Incompressible micromorphic fluid model for turbulence

A theory of incompressible micromorphic fluids is introduced as a rational model for turbulence studies. Balance laws and constitutive equations are given. The theory is then applied to obtain the solution of the turbulent channel flow problem. Turbulent velocity, gyrations, Reynolds stresses, root-mean squares of longitudinal and transverse turbulent velocities, and turbulent shear stress are given.     

A universal approach for mean mechanical energy losses analysis

A vorticity form of mean mechanical energy equation is derived in equipments with inlets and outlets, which establishes a relation between the mean mechanical energy losses and flow parameters such as vorticity, Reynolds stress, etc. The causes of mean mechanical energy losses and distribution of relatively larger losses in the fluid field have been found. The approach in this paper presents a universal tool for energy analysis and mechanism research of drag reduction in complex equipments.     

高浓度固液混合流的湍流模型

建立了高浓度固液混合流的湍流模型，分析了混合流的应力（包括颗粒碰撞应力、粘性应力、湍流应力及Ｃｏｕｌｏｍｂｉｃ摩擦应力）。根据高浓度混合流中颗粒的受力，得出了颗粒运动的力平衡方程。由于引入颗粒碰撞应力和Ｃｏｕｌｏｍｂｉｃ摩擦应力，本模型较其它模型更适合具有高浓度和大颗粒的流场。利用本模型模拟的高浓度含沙水流在水平管道中的流动特性，其数值结果与前人所做的实验结果较一致。     

Two fluid model for two-phase turbulent jets

Eulerian two-fluid models are widely used in nuclear reactor safety and CFD. In these models turbulent diffusion of a dispersed phase must be formulated in terms of the fluctuating interfacial force and the Reynolds stresses. The interfacial force is obtained using the probability distribution function approach by Reeks (1992). This paper is the first application of this force to a case of engineering interest outside homogeneous turbulence. An Eulerian multidimensional two-fluid model for a cylindrical two-phase dispersed particle jet is proposed and compared with experimental data. The averaged conservation equations of mass and momentum are solved for each phase and the turbulent kinetic energy equation is solved for the continuous phase. The turbulent diffusion force and the Reynolds stresses are constituted within the context of the k- model of turbulence. A dissipation term has been added to the k- model for the turbulence modulation by the particles. Once the constitutive relations have been defined, the two-fluid model is implemented in a computational fluid dynamics code. It is shown that when the particles are very small the model is consistent with a convection-diffusion equation for particle transport where the diffusivity is defined according to Taylor's model (Taylor, G.I., 1921. Diffusion by continuous movements. Proc. London Math. Society, A20, pp. 196–211). The two-fluid model is also compared against two experimental data sets. Good agreement between the model and the data is obtained. The sensitivity of the results to various turbulent mechanisms is discussed.     

Theoretical model of a drying system including turbulence aspects

Biological products contain high moisture content in the harvest period. Such moisture could cause their deterioration in storage. Drying is an interesting solution to keep the quality of these products. Generally, drying process is based on contact of a dry air phase with a wet solid. A theoretical model was developed to describe the dynamic behavior of a forced convection drying process. This model takes into account the entire dynamic phenomenon including turbulence, diffusivity and tortuosity effects. Only the mass transfer of water molecules during vaporization was referred to as an empirical expression. The model thus strongly build, was compared to Thompson’s empirical model. Corn grain was used in the validating process. Transient temperature and water content results are presented.     

Mass transfer to clean bubbles at low turbulent energy dissipation

Experimental gas-liquid mass transfer data from a system where single bubbles are kept stationary by a low turbulence downward liquid flow are compared with predictions from theoretical models which take turbulence into account. The data clearly show that, for the turbulence intensities at play, turbulence does not affect mass transfer. Higbie's equation with contact time t_e=d/u may be used for the calculation of the gas-liquid mass transfer coefficient of clean bubbles in systems with levels of turbulent kinetic energy dissipation of, at least, up to .     

