Axial static pressure measurements of water flow in a rectangular microchannel

An experimental investigation of water flow through an aluminum rectangular microchannel with a hydraulic diameter of 169 μm was conducted over a Reynolds number (based upon mean velocity and hydraulic diameter) range from 230 to 4,740. Pressure measurements were simultaneously acquired at eight different axial locations within the channel along with pressure measurements in the inlet and outlet ports. The 27 μm pressure taps were more densely packed near the channel entrance in order to study the developing flow region. The average Poiseuille number for laminar flows was 86.4, which is in excellent agreement with the theoretical value of 86.9. The average critical Reynolds number was found to be 2,370. The limited turbulent friction factor data were in good agreement with the Haaland equation. The inlet to the channel was not well rounded and pressure distributions near the channel entrance show a region of pressure recovery. Entrance length and some minor loss coefficient data were not in agreement with theory, but the cause of these deviations were primarily a function of the inlet geometry and pressure recovery in the microchannel rather than a microscale effect.     

Influence of the mixing of two flows with different total parameters in a laval nozzle on its integral characteristics

A calculation is made of the turbulent zone of mixing of two flows of viscous and heat conducting gas in a Laval nozzle. For such a nozzle of given geometry, a comparison is made of calculations of the integrated characteristics of flows that are nonuniform with respect to the total parameters in the framework of various models: laminar hydraulics, viscous laminar hydraulics, and total mixing without hydraulic losses. The calculations are made for a stationary, nonswlrling flow of a viscous heat conducting gas with nearly discontinuous step distribution of the total parameters at the entrance to an axisymmetric Laval nozzle of given geometry. In this situation, the gas flows with different total parameters at the entrance to the nozzle are separated by a surface near which the profiles of the flow parameters are specified on the basis of boundary-layer theory. In the blocked regime investigated here, the flow in the part where the nozzle becomes narrower and at least at the beginning of the expanding part does not depend on the pressure of the surrounding medium. The integrated characteristics of the nozzle (gas flow rate G, impulse I, specific impulse i = I/G, etc.) depend on the parameter distributions at the entrance to the nozzle, and also on the turbulent mixing of the flows in the mixing zone. To analyze the dependence of the integrated characteristics on the turbulent mixing, the values of these characteristics calculated in the framework of the three models are compared. The model of mixing without hydraulic losses presupposes complete equalization of the parameters of the original inhomogeneous flow in the constant-area chamber in front of the nozzle with conservation of the mass, energy, and momentum fluxes. The model of laminar hydraulics is described in detail in [1, 2]. The model of viscous laminar hydraulics will be described in Sec. 1.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 114–119, July–August, 1979.I thank A. N. Kraiko for supervising the work, A. N. Sekundov for helpful discussions, and I. P. Smirnova and A. B. Lebedev for making available the computer program.     

90°弯管内气固两相湍流流动的数值研究

利用两相湍流KET模型对90°弯管内气固两相湍流流动进行了数值模拟,得到了弯管内两相流动的一些规律,并提出用颗粒动理学压力来定性表征弯管内磨损严重部位,为管道抗磨损设计提供了一定的理论依据。     

Prediction of periodic boundary layers

A relatively simple, yet efficient and accurate finite difference method is developed for the solution of the unsteady boundary layer equations for both laminar and turbulent flows. The numerical procedure is subjected to rigorous validation tests in the laminar case, comparing its predictions with exact analytical solutions, asymptotic solutions, and/or experimental results. Calculations of periodic laminar boundary layers are performed from low to very high oscillation frequencies, for small and large amplitudes, for zero as well as adverse time-mean pressure gradients, and even in the presence of significant flow reversal. The numerical method is then applied to predict a relatively simple experimental periodic turbulent boundary layer, using two well-known quasi-steady closure models. The predictions are shown to be in good agreement with the measurements, thereby demonstrating the suitability of the present numerical scheme for handling periodic turbulent boundary layers. The method is thus a useful tool for the further development of turbulence models for more complex unsteady flows.     

