Transitional Pipe Research Articles

Research on the Jetting Visualization Process and Hydrokinetics of Ink Droplets in Inkjet Imaging System by CAE Technology

Inkjet imaging technology is a typical replication technology, which uses the nozzle to eject the ink droplets on the substrates, and generates the needed color and density through the deposition of the slight droplets on the substrates, and makes the ink droplets form the stable image. In the inkjet imaging system, whether supplying uniform velocity ink droplets from nozzles is the key factor for forming uniform size ink droplets, it is related to the final imaging effects. This paper studied on the jetting visualization process and hydrokinetics of ink droplets based on the CAE (Computer Aided Engineering) technology and the advanced testing equipment. According to the analysis of turbulent flow characteristics and the other jetting flow dynamics factors of the ink droplets, a new type of equipment for inkjet was designed in this paper, including the structure of the transition pipe and nozzles. The shape of the equipment is rectangular, where the flow section is gradually tapered. The experiments and simulations showed that this new inkjet equipment could make the ink droplets distribute under the equal pressure and uniform velocity on the cross direction, and it directly reduced the dot gain phenomenon in the substrates, so it greatly improved the imaging effects in the inkjet imaging system.

Gene Expression Models for the Prediction of Longitudinal Dispersion Coefficients in Transitional and Turbulent Pipe Flow

AbstractLongitudinal 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 evolutionary gene expression programming (GEP) to develop new empirical formulas for the prediction of longitudinal dispersion coefficients in pipe flow using 220 experimental case studies of the dispersion coefficient with a R range of 2,000–500,000 spanning transitional and turbulent pipe flow. Gene expression programming 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. Four GEP models are developed, and the weight and importance of each contro...

Lagrangian approach to laminar–turbulent interfaces in transitional pipe flow

AbstractTransition in shear flows is characterized by localized turbulent regions embedded in the surrounding laminar flow. These so-called turbulent spots or puffs are observed in a variety of shear flows and in certain Reynolds-number regimes, and they are advected by the flow while keeping their characteristic length. We show here for the case of pipe flow that this seemingly passive advection of turbulent puffs involves continuous entrainment and relaminarization of laminar and turbulent fluid across strongly convoluted interfaces. Surprisingly, interface areas are almost two orders of magnitude larger than the pipe cross-section, while local entrainment velocities are much smaller than the mean speed. Even though these velocities were shown to be small and proportional to the Kolmogorov velocity scale (in agreement with a prediction by Corrsin) in a flow without mean shear before, we find that, in pipe flow, local entrainment velocities are about an order of magnitude smaller than this scale. The Lagrangian method used to study the dynamics of the laminar–turbulent interfaces allows accurate determination of the leading and trailing edge speeds. However, to resolve the highly complex interface dynamics requires much higher numerical resolutions than for ordinary turbulent flows. This method also reveals that the volume flux across the leading edge has the same radial dependence but the opposite sign as that across the trailing edge, and it is this symmetry that is responsible for the puff shape remaining constant.

Roughness effects of commercial steel pipe in turbulent flow: universal scaling

The mean turbulent flow over a transitional rough commercial steel pipe is considered in terms of alternate inner roughness variables. The matching of inner layer and outer layer in the overlap region leads to the universal log laws for velocity profile and friction factor, explicitly independent of surface roughness of all kinds. The roughness function, for commercial steel pipe differs from inflectional (sand grain) roughness. The traditional wall law and friction factor depends on type of surface roughness.

An experimental study of transitional pulsatile pipe flow

The transitional regime of a sinusoidal pulsatile flow in a straight, rigid pipe is investigated using particle image velocimetry. The main aim is to investigate how the critical Reynolds number is affected by different pulsatile conditions, expressed as the Womersley number and the oscillatory Reynolds number. The transition occurs in the region of Re = 2250-3000 and is characterized by an increasing number of isolated turbulence structures. Based on velocity fields and flow visualizations, these structures can be identified as puffs, similar to those observed in steady flow transition. Measurements at different Womersley numbers yield similar transition behavior, indicating that pulsatile effects do not play a role in the regime that is investigated. Variations of the oscillatory Reynolds number also appear to have little effect, so that the transition here seems to be determined only by the mean Reynolds number. For larger mean Reynolds numbers, a second regime is observed: here, the flow remains turbulent throughout the cycle. The turbulence intensity varies during the cycle, but has a phase shift with respect to the mean flow component. This is caused by a growth of kinetic energy during the decelerating part and a decay during the accelerating part of the cycle. Flow visualization experiments reveal that the flow develops localized turbulence at several random axial positions. The structures quickly grow to fill the entire pipe in the decelerating phase and (partially) decay during the accelerating phase.

