Laminar Pipe Flow Research Articles

Transient conjugated heat transfer in thermally developing laminar flow in thick walled pipes and minipipes with time periodically varying wall temperature boundary condition

Transient conjugated heat transfer for thermally developing laminar flow in thick walled pipes is analyzed involving two-dimensional wall and axial fluid conduction. A two-regional, initially isothermal pipe is considered and the problem is handled for hydrodynamically developed flow with periodically time-varying outer wall temperature in the downstream region. The problem is solved numerically by a finite-difference method and a parametric study is done to analyse the effects of four defining parameters namely, wall thickness ratio, wall-to-fluid conductivity ratio, wall-to-fluid thermal diffusivity ratio, the Peclet number and also the effect of angular frequency. Considerable amount of heat is transferred through the upstream region due to both wall and fluid axial conduction. Heat transfer characteristics change periodically in time similar to the periodic change in the outer wall temperature. The results are found to be affected by the parameter values and by the angular frequency.

Heat transfer of pulsating laminar flow in pipes with wall thermal inertia

The effects of wall thermal inertia on heat transfer of pulsating laminar flow with constant power density within the pipe wall are investigated theoretically. The energy equation of the fully developed flow and heat transfer is solved by separation of variables and Green's function. The effects of the pulsation amplitude and frequency, the Prandtl number and the wall heat capacity on heat transfer features characterized by temperature, heat flux and Nusselt number are analyzed. The results show that the oscillation of wall heat flux increases along with the wall thermal inertia, while the oscillation of temperature and Nusselt number is suppressed by the wall thermal inertia. The influence of pulsation on the average Nusselt number is also obtained. The pulsating laminar flow can reduce the average Nusselt number. The Nusselt number reduction of pipe flow are a little more remarkable than that of flow between parallel plates, which is mainly caused by differences in hydraulic and thermal performances of the channels.

On scaling pipe flows with sinusoidal transversely corrugated walls: analysis of data from the laminar to the low-Reynolds-number turbulent regime

Direct numerical simulation was used to study laminar and turbulent flows in circular pipes with smoothly corrugated walls. The corrugation wavelength was kept constant at$0.419D$, where$D$is the mean diameter of the wavy-wall pipe and the corrugation height was varied from zero to$0.08D$. Flow rates were varied in steps between low values that generate laminar flow and higher values where the flow is in the post-transitional turbulent regime. Simulations in the turbulent regime were also carried out at a constant Reynolds number,$\mathit{Re}_{{\it\tau}}=314$, for all corrugation heights. It was found that even in the laminar regime, larger-amplitude corrugations produce flow separation. This leads to the proportion of pressure drop attributable to pressure drag being approximately 50 %, and rising to approximately 85 % in transitional rough-wall flow. The near-wall structure of turbulent flow is seen to be heavily influenced by the effects of flow separation and reattachment. Farther from the wall, the statistical profiles examined exhibit behaviours characteristic of smooth-wall flows or distributed roughness rough-wall flows. These observations support Townsend’s wall-similarity hypothesis. The organized nature of the present roughness allows the mean pressure drop to be written as a function of the corrugation height. When this is exploited in an analysis of the mean dynamical equation, the scaling problem is explicitly revealed to result from the combined influences of roughness and Reynolds number. The present results support the recent analysis and observations of Mehdiet al.(J. Fluid Mech., vol. 731, 2013, pp. 682–712), indicating that the length scale given by the distance from the wall at which the mean viscous force loses leading order is important to describing these combined influences, as well as providing a dynamically self-consistent connection to the scaling structure of smooth-wall pipe flow.

The Generalized Lévèque Equation and its application to circular pipe flow

This paper focuses on the application of the Generalized Lévèque Equation (GLE) to circular pipe flow with hydrodynamic and thermal developing flow describing the analogy between heat and momentum transfer. As shown theoretically by other authors, this analogy should be applicable to laminar and turbulent developing flow, in which the hydrodynamic exceeds the thermal boundary layer, i.e. for high Prandtl numbers. The question is, whether this fact can be proven experimentally, and above which Prandtl number is this applicable to a hydrodynamic and thermal developing circular pipe flow. Thus, this paper presents results of an experimental investigation on pressure drop and heat transfer for laminar, turbulent and transition flows in a circular pipe to check the applicability of the GLE for a wide range of Prandtl numbers. Experimental data for heat transfer coefficients are compared to heat transfer coefficients calculated from pressure drop data with the GLE. Reynolds numbers range between 500<Re<15000 and Prandtl numbers between 7<Pr<40. The test fluid is a water–glycol mixture with a mass fraction of water of xm=0.477. The results show that the GLE is applicable to hydrodynamic and thermal developing laminar and turbulent flow in a circular pipe for Pr>30. It is also shown that as soon as the hydrodynamic boundary layer thickness is triple the thermal one, the analogy between momentum and heat transfer according to the GLE is suitable for laminar circular pipe flow.

