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Nasibullayev I.Sh. Two-Dimensional numerical parametric modeling of the capillary microgripper cooling system with unsteady fluid flow. Multiphase Systems. 17 (2022) 3–4. 153–166 (in Russian).
2022. Vol. 17. Issue 3–4, Pp. 153–166
URL: http://mfs.uimech.org/mfs2022.3.014,en
DOI: 10.21662/mfs2022.3.014
Two-Dimensional numerical parametric modeling of the capillary microgripper cooling system with unsteady fluid flow
Nasibullayev I.Sh.
Mavlyutov Institute of Mechanics UFRC RAS, Ufa, Russia

Abstract

The paper presents a parametric analysis of a 2D model of a fluid cooling system for the hot side of a Peltier element of a capillary microgripper. An unsteady flow of coolant in the cooling chamber is considered. The cooling efficiency is studied for three chamber geometries with different radiator locations: monolithic, located on the Peltier element; with one or three ribs. Mathematical models are built: fluid flow through the microgripper chamber; heating the radiator with the hot side of the Peltier element; heat transfer from the radiator to fluid and the removal of the heated fluid from the chamber. The simulation is carried out in the FreeFem++ program until the average change in the temperature of the radiator over the period of fluid oscillations reaches saturation (microgripper operating mode). Using the method of orthogonal central compositional planning, analytical dependences of response functions (maximum temperature on the radiator, amplitude of temperature change on the radiator, and time to establish the operating mode) on model factors (average coolant velocity, heat transfer coefficient, frequency and amplitude of fluid velocity oscillations) are obtained. For each considered geometry and response function, leading and insignificant factors are determined. A parametric analysis of the influence of the physical parameters of the system on the operation of the cooling system was carried out. The simulation results show that the geometry that provides a high degree of cooling and a faster exit to the operating mode (radiator with three fins) has a large amplitude of temperature fluctuations on the radiator and can be used in technical devices that are less sensitive to temperature fluctuations on the radiator. The single fin radiator geometry provides the least radiator temperature fluctuation and can be used to cool capillary microgripper.

Keywords

hydrodynamics,
heat transfer,
capillary microgripper,
fluid cooling system,
finite element method,
orthogonal central composition plan

Article outline

The paper presents a parametric analysis of a two-dimensional model of a liquid cooling system for the hot side of a Peltier element of a capillary microcapture. An unsteady flow of coolant in the cooling chamber is considered. The cooling efficiency is studied for three chamber geometries with different radiator locations: monolithic, located on the Peltier element; with one or three ribs. The first geometry is a vertical section of the cooling chamber and does not take into account the fluid flow around the radiator along the front and rear walls of the chamber, as well as the flow between the radiator fins. The next two geometries represent a horizontal section and do not take into account the flow of fluid along the top wall of the chamber. Mathematical models are built: fluid flow through the microgripper chamber; heating the radiator with the hot side of the Peltier element; heat transfer from the radiator to the fluid and the removal of the heated fluid from the chamber.

Equations of hydrodynamics and thermal conductivity with the corresponding boundary conditions were written in variational form and solved numerically by the finite element method in the FreeFem++ numerical simulation package. Discretization in time was carried out according to the implicit first order Euler’s scheme. Every five time steps, the computational mesh was rebuilt with the density of the finite elements proportional to the fluid velocity gradient. The simulation was carried out until the change in the temperature of the radiator, averaged over the period of flow oscillations, reaches saturation (the operating mode of microgripper). All physical parameters of the coolant (bulk density, dynamic viscosity, isobaric specific heat and thermal conductivity) were considered as temperature-dependent finite element functions with an approximation obtained from tabular data.

For each considered geometry, a series of computational experiments was carried out using the orthogonal central compositional planning method for the following ranges of parameters (factors): average coolant velocity, heat transfer coefficient, frequency and amplitude of fluid velocity oscillations. The following output parameters (response functions) were determined: the maximum temperature on the radiator, the amplitude of the temperature change on the radiator, and the operating mode settling time).