Turbulence-driven secondary flows in a curved pipe

If the torque exerted on a fluid element and the source of streamwise vorticity generation are analyzed, a turbulence-driven secondary flow is found to be possible in a curved pipe. Based on this analysis, it is found that the secondary flow is primarily induced by high anisotropy of the cross-stream turbulent normal stresses near the outer bend (furthest from the center of curvature of the bend). This secondary flow appears as a counterrotating vortex pair embedded in a Dean-type secondary motion. Recent hot-wire measurements provide some evidence for the existence of this vortex pair. To verify the formation and extent of this turbulence-driven vortex pair further, a near-wall Reynolds-stress model is used to carry out a detailed numerical investigation of a curved-pipe flow. The computation is performed specifically for a U-bend with a full developed turbulent flow at the bend entrance and a long straight pipe attached to the exit. Numerical results reveal that there are three vortex pairs in a curved pipe. The primary one is the Dean-type vortex pair. Another pair exists near the pipe core and is a consequence of local pressure imbalance. A third pair is found near the outer bend and is the turbulence-driven secondary flow. It starts to appear around 60° from the bend entrance, grows to a maximum strength at the bend exit, and disappears altogether at about seven pipe diameters downstream of the bend. On the other hand, calculations of developing laminar curved-pipe flows covering a range of pipe-to-bend curvature ratios, Reynolds number, and different inlet conditions fail to give rise to a third cell near the outer bend. Therefore, experimental and numerical evidence together lend support to the formation of a pair of turbulence-driven secondary cells in curved-pipe flows.Research supported by the Office of Naval Research under Grant No. N0014-81-K-0428 and by the David Taylor Research Center, Annapolis, Maryland, under Contract No. N00167-86-K0075.     

Breaking of waves of limiting amplitude over an obstacle

Homogeneous heavy fluid flows over an uneven bottom are studied in a long-wave approximation. A mathematical model is proposed that takes into account both the dispersion effects and the formation of a turbulent upper layer due to the breaking of surface gravity waves. The asymptotic behavior of nonlinear perturbations at the wave front is studied, and the conditions of transition from smooth flows to breaking waves are obtained for steady-state supercritical flow over a local obstacle. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 3–11, May–June, 2006.     

Space and space-time longitudinal velocity correlations in the turbulent far wake of a flat plate in incompressible flow

This paper presents longitudinal space and space-time conventional velocity correlations measured in the wake of a two-dimensional flat-plate at zero incidence, with fully-turbulent boundary layers at its sharp trailing edge. Iso-correlation contour plots are given in the plane of symmetry and normal to this plane in the assumed asymptotic (in the mean velocity sense) part. Comparisons with initially laminar 2-D wake results show that the classical Double-Roller-Eddy model developed for initially laminar wakes is not adapted to initially turbulent wakes; on the other hand, comparison with supersonic wake of the same nature seems to confirm this conclusion. The lack of detailed experimental data in this field is outlined, together with the need of a refined theoretical approach to the coherent structures existing in such flows.     

Pulsed wire velocity anemometry near walls

A new pulsed wire probe for making velocity and turbulence measurements in the near wall region of incompressible, isothermal boundary layers of all kinds is described. Results of careful calibrations of the probe response in both laminar and turbulent flows are presented, with particular emphasis on the effects of diffusion in the very near wall region. Analytic results for the motion and distortion of a heat puff in linear shear flow near a wall are developed and these are shown to validate a very simple approximate theory that accounts for the diffusional effects. It is demonstrated that correction procedures based on the theory can be successfully implemented. Examples of the use of the probe in highly turbulent, separated flows, as well as more standard boundary layers, are given and its response near the wall is contrasted with that of the corresponding (parallel wire) probe used for surface shear stress measurements.     

Effects of pressure work and viscous dissipation on Graetz problem for gas flows in parallel-plate channels

The analytical solutions are obtained for the Graetz problem with pressure work and viscous dissipation in the thermal entrance region of the parallel-plate channels for two basic boundary conditions of uniform wall temperature and uniform wall heat flux involving fully developed laminar gas flows. The asymptotic Nusselt number is found to be zero instead of the conventionally accepted value of 7.54 for the uniform wall temperature case and (140/17)/ [1+(27/17) PrEc] for uniform wall heat flux case. The effects of pressure work and viscous dissipation contribute significantly to the asymptotic results for heat transfer and cannot be neglected under any circumstances in the case of uniform wall temperature. Sample results are presented to illustrate the effects of pressure work and viscous dissipation on heat transfer characteristics in the thermal entrance region.     

Structure of nonpremixed reaction zones in numerical isotropic turbulence

Results from direct numerical simulation of low heat release, turbulent nonpremixed reacting flows modeled using single-step reactions with constant and temperature-dependent rate laws are discussed, and compared with laminar predictions. The mixture fraction and its dissipation rate are statistically independent in regions of intense reaction, partially supporting a commonly made assumption in flamelet-based models. In the presence of a finite rate reverse reaction, the reaction zone spans the entire range of mixture fraction. The joint pdf of the reactive scalars evolves to an equilibrium that is dictated by a balance between the reactive and mixing fluxes in composition space. When the temperature-dependent rate law is implemented, strain-induced extinction is observed for a Zel'dovich (modified) number of 10. As the ratio of local flow to chemical time scale is decreased below unity, a larger fraction of the flow field experiences this mode of extinction. The critical turbulent scalar dissipation rate is compared with laminar values and asymptotic predictions.The first two authors express their acknowledgment to the donors of The Petroleum Research Fund, administered by the American Chemical Society for partial support of this work through a type G grant. We also acknowledge the Council for Research and Creative Writing at the University of Colorado for providing partial financial support.     