Simulation of laminar flow through eccentric annuli using isogeometric variational multiscale method

We present an application of the Residual-based variational multiscale (RBVMS) methodology to the computation of laminar eccentric annular pipe flow with eccentricities of 0.5 and 1. Isogeometric analysis is utilized for higher order approximation of the geometry and solution using Non-uniform rational B-splines (NURBS) functions. The ability of NURBS exactly representing curved circular geometries makes NURBS-based isogeometric analysis attractive for the application to the flow through the eccentric annuli. By using the exact representation of circular boundary, the limiting case of the eccentricity, i.e. the inner circular wall actually touches the outer circular wall, is successfully demonstrated.

Heat transfer enhancement by external magnetic field for paramagnetic laminar pipe flow

Effect of an external magnetic field is numerically investigated on heat transfer of a horizontal constant laminar pipe flow of a paramagnetic fluid. A single current-carrying coil is presumed for the magnet and the pipe is heated at a constant heat flux. It is found that the effect on the heat and fluid flow strongly depends on the coil location, resulting in local heat transfer enhancement/suppression. Only when the coil is placed at threshold of the heating zone, the enhancement is achieved. This is due to the magnetothermal force which attracts cold fluid toward the coil, and the force induces boundary layer thinning behind the coil. In the case, the heat transfer enhancement at the threshold remains approximately 10% at Reynolds number of 10 in no-gravitational field, although the enhancement decreases with the increase of the Reynolds number under constant magnetic induction. Computations in the presence of the gravity reveals that the magnetothermal force becomes effective especially at upper region. It is found that the effectiveness is in a same order as cases without gravity in slow flow field. The contribution of the magnetic field merges to the no-gravity case in higher flow field.

Fully developed laminar flow and heat transfer in serpentine pipes

A serpentine pipe is a sequence of parallel straight pipe segments connected by U-bends. Its geometry is fully characterized by pipe radius, a, bend curvature radius, c and length of the straight segments, l. The repeated curvature inversion forces the recirculation (secondary flow) pattern to switch between two specular configurations, which may enhance mixing and heat or mass transfer with respect to a constant-curvature pipe at the cost of an increase in pressure drop.In the present work, fully developed laminar flow and heat transfer in serpentine pipes were investigated by numerical simulation. The curvature δ = a/c was made to vary between 0.1 and 0.5 while the parameter γ = l/c was made to vary between 0 and 8; for each geometry, the friction velocity Reynolds number Reτ = uτa/ν was made to vary between a very low value (5), yielding almost creeping flow, and the highest value Reτ∗ still yielding steady laminar flow (∼35–40 in most cases). For Reτ≤Reτ∗ results were obtained for values of the Prandtl number between 1 and 100; predicted values of the friction coefficient and of the Nusselt number were compared with experimental results and correlations proposed in the literature. For Reτ>Reτ∗ convergence to steady flow was not achieved and an oscillatory behaviour of the solution was observed, indicating a transition to unsteady regimes which deserves a more focused study.

Dispersion and deposition of ellipsoidal particles in a fully developed laminar pipe flow using non-creeping formulations for hydrodynamic forces and torques

In this study, dispersion and deposition of ellipsoidal particles in fully developed laminar pipe flows were analyzed using new correlations for hydrodynamic forces and torques for non-creeping flow conditions. In these simulations, flow Reynolds numbers up to 400 were considered and the fiber Reynolds numbers in the range of 0.01–6 were studied. The deposition efficiency of ellipsoidal fibers of different sizes and aspect ratios in laminar pipe flows were simulated for various flow and particle Reynolds numbers. A new empirical model for estimating fiber deposition efficiency for finite particle Reynolds numbers was developed. The simulation results were compared with earlier theoretical and numerical studies, as well as the new empirical equation, and good agreement was found. Particular attention was given to the effect of fiber size and aspect ratio on dispersion and deposition of particles under various flow conditions for fully developed laminar pipe flow.

Enhanced mixing by optimized streamwise and angular positioning of longitudinal vorticity

Streamwise vortices can be readily generated to enhance the mass and momentum transfer in continuous static mixers. The topology of these vortices is related to the shape and dimensions of the vortex generator (VG). It is essential to design the VG in such a way that the mass and momentum transfer are obtained for relatively small power dissipation. In the present paper, a streamwise and angular optimization study is performed for the passive scalar mixing enhancement downstream from rectangular wings inserted in a laminar circular pipe flow. The rectangular wing generates streamwise vortices which size is of the same order of the pipe radius. The optimal distance between two successive VGs is determined by analyzing the streamwise intensity of segregation and the pressure drop. The angular positioning of the vortices is also determined via local analysis of the scalar intensity of segregation. Such a study may be applied for other configurations of VGs where streamwise vorticity is used to enhance the mixing process in circular pipe flows.

