Friction factor correlations for laminar, transition and turbulent flow in smooth pipes

In this paper we derive an accurate composite friction factor vs. Reynolds number correlation formula for laminar, transition and turbulent flow in smooth pipes. The correlation is given as a rational fraction of rational fractions of power laws which is systematically generated by smoothly connecting linear splines in log-log coordinates with a logistic dose curve algorithm. This kind of correlation seeks the most accurate representation of the data independent of any input from theories arising from the researchers’ ideas about the underlying fluid mechanics. As such, these correlations provide an objective metric against which observations and other theoretical correlations may be applied. Our correlation is as accurate, or more accurate, than other correlations in the range of Reynolds numbers in which the correlations overlap. However, our formula is not restricted to certain ranges of Reynolds numbers but instead applies uniformly to all smooth pipe flow data for which data is available. The properties of the classical logistic dose response curve are reviewed and extended to problems described by multiple branches of power laws. This extended method of fitting which leads to rational fractions of power laws is applied to data of Marusic and Perry (1995) [1] for the velocity profile in a boundary layer on a flat plate with an adverse pressure gradient, to data of Nikuradse (1932) [2] and McKeon et al. (2004) [3] on friction factors for flow in smooth pipes and to the data of Nikuradse [4] for effectively smooth pipes.     

Physics and mechanics of heat exchange processes in nanofluid flows

Nanofluids present a new type of dispersed fluids consisting of a carrier fluid and solid nanoparticles. Unusual properties of nanofluids, particularly high thermal conductivity, make them eminently suitable for many thermophysical applications, e.g., for cooling of equipment, designing of new heat energy transportation and production systems and so on. This requires a systematic study of heat exchange properties of nanofluids. The present paper contains the measurement results for the heat transfer coefficient of the laminar and turbulent flow of nanofluids on the basis of distilled water with silica, alumina and copper oxide particles in a minichannel with circular cross section. The maximum volume concentration of particles did not exceed 2%. The dependence of the heat transfer coefficient on the concentration and size of nanoparticles was studied. It is shown that the use of nanofluids allows a significant increase in the heat transfer coefficient as compared to that for water. However, the obtained result strongly depends on the regime of flow. The excess of the heat transfer coefficient in the laminar flow is only due to an increase in the thermal conductivity coefficient of nanofluid, while in the turbulent flow the obtained effect is due to the ratio between the viscosity and thermal conductivity of nanofluid. The viscosity and thermal conductivity of nanofluids depend on the volume concentration of nanoparticles as well as on their size and material and are not described by classical theories. That is why the literature data are diverse and contradictory; they do not actually take into account the influence of the mentioned factors (size and material of nanoparticles). It has been shown experimentally and by a molecular dynamics method that the nanofluid viscosity increases while the thermal conductivity decreases with the decreasing dispersed particle size. It is found experimentally for the first time that the nanofluid viscosity coefficient depends on the particle material. The higher is the density of particles, the higher is the thermal conductivity coefficient of nanofluid.     

地源热泵耦合地埋管换热计算若干问题的研究

针对地质构造特点,进行地下一定深度的温度场测试;对耦合地埋管的换热设计计算中的若干问题进行了研究;在简化计算换热模型的基础上,在Excel上用VBA编写宏功能,得到实用的地埋管换热的工程设计计算方法,是一种工程易用的计算软件。同时将这种计算方法应用到了一个实际工程中,并对计算结果进行了验证。     

Incomplete similarity of a plane turbulent wall jet on smooth and transitionally rough surfaces

This study assesses the hypothesis of incomplete similarity for a plane turbulent wall jet on smooth and transitionally rough surfaces. Typically, a wall jet is considered to consist of two regions: an inner layer and an outer layer. The degree to which these two regions reach equilibrium with each other and interact to produce the property of self-similarity remains an open question. In this study, the analysis of the outer and inner regions indicates that each region is characterised by a half-width which exhibits its own distinct dependence on the streamwise distance x from the slot, and a single self-similar structure for both regions does not exist. More specifically, the inner and outer layers of the wall jet exhibit different scaling laws, which results in two self-similar mean velocity profiles, both of which retain a dependence on the slot height H. As such, incomplete similarity of the wall jet on smooth and transitionally rough surfaces is confirmed by this study. In addition, comparison of the experimental results for the transitionally rough surface with the smooth wall case indicates that the surface roughness modifies the development of the mean velocity profile in both the inner and outer regions, although the effect on the outer region is relatively small and close to the experimental uncertainty.     