Flows through plane sudden‐expansions

A calculation method has been developed and used to represent flows downstream of plane symmetric expansions with dimensions and velocities encompassing laminar and turbulent flows. Except for very low Reynolds numbers, the flows are time‐dependent and asymmetric and the calculated results are appraised first in relation to published measurements of laminar flows and then to new measurements obtained at a Reynolds number of 26 500. The time‐dependent laminar simulations indicate that the critical Reynolds numbers are predicted with excellent accuracy for different expansion ratios and the details of the asymmetric velocity profiles are in good agreement with experimental measurements. The laminar flow calculations also show that increasing the thickness of the separating boundary layer leads to longer regions of separation and no dominant frequency for Reynolds numbers up to those at which the third separation region was observed. The turbulent flow simulations made use of the k–ε turbulence model and provided a satisfactory representation of measurements, except in regions close to the wall and within the recirculation regions. Also, the longer reattachment length was underestimated. Limitations are discussed in relation to these and higher‐order assumptions. Copyright © 2000 John Wiley & Sons, Ltd.     

Reynolds number effects on the behavior of a non-buoyant round jet

The behavior of a non-buoyant circular water jet discharged from a contraction nozzle was experimentally investigated. In this experiment, the Reynolds number of the jet, based on the mean velocity results obtained by particle image velocimetry (PIV), ranged from 177 to 5,142. From the experimental results, we found that the cross-sectional profile of the axial velocity for a laminar flow near the nozzle did not show a top-hat distribution, whereas the profiles with Reynolds number higher than 437 were almost top-hat. The length of the zone of flow establishment (ZFE) was found to decrease with increasing Reynolds number. The measured centerline velocity decayed more rapidly and, consequently, approached the theoretical equation earlier near the nozzle as the Reynolds number increased. The decay constant for the centerline velocity of the turbulent cases was relatively lower than that discovered in theory. It is assumed that this probably resulted from the use of the contraction nozzle. Verifying the similarity of the lateral velocity profiles demonstrated that the Gaussian curve was properly approximated only for the turbulent jets and not for the laminar or transitional flows. The jet half width seldom grew for the laminar or transitional flows, whereas it grew with increasing axial distance for the turbulent flows. The spreading rates for the turbulent flows gradually decreased with increasing Reynolds number. The normalized turbulence intensity along the jet centerline increased more rapidly with the axial distance as the Reynolds number increased, and tended to the constant values proposed by previous investigators. The Reynolds shear stress levels were also found to increase as the Reynolds number increased for the turbulent jets.     

Numerical analysis of vortex cell efficiency in laminar and turbulent flows past a circular cylinder with embedded rotating bodies

The effect of flow intensification in small-sized vortex cells on the flow pattern in the near wake downstream of a cylinder and the cylinder drag in laminar and turbulent flows is analyzed on the basis of a numerical simulation of the two-dimensional steady-state flow past a circular cylinder with rotating cylindrical bodies built into the cylinder contour. St. Petersburg, Saratov. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 88–96, July–August, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (projects Nos. 99-01-01115 and 99-01-00772).     

A new evaluation method for Nusselt numbers in naphthalene sublimation experiments in rotating-disk systems

A comparative analysis of theoretical and empirical relations, as well as experimental data for mass transfer of a rotating disk in laminar, transitional and turbulent flows for naphthalene sublimation in air was done. New correlations between local and average Sherwood numbers for the entire disk were offered. A new evaluation approach for Nusselt numbers based on the experimental data for naphthalene sublimation in laminar, transitional and turbulent flows was developed.     

爆轰波透射孔栅形成的高速爆燃波的结构和行为

以实验为主,研究光滑直管中乙炔氧气爆轰波透射孔栅形成的高速爆燃波结构和行为。实验以基于纹影平台的高速转鼓摄影记录孔栅下游近场内初始爆燃波的结构和发展,并以压力传感器跟踪其后继走向。研究发现,高速爆燃波是前驱激波和火焰的组合结构,随着初始压力的提升,它分别表现为紧随于前驱激波的层流和湍流燃烧火焰。入射爆轰胞格尺度小于或与孔栅扰动尺度相当时,湍流燃烧在下游近场迅速形成;层流结构的爆燃波通常无法抵制背景稀疏波而走向衰弱,而湍流燃烧结构可发生加速和向爆轰的转捩;他们之间存在一个不稳定的临界状态,高速爆燃波得以以0.5~0.6倍CJ爆轰速度传播较长距离,这一状态对应于双间断Rankine-Hugoniot关系的等容燃烧解。     

