Articles

A Lagrangian gradient smoothing method for solid‐flow problems using simplicial mesh

SummaryA novel Lagrangian gradient smoothing method (L‐GSM) is developed to solve “solid‐flow” (flow media with material strength) problems governed by Lagrangian form of Navier‐Stokes equations. It is a particle‐like method, similar to the smoothed particle hydrodynamics (SPH) method but without the so‐called tensile instability that exists in the SPH since its birth. The L‐GSM uses gradient smoothing technique to approximate the gradient of the field variables, based on the standard GSM that was found working well with Euler grids for general fluids. The Delaunay triangulation algorithm is adopted to update the connectivity of the particles, so that supporting neighboring particles can be determined for accurate gradient approximations. Special techniques are also devised for treatments of 3 types of boundaries: no‐slip solid boundary, free‐surface boundary, and periodical boundary. An advanced GSM operation for better consistency condition is then developed. Tensile stability condition of L‐GSM is investigated through the von Neumann stability analysis as well as numerical tests. The proposed L‐GSM is validated by using benchmarking examples of incompressible flows, including the Couette flow, Poiseuille flow, and 2D shear‐driven cavity. It is then applied to solve a practical problem of solid flows: the natural failure process of soil and the resultant soil flows. The numerical results are compared with theoretical solutions, experimental data, and other numerical results by SPH and FDM to evaluate further L‐GSM performance. It shows that the L‐GSM scheme can give a very accurate result for all these examples. Both the theoretical analysis and the numerical testing results demonstrate that the proposed L‐GSM approach restores first‐order accuracy unconditionally and does not suffer from the tensile instability. It is also shown that the L‐GSM is much more computational efficient compared with SPH, especially when a large number of particles are employed in simulation.

Experiments on transient growth of turbulent spots

We present detailed experiments on transient growth of turbulent spots induced by external forcing in plane Couette–Poiseuille flow, which are studied in the framework of linear transient growth. The experimental investigation is supplemented with full theoretical analysis. We compare quantitatively the experimental and theoretical results, including maximal gain and the time at which it occurs. We also present the limits of validity for the application of the linear theory at high amplitude perturbation and Reynolds number, showing experiments with self-sustained states.

Particle segregation in turbulent Couette–Poiseuille flow with vanishing wall shear

Inertial particles dispersed in wall-bounded flows in pipes and channels are known to accumulate close to the walls. The segregation ability depends greatly on the inertia-selection effects of the near-wall quasi-coherent turbulent structures, which are formed near both walls where shear stresses are high. Here, however, we investigated if and how particles segregate in the vicinity of walls in absence of mean shear. A tailor-made turbulent Couette–Poiseuille flow was designed such that the mean shear vanished at the moving wall, thereby resulting in an asymmetric flow with conventional near-wall turbulent structures only at one wall. In addition, Large-Scale Structures (LSSs) were observed in the flow, which greatly influenced the distribution of the inertial particles. Particles of five different inertia groups were embedded in the directly simulated turbulence field and examined. It was found that particles of high inertia segregated near the stationary wall where mean shear prevailed, but also near the moving wall where mean shear was absent. However, due to the qualitatively distinct near-wall flow structures, the inertia effects on the actual segregation were different at the two walls. Mechanisms causing the asymmetric wall-normal segregation were explored with the focus on the moving-wall region, where the quasi-coherent turbulent structures were absent, and the local fluid structures were dominated by imprints of the LSSs.

Direct Numerical Simulation and Theory of a Wall-Bounded Flow with Zero Skin Friction.