Pressure drop predictions for laminar pipe flow of carreau and modified power law fluids

Fluids used in many chemical and petroleum industrial processes are often described as complex systems that exhibit non‐Newtonian character. Due to the complex nature of non‐Newtonian fluids, universally accepted flow equations are unavailable. This paper uses the Carreau and modified power law–Cross (MPL‐Cross) rheological models to derive pressure drop–flow rate relationships under laminar flow condition. The aim is to develop simple but effective equations that enable accurate estimation of pressure drop for flow in any pipe size using viscometric data. The new relationships compare favourably with experimental data. Furthermore, new Reynolds number and generalized Reynolds number expressions have been defined.

Neuro-Fuzzy GMDH Approach to Predict Longitudinal Dispersion in Water Networks

Longitudinal dispersion in pipelines leads to changes in the characteristics of contaminants. It is critical to quantify these changes because the contaminants travel through water networks or through chemical reactors. The essential characteristics of longitudinal dispersion in pipes can be described by the longitudinal dispersion coefficient. This paper presents the application of the adaptive Neuro fuzzy group method of data handling to develop new empirical formulae for the prediction of longitudinal dispersion coefficients in pipe flow using 233 experimental case studies of dispersion coefficient with a Re range of 900 to 500,000 spanning laminar, transitional and turbulent pipe flow. The NF-GMDH network was improved using particle swarm optimization based evolutionary algorithm. The group method data handling is used to develop empirical relations between the longitudinal dispersion coefficient and various control variables, including the Reynolds number, the average velocity, the pipe friction coefficient and the pipe diameter. GMDH holds advantage in the case of small data samples due to the optimal choice of the model complexity with automatic adaptation to an unknown level of the data uncertainties. Sensitivity analysis is performed on the developed model and the weight and importance of each control variable is presented. The results indicate that the proposed relations are simpler than previous numerical solutions and can effectively evaluate the longitudinal dispersion coefficients in pipe flow.

Studying nanoparticle distribution in nanofluids considering the effective factors on particle migration and determination of phenomenological constants by Eulerian–Lagrangian simulation

In this study, concentration distribution was obtained for nanofluid laminar flow in circular pipe. The effects of viscosity gradient, shear rate and Brownian diffusion on particle migration were considered. One needs to determine the phenomenological constants in order to find the diffusion fluxes. The two-phase Euler–Lagrange method was used to find these constants, where gravity, drag, Saffman’s lift, Brownian and thermophoretic forces were considered. The constants are not much dependent on the concentration, but they change significantly by varying Peclet number. They increase with increasing Peclet number, which shows that at higher Peclet numbers, the effects of shear rate and viscosity gradient are intensified on particle migration. Meanwhile, by raising Peclet number, the role of shear rate becomes more pronounced in comparison with the viscosity gradient. At lower Peclet numbers with intensified effect of the Brownian diffusion, a more uniform concentration distribution was achieved. Moreover, the particles enlargement considerably intensifies the non-uniformity in concentration distribution. Furthermore, particle migration causes non-uniformity in the properties distribution and consequently reduces the thermal conductivity and viscosity adjacent to the wall due to lower concentration there. Thus, smaller pressure drop and heat transfer coefficient were obtained in comparison with the case of applying uniform properties.

Transient conjugated heat transfer for simultaneously developing laminar flow in thick walled pipes and minipipes

Transient conjugated heat transfer in simultaneously developing laminar pipe flow is analyzed involving two-dimensional wall and fluid axial conduction. The problem is solved numerically by a finite difference method in a thick walled semi-infinite pipe which is initially isothermal, with hydrodynamically and thermally developing flow and with a sudden change in the ambient temperature. A parametric study is done to analyze the effects of six parameters, namely, wall thickness ratio, wall-to-fluid thermal conductivity ratio, wall-to-fluid thermal diffusivity ratio, the Peclet number, the Biot number and the Prandtl number. Heat transfer characteristics are seen to be highly affected by the parameter values.