The Application of a Laminar Flamelet Model to Confined Explosion Hazards

The majority of computational studies of confined explosion hazards apply simple and inaccurate combustion models, requiring adhoc corrections to obtain realistic flame shapes and often predicting an order of magnitude error in the overpressures. This work describes the application of a laminar flamelet model to a series of two-dimensional test cases. The model is computationally efficient applying an algebraic expression to calculate the flame surface area, an empirical correlation for the laminar flame speed and a novel unstructured, solution adaptive numerical grid system which allows important features of the solution to be resolved close to the flame. Accurate flame shapes are predicted, the correct burning rate is predicted near the walls, and an improvement in the predicted overpressures is obtained. However, in these fully turbulent calculations the overpressures are still too high and the flame arrival times too low, indicating the need for a model for the early laminar burning phase. Due to the computational expense, it is unrealistic to model a laminar flame in the complex geometries involved and therefore a pragmatic approach is employed which constrains the flame to propagate at the laminar flame speed. Transition to turbulent burning occurs at a specified turbulent Reynolds number. With the laminar phase model included, the predicted flame arrival times increase significantly, but are still too low. However, this has no significant effect on the overpressures, which are predicted accurately for a baffled channel test case where rapid transition occurs once the flame reaches the first pair of baffles. In a channel with obstacles on the centreline, transition is more gradual and the accuracy of the predicted overpressures is reduced. However, although the accuracy is still less than desirable in some cases, it is much better than the order of magnitude error previously expected. This revised version was published online in July 2006 with corrections to the Cover Date.     

A systematic derivation of a consistent set of “Boussinesq equations”

The often used “Boussinesq equations” for the determination of the coupled flow and temperature field in natural convection are systematically deduced by an asymptotic approach. With the nondimensional temperature difference that drives the flow, ?, as a perturbation parameter the leading order equations are identified as the appropriate equations, named “asymptotic Boussinesq equations”. These equations appear as the distinguished limit $\varepsilon\rightarrow0The often used “Boussinesq equations” for the determination of the coupled flow and temperature field in natural convection are systematically deduced by an asymptotic approach. With the nondimensional temperature difference that drives the flow, ɛ, as a perturbation parameter the leading order equations are identified as the appropriate equations, named “asymptotic Boussinesq equations”. These equations appear as the distinguished limit e?0\varepsilon\rightarrow0 and Ec? 0{Ec}\rightarrow 0 with Ec/e = const.{Ec}/\varepsilon =const. The equations are compared to “Boussinesq equations” of other studies and used to calculate Nusselt numbers in laminar and turbulent flows in infinite vertical channels as an example and for the justification of the asymptotic approach.     

Numerical simulation of magnetohydrodynamic flow in a toroidal duct of square cross-section

We present numerical simulation results of the quasi-static magnetohydrodynamic (MHD) flow in a toroidal duct of square cross-section with insulating Hartmann walls and conducting side walls. Both laminar and turbulent flows are considered. In the case of steady flows, we present a comprehensive analysis of the secondary flow. It consists of two counter-rotating vortex cells, with additional side wall vortices emerging at sufficiently high Hartmann number. Our results agree well with existing asymptotic analysis. In the turbulent regime, we make a comparison between hydrodynamic and MHD flows. We find that the curvature induces an asymmetry between the inner and outer side of the duct, with higher turbulence intensities occurring at the outer side wall. The magnetic field is seen to stabilize the flow so that only the outer side layer remains unstable. These features are illustrated both by a study of statistically averaged quantities and by a visualization of (instantaneous) coherent vortices.     

Evaluation of transient turbulent flow fields using digital cinematographic particle image velocimetry

This paper describes an experimental development for temporal and spatial reconstruction of continuously varying flow fields by means of digital cinematographic particle image velocimetry (PIV). The system uses a copper-vapor laser illumination synchronized with a high-speed camera, and continuously samples at 250 fps to measure transient and non-periodic turbulent flows with relatively low frequencies, i.e., the surf zone turbulence produced by depth-limited wave break in a long laboratory flume. The use of the developed PIV system comprehensively records the temporal development of both phase-averaged and instantaneous turbulent vortex flows descended from the breaking waves to the bottom. Also, the measured power spectra show harmonic frequencies, ranging from the orbital frequency of 0.5 Hz up to the order of 5 Hz, and the well-known −5/3 dependence upon the turbulence fluctuation frequencies thereafter. Received: 2 December 1999/Accepted: 6 September 2000