We study turbulent plane Couette-Poiseuille (CP) flows in which the conditions (relative wall velocity ΔU w ≡ 2U w , pressure gradient dP/dx and viscosity ν) are adjusted to produce zero mean skin friction on one of the walls, denoted by APG for adverse pressure gradient. The other wall, FPG for favorable pressure gradient, provides the friction velocity uτ , and h is the half-height of the channel. This leads to a one-dimensional family of flows of varying Reynolds number Re ≡ U w h/ν. We apply three codes, and cover three Reynolds numbers stepping by a factor of 2 each time. The agreement between codes is very good, and the Reynolds-number range is sizable. The theoretical questions revolve around Reynolds-number independence in both the core region (free of local viscous effects) and the two wall regions. The core region follows Townsend's hypothesis of universal behavior for the velocity and shear stress, when they are normalized with uτ and h; universality is not observed for all the Reynolds stresses, any more than it is in Poiseuille flow or boundary layers. The behavior at very high Re is unknown. The FPG wall region obeys the classical law of the wall, again for velocity and shear stress, but could suggest a low value for the Karman constant κ, possibly near 0.37. For the APG wall region, Stratford conjectured universal behavior when normalized with the pressure gradient, leading to a square-root law for the velocity. The literature, also covering other flows with zero skin friction, is ambiguous. Our results are very consistent with both of Stratford's conjectures, suggesting that at least in this idealized flow geometry the theory is successful like it was for the classical law of the wall. We appear to know the constants of the law within a 10% bracket. On the other hand, again that does not extend to Reynolds stresses other than the shear stress, but these stresses are passive in the momentum equation.

Linear and weakly nonlinear analyses of cylindrical Couette flow with axial and radial flows

Extending previous linear stability analyses of the instabilities developing in permeable Taylor–Couette–Poiseuille flows where axial and radial throughflows are superimposed on the usual Taylor–Couette flow, we further examine the linear behaviour and expand the analysis to consider the weakly nonlinear behaviour of convective-type instabilities by means of the derivation of the fifth-order amplitude equation together with direct numerical simulations. Special attention is paid to the influence of the radius ratio $\unicode[STIX]{x1D702}=r_{in}/r_{out}$, and particularly to wide gaps (small $\unicode[STIX]{x1D702}$) and how they magnify the effects of the radial flow. The instabilities take the form of pairs of counter-rotating toroidal vortices superseded by helical ones as the axial flow is increased. Increasing the radial inflow draws these vortices near the inner cylinder, where they shrink relative to the annular gap, when this gap is wide. Strong axial and radial flows in a narrow annular gap lead to a very large azimuthal wavenumber with steeply sloped helical vortices. Strong radial outflow in a wide annular gap results in very large helical vortices. The analytical and numerical saturated vortices match quite well. In addition, radial inflows or outflows can turn the usually supercritical bifurcation from laminar to vortical flow into a subcritical one. The radial flow above which this change occurs decreases as the radius ratio $\unicode[STIX]{x1D702}$ decreases. A practical motivation for this weakly nonlinear analysis is found in modelling dynamic filtration devices, which rely on vortical instabilities to reduce the processes of accumulation on their membranes.

Design method of a vertical screw conveyor based on Taylor–Couette–Poiseuille stable helical vortex

This article investigates gas–solid two-phase flow in a vertical screw conveyor and analyzes the distribution function of the circumferential velocity of particles in the radial direction. Theoretical analysis combined with EDEM+FLUENT simulation analysis is performed to determine the best fill rate, the best screw speed, and critical Reynolds number when Taylor–Couette–Poiseuille flow stable helical vortex forms in the vertical screw conveyor. The formula for the critical Reynolds number and the best throughput is determined under different friction coefficients to establish an efficient design method based on Taylor–Couette–Poiseuille stable helical vortex flow. The method greatly benefits the design of vertical screw conveyors.

