Lengths Of Flows Research Articles

Pipe Inlays to Shorten the Development Lengths of Laminar Pipe Flows: A Numerical Study

Pipe Inlays to Shorten the Development Lengths of Laminar Pipe Flows: A Numerical Study

Entry Length Requirements for Two- and Three-Dimensional Laminar Couette–Poiseuille Flows

In this study, we examine the development length requirements for laminar Couette–Poiseuille flows in a two-dimensional (2D) channel as well as in the three-dimensional (3D) case of flow through a square duct, using a combination of numerical and experimental approaches. The parameter space investigated covers wall to bulk velocity ratios, r, spanning from 0 (purely pressure-driven flow) to 2 (purely wall driven-flow; 4 in the case of a square duct) and a wide range of Reynolds numbers (Re). The results indicate an increase in the development length (L) with r. Consistent with the findings of Durst et al. (2005, “The Development Lengths of Laminar Pipe and Channel Flows,” ASME J. Fluids Eng., 127(6), pp. 1154–1160), L was observed to be of the order of the channel height in the limit as Re→0, irrespective of the condition at the inlet. This, however, changes at high Reynolds numbers, with L increasing linearly with Re. In all the cases considered, a uniform velocity profile at the inlet was found to result in longer entry lengths than in a flow developing from a parabolic inlet profile. We show that this inlet effect becomes less important as the limit of purely wall-driven flow is approached. Finally, we develop correlations for predicting L in these flows and, for the first time, also present laser Doppler velocimetry (LDV) measurements of the developing as well as fully-developed velocity profiles, and observe good agreement between experiment, analytical solution, and numerical simulation results in the 3D case.

Numerical Study on Entrance Length in Thermal Counterflow of Superfluid $$^4$$He

Three-dimensional numerical simulations in a square duct were conducted to investigate entrance lengths of normal fluid and superfluid flows in a thermal counterflow of superfluid $^4$He. The two fluids were coarse-grained by using the Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model and were coupled through mutual friction. We solved the HVBK equations by parameterizing the coefficient of the mutual friction to consider the vortex line density. A uniform mutual friction parameter was assumed in the streamwise direction. Our simulation showed that the entrance length of the normal fluid from a hot end becomes shorter than that of a single normal fluid due to the mutual friction with the parabolically developed superfluid flow near the hot end. As the mutual friction increases, the entrance length decreases. Same as that, the entrance length of the superfluid from a cold end is affected by the strength of the mutual friction due to the parabolically developed normal fluid flow near the cold end. Aside from the entrance effect, the realized condition of a tail-flattened flow is discussed by parameterizing the superfluid turbulent eddy viscosity and the mutual friction.

Entry Lengths of Laminar Pipe and Channel Flows

Numerical simulations of laminar pipe and channel flows were carried out: (i) to understand the effect of inlet conditions, viz., flat inlet and streamtube inlet, on entry lengths, and (ii) to investigate the flow development in radial/transverse locations. Results show that hydrodynamic entry lengths from the streamtube inlet simulations are significantly lower compared to the entry lengths from the flat inlet simulations for low Reynolds numbers. Moreover, results from the current study (Newtonian flow with no-slip) as well as the results from the literature (non-Newtonian flow with no-slip) showed that for many flow situations, the slowest development of axial velocity in the transverse location happens to be very near to the wall. For the above cases, the existing entry length criteria (centerline as well as global entry length) are not appropriate to define the entry length. We have proposed a new entry length criterion based on the displacement thickness which is an integral measure of the velocity profile. A new entry length correlation using the displacement thickness criterion is proposed for Newtonian flows in pipe and channel based on simulations with the streamtube inlet condition.

Modeling the October 2005 lahars at Panabaj (Guatemala)

An extreme rainfall event in October of 2005 triggered two deadly lahars on the flanks of Toliman volcano (Guatemala) that caused many fatalities in the village of Panabaj. We mapped the deposits of these lahars, then developed computer simulations of the lahars using the geologic data and compared simulated area inundated by the flows to mapped area inundated. Computer simulation of the two lahars was dramatically improved after calibration with geological data. Specifically, detailed field measurements of flow inundation area, flow thickness, flow direction, and velocity estimates, collected after lahar emplacement, were used to calibrate the rheological input parameters for the models, including deposit volume, yield strength, sediment and water concentrations, and Manning roughness coefficients. Simulations of the two lahars, with volumes of 240,200 ± 55,400 and 126,000 ± 29,000 m3, using the FLO-2D computer program produced models of lahar runout within 3% of measured runouts and produced reasonable estimates of flow thickness and velocity along the lengths of the simulated flows. We compare areas inundated using the Jaccard fit, model sensitivity, and model precision metrics, all related to Bayes’ theorem. These metrics show that false negatives (areas inundated by the observed lahar where not simulated) and false positives (areas not inundated by the observed lahar where inundation was simulated) are reduced using a model calibrated by rheology. The metrics offer a procedure for tuning model performance that will enhance model accuracy and make numerical models a more robust tool for natural hazard reduction.