For each considered geometry and response functions, leading and insignificant factors are determined. A parametric analysis of the influence of the physical parameters of the system on the operation of the cooling system was carried out. It was found that, on average, the third geometry, compared to the second, provides better cooling (by 1.8 times) and less time to reach the operating mode (by 1.7 times), but has large temperature fluctuations on the radiator (by 2 times), which can lead to to premature failure of the held object. The simulation results show that the geometry that provides a high degree of cooling and a faster exit to the operating mode (radiator with three fins) has a large amplitude of temperature fluctuations on the radiator and can be used in technical devices that are less sensitive to temperature fluctuations on the radiator. The single fin radiator geometry provides the least radiator temperature fluctuation and can be used to cool capillary micro grippers.

References

  1. Mishra M.K., Dubey V., Mishra P.M., Khan I. MEMS Technology: A Review. Journal of Engineering Research and Reports. 2019. Vol. 4, No. 1. Pp. 1–24.
    DOI: 10.9734/jerr/2019/v4i116891
  2. Convery N., Gadegaard N. 30 years of microfluidics. Micro and Nano Engineering. 2019. Vol. 2. Pp. 76–91.
    DOI: 10.1016/j.mne.2019.01.003
  3. Microfluidics Based Microsystems: Fundamentals and Applications. Eds. by Kakaç S., Kosoy B., Li D., Pramuanjaroenkij A. Dordrecht: NATO Science for Peace and Security Series A: Chemistry and Biology. Springer. 2010. 618 p.
    DOI: 10.1007/978-90-481-9029-4
  4. Kleinstreuer C., Li J. Microscale Cooling Devices. In: Li, D. (eds) Encyclopedia of Microfluidics and Nanofluidics. Springer, New York, NY. 2015.
    DOI: 10.1007/978-1-4614-5491-5_1008
  5. Laser D.J., Santiago J.G. A review of micropumps. Journal of Micromechanics and Microengineering. 2004. Vol. 14. Pp. R35–R64.
    DOI: 10.1088/0960-1317/14/6/R01
  6. Patankar S.V. Numerical heat transfer and fluid flow. Taylor and Francis. 1980.[7] Cotta R. M., Knupp D. C., Naveira-Cotta C. P. Analytical Heat and Fluid Flow in Microchannels and Microsystems. Cham: Springer. 2016. 164 p.
    DOI: 10.1007/978-3-319-23312-3
  7. Drabiniok E., Neyer A. Micro porous polymer foil for application in evaporation cooling. Microsystem Technologies. 2014. Vol. 20. Pp. 1913–1918.
    DOI: 10.1007/s00542-013-1983-9
  8. Koca F., Zabun M. The effect of outlet location on heat transfer performance in micro pin-fin cooling used for a CPU. The European Physical Journal Plus. 2021. Vol. 136. Art. no 1115.
    DOI: 10.1140/epjp/s13360-021-02113-4
  9. Mishra A., Paul A.R., Jain A., Alam F. Design and Analysis of Synthetic Jet for Micro-channel Cooling. In: Wen, C., Yan, Y. (eds) Advances in Heat Transfer and Thermal Engineering. Springer, Singapore. 2021.
    DOI: 10.1007/978-981-33-4765-6_55
  10. Afshari F. Experimental and numerical investigation on thermoelectric coolers for comparing air-to-water to air-to-air refrigerators. Journal of Thermal Analysis and Calorimetry. 2021. Vol. 144. Pp. 855–868.
    DOI: 10.1007/s10973-020-09500-6
  11. Tullius J.F., Vajtai R., Bayazitoglu Y. A Review of Cooling in Microchannels. Heat Transfer Engineering. 2011. Vol. 32, No, 7–8. Pp. 527–541.
    DOI: 10.1080/01457632.2010.506390
  12. Nasibullayev I.Sh., Nasibullaeva E.Sh. [The effect of temperature on the fluid flow dynamics in technical systems with jets]. Transactions of the Institute of Mechanics named after R.R. Mavlyutov, Ufa Scientific Center, Russian Academy of Sciences [Trudy Instituta mehaniki im. R.R. Mavlyutova], Ufimskiy Nauchnyi Centr RAN]. 2016. V. 11, No. 1. P. 1–9 (In Russian).
