Friction factor evaluation of compressible microflows using 1D Fanno flow-based numerical model

A numerical model based on the conventional Fanno flow theory for the friction factor evaluation of the gas flows inside microchannels has recently been developed by Cavazzuti et al. [1]. The current work aims to compare this numerical model with experimental results of microchannels. Pressure drop experiments are performed for a circular cross sectional microtube and a rectangular microchannel with Nitrogen gas as working fluid. The hydraulic diameters of microtube and microchannel are 100 \u3bcm and 69.4 \u3bcm respectively. Rectangular microchannel with an aspect ratio (height to width) of 0.036 is chosen for the comparison. This allows to treat the rectangular microchannel as parallel plate in the numerical Fanno model. During experiments stagnation pressure at the inlet is increased such that maximum Reynolds number is 3000 in the case of microchannel and 7600 for microtube. Results show that for the evaluation of average friction factor in both considered geometries, there exists a good match between Fanno-based 1D numerical model and experimental results in the laminar regime whereas comparison worsens as the flow approaches choking. Limitations as well as the potential reasons for the discrepancies between the developed model and experiments will be discussed

Turbulent temperature profile in the quasi-fully developed region of a micro-tube

Turbulent temperature profiles in the quasi-fully developed region of a micro-tube were obtained numerically by solving the energy equation including the substantial derivative of pressure and viscous dissipation terms for the case of constant wall temperature. The fluid was assumed to be an ideal gas with constant density over the cross-section. The turbulent velocity profile was approximated by the three-layer model of Von Kármán. The temperature profiles were compared with the laminar flow and previous numerical solutions. The total temperature was higher than the wall temperature depending on the Mach number. The static temperature in the quasi-fully developed region agrees well with the temperature results for an ideal gas flow obtained by solving the Navier-Stokes and energy equations

Experiments on measurement of heat transfer rate of gas flow through microchannel with constant wall temperature

Experimental results for the measurement of heat transfer rates in microchannel gas flow are crucial for gas to gas micro heat exchangers. A critical overview of the main factors that play an important role in the determination of heat transfer rate is presented. The experimental and numerical data obtained from authors' previous studies are used in order to highlight the characteristics of convective heat transfer of gas through microchannels with constant wall temperature. It is suggested to obtain heat transfer rates by determining the difference between the gas enthalpy at the inlet and outlet by measuring local temperature and pressure. The heat transfer rates obtained in the present study were compared with those determined by the difference in total temperatures and incompressible flow Nusselt number

Notes on factitious shear work of slip flow in a channel

Gas slip flow is observed in a micro scale channel whose characteristic length is less than about 10 μm under atmospheric conditions. To analyze the slip flow, the energy equation with the viscous dissipation term is solved with a boundary condition which includes a factitious sliding shear work term due to the slip at the wall to compensate the energy balance. Recently, an alternate method which uses the boundary condition without inclusion of the factitious sliding shear work term has been proposed. However, it seems that physics of the slip flow has not been properly understood by researchers. In this paper to clarify the issue, a very simple configuration, a steady state laminar slip flow in a hydro-dynamically fully developed region of a circular micro-tube with an adiabatic wall, is considered. Also all thermo-physical properties of the fluid are assumed to be constant. Theoretical justification to the boundary condition of the energy equation is provided using the discontinuity of the velocity of the slip flow on the wall

Friction factor correlations of slip flow in micro-tubes

Poiseuille number, the product of friction factor and Reynolds number (f·Re) for quasi-fully developed flow in a micro-tube was obtained in slip flow regime. The numerical methodology is based on the Arbitrary- Lagrangian-Eulerian (ALE) method. Two-dimensional compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers with two thermal boundary conditions: CWT (constant wall temperature) and CHF (constant heat flux), respectively. The tube diameter ranges from 3 to 10μm and the tube aspect ratio is 200. The stagnation pressure, pstg is chosen in such away that the exit Mach number ranges from 0.1 to 1.0. The outlet pressure is fixed at the atmospheric pressure. In slip flow, Mach and Knudsen numbers are systematically varied to determine their effects on f·Re. The correlation for f·Re is obtained from numerical results. It was found that f·Re is mainly a function of Mach number and Knudsen number and is different from the values obtained by 64/(1+8Kn) for slow flow. The obtained f·Re correlations are applicable to both no-slip and slip flow regimes. Copyright © 2007 by ASME

On temperature jump condition for turbulent slip flow in a quasi-fully developed region of micro-channel with constant wall temperature

Temperature variation of turbulent slip flows in the quasi-fully developed region of a micro-tube were obtained numerically by solving the energy equation including the substantial derivative of pressure and viscous dissipation terms for the case of constant wall temperature. The fluid was assumed to be an ideal gas with constant density over the cross-section. The turbulent velocity profile was approximated by the three-layer model of Von Kármán. Although the shear work term is not included in the conventional temperature jump boundary condition explicitly, it is verified that the conventional temperature jump boundary condition is valid for a slip flow in a micro-tube with constant wall temperature when both viscous dissipation and substantial derivative of pressure terms are included in the energy equation. The total temperature in the quasi-fully developed region was lower than the wall temperature in the case of Kn ≥ 0.01

Experimental investigations of local friction factors of laminar and turbulent gas flows in smooth micro-tubes

Local friction factors of laminar and turbulent gas flows including choked flows through micro-tubes were experimentally investigated under atmospheric back pressure and variable inlet pressure. The experiments were carried out using two glass micro-tubes with D = 265.7 and 399.9 μm and a fused silica micro-tube with D = 531.2 μm. Two to three pressure tap holes were drilled into the micro-tube wall at intervals of 5 ~ 6 mm to measure local pressures. The local Mach numbers, temperatures and friction factors were obtained by using stagnation temperatures and pressures, local pressures and mass flow rates. The results for wide range of Reynolds numbers and Mach numbers were obtained including choked flows. Both the local Fanning and the local Darcy friction factors were obtained under the assumption of both Fanno flow (adiabatic wall) and isothermal flow, respectively. Since the measured values of the inner relative surface roughness of the micro-tubes were less than 0.02 %, only the effect of compressibility on friction factors was assessed. The difference between Fanning and Darcy friction factors was described and compared with the ff and fd correlation as a function of Mach number. The friction factor difference obtained under the assumption of Fanno and isothermal flows was also compared with the available literature and numerical results. In the turbulent flow region including the choked flow, the local Fanning friction factors under the assumption of Fanno flow nearly coincided with Blasius correlation