Turbulent Couette–Poiseuille flow with zero wall shear

A particular pressure-driven flow in a plane channel is considered, in which one of the walls moves with a constant speed that makes the mean shear rate and the friction at the moving wall vanish. The Reynolds number considered based on the friction velocity at the stationary wall (uτ,S) and half the channel height (h) is Reτ,S = 180. The resulting mean velocity increases monotonically from the stationary to the moving wall and exhibits a substantial logarithmic region. Conventional near-wall streaks are observed only near the stationary wall, whereas the turbulence in the vicinity of the shear-free moving wall is qualitatively different from typical near-wall turbulence. Large-scale-structures (LSS) dominate in the center region and their spanwise spacing increases almost linearly from about 2.3 to 4.2 channel half-heights at this Reτ,S. The presence of LSS adds to the transport of turbulent kinetic energy from the core region towards the moving wall where the energy production is negligible. Energy is supplied to this particular flow only by the driving pressure gradient and the wall motion enhances this energy input from the mean flow. About half of the supplied mechanical energy is directly lost by viscous dissipation whereas the other half is first converted from mean-flow energy to turbulent kinetic energy and thereafter dissipated.

Nonlinear coupling of interfacial instabilities with resonant wave interactions in horizontal two-fluid plane Couette–Poiseuille flows: numerical and physical observations

We investigate mechanisms governing the initial growth and nonlinear evolution of interfacial waves in horizontal two-fluid plane Couette–Poiseuille flows. Nonlinear coupling of the Kelvin–Helmholtz interfacial instability with resonant wave interactions has been shown to be capable of rapidly generating long waves through the transfer of energy from linearly unstable short waves to stable long-wave components within the context of potential flow theory. The objective of this work is to determine whether that coupled mechanism persists in laminar and turbulent viscous flows. Utilizing both theoretical and computational methods, we analyse the initial Orr–Sommerfeld instability to quantify the frequencies and growth/decay rates of each wave mode for two-fluid laminar and turbulent channel flows. The obtained dispersion relation allows for the identification of resonant and/or near-resonant triads among (unstable and damped) wave components in an interfacial wave spectrum. We perform direct numerical simulations (DNS) of the two-phase Navier–Stokes equations with a fully nonlinear interface to formally establish the validity of our theoretical predictions for viscous flows. DNS results show the existence of a nonlinear energy cascade from unstable short- to damped long-wavelength waves due to resonant subharmonic and/or triadic interactions in both laminar Couette and turbulent Poiseuille flows. Spectral analysis of the interfacial evolution confirms that the combined instability–resonance mechanism persists in the presence of viscosity despite being derived under the assumption of potential flow theory. Finally, we perform a detailed examination of experimentally measured wave power spectra from Jurman et al. (J. Fluid Mech., vol. 238, 1992, pp. 187–219) and carry out a numerical sensitivity study of the flow conditions to demonstrate and verify the existence of the coupled instability–resonance mechanism in physical systems. Our analysis accurately predicts the initial instability and the resulting nonlinear energy cascade through subharmonic and triadic interfacial wave resonances.

Drag flow analysis of Oldroyd eight constant fluid

This article presents the steady drag flow problems. The incompressible Oldroyd eight constant fluid flow is considered between two infinite parallel plates. Three flow problems including the Couette flow, Poiseuille flow and Couette–Poiseuille flow are modeled. The source term appearing in the nonlinear differential equation for each case is simplified with the application of modified homotopy perturbation method, and thus the general solution is obtained. The validity of second order approximate analytic solutions is tested with the aid of a numerical technique. The order of accuracy has been obtained in tabular form and the graphs are presented to demonstrate the difference between the three flow regimes.