    DOI: 10.21662/uim2016.1.001
  13. Nonino C., Del Giudice S., Savino S. Temperature-Dependent Viscosity and Viscous Dissipation Effects in Microchannel Flows With Uniform Wall Heat Flux. Heat Transfer Engineering. 2010. Vol. 31, No. 8. Pp. 682–691.
    DOI: 10.1080/01457630903466670
  14. Nasibullayev I.Sh. [Analytical analysis of operating mode switching in a 2D model of a fluid cooling system of the micro-gripper] Analiticheskiy analiz pereklyucheniya rabochego rezhima v dvumernoy modeli sistemy zhidkostnogo okhlazhdeniya mikrozakhvata. Vestnik USATU [Vestnik UGATU]. 2021. Vol. 25, N. 3 (93). Pp. 120–131 (in Russian).
    DOI: 10.54708/19926502_2021_25393120
  15. Choi J.T., Kwon O.K., Cha D.A. A numerical study of the heat transfer and fluid flow of micro-channeled water block for computer CPU cooling. Journal of Mechanical Science and Technology. 2011. Vol. 25. Art. no. 2657.
    DOI: 10.1007/s12206-011-0616-4
  16. Chien-Yuh Yang, Chun-Ta Yeh , Wei-Chi Liu, Bing-Chwen Yang. Advanced Micro-Heat Exchangers for High Heat Flux. Heat Transfer Engineering. 2007. Vol. 28, No. 8–9. Pp. 788-794.
    DOI: 10.1080/01457630701328676
  17. Xu S., Hu G., Qin J., Yang Y. A numerica1 study of fluid flow and heat transfer in different microchannel heat sinks for electronic chip cooling. Journal of Mechanical Science and Technology. 2012. Vol. 26. Pp. 1257–1263.
    DOI: 10.1007/s12206-012-0209-x
  18. Luo X., Liu S., Jiang X., Cheng. T. Experimental and numerical study on a micro jet cooling solution for high power LEDs. Science in China Series E: Technological Sciences. 2007. Vol. 50. Pp. 478–489.
    DOI: 10.1007/s11431-007-0028-y
  19. Bose J.R., Ahammed N., Asirvatham L.G. Thermal performance of a vapor chamber for electronic cooling applications. Journal of Mechanical Science and Technology. 2017. Vol. 31. Pp. 1995–2003.
    DOI: 10.1007/s12206-017-0349-0
  20. Hendricks T.J., Karri N.K. Micro- and Nano-Technology: A Critical Design Key in Advanced Thermoelectric Cooling Systems. Journal of Electronic Materials. 2009. Vol. 38, N. 7. P. 1257–1267.
    DOI: 10.1007/s11664-009-0709-3
  21. Chen L., Meng F., Sun F. Thermodynamic analyses and optimization for thermoelectric devices: The state of the arts. Science China Technological Sciences. 2016. Vol. 59. Pp. 442–455.
    DOI: 10.1007/s11431-015-5970-5
  22. Bar-Cohen A., Wang P. On-chip Hot Spot Remediation with Miniaturized Thermoelectric Coolers. Microgravity Science and Technology. 2009. Vol. 21. Pp. 351–359.
    DOI: 10.1007/s12217-009-9162-4
  23. Nasibullayev I.Sh., Darintsev O.V. [Computer 2D modelling of a micro-grip fluid cooling system]. Vychislitel’nyye tekhnologii [Computational technologies]. 2021. V. 26. No. 2. Pp. 4–20 (in Russian).
    DOI: 10.25743/ICT.2021.26.2.002
  24. Darintsev O.V., Migranov A.B. [Capillary micro-grip with feedback] Capilarnyi microzahvat s obratnoi svazju. Patent RF No. 2261795 RU, [Published] Opublikovano 10.10.2005. Byul. N. 28 (in Russian).
    https://www1.fips.ru/registers-doc-view/fips_servlet?DB=RUPAT&DocNumber=2261795&TypeFile=html
  25. Darintsev O. Microgrippers: Principle of Operation, Construction, and Control Method. Smart Innovation, Systems and Technologies. 2021. Vol. 187. Pp. 25–37. Springer, Singapore. DOI: 10.1007/978-981-15-5580-0_2