Surface wettability effect on fluid transport in nanoscale slit pores

The surface wettability effect on fluid transport in nanoscale slit pores is quantitatively accessed by using non‐equilibrium molecular dynamics (NEMD) simulation incorporating with density functional theory (DFT). In particular, the slip lengths of benzene steady flows under various wetting conditions are computed with NEMD simulations and a quasi‐general expression is given, while the structural properties are investigated with DFT. By taking into account the inhomogeneity of fluid density inside pore, we find that the conventional flux enhancement rate is associated with both the molecule slipping and geometrical confinement, and it becomes drastically high in solvophobic pores especially when the pore size is of several fluid diameters. In good agreement with experimental results, we further show that the wettability effect competes with pore size effect in determining the flux after pore inner surface modification, and a high flux can be achieved when the deposited layer is solvophobic yet thin. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1704–1714, 2017

Flow development during low Reynolds number mixed convection

An experimental study was conducted to investigate the flow development inside a horizontal channel subjected to bottom wall heating at low Reynolds numbers. Velocity fields were measured in the vertical mid-plane at five locations along the channel heated section using Particle Image Velocimetry (PIV) technique. The developing lengths of mean and turbulent flows as well as the temperature field showed a strong dependency on the flow rate and the wall temperature. The developing length was found to increase with the increase of bottom wall temperature and/or the decrease of flow rate (i.e. increasing Gr/Re2). A strong correlation between the hydrodynamic and thermal development in the heated section was also observed. The Proper Orthogonal Decomposition (POD) was performed on the turbulent velocity fields. The results revealed the presence of local convective cells near the heated wall along the channel length. The results also showed an influence of flow rate on the size of the convective cell, however, no temperature dependency was observed.

Computation of Turbulent Flows in Natural Gas Pipes with Different Rectifiers

With the development of natural gas industry, improving the accuracy of the flowmeter systems is becoming the common concerned problem both corporations and customers. Many experiments demonstrate that the different flow field structures in pipes with diverse baffle installations have great influence on the measure accuracy of flowmeters. In order to measure the flux in pipes more accurate, the flowmeters must be installed downstream the baffles far away so that the irregular flows induced by baffles have less influence on the flowmeters. However, the installation lengths downstream baffles for flowmeters in ISO are are usually much longer than the allowable lengths for the local flowmeters. To decrease the installation lengths and loss measure accuracy of flowmeters as little as possible, it is necessary to study the flows in pipes with baffles. CFD is a good tool for the study. Here, the flows in a diffusive pipe with various rectifiers are computed as examples. The lengths of the irregular flows induced by the diffuser and rectifier are shown. By analyzing and comparison the numerical results, the installation lengths for flowmeters and the rectification of the different rectifiers are confirmed. The study conclusions will be very useful for guiding the local flowmeter selection and installation in the future.

Classification of flow patterns in rectangular shallow reservoirs

This work focuses on the experimental classification of flow patterns in rectangular shallow reservoirs, including symmetric flows without any reattachment point to asymmetric flows with one reattachment point, two reattachment points, or two reattachment points and one detachment point. The median position and the natural variability of the reattachment lengths of asymmetric flows were measured for 40 geometric and hydraulic conditions. The effects of dimensionless flow depth, Froude number, lateral expansion ratio and dimensionless length on the median reattachment lengths were analysed. A number of regression equations were proposed. For “high” dimensionless flow depths and a Froude number of 0.20, a shape parameter was proposed for predicting the transition between symmetric and asymmetric flows. The results of this study are useful knowledge for improving current methods to predict the trapping efficiency and the preferential regions of deposition in reservoirs.

Fuzzy optimization model for integrated management of total nitrogen loads from distributed point and nonpoint sources in watershed

A fuzzy optimization model is developed to allocate allowable total nitrogen (T-N) loads to distributed nonpoint sources (NPSs) and point sources (PSs) in a watershed for river water quality management using the linear programing technique. The watershed is divided into uniform grid cells on which T-N loads issuing from NPSs such as paddy fields, upland crop fields and cities are controlled. A geographic information system integrated with the digital elevation model facilitates computation of route lengths of surface and subsurface flows from cells to a river running through the watershed. The T-N loads discharged from their sources are assumed to decay, subject to distance-related first-order kinetics. As management goals, maximizations of total allowable NPS loads, total allowable PS loads and total yield of rice are considered from environmental and economic viewpoints. A prime constraint is an effluent limitation standard for the aggregate amount of loads that arrive at the downstream end of the river. The fuzzy sets theory helps appropriately describe vague attitudes of decision-makers (i.e., stakeholders and management authorities) in terms of constraints and conflicting goals. An application of the fuzzy optimization model, developed as an improvement over our last nonfuzzy model, to a real watershed in Shiga prefecture, Japan, demonstrates that the fuzzy model embodies our last model, and is capable of creating management alternatives for T-N load allocation in a more practical and flexible manner.