On the generalization of velocity slip in fluid flows using a steady-state series expansion of the wall shear stress: Case of simple Newtonian fluids

This paper is one of two articles, where we present a new wall slip formulation based on a series expansion involving both differential in space and exponential forms of wall shear stress. In the first of these articles, we presented and described this new formulation using Phan-Thien–Tanner fluid as case study. Meanwhile, this second paper analyzes the new slip formulation for Newtonian Fluid. Unlike in the first paper, here, we have considered both the exponential and differential forms, though truncated at three terms each. Thus, we use our new truncated triple-slip-coefficients wall slip law to analyze Newtonian fluid in different systems. In particular, we study the planar Couette and planar Poiseuille problem, where two infinitely long and parallel plates have been used.For this part also, slip velocities and shear stresses at the walls are scrutinized for both problems. Further, as the Couette problem is pressure independent; the differential form of the slip law is considered for Poiseuille problem only. In addition, the pressure and flow-rate are studied for various slip coefficients for Poiseuille flow case using condensed forms of the triple-slip-coefficients. Our results obtained prove reasonable as represented by physically realistic plots herein. This feasibility is especially dictated by the velocity profile across channel width for both application problems. More importantly, results obtained for Poiseuille problem is corroborated with experimental data. Therefore, we can infer from all these, that this new model has the potential of providing results which can match experimental data, that is, if the three slip-coefficients are properly chosen.

A multiscale SPH method for simulating transient viscoelastic flows using bead-spring chain model

In this article, a multiscale smoothed particle hydrodynamics (SPH) method is proposed to simulate transient viscoelastic flows by using a bead-spring chain description of polymer molecule. This methodology couples macroscopic conservation equations for mass and momentum with a stochastic differential equation for bead-spring chain dynamics, which can be solved by a three-step semi-implicit algorithm to obtain the polymeric stress. Accordingly, a closed-form constitutive equation is not required. The multiscale SPH method is firstly verified by the plane Couette flow with Hookean and finitely extendable non-linear elastic (FENE) bead-spring chain models with the number of beads M=2, which correspond to Hookean and FENE dumbbell models, respectively. Results for the velocity and shear stress are in excellent agreement with the available numerical and analytical solutions in literature. Then, the numerical method is extended to simulate the plane Couette flow and Poiseuille flow with FENE bead-spring chain model with M >2. In particular, some molecular information of bead-spring chain such as the molecular stretch, the orientation angle and the mean configuration thickness are displayed. The influence of the number of beads M on the evolutions of the molecular information is also analyzed in detail. It is demonstrated that the multiscale SPH method proposed here is a promising computational tool for the multiscale simulations of transient viscoelastic flows.

Enhancement of forced convection in wide cylindrical annular channel using rotating inner pipe with interrupted helical fins

This paper presents the results of heat transfer and pressure drop in concentric annular wide channel with inner plain or finned pipe under stationary and rotating conditions in Taylor–Couette–Poiseuille flow. The experiments are conducted for one plain pipe and three finned pipes with helical fin spacing of 75, 110 and 150mm at rotating speeds of 0, 200, 250, 300, 350 and 400rpm. The experiments cover axial Reynolds number of 8.07×104–1.82×105, rotational Reynolds number of 0 and from 1428 to 3008, corresponds to Taylor number of 0 and from 1.22×106 to 8.32×106. The reported results in the form of Nusselt numbers and friction factors are correlated in terms of Re, Ta, Pr and fin geometrical parameters. The results proved that at Re=1.5×105, the wide annular channel with inner pipe of helical fin spacing 75mm that rotates at 400rpm enhances Nu by a factor of 7.5 and also boosts the ratio of heat exchange to pumping power by a factor of 7.6, compared to the case for plain stationary pipe.

The Couette–Poiseuille flow of a suspension modeled as a modified third-grade fluid

In this paper, we modify the thermodynamically compatible third-grade fluid model by introducing a shear-rate- and volume-fraction-dependent viscosity into the equation. With this new model, it is possible to predict not only the normal stress differences, but also the variable viscosity observed in many suspensions. We study the Couette–Poiseuille flow of such a fluid between two horizontal flat plates. The steady fully developed flow equations are made dimensionless and are solved numerically; the effects of different dimensionless numbers are discussed.

