Turbulent dispersion of droplets for air flow in a pipe

An optical technique was used to study the dispersion of 50 m, 90 m and 150 m droplets downstream of a source located in the center of a vertical pipe through which turbulent air is flowing. A turbulent dispersion coefficient, _P, and a mean-square of the fluctuations in the turbulent velocity, v _p ² , are determined from the change of the measured mean-square displacement of the droplets over the pipe cross section with time. The interesting aspect of the experiments is that they explored conditions where the inertia of the particles is believed to be a much more important effect than that of the crossing of trajectories associated with the inequality of the average velocities of the particles and the fluid.     

Turbulent flow in a pipe

Summary The model used to describe turbulent flow is based on a non linear relation between the stress tensor and the rate-of-strain tensor. The turbulent velocity distribution for incompressible, one-dimensional flow is examined.     

Free-surface non-Newtonian fluid flow in a round pipe

Free-surface pseudoplastic and viscoplastic fluid flows in a round pipe were studied for the case where the direction of motion coincides with the direction of gravity. Numerical modeling was performed using a technique based on a combination of the SIMPLE algorithm and the method of invariants. Three characteristic filling regimes were found to exist: a complete filling regime, a regime characterized by air-cavity formation on the solid wall, and a jet regime. Critical parameter values separating the regions of existence of these regimes were calculated. The evolution of quasisolid cores was studied for flow of a fluid with an yield point.     

Turbulent air flow over a moving curved surface

A numerical model of turbulent air flow over a curved surface is described. The model is based on two-dimensional nonlinear Reynolds equations and continuity equations written in a coordinate system moving with the profile of the curved surface. The Reynolds stresses are represented in the form of the product of the isotropic turbulent viscosity coefficient, which increases linearly with height, and the deformation tensor of the mean velocity field. Flow over a stationary sinusoidal surface and a sinusoidal gravity wave on water is simulated. The structure of the velocity and pressure wave fields is obtained. The differences in flow over stationary and moving surfaces are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 20–24, September–October, 1986.     

Turbulent heat transfer characteristics of water flow in a rotating pipe

Large-Eddy-Simulation of turbulent heat transfer for water flow in rotating pipe is performed, for various rotation ratios (0 ≤ N ≤ 14). The value of the Reynolds number, based on the bulk velocity and pipe diameter, is Re = 5,500. The aim of this study is to examine the effect of the rotating pipe on the turbulent heat transfer for water flow, as well as the reliability of the LES approach for predicting turbulent heat transfer in water flow. Some predictions for the case of non-rotating pipe are compared to the available results of literature for validation. To depict the influence of the rotation ratio on turbulent heat transfer, many statistical quantities are analyzed (distributions of mean temperature, rms of fluctuating temperature, turbulent heat fluxes, higher-order statistics). Some contours of instantaneous temperature fluctuations are examined.     

Auto-ignitions of a methane/air mixture at high and intermediate temperatures

A rapid compression machine (RCM) and a shock tube (ST) have been employed to study ignition delay times of homogeneous methane/air mixtures at intermediate-to-high temperatures. Both facilities allow measurements to be made at temperatures of 900–2000 K, at pressures of 0.38–2.23 MPa, and at equivalence ratios of 0.5, 1.0, and 2.0. In ST experiments, nitrogen served as a diluent gas, whereas in RCM runs the diluent gas composition ranged from pure nitrogen to pure argon. Recording pressure, UV, and visible emissions identified the evolution of chemical reactions. Correlations of ignition delay time were generated from the data for each facility. At temperatures below 1300 K, a significant reduction of average activation energy from 53 to 15.3 kcal/mol was obtained. Moreover, the RCM data showed significant scatter that dramatically increased with decreasing temperature. An explanation for the abnormal scatter in the data was proposed based on the high-speed visualization of auto-ignition phenomena and experiments performed with oxygen-free and fuel-free mixtures. It is proposed that the main reason for such a significant reduction of average activation energy is attributable to the premature ignition of ultrafine particles in the reactive mixture.     

Flow pattern and pressure fluctuation in air-solid two-phase flow in a pipe at low air velocities

An experiment was made on an air-solid two-phase flow in a horizontal pipe. The main concern was the relation between flow patterns and pressure fluctuation at low air velocities. First, the flow patterns were classified into five different types depending on the air and particle flow rates. Next, it was shown how the properties of pressure fluctuation change as the air velocity decreases. Further, fluctuation signals were analyzed in detail and differences due to the flow patterns and particle size were discussed.     