Modeling the transition to turbulence in shear flows

One-dimensional models are presented for transitional shear flows. The models have two variables corresponding to turbulence intensity and mean shear. These variables evolve according to simple equations based on known properties of transitional turbulence. The first model considered is for pipe flow. A previous study modeled turbulence using a chaotic tent map. In the present work turbulence is modeled instead as multiplicative noise. This model captures the character of transitional pipe flow and contains metastable puffs, puff splitting, and slugs. These ideas are extended to a limited model of plane Couette flow.

Turbulent flow in a machine honed rough pipe for large Reynolds numbers: General roughness scaling laws

An alternate inner wall variable, for flow over a transitional rough pipe surface, is defined as the ratio of normal coordinate measured above the mean roughness level to the wall roughness scale. The Reynolds equations for mean turbulent flow in a transitional rough pipe, in two layers (inner and outer) are considered. The predictions of the mean velocity and friction factor in fully developed turbulent flow in a rough pipe flow, presented here, covers all types of roughness. The data for a particular case of the machine honed Princeton superpipe roughness, analogous to inflectional type roughness of Nikuradse, is presented, as two expressions using our roughness scale. The velocity profile and friction factor, on a transitional rough wall, are shown to be governed by the new log laws, which are explicitly independent of the transitional wall roughness. Further, the inflectional roughness has also been connected with geometric roughness parameters; like, arithmetic mean roughness, mean peak to valley heights roughness, root mean square (rms), roughness based on texture measure; and the friction factor implicit and approximate explicit formulas have also been proposed. In entire transition region between fully smooth and fully rough wall, monotonic roughness of Colebrook (Moody Chart) over estimaton the friction factor when compared with present inlectional roughness.

Simplifying the complexity of pipe flow

Transitional pipe flow is modeled as a one-dimensional excitable and bistable medium. Models are presented in two variables, turbulence intensity and mean shear, that evolve according to established properties of transitional turbulence. A continuous model captures the essence of the puff-slug transition as a change from excitability to bistability. A discrete model, which additionally incorporates turbulence locally as a chaotic repeller, reproduces almost all large-scale features of transitional pipe flow. In particular, it captures metastable localized puffs, puff splitting, slugs, localized edge states, a continuous transition to sustained turbulence via spatiotemporal intermittency (directed percolation), and a subsequent increase in turbulence fraction toward uniform, featureless turbulence.

Numerical modelling of unsteady turbulent flow in tubes, including the effects of roughness and large changes in Reynolds number

A method has been developed for predicting unsteady turbulent friction in smooth, transitional, and rough pipe flows. For transitional and rough pipe flows the effective viscosity at the wall is varied depending on Reynolds number and roughness. An approximation has been made for the transition region using a cubic spline for the friction factor between the smooth and rough regions. This turbulence model can be implemented readily in several types of numerical model for pipe flow, including simple lumped parameter models, finite difference/finite element methods, and the method of characteristics. An approximate method for representing changes in turbulence energy is discussed. Using this, the method is suitable for small and large changes in flow, and for short and long time scales, but further validation is needed.

Study on the Uniform Distributed Mechanics of Ink Droplet in Inkjet Printing Equipment

This paper studied on the hydrokinetics and uniform distributed mechanics of supplying ink pressure for the inkjet printing system based on the, and the advanced testing equipment. According to the analysis of theoretical calculation and CFD, we designed a new type of equipment for supplying ink, including the structure of the transition pipe. This supplying ink equipment could make the ink droplets distribute under the equal pressure on the cross direction. The experiments showed that this new supplying ink equipment could make the ink droplets distribute under the equal pressure and uniform velocity on the cross direction, so it greatly improved the imaging effects for the inkjet printing system.