  26. Bruus H. Theoretical microfluidics. Lecture notes third edition. MIC Department of Micro and Nanotechnology Technical University of Denmark. 2006. 237 p.[28] Nasibullayev I.Sh., Nasibullaeva E.Sh., Denisova E.V. [Dynamics of fluid flow in technical systems with jets] Dinamika techeniya zhidkosti v tekhnicheskikh sistemakh s zhiklerami. Bulletin of the Ufa Scientific Center of the Russian Academy of Sciences [Izvestiya Ufimskogo Nauchnogo Centra RAN]. 2015. No. 4. Pp. 20–25 (In Russian).
    eLIBRARY ID: 25732231
  27. Kuzmin D., Hämäläinen J. Finite Element Methods for Computational Fluid Dynamics: A Practical Guide. Computational Science & Engineering. SIAM. 2014.
    DOI: 10.1137/1.9781611973617
  28. Nasibullayev I.Sh., Nasibullaeva E.Sh. [The fluid flow through the related element system of technical device such as pipe– hydraulic resistance–pipe] Techeniye zhidkosti cherez sistemu svyazannykh elementov tekhnicheskogo ustroystva tipa truba–gidrosoprotivleniye–truba. Transactions of the Institute of Mechanics named after R.R. Mavlyutov, Ufa Scientific Center, Russian Academy of Sciences [Trudy Instituta mehaniki im. R.R. Mavlyutova], Ufimskiy Nauchnyi Centr RAN]. 2016. V. 11, No. 2. Pp. 141–149 (In Russian).
    DOI: 10.21662/uim2016.2.021
  29. Chiang Ch.-Yu, Pironneau O., Sheu T., Thiriet M. Numerical Study of a 3D Eulerian Monolithic Formulation for Incompressible Fluid- Structures Systems. Fluids. 2017. V. 2, No. 2. P. 34–53.
    DOI: 10.3390/fluids2020034
  30. Hecht F. New development in FreeFem++ // Journal of Numerical Mathematics. 2012. V. 20, No. 3–4. Pp. 251–265.
    DOI: 10.1515/jnum-2012-0013
  31. Nasibullayev I.Sh. [Application of free software FreeFem++/Gmsh and FreeCAD/CalculiX for simulation of static elasticity problems] Primeneniye svobodnykh programm FreeFem++/Gmsh i FreeCAD/CalculiX dlya modelirovaniya staticheskikh strukturnykh zadach. Multiphase Systems [Mnogofaznyye sistemy]. 2020. V. 15, No. 3–4. Pp. 183–200 (In Russian).
    DOI: 10.21662/mfs2020.3.129
  32. Sadaka G., Dutykh D. Adaptive Numerical Modeling of Tsunami Wave Generation and Propagation with FreeFem++. Geosciences. 2020. Vol. 10, No. 9. Art. no. 351.
    DOI: 10.3390/geosciences10090351
  33. Nasibullayev I.Sh. [Application of free software to visualize the results of simulation of dynamic processes] Ispol’zovaniye svobodnogo PO dlya vizualizatsii rezul’tatov modelirovaniya dinamicheskikh protsessov. Multiphase Systems [Mnogofaznyye sistemy]. 2021. V. 16, No 3–4. Pp. 121– 143 (In Russian).
    DOI: 10.21662/mfs2021.3.016
  34. Nasibullayev I.Sh., Darintsev O.V., [Two-dimensional dynamic model of the interaction of a fluid and a piezoelectric bending actuator in a plane channel] Dvumernaya dinamicheskaya model’ vzaimodeystviya zhidkosti i p’yezoelektricheskogo privoda s poperechnym izgibom v ploskom kanale. Multiphase Systems [Mnogofaznyye sistemy]. 2019. V. 14, No. 4. Pp. 220–232 (In Russian).
    DOI: 10.21662/mfs2019.4.029
  35. Sadaka G., Rakotondrandisa A., Tournier P.-H., Luddens F., Lothodé C., Danaila I. Parallel finite-element codes for the simulation of two- dimensional and three-dimensional solid–liquid phase-change systems with natural convection. Computer Physics Communications. 2020. Vol. 257. P. 107492.
    DOI: 10.1016/j.cpc.2020.107492
  36. Nasibullayev I.Sh., Nasibullaeva E.Sh. [Fluid flow through the hydraulic resistance with a dynamically variable geometry] Techeniye zhidkosti cherez gidrosoprotivleniye s dinamicheski izmenyayemoy geometriyey. Transactions of the Institute of Mechanics named after R.R. Mavlyutov, Ufa Scientific Center, Russian Academy of Sciences [Trudy Instituta mehaniki im. R.R. Mavlyutova], Ufimskiy Nauchnyi Centr RAN]. 2017. V. 12, No. 1. Pp. 59–66 (In Russian).
