Laminar Pipe Flow Research Articles

New method for the determination of convective heat transfer coefficient in fully-developed laminar pipe flow

New method for the determination of convective heat transfer coefficient in fully-developed laminar pipe flow

Parametric study of cone angle influence on bubble vortex breakdown onset in laminar conical flow at various swirl numbers

The current work studies a swirling laminar viscous pipe flow with a controllable swirl number and varying pipe divergence cone angle. Such flows are widely used in various engineering applications. When a certain level of flow swirl is reached, a phenomenon called vortex breakdown occurs, the characteristics of which depend on the intensity of swirling of the flow and the Reynolds number. However, in addition to these two parameters, an important influence is exerted by the pipe opening angle, which often does not allow generalizing the results obtained in the pipe flow with even slightly different angles. Since experimentally it is quite difficult and expensive to change the pipe angle, especially considering the water as working fluid, this issue could be solved using CFD techniques. Using the design study, 63 different combinations of S and α are considered. The effect of the pipe divergence angle on the position of the bubble vortex breakdown and its properties is demonstrated. It is shown that there is a nonlinear relationship between the position of the bubble breakdown onset and the minimum value of the axial velocity at the axis depending on the opening angle of the cone.

Experimental investigation of the thermal development of two nanofluids in laminar flow

In this study, we conducted an experimental investigation of the thermal development of two nanofluids (γ-Al2O3 and TiO2 in deionized water) in a laminar pipe flow. To do so, the local Nusselt number is determined for Reynolds numbers from 650 to 1800. Experiments were carried out with water and two concentrations of water-based nanofluids with aluminum oxide and titanium oxide nanoparticles. The results show that the local Nusselt number remains unchanged with increasing mass concentration and that the process of thermal development is similar to that of water. Similarly, the friction factor is not affected by the addition of the nanoparticles, suggesting that these nanofluids behave like a homogeneous mixtures.

Non-Newtonian laminar flow in pipes using radius, stress, shear rate or velocity as the independent variable

The flow of a non-Newtonian fluid in a circular pipe is a classic introductory transport phenomena problem, familiar to readers of Robert Byron Bird textbooks. A characteristic of Bird's work was taking the time to explore alternative ways to describe a problem and refine the results into elegant and readable formulas. Inspired by that approach, we compare methods for pipe flow solutions that differ on the independent variable used (radius, stress, shear rate) to obtain flow rate and residence time distributions for generalized Newtonian fluids. We highlight cases where using the shear rate as the independent variable has advantages for analytical and numerical solutions. We describe a method to use velocimetry experimental data coupled with a pressure drop measurement to directly construct a curve of flow rate vs pressure drop without the need of fitting the data to any rheological models. We present a geometrical interpretation of velocity profiles as areas in the stress–shear rate plane and derive analytical solutions for a three-parameter model of soft glassy materials [Caggioni et al., “Variations of the Herschel–Bulkley exponent reflecting contributions of the viscous continuous phase to the shear rate-dependent stress of soft glassy materials,” J. Rheol. 64, 413 (2020)] and a four-parameter model for chocolate melts [H. D. Tscheuschner, “Rheologische eigenschaften von lebensmittelsystemen,” in Rheologie Der Lebensmittel, edited by D. Weipert, H. Tscheuschner, and E. Windhab (Behr's Verlag, Hamburg, 1993), pp. 101–172]. We also compare the speed of various numerical approaches for a fractional viscoelastic model [A. Jaishankar and G. H. McKinley, “A fractional K-BKZ constitutive formulation for describing the nonlinear rheology of multiscale complex fluids,” J. Rheol. 58, 1751 (2014)].

Rational Approximation of Unsteady Friction Weighting Functions in the Laplace Domain

AbstractThis paper aims at improving the weighting function based-method (WFB) for modeling the transient behavior of a laminar flow in cylindrical pipes in a one-dimensional approach. Two improvem...