Turbulent particle mass flux in a two-phase shear flow

This paper presents measurements of mean and rms of fluctuations of concentration, particle turbulent velocities, shear stress and covariance of the fluctuations of particle number density and particle velocities in a horizontal plane shear layer. Particle Image Velocimetry (PIV) was used to obtain simultaneously particle velocities and number densities to evaluate models for the prediction of particle dispersion in Reynolds-Averaged Navier-Stokes calculation approaches. The flow was horizontal with the low speed side on top and laden with nearly mono-dispersed 55 and 90 µm glass beads, which were injected at the upper, low speed side of the flow. The Stokes number of the particles was in the range of 0.41 to 4.3 and the drift parameter due to gravity was in the range 0.18 to 1.5. The experimental results quantified how particle ‘centrifuging’ by the large fluid vortices influenced the measured quantities. The turbulent particle mass flux was compared with models based on the gradient of mean particle concentration. Different dispersion coefficients were evaluated by introducing the measured quantities into the model equation and it was found that dispersion coefficients based on the fluid eddy diffusivity performed poorly leading to an order of magnitude errors. A dispersion coefficient in tensor form, based on the product of particle shear stress and particle integral time scale, led to good agreement with measured turbulent particle mass fluxes with errors between 0 and 50%.     

Use of angle resolved PIV to estimate local specific energy dissipation rates for up- and down-pumping pitched blade agitators in a stirred tank

Up-pumping pitched blade turbines (and similar impellers) have recently been shown to be particularly effective for achieving a variety of mixing duties. Here, their turbulent flow characteristics are analysed by angle-resolved particle image velocimetry (PIV) for the first time and compared with their down-pumping equivalent, the usual time-averaged parameters also being determined for each. The work was conducted in 0.15 m diameter vessel (T) with a 45° impeller of diameter D (=0.45T) in water. The angle-resolved PIV enables a number of novel features to be identified. Firstly, the two pumping directions are shown to give very different vortex structures, even though the flow numbers, Fl, are the same (=0.79). In addition, the ‘spottiness’ of the normalized kinetic energy along a radius as the trailing vortex moved away from each impeller can be identified, which is not shown from time-averaged data. Often, the most important parameter for processing is the local normalized specific energy dissipation rate, and this is estimated using three methodologies: by measurement of the components of the stress tensor directly, ; by dimensional analysis, , with measured integral length scales (ILS); and by the Smagorinsky closure method, , to model unresolved scales (with a Smagorinsky constant used in the literature on stirred vessels). Again, only the angle-resolved results show the spottiness of and also higher values than the time-averaged. Differences in the values obtained by the three methods are discussed and compared with the existing literature. Most importantly, for the first time, the power input in the PIV-interrogated region is calculated from the three methods and compared to the input based on the impeller torque. Both DA and SGS methods are shown to overestimate the true power by a factor of 5 and 2, respectively, whilst the DE method provided a significant underestimate (1/5th) due to the limitation of the resolved length scales. The SGS method shows the greatest promise and by changing the value of the Smagorinsky constant in accordance with recent recommendations, good agreement is obtained. Nevertheless, it is concluded that there is still a need for improved methods for determining the important mixing parameter, .     

Population balance modelling of protein precipitates exhibiting turbulent flow through a circular pipe

The breakage of liquid-liquid, solid-liquid and solid-gas dispersions occurs in many industrial processes during the transport of particulate materials. In this work, breakage of whey protein precipitates passing through a capillary pipe is examined and an experimentally derived breakage frequency is applied to construct a suitable population balance model to characterize the breakage process. It has been shown that the breakage frequency of precipitate particles is highly dependent on their shear history and on the turbulent energy dissipation rate in the pipe. The population balance equation (PBE) uses a volume density based discrete method which is adapted from mass density based discretization. In addition to comparing the model with experimental data, predicted results at different velocities are presented. It was found that the population balance breakage model provides satisfactory results in terms of predicting particle size distributions for such processes.     

Multi-fluid simulation of turbulent bubbly pipe flows

Radial distributions of void fraction α_G, bubble aspect ratio E, phasic velocities V_G and V_L and turbulent kinetic energy k in bubbly pipe flows are measured using an image processing method and a laser Doppler velocimetry. Multi-fluid simulations are conducted to examine applicability of state-of-the-art closure relations to the turbulent bubbly pipe flows. The experimental results indicate that aspect ratio of bubbles in the near wall region takes a higher value than that of free rising bubbles due to the presence of wall, and that the change in the aspect ratio induces decrease in relative velocity between bubbles and liquid in the near wall region. Drag coefficient C_D of a bubble in a bubbly pipe flow tends to increase with magnitude of shear flow, and the effect of shear flow on C_D is estimated by the correlation proposed by Legendre and Magnaudet (1998). Comparison between the simulated and the measured results indicate that the effects of bubble shape and shear flow on drag force acting on bubbles should be taken into account for accurate predictions of bubbly pipe flows. The turbulence models proposed by Lopez de Bertodano et al. (1994) and by Hosokawa and Tomiyama (2004a) give good predictions for turbulence modification caused by bubbles.