    DOI: 10.21662/uim2017.1.009
  37. Nasibullayev I.Sh., Nasibullaeva E.Sh., Darintsev O.V. [Study of fluid flow through a channel deformed by piezoelement] Izucheniye techeniya zhidkosti cherez deformiruyemyy p’yezoelementom kanal. Mnogofaznyye sistemy [Multiphase Systems]. 2018. V. 13, No. 3. Pp. 1–10 (In Russian).
    DOI: 10.21662/mfs2018.3.001
  38. Cheng CH, Tseng YP. Characteristic studies of the piezoelectrically actuated micropump with check valve. Microsystem Technologies. 2013. Vol. 19. Pp. 1707–1715.
    DOI: 10.1007/s00542-013-1857-1
  39. Guo L., Yan W., Xu, Y., Chen Y. Valveless piezoelectric micropump of parallel double chambers. International Journal of Precision Engineering and Manufacturing. 2012. Vol. 13. Pp. 771–776.
    DOI: 10.1007/s12541-012-0101-8
  40. Nasibullayev I.Sh., Nasibullaeva E.Sh., Darintsev O.V., [Simulation of fluid flow through a elastic microchannel deformed by a piezoelement in microgrip cooling systems] Modelirovaniye techeniya zhidkosti cherez deformiruyemyy p’yezoelementom elastichnyy mikrokanal sistemy okhlazhdeniye mikrozakhvata. Mechatronics, automation, control [Mekhatronika, Avtomatizatsiya, Upravlenie]. 2019. V. 20, No. 12. Pp. 740– 750 (In Russian).
    DOI: 10.17587/mau.20.740-750
  41. Nasibullayev I.Sh., Darintsev O.V., Nasibullaeva E.Sh. and Bogdanov D.R. Piezoelectric Micropumps for Microrobotics: Operating Modes Simulating and Analysis of the Main Parameters of the Fluid Flow Generation. Smart Innovation, Systems and Technologies. 2021. V. 187. Pp. 525–536. Springer, Singapore.
    DOI: 10.1007/978-981-15-5580-0_43
  42. Nasibullayev I.Sh., Nasibullaeva E.Sh., Darintsev O.V. Computer Axisymmetric Model of a Piezoelectric Micropump. Journal of Engineering Science and Technology Review. 2021. Vol. 14, No. 2. Pp. 152–164.
    DOI: 10.25103/jestr.142.19
  43. Nasibullayev I.Sh., Nasibullaeva E.Sh., Darintsev O.V. Dependence of the Piezoelectric Micropump Operating Mode on Its Geometry. Journal of Physics: Conference Series. 2021. V. 2096, No. 1. P. 012081.
    DOI: 10.1088/1742-6596/2096/1/012081[46] Nasibullayev I.Sh. [The development of a computer model for the main element of the fuel metering unit] Razrabotka kompyuternoy modeli osnovnogo elementa agregata dozirovaniya topliva. Vychislitelnye tehnologii [Computational Technologies]. 2016. V. 21, No. 2. Pp. 26–41. (In Russian).
    eLIBRARY ID: 28886942
  44. Nasibullayev I.Sh. [Application of free software for processing and visualization of scientific research results] Ispol’zovaniye svobodnykh programm dlya obrabotki i vizualizatsii rezul’tatov nauchnykh issledovaniy. Multiphase Systems [Mnogofaznyye sistemy]. 2021. V. 16, No 2. Pp. 58–71 (In Russian).
    DOI: 10.21662/mfs2021.2.009
  45. Landau L.D., Lifshitz E.M. [Theoretical physics. V. 6. Fluid Mechanics. M.: Nauka] Teoreticheskaya fizika. T. 6. Gidrodinamika. M.: Nauka. 1988. 736 p. (In Russian).
  46. Sivukhin D.V. [General course of physics. V. I. Mechanics. M.: Science] Obshchiy kurs fiziki. M.: Nauka. 1979. T. I. Mekhanika. 1979. 520 p. (In Russian)
  47. GOST 15527-2004. Alloys copper-zinc (brass), processed by pressure.
  48. Shlyakhin P.N., Bershadsky M.L. [Brief guide to steam turbine installations] Kratkiy spravochnik po paroturbinnym ustanovkam. M.- L.: Gosenergoizdat. 1961. 128 p.