Direct numerical simulation of two-phase pipe flow: Influence of the domain length on the flow regime

We investigate the dynamics of a kerosene–water mixture in a vertical pipe flow by solving the Cahn–Hilliard–Navier–Stokes equations. We compute the linear stability of laminar core-annular flow in a vertical pipe and find that it is highly unstable. By performing direct numerical simulations initialized with a slightly perturbed core-annular flow, we show that the system transitions to turbulence and finally relaxes into a turbulent slug flow regime provided that the pipe is sufficiently long. This configuration presents mild turbulence and large scale three-dimensional recirculation patterns. Our work highlights the need for applying nonlinear-dynamics approaches and carefully selecting the domain length to investigate the patterns observed in two-phase pipe flows and demonstrates the capabilities of phase-field methods to reliably simulate flows under realistic experimental conditions.

Prediction of multiphase flows with sharp interfaces using anisotropic mesh optimisation

We propose an integrated, parallelised modelling approach to solve complex multiphase flow problems with sharp interfaces. This approach is based on a finite-element, double control-volume methodology, and employs highly-anisotropic mesh optimisation within a framework of high-order numerical methods and algorithms, which include adaptive time-stepping, metric advection, flux limiting, compressive advection of interfaces, multi-grid solvers and preconditioners. Each method is integral to increasing the fidelity of representing the underlying physics while maximising computational efficiency, and, only in combination, do these methods result in the accurate, reliable, and efficient simulation of complex multiphase flows and associated regime transitions. These methods are applied simultaneously for the first time in this paper, although some of the individual methods have been presented previously. We validate our numerical predictions against standard benchmark results from the literature and demonstrate capabilities of our modelling framework through the simulation of laminar and turbulent two-phase pipe flows. These complex interfacial flows involve the creation of bubbles and slugs, which involve multi-scale physics and arise due to a delicate interplay amongst inertia, viscous, gravitational, and capillary forces. We also comment on the potential use of our integrated approach to simulate large, industrial-scale multiphase pipe flow problems that feature complex topological transitions.

Sedimentation effects on particle position and inertial deposition in 90° circular bends

Laminar fluid-particle flows in bend geometries are present in many industrial, pharmaceutical, and biomedical applications. Particle deposition has been studied extensively; however, little attention has been paid to the effect of particle sedimentation on particle position and deposition in different pipe geometry combinations. This study presented a comprehensive analysis of sedimentation effects on particle flow behaviour in 90° circular pipe bends of micron particles in laminar pipe flows. Pipe geometry combinations consisted of eight pipe diameters, nine bend radii, and 30 particle diameters in a range of 1 to 100 μm. The results demonstrated the locations of particles that sedimented to the bottom half of the straight pipe section, and the particle positions upstream from the pipe bend entrance, which was no longer in a fully developed profile. These new locations represent the effects of gravity, pulling the particles down. While obtaining these positions can be found through CFD analysis, we proposed an analytical solution to predict the particle trajectory from different release locations that would help to identify the initial particle distribution at locations upstream to the bend, to obviate the need for long upstream straight pipe sections in the CFD analysis.

Convective Heat Transfer of Laminar Swirling Pipe Flow With Viscous Dissipation Effects

Abstract The oil-water-gas separation is a critical aspect of the treatment of production flows in the oil industry. The segregation of gas bubbles and/or water droplets dispersed in viscous oil by an in-line swirling flow separator has been considered by the oil industry for topside and subsea applications. For high viscosity oils, heat transfer processes can be affected. Works addressing these applications are rare in the literature. In this way, the article presents a numerical investigation on heat transfer characteristics in a decaying swirling flow, considering the effects of viscosity dissipation due to the high viscosity of the fluid. The flow has both velocity and temperature profiles developing simultaneously in a tube with a constant diameter having a uniform wall heat flux in a laminar flow regime, particularly the behavior of heat transfer characteristics for strongly swirling numbers considering viscous dissipation. Three swirl numbers (S = 0.0, 0.3, and 0.7) and five Brinkman numbers (Br = 0.0, 0.1, 0.5, 1.0, and 10.0) were investigated and the effects of those parameters on the dimensionless temperature profiles, Nusselt number and viscous dissipation function were examined. The heat transfer analysis indicated that the swirling flow affects the fluid's axial and radial temperature distribution. They promoted increased fluid in wall temperature and bulk temperature and affected the local Nusselt number distribution.