Aspect ratio effects in turbulent duct flows studied through direct numerical simulation

Three-dimensional effects in turbulent duct flows, i.e., sidewall boundary layers and secondary motions, are studied by means of direct numerical simulation (DNS). The spectral element code Nek5000 is used to compute turbulent duct flows with aspect ratios 1–7 (at Re_{b, c} = 2800, Re_{τ, c} ? 180) and aspect ratio 1 (at Re_{b, c} = 5600, Re_{τ, c} ? 330), in streamwise-periodic boxes of length 25h. The total number of grid points ranges from 28 to 145 million, and the pressure gradient is adjusted iteratively in order to keep the same bulk Reynolds number in the centreplane with changing aspect ratio. Turbulence is initiated via a trip forcing active during the initial stages of the simulation, and the statistical convergence of the data is discussed both in terms of transient approach and averaging period. Spanwise variations in wall shear, mean-flow profiles, and turbulence statistics are analysed as a function of aspect ratio, and also compared with the spanwise-periodic channel (as idealisation of an infinite aspect ratio duct). The computations show good agreement with experimental measurements carried out in parallel at the Illinois Institute of Technology (IIT) in Chicago, and highlight the relevance of sidewall boundary layers and secondary vortices in the physics of the duct flow. The rich array of secondary vortices extending throughout the upper and lower walls of the duct, and their dependence on Reynolds number and aspect ratio, had not been reported in the literature before.     

Noise of a turbulent boundary layer flow over smooth and rough plates at low mach numbers

The spectral levels of the quadrupole noise generated by a boundary layer flow over a smooth surface are calculated. Explicit dependences of the noise levels on the Reynolds number are obtained for the low-frequency and high-frequency ranges. It is shown that the logarithmic zone of the velocity profile is responsible for the region of the quadrupole noise spectrum with a hyperbolic dependence on frequency. A method of calculating the dipole noise of a boundary layer flow over a rough surface is developed. The method is based on the use of the combined probability density for the turbulent velocity fluctuations and the random dimensions of protuberances of the rough surface. The two constants involved in this theory are determined from a special experiment. It is shown that the surface roughness noticeably increases the radiation levels of a boundary layer flow in a certain frequency range.     

The evolution of velocity profiles and turbulent viscosity in a system of currents with wind-induced and density flows

The results of an in-situ study and mathematical modeling of a system of currents with wind-induced and density flows are presented. The model is based on the obtained dependences of its key parameters on the density-field characteristics, changes in the water level, and the water-reservoir topography. The revealed features of the of shear-velocity profile are indicated and a function of its distribution from the bottom to the open surface of the water is given. The model that was developed is verified by the data from measuring the parameters of currents and composition of water in the Petrozavodsk Bay of Onega Lake in September 2007. The regularities for the evolution of distributions of the coefficient of the turbulent exchange and current velocity over depth and in time are revealed.     

Residence-time distributions for chaotic flows in pipes

In this paper we derive two rigorous properties of residence-time distributions for flows in pipes and mixers motivated by computational results of Khakhar et al. [Chem. Eng. Sci. 42, 2909 (1987)], using some concepts from ergodic theory. First, a curious similarity between the isoresidence-time plots and Poincare maps of the flow observed in Khakhar et al. is resolved. It is shown that in long pipes and mixers, Poincare maps can serve as a useful guide in the analysis of isoresidence-time plots, but the two are not equivalent. In particular, for long devices isoresidence-time sets are composed of orbits of the Poincare map, but each isoresidence-time set can be comprised of many orbits. Second, we explain the origin of multimodal residence-time distributions for nondiffusive motion of particles in pipes and mixers. It is shown that chaotic regions in the Poincare map contribute peaks to the appropriately defined and rescaled axial distribution functions. (c) 1999 American Institute of Physics.     