Using Heavy-Tailed Feature to Estimate Flow Length Distributions

Routers have the ability to output statistics about packets and flows of packets that traverse them. Passive traffic measurement increasingly employs sampling at the packet level. However, knowing the number and length of the original flows is necessary for some applications. This paper provides an algorithm that uses flow statistics formed from sampled packet stream to infer the absolute frequencies of lengths of flows in the unsampled stream. We achieve this through statistical inference and by exploiting heavy-tailed feather. We also investigate the impact on our results of different packet sampling rate. The theoretical analysis demonstrates that the computational complexity is well under control, and the experiment results show the inferred distributions are accurate in most cases.

Development-Length Requirements for Fully Developed Laminar Pipe Flow of Inelastic Non-Newtonian Liquids

In the current study, we report the results of a detailed and systematic numerical investigation of developing pipe flow of inelastic non-Newtonian fluids obeying the power-law model. We are able to demonstrate that a judicious choice of the Reynolds number allows the development length at high Reynolds number to collapse onto a single curve (i.e., independent of the power-law index n). Moreover, at low Reynolds numbers, we show that the development length is, in contrast to existing results in the literature, a function of power-law index. Using a simple modification to the recently proposed correlation for Newtonian fluid flows (Durst, F. et al., 2005, “The Development Lengths of Laminar Pipe and Channel Flows,” J. Fluids Eng., 127, pp. 1154–1160) to account for this low Re behavior, we propose a unified correlation for XD∕D, which is valid in the range 0.4<n<1.5 and 0<Re<1000.

The Development Lengths of Laminar Pipe and Channel Flows

Abstract The authors’ research work into fully developed pulsating and oscillating laminar pipe and channel flows raised questions regarding the development length of the corresponding steady flow. For this development length, i.e., the distance from the entrance of the pipe to the axial position where the flow reaches the parabolic velocity profile of the Hagen-Poiseuille flow, a wide range of contradictory data exists. This is shown through a short review of the existing literature. Superimposed diffusion and convection, together with order of magnitude considerations, suggest that the normalized development length can be expressed as L∕D=C0+C1Re and for Re→0 one obtains C0=0.619, whereas for Re→∞ one obtains C1=0.0567. This relationship is given only once in the literature and it is presumed to be valid for all Reynolds numbers. Numerical studies show that it is only valid for Re→0 and Re→∞. The development length of laminar, plane channel flow was also investigated. The authors obtained similar results to those for the pipe flow: L∕D=C0′+C1′; Re, where C0′=0.631 and C1′=0.044. Finally, correlations are given to express L∕D analytically for the entire Re range for both laminar pipe and channel flows.

Fracturing as a quantitative indicator of lava flow dynamics

The traditional classification of lava flows into pahoehoe, aa and blocky varieties reflects differences in how a flow can fracture its surface during advance. Pahoehoe and aa lavas have a low strength upon eruption and require surface cooling to produce a crust that can fracture. Among pahoehoe lavas, applied stresses are small enough to allow the growth of a continuous crust, which is broken intermittently as the flow advances by propagating a collection of lava tongues. Among aa lavas, in contrast, applied stresses are large enough to maintain persistent crustal failure. Blocky lavas are distinguished by having a significant strength upon eruption, so that motion can induce surface fracturing even without cooling. The transition from pahoehoe to aa thus coincides with a change from intermittent to persistent failure of chilling crust, whereas the transition from aa to blocky lava occurs when lava beneath the crust can also autobrecciate. These fracturing characteristics have been used to quantify the transitions between flow regimes and suggest that shear fracture may dominate tensile failure. They also (1) explain the restricted variations with slope of pahoehoe and aa flow thickness, as well as the maximum advance rate for which pahoehoe can form, equivalent to the minimum rate required for aa lava, and (2) provide a revised method for forecasting the maximum potential lengths of aa flows. Applications include improved hazard assessments during effusive eruptions and new evaluations of the emplacement conditions for very large-volume pahoehoe lava flows.

