Abstract
Fanno theory provides an analytical model for one-dimensional confined viscous compressible flows. The model holds under the assumptions of adiabatic flow and constant cross-section channel. From theory, the differential of every flow-related quantity is expressed as a function of Mach number and friction factor. One-dimensional flow numerical models can be derived by discretizing Fanno equations. However, theory does not assess how to evaluate friction, while the model works properly only if friction is estimated correctly. Compressibility and turbulence act by deforming the velocity profile making it flatter. Assuming the friction factor function of the Reynolds number alone, in line with incompressible flow theory, is thus not correct. Better correlations should include the Mach number to address compressibility effects. Here, the impact of turbulence and compressibility on the velocity profiles in a micro-channel is analysed by means of CFD simulations. Friction factor correlations are deduced for turbulent micro-flows. The impact of the velocity profile on other quantities, such as dynamic pressure and bulk temperature, needed for the numerical model operation, is also evaluated. Additional correlations for these quantities overcome the instrinsic limits of the one-dimensional model, necessarily unaware of local velocity profiles, in a quasi-2D fashion significantly improving its predicting capabilities.
Highlights
Micro-scale fluid flow is attracting a growing interest thanks to miniaturization in many technological fields
Other works investigate the problem from a more theoretical or analytical point of view as the understanding of the fundamental physics behind micro-scale fluid flow and heat transfer still represents a challenge for the scientific community with regard to many aspects including multi-phase flows, boiling flows, rarefied gas condition, heat transfer, friction, and compressibility effects, either under laminar or turbulent flow condition
Compressible friction factors in micro-channels were investigated in [9, 10] where laminar and turbulent correlations were proposed, respectively
Summary
Micro-scale fluid flow is attracting a growing interest thanks to miniaturization in many technological fields. Other works investigate the problem from a more theoretical or analytical point of view as the understanding of the fundamental physics behind micro-scale fluid flow and heat transfer still represents a challenge for the scientific community with regard to many aspects including multi-phase flows, boiling flows, rarefied gas condition, heat transfer, friction, and compressibility effects, either under laminar or turbulent flow condition. Compressible friction factors in micro-channels were investigated in [9, 10] where laminar and turbulent correlations were proposed, respectively. The correlations are derived from a detailed analysis of the velocity profiles from a set of CFD simulations As such they are able to include additional information that normally would not be available in a one-dimensional model where at each section every flow characteristic is represented by a single average value. The superposition of compressibility and turbulence effects on the shape of the velocity profiles is more complicated and nonlinear, requiring more elaborated correlations to be modelled
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Communications in Heat and Mass Transfer
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