Turbulent flow in a channel at a low Reynolds number

A two-component laser Doppler velocimeter with high spatial and temporal resolution was used to obtain measurements for fully developed turbulent flow of water through a channel with an aspect ratio of 12 : 1 at Re=5700 (based on the centerline velocity and the half-height of the channel). Statistical quantities that were determined are the mean streamwise velocity, the root-mean-square of the fluctuations of the streamwise and the normal velocities, the Reynolds shear stress and higher order moments. Turbulence production is calculated from these quantities. Turbulence statistics obtained from experiments are compared with results from a direct numerical simulation at the same Reynolds number. The good agreement validates a recent DNS, at Re=5700, which is approximately twice as large as used in most previous studies. Received: 12 May 1997 / Accepted: 8 April 1998     

Turbulent forced convective heat transfer in two-phase evaporating droplet flow through a vertical pipe

A physical model was developed to study heat transfer in turbulent dispersed flow at very high vapor quality in a vertical pipe by numerically solving the coupling governing differential equations for both phases. Major heat transfer mechanisms included in the model were the thermal nonequilibrium effects, droplet vaporization, droplet deposition on the duct wall and thermal radiative transfer. The predicted results indicated that vapor superheating is dominant for the cases with high wall superheat, otherwise droplet vaporization dominates the energy transport processes. Heat transfer during the droplet-wall interaction only exists at low wall superheat but in small amounts.     

Turbulent heat transfer for pipe flow with uniform heat generation

An Analytic solution is presented of the problem of turbulent heat transfer in pipes with internal heat generation and insulated wall by applying a recently-developed eddy conductivity model. The results agree closely with available experimental data for a wide range of Prandtl number (0.02–10.5).     

Heat transfer to air–water annular flow in a horizontal pipe

Two-phase air–water flow and heat transfer in a 25 mm internal diameter horizontal pipe were investigated experimentally. The water superficial velocity varied from 24.2 m/s to 41.5 m/s and the air superficial velocity varied from 0.02 m/s to 0.09 m/s. The aim of the study was to determine the heat transfer coefficient and its connection to flow pattern and liquid film thickness. The flow patterns were visualized using a high speed video camera, and the film thickness was measured by the conductive tomography technique. The heat transfer coefficient was calculated from the temperature measurements using the infrared thermography method. It was found that the heat transfer coefficient at the bottom of the pipe is up to three times higher than that at the top, and becomes more uniform around the pipe for higher air flow-rates. Correlations on local and average Nusselt number were obtained and compared to results reported in the literature. The behavior of local heat transfer coefficient was analyzed and the role of film thickness and flow pattern was clarified.     

Turbulent structure of air flow over wind-induced gravity waves

This is the second paper in a group of three that reports the systematic measurements of wind-generated water waves in a wind tunnel experiment. Here, the structure of the boundary layer on the air side of the water?Cair interface was analysed and compared with the boundary layer over a smooth plane rigid wall. The contribution of the wave-induced Reynolds stress was detected through filtering the spectrum of velocity fluctuations. Wave-induced Reynolds stresses became negligible for z?>?5 H _rms. The intermittency factor in the boundary layer over water waves was similar to that in a boundary layer over a rigid plane wall, with several differences near the interface. Here, the presence/absence of water damps out the turbulence. The quadrant analyses revealed that ejection and sweep events were dominant and more concentrated. At small fetches, the large-amplitude negative streamwise perturbations were preferentially lifted. Turbulence energy production peaked at z/???=?0.2 and had a distribution similar to that observed for a self-preserving boundary layer with a strong adverse gradient pressure. The quadrant analysis contribution to the energy production revealed that ejections still dominated the balance and that the production was spatially modulated in the wind direction with a couple of cells and with a minimum in the area of the free surface wave height reduction.     

Turbulent boundary layer at the initial portion of a pipe with rough walls

The development of a turbulent boundary layer at the initial portion of a pipe with rough walls is considered in the framework of the boundary-layer theory. It is shown that the consideration of roughness can be carried out by introducing into the standard law of friction a function which takes into account this factor. An experimental investigation is carried out on a test portion of a pipe with natural roughness whose relative value equals 10^–3. The range of Reynolds numbers is 5.1 · 10⁴-3.4 · 10⁵. The method of calculation proposed here leads to results which satisfactorily agree with the data of the experimental investigation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 109–116, September–October, 1971.     