Evaporating droplets in turbulent reacting flows

Three-dimensional direct numerical simulations are carried out to determine the effects of turbulence on the preferential segregation of an evaporating spray and then to study the evolution of the resulting mixture fraction topology and propagating flame. First, the mixing between an initially randomly dispersed phase and the turbulent gaseous carrier phase is studied with non-evaporating particles. According to their inertia and the turbulence properties, the formation of clusters of particles is analyzed (formation delay, cluster characteristic size and density). Once the particles are in dynamical equilibrium with the surrounding turbulent flow, evaporation is considered through the analysis of the mixture fraction evolution. Finally, to mimic ignition, a kernel of burnt gases is generated at the center of the domain and the turbulent flame evolution is described.     

Helicity generation in turbulent MHD flows

We study turbulent flow of a conducting liquid in a uniform external magnetic field. It is shown that intense helicity generation is possible in the presence of a mean shear flow. It is noted that even though the mean helicity of the initial flow can be zero, the presence of internal topological structure of the flow, for example the presence of helicity of different signs at different scales, is nevertheless necessary for helicity generation. Zh. éksp. Teor. Fiz. 114, 946–955 (September 1998)     

Velocity correlations in dense granular flows

Velocity fluctuations of grains flowing down a rough inclined plane are experimentally studied. The grains at the free surface exhibit fluctuating motions, which are correlated over a few grain diameters. The characteristic correlation length is shown to depend on the inclination of the plane and not on the thickness of the flowing layer. This result strongly supports the idea that dense granular flows are controlled by a characteristic length larger than the particle diameter.     

Effects of forcing in three-dimensional turbulent flows

We present the results of a numerical investigation of three-dimensional homogeneous and isotropic turbulence, stirred by a random forcing with a power-law spectrum, E(f)(k) approximately k(3-y). Numerical simulations are performed at different resolutions up to 512(3). We show that at varying the spectrum slope y, small-scale turbulent fluctuations change from a forcing independent to a forcing dominated statistics. We argue that the critical value separating the two behaviors, in three dimensions, is y(c)=4. When the statistics is forcing dominated, for yy(c), we find the same anomalous scaling measured in flows forced only at large scales. We connect these results with the issue of universality in turbulent flows.     

Structure analysis of turbulent mixing patterns in inert and reactive turbulent liquid flows

The paper contains an extended summary of an invited plenary talk given at the Workshop on Active Chaos at the Los Alamos National Laboratory on 29-31 May 2001 by one of us (F.S.R.). (c) 2002 American Institute of Physics.     

Statistics of Lagrangian velocities in turbulent flows

We present a generalized Fokker-Planck equation for the joint position-velocity probability distribution of a single fluid particle in a turbulent flow. Based on a simple estimate, the diffusion term is related to the two-point two-time Eulerian acceleration-acceleration correlation. Dimensional analysis yields a velocity increment probability distribution with normal scaling v approximately t(1/2). However, the statistics need not be Gaussian.     

Velocity profiles in shear-banding wormlike micelles

Using dynamic light scattering in heterodyne mode, we measure velocity profiles in a much studied system of wormlike micelles (CPCl/NaSal) known to exhibit both shear-banding and stress plateau behavior. Our data provide evidence for the simplest shear-banding scenario, according to which the effective viscosity drop in the system is due to the nucleation and growth of a highly sheared band in the gap, whose thickness linearly increases with the imposed shear rate. We discuss various details of the velocity profiles in all the regions of the flow curve and emphasize the complex, non-Newtonian nature of the flow in the highly sheared band.