Cell specific variation in viability in suspension in in vitro Poiseuille flow conditions

The influence of Poiseuille flow on cell viability has applications in the areas of cancer metastasis, lab-on-a-chip devices and flow cytometry. Indeed, retaining cell viability is important in the emerging field of adoptive cell therapy, as cells need to be returned to patients’ bodies, while the viability of other cells, which are perhaps less accustomed to suspension in a fluidic environment, is important to retain in flow cytometers and other such devices. Despite this, it is unclear how Poiseuille flow affects cell viability. Following on from previous studies which investigated the viability and inertial positions of circulating breast cancer cells in identical flow conditions, this study investigated the influence that varying flow rate, and the corresponding Reynolds number has on the viability of a range of different circulating cells in laminar pipe flow including primary T-cells, primary fibroblasts and neuroblastoma cells. It was found that Reynolds numbers as high as 9.13 had no effect on T-cells while the viabilities of neuroblastoma cells and intestinal fibroblasts were significantly reduced in comparison. This indicates that in vitro flow devices need to be tailored to cell-specific flow regimes.

Effect of viscosity on entropy generation for laminar flow in helical pipes

Entropy generation for fully developed laminar flow in a helical pipe carrying high viscous fluid under constant temperature boundary conditions is investigated analytically. This work focuses on geometrical, fluid, and thermal aspects and their influence on irreversibilities in helical coils. The effect of viscosity on the irreversibilities and its influence on the operating parameters of the helical coil are studied with the second law of thermodynamics. The most commonly used relationships for estimating viscosity change due to temperature are selected for analysis. The entropy generation and avoidable exergy destruction in each case are presented. Bejan number is plotted for varying viscosities under different wall temperatures for both heat transfer to and from the fluid. The thermodynamic potential of improvement based on avoidable and unavoidable exergy destruction concepts showed that the potential of improvement for heating and the cooling condition is considerable for a given operating condition in helical tubes. The selected model for estimating viscosity influences the optimum operating wall temperature, thereby giving an insight into a selection of a proper viscosity model. The optimum helical number is not affected by fluid properties and wall temperature. The heat transfer to pumping ratio is evaluated and it is found that the optimal value is influenced by the change in viscosity.

An Encounter With Lattice Boltzmann for Biomedical Applications: Interactive Simulation to Support Clinical and Design Decisions

Abstract Medical device design for personalized medicine requires sophisticated tools for optimization of biomechanical and biofluidic devices. This paper investigates a new real-time tool for simulating structural and fluid scenarios—ansys Discovery Live—and we evaluate its capability in the fluid domain through benchmark flows that all involve steady-state flow at the inlet and zero pressure at the outlet. Three scenarios are reported: (i) Laminar flow in a straight pipe, (ii) vortex shedding from the Karman vortex, and (iii) nozzle flows as characterized by an FDA benchmark geometry. The solver uses a lattice Boltzmann method requiring a high-performance GPU (nVidiaGTX1080, 8GB RAM). Results in each case were compared with the literature and demonstrated credible solutions, all delivered in near real-time: (i) The straight pipe delivered parabolic flow after an appropriate entrance length (plug flow inlet conditions), (ii) the Karman vortex demonstrated appropriate vortex shedding as a function of Reynolds number, characterized by Strouhal number in both the free field and within a pipe, and (iii) the FDA benchmark geometry generated results consistent with the literature in terms of variation of velocity along the centerline and in the radial direction, although deviation from experimental validation was evident in the sudden expansion section of the geometry. This behavior is similar to previously reported results from Navier–Stokes solvers. A cardiovascular stenosis example is also considered, to provide a more direct biomedical context. The current software framework imposes constraints on inlet/outlet boundary conditions, and only supports limited control of solver discretization without providing full field vector flow data outputs. Nonetheless, numerous benefits result from the interactive interface and almost real-time solution, providing a tool that may help to accelerate the arrival of improved patient-specific medical devices.

Influence of high shear on the effective thermal conduction of spherical micro- and nanoparticle suspensions in view of particle rotation

