http://orcid.org/0000-0002-8807-1430
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ABSTRACT
The use of Tesla valves for flow control and rectification in mini and microfluidic applications is appealing due to their passive operation and no-moving-parts design. The effectiveness of such valves can be increased through their in-series arrangement, i.e., a multistaged Tesla valve (MSTV). In this study, the effect of inlet Reynolds number (25–200) on the flow rectification and thermal enhancement capabilities of a single Tesla valve and MSTV (up to 10 stages) is numerically investigated through 3D computational fluid dynamics. Based on the simulation results, power-law correlations for MSTV design and performance in terms of Nusselt number, Darcy friction factor, pressure diodicity, and thermal diodicity are derived and provided. The results demonstrate that heat transfer enhancement during reverse flow through the Tesla valve structure is attributable to flow bifurcation, stagnation, and mixing mechanisms; average Nusselt numbers as high as 7.1 were observed for Re = 200. The ability of a Tesla valve to function as a mini-to-micro-type heat exchanger, thermal diode, and/or check valve can benefit several thermal/flow control applications.
Nomenclature
| Ac | = | cross-sectional area (m2) |
| cp | = | isobaric specific heat capacity (J/kg · K) |
| D | = | diameter (m) |
| DH | = | hydraulic diameter (m) |
| Dip | = | pressure diodicity |
| Dit | = | thermal diodicity |
| E | = | total energy (J) |
| e | = | total specific energy (J/kg) |
| f | = | friction factor |
| = | average friction factor | |
| = | running average friction factor | |
| H | = | height (m) |
| = | average heat transfer coefficient (W/m2 • K) | |
| kf | = | thermal conductivity (W/m•K) |
| = | mass flow rate (kg/s) | |
| = | average Nusselt number | |
| = | running average Nusselt number | |
| N | = | number of Tesla valves (stages) |
| P | = | static pressure (Pa) |
| Pr | = | Prandtl number |
| q | = | heat transfer rate (W/m2) |
| Re | = | Reynolds number |
| ΔT | = | temperature difference (K) |
| ΔTLM | = | log-mean temperature difference |
| u | = | velocity (m/s) |
| Greek symbols | = | |
| δ | = | momentum boundary layer entrance length (m) |
| μ | = | dynamic viscosity (Pa • s) |
| ν | = | kinematic viscosity (m2/s) |
| ρ | = | density (kg/m3) |
| тeff | = | effective viscous dissipation |
| Subscripts | = | |
| 1 | = | first valve |
| f | = | forward flow |
| i | = | inlet |
| l,j | = | index |
| o | = | outlet |
| r | = | reverse flow |
| w | = | wall |
| ∞ | = | periodic/fully developed valve |
Nomenclature
| Ac | = | cross-sectional area (m2) |
| cp | = | isobaric specific heat capacity (J/kg · K) |
| D | = | diameter (m) |
| DH | = | hydraulic diameter (m) |
| Dip | = | pressure diodicity |
| Dit | = | thermal diodicity |
| E | = | total energy (J) |
| e | = | total specific energy (J/kg) |
| f | = | friction factor |
| = | average friction factor | |
| = | running average friction factor | |
| H | = | height (m) |
| = | average heat transfer coefficient (W/m2 • K) | |
| kf | = | thermal conductivity (W/m•K) |
| = | mass flow rate (kg/s) | |
| = | average Nusselt number | |
| = | running average Nusselt number | |
| N | = | number of Tesla valves (stages) |
| P | = | static pressure (Pa) |
| Pr | = | Prandtl number |
| q | = | heat transfer rate (W/m2) |
| Re | = | Reynolds number |
| ΔT | = | temperature difference (K) |
| ΔTLM | = | log-mean temperature difference |
| u | = | velocity (m/s) |
| Greek symbols | = | |
| δ | = | momentum boundary layer entrance length (m) |
| μ | = | dynamic viscosity (Pa • s) |
| ν | = | kinematic viscosity (m2/s) |
| ρ | = | density (kg/m3) |
| тeff | = | effective viscous dissipation |
| Subscripts | = | |
| 1 | = | first valve |
| f | = | forward flow |
| i | = | inlet |
| l,j | = | index |
| o | = | outlet |
| r | = | reverse flow |
| w | = | wall |
| ∞ | = | periodic/fully developed valve |
Acknowledgments
The authors acknowledge the support and resources provided by Mississippi State University’s Center for Advanced Vehicular Systems and High Performance Computing Collaboratory (HPC2).