DRAG COEFFICIENT OF A SOLID SPHERE UNDER NON-ISOTHERMAL CONDITIONS

The results of an experimental study of gravitational settling of a cooled (T = 82 K, 250 K) and a heated (T = 373 K, 473 K, 573 K) steel ball in glycerin and polymethylsiloxane liquids (PDMS-10000, PDMS-30000) in the range of the Reynolds numbers Re = 10−3–1 are presented. It is shown that the stationary velocity of gravitational settling of a particle decreases with its cooling and, conversely, it increases with heating of the particle. A time dependence of the distance traveled by the particle is found to be linear for both heated, cooled, and etalon (T = Tl) solid spheres. The effect of the difference in the particle and carrier medium temperatures on the drag coefficient of the solid sphere is analyzed. For the considered Reynolds numbers, it is revealed that the drag coefficient of a single solid sphere is determined by CD = a /Re , where a is the empirical coefficient depending on the ratio of the particle and liquid temperatures T = T /Tl . Using the regression analysis method, the expression for a drag coefficient of a solid particle under non-isothermal conditions at T >> 1 is found to be similar to the Hadamard –Rybczynski expression CD = 16/Re, which is obtained for a spherical bubble (or a drop). The empirical dependences of the drag coefficient for a cooled and a heated solid sphere on the difference in the particle and liquid temperatures δТ = 1− T are obtained.

Нелинейные эффекты в поле вязких волн, возбужденном пластиной конечных размеров

The numerical study of nonlinear non-stationary velocity and pressure fields close to an absolutely rigid plate oscillating in incompressible viscous fluid along its length was performed. The plate had an infinitesimal thickness and finite length. The study showed that limiting the length of the plate leads to the problem non-linearity, which appears even with a small amplitude of the plate surface oscillations. We also studied the velocity and pressure fields with large amplitudes of the plate surface oscillations. The arising of the plug flows during the oscillations of the plate of infinitesimal thickness and finite length was explained in terms of viscous waves. The instant vortex motion formation mechanism in viscous fluid was uncovered.

Model and Stability of the Traffic Flow Consisting of Heterogeneous Drivers

Although traffic flow has attracted a great amount of attention in past decades, few of the studies focused on heterogeneous traffic flow consisting of different types of drivers or vehicles. This paper attempts to investigate the model and stability analysis of the heterogeneous traffic flow, including drivers with different characteristics. The two critical characteristics of drivers, sensitivity and cautiousness, are taken into account, which produce four types of drivers: the sensitive and cautious driver (S-C), the sensitive and incautious driver (S-IC), the insensitive and cautious driver (IS-C), and the insensitive and incautious driver (IS-IC). The homogeneous optimal velocity car-following model is developed into a heterogeneous form to describe the heterogeneous traffic flow, including the four types of drivers. The stability criterion of the heterogeneous traffic flow is derived, which shows that the proportions of the four types of drivers and their stability functions only relating to model parameters are two critical factors to affect the stability. Numerical simulations are also conducted to verify the derived stability condition and further explore the influences of the driver characteristics on the heterogeneous traffic flow. The simulations reveal that the IS-IC drivers are always the most unstable drivers, the S-C drivers are always the most stable drivers, and the stability effects of the IS-C and the S-IC drivers depend on the stationary velocity. The simulations also indicate that a wider extent of the driver heterogeneity can attenuate the traffic wave.