PSI - Issue 65

Golodnova A.I. et al. / Procedia Structural Integrity 65 (2024) 97–101 Golodnova A.I., Erpalov M.V. / Structural Integrity Procedia 00 (2024) 000–000

99 3

1. The nature of the movement in the channels should be laminar (Re ≤ 2300). Therefore, the Reynolds criterion (Re) is determined: Re= ν d g υ = ν d g ·ρ ƞ , (1) where d g is the hydraulic diameter of the channel, m; υ are the kinematic viscosity of the gas mixture, ν are the flow velocity, ƞ are the dynamic viscosity of the flow, ρ are the flow density. 2. Under conditions of constant gas stoichiometry, small channels pass gas faster than large channels, and the gas velocity is proportional to the flow rate, as explained in equations (2) and (3) N=ν А=ν А n ·n , (2) where N, A, ν, n, Ai are denote the total volumetric flow rate, the total cross-sectional area of the flow channels, the flow velocity, the number of flow channels and the individual cross-sectional area of each flow channel, respectively. 2.1 Under conditions of the presence of braking elements, the velocity ratio maintain: ν 1 λ 1 =ν 2 λ 2 , (3) where ν1 ν2 are the flow velocity before and after the turn, λ1, λ2 are the coefficient of friction losses before and during the turn. 3.1 One of the main parameters of gas movement through channels is the pressure drop. It is noted that the greater the pressure drop, the higher the flow velocity. This is explained by the fact that a large pressure drop creates a large driving force, leading to flow acceleration. At the same time, according to the Darcy-Weisbach equation, the pressure drop also depends on the channel length: P=λ·ρ· L d · ν 2 2 (4) where ΔР are the pressure loss due to hydraulic resistance; λ are the coefficient of friction losses along the length; ν are the average velocity of the gas flow, m/s; ρ is the density of gases, kg/m3; d is the hydraulic diameter; L are the channel length [11]. Since the condition of laminar type (Re ≤ 2300) are set, which corresponds to laminar gas flow, the coefficient of friction losses depending on the trajectory along the length is selected as: without turns

64 Rе

λ 1 =

(5)

with turns

λ 2 =λ 1 ·K ,

(6)

where Re are the Reynolds criterion; K are the coefficient taking into account the influence of wall roughness for microchannels, where the cross-section before and after the turn does not change according to reference data taking into account the roughness of the channel surfaces is taken as 1.15. 3. Discussion of results To obtain the calculation results using the KOMPAS software package, the above trajectories with different channel sizes were constructed in the software package on a 5x5 cm plate.