Evidence for episodicity in the magma supply to the large Tharsis volcanoes

The volumes and estimated total lifetimes of the Tharsis shield volcanoes on Mars imply that they were built with an average magma supply rate within a factor of 2–3 of ∼0.05 m3 s−1. The morphologies and positions of the summit calderas of these volcanoes, specifically the overlapping relationships between the calderas, are evidence that multiple magma reservoirs existed within them, centered on distinctly different locations at various times. The requirement that the magma in an older reservoir must have cooled below its solidus temperature in order to change the local stresses in such a way that a new reservoir grew at a different location argues for long time gaps (probably tens of Myr) during which the supply rate of magma from the mantle was much smaller than at other times. Conversely, the need to offset conductive cooling to the surface once an active magma reservoir was established implies that the magma supply rate was large, ∼1–10 m3 s−1, for times of order 0.1 Myr. An initial pulse involving rates of more than 150 m3 s−1 acting for at least a few weeks was needed to initiate each new reservoir. The lengths of numerous long lava flows on the flanks of the Tharsis Montes imply that lava must have been erupted at rates of ∼100–300 m3 s−1 for periods of a few years to a few tens of years. The volumes of many of these flows exceed the amounts of magma that could be released from overpressured magma reservoirs of the sizes implied by the dimensions of the summit calderas with the surrounding rocks behaving elastically. A maintained high magma supply rate from the mantle (leading to buffered eruption conditions) is almost certainly required for such flows, whereas inelastic caldera collapse events (unbuffered eruption conditions) can explain the emplacement of other flows. Taken together, the various lines of evidence suggest that the Tharsis volcanoes were built episodically with active phases lasting less than 1 Myr alternating with ∼100 Myr quiet phases. We comment on the implications of these issues for the episodicity of the generation of magma in the mantle and for the mode of transport of the magma in dikes or diapirs.

Generalized Culvert Design Diagram

The features of culvert flow in a basic arrangement are highlighted. Four fundamental flow types may be identified, namely critical flow, uniform flow, gated flow, and pressurized flow. A generalized design diagram is presented for the circular barrel that gives the possible transitions between various flow types. Further, the lengths of free surface flows with a central pressurized flow portion are determined as a function of the pipe Froude number. Photographs of model tests illustrate the complex flow patterns that may occur even in a simple culvert arrangement. Of particular relevance are choking conditions and features of two-phase flow in a culvert. The effects of friction coefficient, bottom slope, relative pipe length, and upstream head are detailed for free culvert outlet conditions.

Factors controlling the lengths of channel-fed lava flows

Factors which control lava flow length are still not fully understood. The assumption that flow length as mainly influenced by viscosity was contested by Walker (1973) who proposed that the length of a lava flow was dependent on the mean effusion rate, and by Malin (1980) who concluded that flow length was dependent on erupted volume. Our reanalysis of Malin's data shows that, if short duration and tube-fed flows are eliminated, Malin's Hawaiian flow data are consistent with Walker's assertion. However, the length of a flow can vary, for a given effusion rate, by a factor of 7, and by up to 10 for a given volume. Factors other than effusion rate and volume are therefore clearly important in controlling the lengths of lava flows. We establish the relative importance of the other factors by performing a multivariate analysis of data for recent Hawaiian lava flows. In addition to generating empirical equations relating flow length to other variables, we have developed a non-isothermal Bingham flow model. This computes the channel and levee width of a flow and hence permits the advance rates of flows and their maximum cooling-limited lengths for different gradients and effusion rates to be calculated. Changing rheological properties are taken into account using the ratio of yield strength to viscosity; available field measurements show that this varies systematically from the vent to the front of a lava flow. The model gives reasonable agreement with data from the 1983–1986 Pu'u ‘O’o eruptions and the 1984 eruption of Mauna Loa. The method has also been applied to andesitic and rhyolitic lava flows. It predicts that, while the more silicic lava flows advance at generally slower rates than basaltic flows, their maximum flow lengths, for a given effusion rate, will be greater than for basaltic lava flows.

Factors controlling the lengths of channel-fed lava flows

Factors controlling the lengths of channel-fed lava flows

Lengths of Hawaiian lava flows

Comparison of length, volume, and effusion rate for 87 historic Hawaiian basaltic lava flows shows little support for a direct relationship between flow length and effusion rate. A statistically more significant relationship exists between flow length and total volume of material extruded. Cross-sectional area, effusion rate, and volume all play important roles in governing the emplacement of lava flows in Hawaii; no single factor appears most important. One reason for the observed relationships in Hawaii may be that tube-fed flows, with approximately constant cross-sectional area, advance farther than other types of flows for similar effusion rates and volumes.

Volcanic features of the nearside equatorial lunar maria

A map is presented of the distribution of volcanic features in the lunar maria between longitudes 50°E. and 100°W, and latitudes 50°N. and S. Flood basaltic flows predominate, and where individual flow units can be identified they may be hundreds of kilometres long. Sinuous rilles are considered to be tubes and channels associated with flood volcanism and to indicate directions and lengths of flows. The large areal extent of the flood basalts may result from an exeedingly high eruption rate of low viscosity lava. Mare ridges are thought to be generally shallow in origin and result from magma movement in extensive shallow sills. Other types of volcanism include caldera collapse, shield volcanoes and viscous extrusions together with pyroclastic cones.