Turbulent structure during transition to self-similarity in a round jet

 The developing turbulent region of a round jet was investigated using an improved implementation of digital particle image velocimetry (DPIV). The two-dimensional flow field in planes normal and parallel to the axial velocity was measured at locations between 15 and 30 diameters downstream, for two Reynolds numbers of 5500 and 16,000. The study consisted of instantaneous snapshots of the velocity and vorticity fields as well as measurements of velocity correlations up to third order. In this regime, the Reynolds number had a significant effect on both the instantaneous flow structure and the profiles of mean velocity across the jet. Coherent streamwise structures were present in the jet core for the lower Reynolds number. Additional structures whose evolution was governed by time scales two orders of magnitude larger than the convective scale inside the jet were observed in the entrainment field. The velocity correlations provided further support for the validity of DPIV turbulence measurements. The data was consistent with the equations of motion and momentum was conserved. DPIV measurements of turbulent kinetic energy components agreed with the hot-wire measurements of previous studies. Received: 27 November 1996/Accepted: 14 July 1997     

Pulsating turbulent pipe flow in the current dominated regime at high and very-high frequencies

The paper presents Direct Numerical Simulations of sinusoidal pulsating turbulent flow, at low bulk Reynolds numbers, with high frequency, in a straight pipe. Our objective is to study pulsating flow considering it as the superposition of a temporal unsteadiness on a mean current, and from this viewpoint, to decompose the flow in a mean and an oscillating part. Firstly, we examine the time-averaged statistics, which show that the parent flow retains its properties. Then, we analyze the oscillating part of the flow, and confirm the notion that for rapidly pulsating flow, the amplitude of the streamwise velocity and the phase lag at different radial locations follow the solution of the laminar Stokes problem. In addition, we find that the modulation of the turbulent fluctuations follows approximately the sinusoidal form of the imposed pulsation, and that the ratio of the frequency parameter to the amplitude of the streamwise velocity can be used as a scaling factor. We investigate the effects of the amplitude and the frequency of the imposed unsteadiness on the modulation of the time-averaged properties and the turbulence statistics, through a systematic analysis. Finally, we examine the time evolution of the mean velocity and the turbulent fluctuations. These results indicate that a lower limit for the high frequency regime can be identified, based on the level of conformity of the phase-averaged profiles on their steady-state counterparts. For very high frequencies, we find that that the flow behavior does not change, indicating the absence of an upper limit for the high frequency regime.     

Laminar flow in a pipe at low and moderate reynolds numbers

Summary The laminar flow of a homogeneous viscous liquid in the inlet of a pipe is investigated numerically for a range of small and moderate Reynolds numbers where the boundary layer approximation is inapplicable. Velocity profiles and other characteristics of the flow are calculated and the results compared with approximate results obtained by other methods. The limiting case of vanishingly small Reynolds number is also treated analytically.Part of this work was performed while the second author was a summer visitor in the Applied Mathematics Department, Brookhaven National Laboratory, Upton (L.I.), New York.     

Correlation of powder flow properties to interparticle interactions at ambient and high temperatures

A combination of a continuum approach and a particle–particle approach to describe the multi-scale nature of the mechanical properties of bulk solids may be beneficial to scientific and engineering applications. In this paper, a procedure is proposed to estimate the interparticle forces beginning with the bulk flow properties as measured with standardized techniques. In particular, the relationship between interparticle forces and bulk solid tensile strength is adopted based on the microscale approaches of Rumpf(1970) and Molerus(1975). The flow properties of fluid cracking catalyst(FCC), corundum and glass bead powders were all characterized with a modified Schulze ring shear cell capable of operating at temperatures up to 500℃. The powder test conditions were selected such that the van der Waals forces were the most significant particle–particle interactions. The model equations describe two cases, in which either elastic or plastic deformation of the contact points is assumed. The results indicate that the model provides the correct order of magnitude for the values of the tensile strength when proper values for the mean curvature radius at the contact points are taken into account. A sensitivity analysis for the main parameters in the model was performed. This analysis indicated that the assumption of plastic deformation at contact surfaces coupled with a decrease in porosity justified an increase of the tensile strength with consolidation stress. Furthermore, the effect of temperature on the measured flow behavior can be explained as a change in the strength of the material.     

Correlation of powder flow properties to interparticle interactions at ambient and high temperatures

A combination of a continuum approach and a particle–particle approach to describe the multi-scale nature of the mechanical properties of bulk solids may be beneficial to scientific and engineering applications. In this paper, a procedure is proposed to estimate the interparticle forces beginning with the bulk flow properties as measured with standardized techniques. In particular, the relationship between interparticle forces and bulk solid tensile strength is adopted based on the microscale approaches of Rumpf (1970) and Molerus (1975). The flow properties of fluid cracking catalyst (FCC), corundum and glass bead powders were all characterized with a modified Schulze ring shear cell capable of operating at temperatures up to 500 °C. The powder test conditions were selected such that the van der Waals forces were the most significant particle–particle interactions. The model equations describe two cases, in which either elastic or plastic deformation of the contact points is assumed. The results indicate that the model provides the correct order of magnitude for the values of the tensile strength when proper values for the mean curvature radius at the contact points are taken into account. A sensitivity analysis for the main parameters in the model was performed. This analysis indicated that the assumption of plastic deformation at contact surfaces coupled with a decrease in porosity justified an increase of the tensile strength with consolidation stress. Furthermore, the effect of temperature on the measured flow behavior can be explained as a change in the strength of the material.