On the numerical study of bubbly flow created by ventilated cavity in vertical pipe

The dispersion of bubbles into a down-liquid flow in a vertical pipe is investigated. At low flow rates, the intended design of a swarm of discrete bubbles is achieved. At high flow rates, a ventilated cavity is nonetheless formed, which is attached close to the gas sparger. Behind this ventilated cavity, three different flow regimes characterize the complex bubbly flow field downstream of the down-liquid flow: vortex region with high void fraction, transitional region and pipe flow region. In this study, a numerical model that solved the entire development of the gas–liquid flow including the extended single-phase liquid region upstream to the wall-jet and recirculating-vortex zones in order to allow a more realistic determination of the boundary conditions of the down-liquid flow was adopted. Coupling with the Eulerian–Eulerian two-fluid model to solve the respective gas and liquid phases, a population balance model was also applied to predict the bubble size distribution in the wake right below the cavity base as well as further downstream in the transitional and fully-developed pipe flow regions. The numerical model was evaluated by comparing the numerical results against the data derived from theoretical, numerical and experimental approaches. Prediction of the Sauter mean bubble diameter distributions by the population balance approach at different axial locations confirmed the dominance of breakage due to the high turbulent intensity below the ventilated cavity which led to the generation of small gas bubbles at high void fraction. Further downstream, the coalescence effect dominated leading to merging of the small bubbles to form bigger bubbles.

Distinct large-scale turbulent-laminar states in transitional pipe flow

When fluid flows through a channel, pipe, or duct, there are two basic forms of motion: smooth laminar motion and complex turbulent motion. The discontinuous transition between these states is a fundamental problem that has been studied for more than 100 yr. What has received far less attention is the large-scale nature of the turbulent flows near transition once they are established. We have carried out extensive numerical computations in pipes of variable lengths up to 125 diameters to investigate the nature of transitional turbulence in pipe flow. We show the existence of three fundamentally different turbulent states separated by two distinct Reynolds numbers. Below Re (1) approximately equal 2,300, turbulence takes the form of familiar equilibrium (or longtime transient) puffs that are spatially localized and keep their size independent of pipe length. At Re (1) the flow makes a striking transition to a spatio-temporally intermittent flow that fills the pipe. Irregular alternation of turbulent and laminar regions is inherent and does not result from random disturbances. The fraction of turbulence increases with Re until Re (2) approximately equal 2,600 where there is a continuous transition to a state of uniform turbulence along the pipe. We relate these observations to directed percolation and argue that Re (1) marks the onset of infinite-lifetime turbulence.

Transition in Localized Pipe Flow Turbulence

Direct numerical simulation of transitional pipe flow is carried out in a long computational domain in order to characterize the dynamics within the saddle region of phase space that separates laminar flow from turbulent intermittency. For Reynolds numbers ranging from Re=1800 to 2800, a shoot and bisection method is used to compute critical trajectories. The chaotic saddle or edge state approached by these trajectories is studied in detail. For Re< or =2000 the edge state and the corresponding intermittent puff are shown to share similar averaged global properties. For Re> or =2200, the puff length grows unboundedly whereas the edge state varies only little with Re. In this regime, transition is shown to proceed in two steps: first the energy grows to produce a localized turbulent patch, which then, during the second stage, spreads out to fill the pipe.

Asymmetry in transitional pipe flow of drag-reducing polymer solutions

New experimental data are presented and discussed for fully developed pipe flow of shear-thinning, viscoelastic polymer solutions in the transitional regime between laminar and turbulent flow. The data confirm that such transitional flows exhibit significant departures from axisymmetry in contrast to the fully developed pipe flow of Newtonian fluids or both laminar and turbulent flows of such drag-reducing liquids. The azimuthal structure of the asymmetry is investigated together with its axial development and also the velocity fluctuation levels. These data do not lead to an explanation for the asymmetry but do suggest that the influence of the flow geometry both upstream and downstream can be ruled out.

Study on the equal pressure distributed hydrokinetics of the supplying ink for continuous inkjet printing system

Supplying uniform pressure ink in continuous inkjet printing system is the key factor for forming uniform and constant speed ink droplets, it is related to the final imaging effects, this research has seldom been reported in these years. This paper studied on the hydrokinetics and uniform distributed mechanics of supplying ink pressure for the continuous inkjet printing system based on the theoretical calculation, CFD (Computational Fluid Dynamics) and the advanced testing equipment. According to the analysis of laminar flow characteristics and the other jetting flow dynamics factors of the ink, a new type of equipment for supplying ink was designed in this paper, including the structure of the transition pipe and nozzle. The shape of the equipment is rectangular, where the flow section is gradually tapered. This supplying ink equipment can make the ink droplets distribute under the equal pressure on the cross direction. This study educed the optimally hydrokinetics parameters for the continuous inkjet printing. The experiments showed that this new supplying ink equipment could make the ink droplets distribute under the equal pressure and uniform velocity on the cross direction, so it greatly improved the imaging effects for the continuous inkjet printing system.