In the past three decades, different physical models to describe the thermal conductivity enhancements of suspensions with micro- and nanoparticles with respect to particle sizes, shape, volume fraction etc. were established. However, none of these models considered the effect of shear, although an influence has been observed experimentally in a few studies for very high shear rates. Possible underlying mechanisms for shear induced thermal conductivity enhancement have not been explained in detail yet.In this article, the finite element method is used to evaluate how shear induced particle rotation and the velocity field around the rotating particle drives thermal conductivity enhancement. For nanoparticles it is found that particle rotation does not enhance the heat transfer inside the particle. However, within the Péclet number (Pe=γ˙d2/a) range of 0−300, particle rotation linearly enforces the heat transport up to 5−30%, mainly due to advective motion (eddies) around the particle. For high shear rates (Pe>500), the enhancement approaches a constant value, at which the particle material becomes irrelevant for the effective conductivity enhancement. In this case, asymmetric advective motion around the particle dominates the heat transfer. Note that the Péclet number range for which an advective motion plays a significant role is relevant for suspensions with micrometer-size particles but not for nanoparticle suspensions.In a final step, the influence of the shear-affected thermal conductivity is evaluated for a forced-convection laminar pipe flow with a parabolic velocity profile. Utilizing a thermal conductivity model which accounts for the local shear, the overall heat transfer enhancement in the channel flow is determined. It is found that a 65% cross-section saturation with shear-induced enhancement is hard to be reached within the laminar flow region. Thus, the shear enforcements mainly take effect close to the pipe wall.

Wall and interfacial shear stresses in laminar two-phase stratified flow in pipes

Exact solutions for separated two-phase flows are useful as a benchmark for numerical codes and for testing closure relations for simplified 1D Two-Fluid models. In particular, the correct representation of the wall and interfacial shear stresses is essential for the modeling of these flows. In this study, a complete set of exact solutions for laminar stratified two-phase flows in inclined pipes is used to explore the wall and interfacial shear stresses. We examine all possible configurations with concave and convex interfaces, which are related to the contact angle of the phases with the pipe surface. A closed-form analytical expression for the average interfacial shear stress was obtained for all cases of stratified two-phase flow. The limiting behavior of the local shear stresses at the triple-point (TP) region, where the interface meets the pipe wall, is determined by residue calculus. It is shown that the shear stresses behavior upon approaching the TP is determined by the fluid's viscosity ratio and the contact angle. The combinations of those parameters that result in convergence or divergence of the shear stresses at the TP are identified. The usefulness of the analytical expressions obtained for correctly predicting the shear stresses variation upon approaching the TP is demonstrated and discussed.

Rheological Characterization of a Concentrated Phosphate Slurry

Phosphate ore slurry is a suspension of insoluble particles of phosphate rock, the primary raw material for fertilizer and phosphoric acid, in a continuous phase of water. This suspension has a non-Newtonian flow behavior and exhibits yield stress as the shear rate tends toward zero. The suspended particles in the present study were assumed to be noncolloidal. Various grades and phosphate ore concentrations were chosen for this rheological investigation. We created some experimental protocols to determine the main characteristics of these complex fluids and established relevant rheological models with a view to simulate the numerical flow in a cylindrical pipeline. Rheograms of these slurries were obtained using a rotational rheometer and were accurately modeled with commonly used yield-pseudoplastic models. The results show that the concentration of solids in a solid–liquid mixture could be increased while maintaining a desired apparent viscosity. Finally, the design equations for the laminar pipe flow of yield pseudoplastics were investigated to highlight the role of rheological studies in this context.

Analytical solutions for the incompressible laminar pipe flow rapidly subjected to the arbitrary change in the flow rate

A one-dimensional mathematical model is developed for an unsteady incompressible laminar flow in a circular pipe subjected to a rapid change in the flow rate from an initial flow with flow rate, Qi, to a final flow with flow rate, Qf, in a step-like fashion at an arbitrary time, tc. The change in the flow rate may either be an increment, Qf > Qi, or a decrement, Qf < Qi. The change time, tc, may either belong to the initial flow remaining in a temporally developing state or temporally developed state. The developed model is solved using the Laplace transform method to deduce generalized analytical expressions for the flow characteristics, viz., velocity, pressure gradient, wall shear stress, and skin friction factor, CfRe, where Re is Reynolds number based on the cross-sectional area-averaged velocity and pipe radius. Exact solutions for λa=Qi/Qf=0 and λd=Qf/Qi=0 with tc≥tsi are available in the literature and the present generalized analytical solutions fill the remaining range of parameters, 0<λa<1 and 0<λd<1 with 0<tc<tsi and tc≥tsi, where tsi is the time at which the initial flow reaches the temporally developed state. Exact solutions for canonical pipe flow problems reported in the literature are deduced as subsets of the derived generalized solutions. The parametric study reveals the effects of varying λa or λd and tc on the quantities of practical importance, viz., τs and CfRe, where τs is the time required for the final flow to reach the temporally developed state.

