Use of concentration-pulsation equation in the calculation of jet-type turbulent flows

Research of the petroleum road bitumen modification process with secondary polyethylene terephthalate

“…Using the probabilistic approach [13][14][15][16][17], we first describe a set of elements of the phase space 𝑑𝑑𝑑𝑑, which in this case will be a combination of the random velocity of the PET -v particle and its random size D. It corresponds to the mechanism of formation of PET particles from the melt in the process of temperature reduction [13,15]:…”

“…Where 𝐽𝐽 𝑧𝑧 = 2 5 𝑚𝑚𝑚𝑚 2 is the moment of inertia of the PET particle, 𝜔𝜔 is the angular velocity of its rotation, which can be considered proportional to the velocity v, or 𝜔𝜔 = 2𝑑𝑑 0 𝑤𝑤𝑑𝑑 0 𝑑𝑑 𝑏𝑏 −1 . The surface energy of the particles is determined by the formula [13,14]:…”

“…The expression for the differential particle size distribution function PET according to [12][13][14] will be formed for the reduced elementary phase volume 𝑑𝑑𝑑𝑑′ = 𝑑𝑑𝑤𝑤:…”

“…The values 𝑘𝑘 0 , 𝑘𝑘 3 -𝑘𝑘 8 are determined in accordance with the formulas: The graph of the probability density function of the number of PET particles over a nondimensional parameter 𝐷𝐷 𝑏𝑏 is shown in Figure 1. The main average characteristics of the process (non-dimensional diameter 𝐷𝐷 𝑏𝑏 , particle surface S, and volume V) of the formation of PET particles according to [13,14] After integrating expressions (20) we have:…”