Analytical solutions for the incompressible laminar pipe flow rapidly subjected to the arbitrary change in the flow rate

Ashok Kannaiyan; Thirumaran Varathalingarajah; Sekarapandian Natarajan

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Analytical solutions for the incompressible laminar pipe flow rapidly subjected to the arbitrary change in the flow rate

机译：Analytical solutions for the incompressible laminar pipe flow rapidly subjected to the arbitrary change in the flow rate

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A one-dimensional mathematical model is developed for an unsteady incompressible laminar flow in a circular pipe subjected to a rapid change in the flow rate from an initial flow with flow rate, Q_i, to a final flow with flow rate, Q_f, in a step-like fashion at an arbitrary time, t_c. The change in the flow rate may either be an increment, Q_f > Q_i, or a decrement, Q_f < Q_i. The change time, t_c, may either belong to the initial flow remaining in a temporally developing state or temporally developed state. The developed model is solved using the Laplace transform method to deduce generalized analytical expressions for the flow characteristics, viz., velocity, pressure gradient, wall shear stress, and skin friction factor, C_f Re, where Re is Reynolds number based on the cross-sectional area-averaged velocity and pipe radius. Exact solutions for λ_a = Q_i/Q_f = 0 and λ_d = Q_f /Q_i = 0 with t_c ≥ t_(si) are available in the literature and the present generalized analytical solutions fill the remaining range of parameters, 0 < λ_a < 1 and 0 < λ_d < 1 with 0 < t_c < t_(si) and t_c ≥ t_(si), where tsi is the time at which the initial flow reaches the temporally developed state. Exact solutions for canonical pipe flow problems reported in the literature are deduced as subsets of the derived generalized solutions. The parametric study reveals the effects of varying λ_a or λ_d and t_c on the quantities of practical importance, viz., τ_s and C_f Re, where τ_s is the time required for the final flow to reach the temporally developed state.

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来源
《Physics of fluids》 |2021年第1期|043601-1-043601-14|共14页
作者
Ashok Kannaiyan; Thirumaran Varathalingarajah; Sekarapandian Natarajan;
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作者单位

Faculty of Mathematics, Technical University of Chemnitz, Chemnitz, Saxony 09111, Germany;

Computational Fluid Dynamics Laboratory, School of Mechanical Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu 632014, India;

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正文语种英语
中图分类流体力学;
关键词
Analytical; incompressible laminar; pipe flow rapidly subjected;

Analytical solutions for the incompressible laminar pipe flow rapidly subjected to the arbitrary change in the flow rate

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