Interfacial instability in two-layer Couette–Poiseuille flow of viscoelastic fluids

The temporal linear stability analysis of shear flow of two-layer viscoelastic fluids, both described using the upper convected Maxwell (UCM) model, is carried out. The plane Couette flow under creeping flow conditions both in the absence and presence of pressure gradient is examined to study the role of unmatched elasticities in the interfacial instability. As the most critical disturbance is known to be of finite wavelength of the order of channel width, the numerical analysis examines the entire range of disturbance wavenumbers and the stability map is constructed in the parametric space of fluid Weissenberg numbers to indicate the region of stable interface. With a focus on optical fiber coating process, the analysis investigates the role of pressure gradient imposed on the plate-driven flow. Both the adverse and favorable pressure gradients are analyzed to identify the region for stable coating flow. In the presence of pressure gradient, the region of stable interface broadens when the high elasticity fluid occupies the region of low shear rate, which is the bottom (top) layer for the adverse (favorable) pressure gradient. For the two fluids of unmatched rheology, in addition to elastic instability, the role of viscosity stratification leading to a jump in the shear rate at interface is also examined. The adverse pressure gradient has a stabilizing effect when more viscous fluid is more elastic, whereas the favorable pressure gradient tends to stabilize the interface when the less viscous fluid has higher elasticity than the more viscous fluid.

Simplified Explicit Flow Equations for Herschel-Bulkley Fluids in Couette-Poiseuille Flow—For Real-Time Surge and Swab Modeling in Drilling

SummarySimplified flow equations are developed for Herschel-Bulkley (HB) fluids in laminar Couette-Poiseuille (CP) flow. Such flow problems are encountered in drilling when the drillstring is moved longitudinally (surge and swab operations). The new equations give the frictional-pressure gradient explicitly as a function of the bulk-flow rate. This makes them very well-suited for applications in fast, robust dynamic models for real-time applications. Incorporating these equations in a dynamic model based on ordinary differential equations (ODEs) enables coupling with system identification and control-system theory. This is a great advantage in drilling applications where there are many uncertain parameters and few measurements. Thorough analysis of relevant analytical solutions is performed to replace the most complex (implicit) parts of the solution with simpler approximations. The accuracy of the new equations, in comparison with numerical simulations and available analytical solutions, is shown to be acceptable for most practical applications.

Numerical Simulation of Rarefied Gas Flows with Specified Heat Flux Boundary Conditions

AbstractWe investigate unidirectional rarefied flows confined between two infinite parallel plates with specified heat flux boundary conditions. Both Couette and force-driven Poiseuille flows are considered. The flow behaviors are analyzed numerically by solving the Shakhov model of the Boltzmann equation. We find that a zero-heat-flux wall can significantly influence the flow behavior, including the velocity slip and temperature jump at the wall, especially for high-speed flows. The predicted bimodal-like temperature profile for force-driven flows cannot even be qualitatively captured by the Navier-Stokes-Fourier equations.

Interactions of Vortices of a Square Cylinder and a Rectangular Vortex Generator Under Couette–Poiseuille Flow

This study focuses on interactions of vortices generated by a family of eddy-promoting upstream rectangular cylinders (of different heights a* and widths b*) with the shear layers of a downstream square cylinder (of height A*) placed near a plane in an in-line tandem arrangement under the incidence of Couette–Poiseuille flow based nonuniform linear/nonlinear velocity profile. The dimensionless operational parameters are cylinders spacing distance S, ratio of heights r2=a*/A* (≤1), aspect ratio r1=b*/a* (≤1), Reynolds number Re (based on the velocity at height A* for Couette flow), ReU2 (based on the velocity at height 10A* for Couette–Poiseuille flow), and nondimensional pressure gradient P at the inlet. The governing equations are solved numerically through a pressure-correction-based iterative algorithm (SIMPLE) with the quadratic upwind interpolation for convective kinematics (QUICK) scheme for convective terms. The major issue of appearing multiple peaks in the spectrum of the fluctuating lift coefficient of the downstream cylinder is addressed and justified exhibiting the flow patterns. While considering the rectangular shape (for the upstream cylinder) and nonlinear velocity (at the inlet), the possibility of generating the unsteadiness in the steady wake flow of the downstream cylinder at a Re (based on height a*) less than the critical Re for the downstream cylinder is documented here. The dependence of flow characteristics of the downstream cylinder on the angle of incident linear velocity at specific S and r1 is also demonstrated here. It is observed that the discontinuous jump in the aerodynamic characteristics (due to a sudden change from one distinct flow pattern to the other in the critical spacing distance regime) is directly proportional to the height of the vortex generator. Increasing P under the same characteristic velocity causes the steady flow of cylinder(s) to convert to a periodic flow and reduces the critical spacing distance for the vortex generator.

