Compressibility Effects on Kinetic Energy Correction Factors for Laminar and Turbulent Gas Flows

Abstract

Abstract. This study investigates the effect of compressibility on the kinetic energy correction factor, α, in both laminar and turbulent gaseous flows. In Bernoulli's equation, α is defined as the ratio of kinetic energy based on the integrated nonuniform velocity distribution to that based on a uniform distribution. For incompressible flows, α assumes the characteristic values of 2 for laminar flow with a parabolic velocity profile and approximately 1 for turbulent flow with a nearly uniform profile. In compressible gas flows, however, the velocity and temperature distributions can deviate substantially from their incompressible counterparts. To quantify these effects, numerical simulations were performed using the arbitrary Lagrangian–Eulerian (ALE) method to solve the two-dimensional compressible momentum and energy equations. The simulations covered a wide range of Reynolds numbers for both laminar and turbulent regimes under adiabatic wall conditions, with tube diameters ranging from 10 μm to 10 mm and a fixed length-to-diameter ratio (L/D) of 200. The results show that, in laminar flow, velocity profiles progressively depart from the classical parabolic form as the Mach number increases along the tube length. In turbulent flow, velocity distributions deviate from the conventional power-law profile, with the extent of deviation depending on the Reynolds number. Overall, the findings indicate that α decreases with increasing Mach number in laminar flow, whereas it remains essentially constant and largely independent of Mach number in turbulent flow.