Laminar Pipe Flow with Mixed Convection under the Influence of Magnetic Field.

Magnetic influence on ferronanofluid flow is gaining increasing interest from not only the scientific community but also industry. The aim of this study is the examination of the potentials of magnetic forces to control heat transfer. Experiments are conducted to investigate the interaction between four different configurations of permanent magnets and laminar pipe flow with mixed convection. For that purpose a pipe flow test rig is operated with a water-magnetite ferronanofluid. The Reynolds number is varied over one order of magnitude (120–1200). To characterise this suspension, density, solid content, viscosity, thermal conductivity, and specific heat capacity are measured. It is found that, depending on the positioning of the magnet(s) and the Reynolds number, heat transfer is either increased or decreased. The experiments indicate that this is a local effect. After relaxation lengths ranging between 2 and 3.5 lengths of a magnet, all changes disappeared. The conclusion from these findings is that magnetic forces are rather a tool to control heat transfer locally than to enhance the overall heat transfer of heat exchangers or the like. Magnetically caused disturbances decay due to viscous dissipation and the flow approaches the basic state again.

Forced Convective Laminar flow In Elliptic Pipes of Different Aspect Ratios.(Dept.M)

The present analysis investigates non-Darcy forced convective heat transfer in a cylindrical pipe filled with spherical beads saturated with non-Newtonian drag reducing fluid. The cylindrical pipe is subjected to either a uniform heat flux (UHF) or a constant wall temperature (CWT). In modeling the flow, both the energy equation and a modified momentum (Darcy-Forschheimer-Brinkman) equation are used , in which the variable porosity, flow inertia, Brinkman viscous friction (non-Darcian effects) besides the elongational viscosity of drag reducing fluids are taken into consideration and the finite difference technique is used. The results are obtained for a non-Newtonian drag parameter range of 0≤up≤5000, and nondimensional pressure gradient B up to 108. The results show that the non-Newtonian character of drag reducing fluids have a significant influence on the entrance length, beat transfer characteristics and the temperature profiles. Important results documenting and analyzing the behavior of the entrance length and the heat characteristics and its dependence on the non-Newtonian drag parameter are also reported. To examine the adequacy of the present heat transfer model. The governing equations were solved under conditions corresponding to those in Poulikakos and Renken [20]. The comparison of the calculated Nuf with that of Poulikakos and Renken[20]for d=3 and 5mm,up=0.0.05≤D≤0.15 and 104≤B≤106 shows good agreement and validates the presented heat transfer model.

Do extreme events trigger turbulence decay? – a numerical study of turbulence decay time in pipe flows

Abstract

The influence of cell elastic modulus on inertial positions in Poiseuille microflows

Microchannels are used as a transportation highway for suspended cells both in vivo and ex vivo. Lymphatic and cardiovascular systems transfer suspended cells through microchannels within the body, and microfluidic techniques such as lab-on-a-chip devices, flow cytometry, and CAR T-cell therapy utilize microchannels of similar sizes to analyze or separate suspended cells ex vivo. Understanding the forces that cells are subject to while traveling through these channels are important because certain applications exploit these cell properties for cell separation. This study investigated the influence that cytoskeletal impairment has on the inertial positions of circulating cells in laminar pipe flow. Two representative cancer cell lines were treated using cytochalasin D, and their inertial positions were investigated using particle streak imaging and compared between benign and metastatic cell lines. This resulted in a shift in inertial positions between benign and metastatic as well as treated and untreated cells. To determine and quantify the physical changes in the cells that resulted in this migration, staining and nanoindentation techniques were then used to determine the cells’ size, circularity, and elastic modulus. It was found that the cells’ exposure to cytochalasin D resulted in decreased elastic moduli of cells, with benign and metastatic cells showing decreases of 135 ± 91 and 130 ± 60 Pa, respectively, with no change in either size or shape. This caused benign, stiffer cancer cells to be more evenly distributed across the channel width than metastatic, deformable cancer cells; additionally, a decrease in the elastic moduli of both cell lines resulted in increased migration toward the channel center. These results indicate that the elastic modulus may play more of a part in the inertial migration of such cells than previously thought.