Lifetime statistics in transitional pipe flow

Several experimental and numerical studies have shown that turbulent motions in circular pipe flow near transitional Reynolds numbers may not persist forever, but may decay. We study the properties of these decaying states within direct numerical simulations for Reynolds numbers up to 2200 and in pipes with lengths equal to 5, 9, and 15 times the diameter. We show that the choice of the ensemble of initial conditions affects the short time parts of lifetime distributions, but does not change the characteristic decay rate for long times. Comparing lifetimes for pipes of different length we notice a linear increase in the characteristic lifetime with length, which reproduces the experimental results when extrapolated to 30 diameters, the length of an equilibrium turbulent puff at these Reynolds numbers.

Experimental and theoretical progress in pipe flow transition

There have been many investigations of the stability of Hagen-Poiseuille flow in the 125 years since Osborne Reynolds' famous experiments on the transition to turbulence in a pipe, and yet the pipe problem remains the focus of attention of much research. Here, we discuss recent results from experimental and numerical investigations obtained in this new century. Progress has been made on three fundamental issues: the threshold amplitude of disturbances required to trigger a transition to turbulence from the laminar state; the threshold Reynolds number flow below which a disturbance decays from turbulence to the laminar state, with quantitative agreement between experimental and numerical results; and understanding the relevance of recently discovered families of unstable travelling wave solutions to transitional and turbulent pipe flow.

Recurrence of travelling waves in transitional pipe flow

The recent theoretical discovery of families of unstable travelling-wave solutions in pipe flow at Reynolds numbers lower than the transitional range, naturally raises the question of their relevance to the turbulent transition process. Here, a series of numerical experiments are conducted in which we look for the spatial signature of these travelling waves in transitionary flows. Working within a periodic pipe of 5D (diameters) length, we find that travelling waves with low wall shear stresses (lower branch solutions) are on a surface in phase space which separates initial conditions which uneventfully relaminarize and those which lead to a turbulent evolution. This dividing surface (a separatrix if turbulence is a sustained state) is then minimally the union of the stable manifolds of all these travelling waves. Evidence for recurrent travelling-wave visits is found in both 5D and 10D long periodic pipes, but only for those travelling waves with low-to-intermediate wall shear stress and for less than about 10% of the time in turbulent flow at Re = 2400. Given this, it seems unlikely that the mean turbulent properties such as wall shear stress can be predicted as an expansion solely over the travelling waves in which their individual properties are appropriately weighted. Instead the onus is on isolating further dynamical structures such as periodic orbits and including them in any such expansion.

Statistical analysis of coherent structures in transitional pipe flow

Numerical and experimental studies of transitional pipe flow have shown the prevalence of coherent flow structures that are dominated by downstream vortices. They attract special attention because they contribute predominantly to the increase of the Reynolds stresses in turbulent flow. In the present study we introduce a convenient detector for these coherent states, calculate the fraction of time the structures appear in the flow, and present a Markov model for the transition between the structures. The fraction of states that show vortical structures exceeds 24% for a Reynolds number of about Re=2200 , and it decreases to about 20% for Re=2500 . The Markov model for the transition between these states is in good agreement with the observed fraction of states, and in reasonable agreement with the prediction for their persistence. It provides insight into dominant qualitative changes of the flow when increasing the Reynolds number.

Heat transfer of a non-Newtonian fluid (Carbopol aqueous solution) in transitional pipe flow

An experimental study of the forced convection heat transfer for non-Newtonian fluid flow in a pipe is presented. We focus particularly on the transitional regime. A wall boundary heating condition of heat flux is imposed. The non-Newtonian fluid used is Carbopol (polyacrylic acid) aqueous solutions. Detailed rheology as well as the variation of the rheological parameters with temperature are reported. Newtonian and shear thinning fluids are also tested for comparative purposes. The characterization of the flow and the thermal convection is made via the pressure drop and the wall temperature measurements over a range of Reynolds number from laminar to turbulent regime. Our measurements show that the non-Newtonian character stabilizes the flow, i.e., the critical Reynolds number to transitional flow increases with shear thinning and yield stress. The heat transfer coefficients are given and compared with heat transfer laws for different regime flows. Details when the heat transfer coefficient loses rapidly its local dependence on the Reynolds number are analyzed.