A polynomial expansion of axial velocity profiles to solve transient laminar flow in elastic pipe

A polynomial expansion of axial velocity profiles to solve transient laminar flow in elastic pipe

Numerical study of a particle separation method based on the Segré‐Silberberg effect

AbstractParticles that are placed in a laminar pipe flow rotate and migrate transversally to a radial equilibrium position. This so called Segré‐Silberberg effect is used in a new method for size separation of particles. The particles to be separated are placed in a pipe flow and subsequently enter an expansion chamber, where the flow is split and the particles are divided into two fractions. This paper reports the results of two‐dimensional Euler‐Lagrange simulations of the motion of neutrally‐buoyant particles inside the expansion chamber. The simulation results agree well with experimental data on the separation and show that the Saffman force has a significant impact onto the particle trajectories. (© 2014 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Friction factor and heat transfer of nanofluids containing cylindrical nanoparticles in laminar pipe flow

Numerical simulations of polyalphaolefins-Al2O3 nanofluids containing cylindrical nanoparticles in a laminar pipe flow are performed by solving the Navier-Stokes equation with term of cylindrical nanoparticles, the general dynamic equation for cylindrical nanoparticles, and equation for nanoparticle orientation. The distributions of particle number and volume concentration, the friction factor, and heat transfer are obtained and analyzed. The results show that distributions of nanoparticle number and volume concentration are non-uniform across the section, with larger and smaller values in the region near the pipe center and near the wall, respectively. The non-uniformity becomes significant with the increase in the axial distance from the inlet. The friction factor decreases with increasing Reynolds number. The relationships between the friction factor and the nanoparticle volume concentration as well as particle aspect ratio are dependent on the Reynolds number. The Nusselt number of nanofluids, directly proportional to the Reynolds number, particle volume concentration, and particle aspect ratio, is higher near the pipe entrance than at the downstream locations. The rate of increase in Nusselt number at lower particle volume concentration is more than that at higher concentration. Finally, the expressions of friction factor and Nusselt number as a function of particle volume concentration, particle aspect ratio, and Reynolds number are derived based on the numerical data.

Prognosis the Erosion-Corrosion Rates for Slurry Seawater Flow in Steel Pipeline Using Neural System

The work of this paper proposes a new technique for estimating and predicting erosion corrosion rate for laminar and turbulent flow in pipes. The technique depends on the neural networks Artificial Intelligent algorithms. Based on experimental results, which was applied to A 106 carbon-steel pipes, the networks are trained. Four velocities (Reynolds numbers) are used for laminar and four for turbulent regimes. The experiments also used seawater containment three different concentrations of sand. For each experiment the iron losses were measured six times in three hours’ time interval. The proposed estimating/predicting system managed to find values between the readings as well as predict the behavior of the erosion corrosion rate for extra three hours. The estimated/predicted results have been developed to find the transient zone between the Laminar and Turbulent flow regimes and investigating its effects on the erosion-corrosion behavior.

A solution to the turbulent Graetz problem by matched asymptotic expansions for an axially rotating pipe subjected to external convection

Abstract Heat transfer in an axially rotating pipe subjected to turbulent internal flow is strongly suppressed by tube rotation. For increasing rotational speeds of the pipe wall, the flow starts to laminarize and eventually the axial velocity profile of the hydrodynamically fully developed flow approaches the one of a laminar pipe flow. The solution for the heat transfer of a fluid with a hydrodynamically fully developed velocity profile in an axially rotating pipe subjected to external convection leads to a Sturm–Liouville eigenvalue problem. Asymptotic expressions are shown for the eigenvalues and constants based on a matched asymptotic expansion approach. These values are compared with numerical calculations and good agreement is found.

Inertial focusing in microfluidics.

When Segré and Silberberg in 1961 witnessed particles in a laminar pipe flow congregating at an annulus in the pipe, scientists were perplexed and spent decades learning why such behavior occurred, finally understanding that it was caused by previously unknown forces on particles in an inertial flow. The advent of microfluidics opened a new realm of possibilities for inertial focusing in the processing of biological fluids and cellular suspensions and created a field that is now rapidly expanding. Over the past five years, inertial focusing has enabled high-throughput, simple, and precise manipulation of bodily fluids for a myriad of applications in point-of-care and clinical diagnostics. This review describes the theoretical developments that have made the field of inertial focusing what it is today and presents the key applications that will make inertial focusing a mainstream technology in the future.

Mass Transfer Effects on Viscous Flow in an Expanding or Contracting Porous Pipe with Chemical Reaction

In this paper, an analysis is performed to study the effects of mass transfer and chemical reaction on laminar flow in a porous pipe with an expanding or contracting wall. The pipe wall expands or contracts uniformly at a time dependent rate. The governing equations are reduced to ordinary differential equations by using a similarity transformation. An analytical approach, namely, the homotopy analysis method is applied in order to obtain the solutions of the ordinary differential equations. The convergence of the obtained series solutions is analyzed. The effects of various parameters on flow variables have been discussed. It is noticed that the wall expansion ratio significantly increases the axial velocity and the concentration for the case of wall expansion and it decreases the axial velocity for the case of wall contraction irrespective of injection or suction. Further, it is observed that the concentration (ϕ) decreases for a destructive chemical reaction () and increases for a generative chemical reaction (). The concentration reduces as Schmidt number () increases. The corresponding problem related to the porous pipe flow with a stationary wall can be recovered from the present analysis in the limiting case where the wall expansion ratio approaches to zero (i.e., ).