Effect of Asymmetric Boundary Conditions on Couette–Poiseuille Flow of Power-Law Fluid

The effect of viscous dissipation on forced convective heat transfer for a Couette–Poiseuille flow of a power-law fluid subjected to asymmetric thermal boundary conditions is investigated here. The Couette–Poiseuille flow studied is limited to one with a maximum velocity, where the location that corresponds to the maximum velocity has to be solved numerically. A new analytical expression is obtained for the Nusselt number, in terms of the heat flux ratio applied to the top and bottom parallel plates and in terms of the Brinkman number as defined for the power-law fluid. Present results, when reduced to a few special cases, are in excellent agreement with published results. An asymptotic Brinkman number is observed in the Nusselt number versus Brinkman number plot, which shows a sign change in for the range of power-law indices tested.

Effect of conjugate heat transfer on the irreversibility generation rate in a combined Couette–Poiseuille flow between asymmetrically heated parallel plates: The entropy minimization analysis

We investigate the entropy transport dynamics of a Newtonian fluid in a parallel-plate channel considering the effect of conjugate heat transfer into the analysis. We consider that the flow to be actuated by the combined influences of externally applied pressure gradient and movement of the upper plate of the channel. Using an analytical scheme associated with the thermal boundary conditions of third kind at the outer boundaries of the channel, we bring out the alteration in the underlying thermal transport characteristics of heat as attributable to the nonlinear interactions between flow dynamics and viscous heating. Our analysis demonstrates the influential role of different performance index parameters viz., the geometric parameters, material properties, flow conditions on the irreversibility generation rate of the system. In particular, we unveil an optimum value of wall thickness and wall to fluid conductivity ratio that leads to minimization of the entropy generation rate in the system owing to intricate interplay between the heat flow dynamics and viscous heating. Our results may have far ranging consequences in the design of various cooling and heat removal devices and systems, which are often used in different engineering applications.

In an attempt to generalize wall slip in fluid flows using a series expansion of the wall shear stress: Case of non-Newtonian [Phan–Thien–Tanner fluid

In this paper, we address a new wall slip formulation based on a series expansion of both differential and exponential forms of wall shear stress. As this is initially considered as an infinite series, we use a truncated version of it to get a slip law having three slip coefficients, where we have considered the exponential form only. We use our new truncated triple-slip-coefficients wall slip law to analyze a particular class of viscoelastic non-Newtonian fluid. This special case follows the Phan–Thien–Tanner fluid model. Moreover, for this fluid, we identify Weissenberg number as one salient parameter affecting slip. In particular, our new model is tested on a familiar planar Couette and planar Poiseuille flow problem, where two parallel and infinitely long plates have been used. Furthermore, slip-dependent analytical expressions for field quantities such as velocity and shear stress at the walls and beyond, are derived and numerically analyzed for both problems. In addition, the pressure and flow-rate are derived for various slip coefficients for Poiseuille flow case.Our results obtained prove reasonable as represented by physically realistic plots herein. This feasibility is especially dictated by the velocity profile across channel width for both application problems. Thus, we can infer from all these, that this new model has the potential of providing results which can match experimental data, that is, if the three slip-coefficients are properly chosen.