rom Poiseuille theory, it is known that incompressible laminar fullydeveloped flow of a Newtonian fluid in a constant crosssection channel is characterised by steady parabolic velocity profiles after a fullydeveloped flow condition is attained. In turbulent fullydeveloped flow the velocity profiles are nonparabolic and become more flat for higher Reynolds numbers. When the incompressible hypothesis does not hold, as in the case of high velocity ideal gas flow, the velocity profile becomes flatter, as if more turbulent, due to the superposition of compressibility and turbulence effects, if applicable. This is typical in microchannel flows, where pressure gradients are high and the gas is rapidly accelerating, eventually up to the sound velocity. As the flow accelerates the effects of compressibility grow stronger and the velocity profile keeps changing shape. The radial velocity component does not zero as in fullydeveloped flow but reverses after the entrance effects have damped out and grows with the Mach number. A net mass transfer toward the walls is thus generated making the velocity profile more flat. This affects the friction factor which is no longer constant, being proportional to the normaltowall velocity gradient, and needs to be evaluated. In the present work, the compressible friction factor is numerically investigated and correlations are proposed based on the velocity profile shape evolution as a function of the Mach number. This, together with other considerations on the velocity profile shape change, is shown to enhance the predictive capability of the Fanno theory for compressible flows.
Velocity profile development and friction in compressible microflows / Cavazzuti, Marco; Corticelli, Mauro A.; Karayiannis, Tassos G..  2191:(2019). (Intervento presentato al convegno 74th Conference of the Italian Thermal Machines Engineering Association, ATI 2019 tenutosi a Modena nel 1113/9/2019) [10.1063/1.5138775].
Velocity profile development and friction in compressible microflows
Marco Cavazzuti;Mauro A. Corticelli;
2019
Abstract
rom Poiseuille theory, it is known that incompressible laminar fullydeveloped flow of a Newtonian fluid in a constant crosssection channel is characterised by steady parabolic velocity profiles after a fullydeveloped flow condition is attained. In turbulent fullydeveloped flow the velocity profiles are nonparabolic and become more flat for higher Reynolds numbers. When the incompressible hypothesis does not hold, as in the case of high velocity ideal gas flow, the velocity profile becomes flatter, as if more turbulent, due to the superposition of compressibility and turbulence effects, if applicable. This is typical in microchannel flows, where pressure gradients are high and the gas is rapidly accelerating, eventually up to the sound velocity. As the flow accelerates the effects of compressibility grow stronger and the velocity profile keeps changing shape. The radial velocity component does not zero as in fullydeveloped flow but reverses after the entrance effects have damped out and grows with the Mach number. A net mass transfer toward the walls is thus generated making the velocity profile more flat. This affects the friction factor which is no longer constant, being proportional to the normaltowall velocity gradient, and needs to be evaluated. In the present work, the compressible friction factor is numerically investigated and correlations are proposed based on the velocity profile shape evolution as a function of the Mach number. This, together with other considerations on the velocity profile shape change, is shown to enhance the predictive capability of the Fanno theory for compressible flows.File  Dimensione  Formato  

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