Journal of Computational & Applied Research in Mechanical Engineering (JCARME)

Document Type : Research Paper

Authors

Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran

https://doi.org/10.22061/jcarme.2022.8001.2068

Abstract

In this study, comprehensive numerical simulations were conducted to examine laminar pulsatile developing flows through flat channels. The developing velocity fields and the hydrodynamic entry length were explored for the Reynolds numbers from 20 to 200, and the low and intermediate non-dimensional pulsation frequency or the Womersley number (1.08 ≤Wo≤ 8.86). For all simulations, the pulsating amplification factor was considered from zero to one, (0 ≤A≤ 1), and to achieve more practical and relevant outcomes, time-dependent parabolic inlet velocity profiles were applied. The outcomes reveal that for the higher values of the pulsation frequency or the Womersley number (6 ≤ Wo ≤ 8.66), the maximum pulsatile entranced length during a cycle is close to the inlet length of the mean component of the flow. On the other hand, for the rest of the Womersley number range (1.08 ≤ Wo < 6), and high amplification factor (0.5 ≤ A), the value of the entrance length increases and is significantly different from the development length of the steady component. Moreover, the results demonstrate that the entry length correlates with the Womersley number through a power-law function, whilst it has linear correlations with the Reynolds number and the amplification factor. Further, using the result of the accomplished numerical study, a practical correlation of the entrance length is offered to be used in the design phase for any type of pulsatile flow through the flat channels.

Graphical Abstract

Keywords

dor

20.1001.1.22287922.2023.12.2.8.3

Main Subjects

Computational Fluid Dynamics (CFD)

References

[1] T. Lieuwen and B. T. Zinn, "The role of equivalence ratio oscillations in driving combustion instabilities in low NOx gas turbines," in Symposium (International) on combustion, Elsevier, Vol. 27, No. 2, pp. 1809-1816, (1998).

[2] J. Majdalani and H. Chibli, "Pulsatory channel flows with arbitrary pressure gradients," in 3rd Theoretical Fluid Mechanics Meeting, St. Louis, Missouri, pp. 2-13, (2002).

[3] N. MILLER, E. POWELL, F. CHEN, and B. ZINN, "The use of air staging to reduce the NOx emissions from coal burning Rijke pulse combustors," Combustion science and technology, Vol. 94, No. 1-6, pp. 411-426, (1993).

[4] R. Raun, M. Beckstead, J. Finlinson, and K. Brooks, "A review of Rijke tubes, Rijke burners and related devices," Progress in Energy and Combustion Science, Vol. 19, No. 4, pp. 313-364, (1993).

[5] G. Richards, R. Logan, C. Meyer, and R. Anderson, "Ash deposition at coal-fired gas turbine conditions: surface and combustion temperature effects," J. Eng. Gas Turbines Power, Vol. 114, No.1, pp. 132-138, (1992).

[6] S. Yavuzkurt, M. Ha, G. Koopmann, and A. Scaroni, "A model of the enhancement of coal combustion using high-intensity acoustic fields," J. Energy Resour. Technol. Vol.113, No.4, pp. 277-285, (1991).

[7] N. H. Brooks, Engineering Fluid Mechanics Workshop Report. American Society of Mechanical Engineers, AIAA, Nashville,TN, pp.40-50 (1990).

[8] D. J. Laser and J. G. Santiago, "A review of micropumps," J. Micromech. Microeng, Vol. 14, No. 6, p. R35, (2004).

[9] B. D. Iverson and S. V. Garimella, "Recent advances in microscale pumping technologies: a review and evaluation," Microfluidics and nanofluidics, Vol. 5, No. 2, pp. 145-174, (2008).

[10] R. K. Shah and A. L. London, Laminar flow forced convection in ducts: a source book for compact heat exchanger analytical data. Academic press, New York, pp.55-63, (2014).

[11] H. B. Atabek and C. C. Chang, "Oscillatory flow near the entry of a circular tube," Zeitschrift für angewandte Mathematik und Physik ZAMP, Vol. 12, No. 3, pp. 185-201, (1961).

[12] J. Krijger, B. Hillen, and H. Hoogstraten, "Pulsating entry-flow in a plane channel," Zeitschrift für angewandte Mathematik und Physik ZAMP, Vol. 42, No. 1, pp. 139-153, (1991).

[13] X. He and D. N. Ku, "Unsteady entrance flow development in a straight tube," J Biomech Eng., Vol. 116, No.3, pp. 355-360, (1994).

[14] H. Cho and J. M. Hyun, "Numerical solutions of pulsating flow and heat transfer characteristics in a pipe," International Journal of Heat and Fluid Flow, Vol. 11, No. 4, pp. 321-330, (1990).

[15] W. Chan, S. Lee, and C. Liu, "Effects of frequency and amplitude of oscillation on low Reynolds number pulsating flow in a circular pipe," Engineering Computations, Vol. 19, pp. 119-132, (2002).

[16] S. Ray, B. Ünsal, and F. Durst, "Development length of sinusoidally pulsating laminar pipe flows in moderate and high Reynolds number regimes," International journal of heat and fluid flow, Vol. 37, pp. 167-176, (2012).

[17] R. Blythman, N. Jeffers, T. Persoons, and D. Murray, "Localized and time-resolved velocity measurements of pulsatile flow in a rectangular channel," International Journal of Mechanical and Mechatronics Engineering, Vol. 10, No. 2, pp. 243-249 (2016).

[18] W. Rydlewicz, M. Rydlewicz, and T. Pałczyński, "Experimental investigation of the influence of an orifice plate on the pressure pulsation amplitude in the pulsating flow in a straight pipe," Mechanical Systems and Signal Processing, Vol. 117, pp. 634-652, (2019).

[19] M. Purdin and D. Ksenok, "Resistance in a Developing Low-Amplitude Pulsating Laminar Flow in a Flat Channel," International Journal of Engineering Research and Technology, Vol. 12, No. 4, pp. 570-578 (2019).

[20] OJ. Lobo, D. Chatterjee, " Development of flow in a square mini-channel: Effect of flow oscillation," Physics of Fluids, Vol. 30, No. 4, pp. 042003 (2018).

[21] M. Amaratunga, HA. Rabenjafimanantsoa, RW. Time, "Comparison of oscillatory flow conditions in Newtonian and non-Newtonian fluids using PIV and high-speed image analysis," Flow Measurement and Instrumentation, Vol. 70, No. 1, pp. 101628 (2019).

[22] G. Shajari, M. Abbasi, and M. K. Jamei, "Entrance length of oscillatory flows in parallel plate microchannels," Proc IMechE Part C: J Mechanical Engineering Science, Vol.11, No.1, p.0954406220968125, (2020).

[23] G. Beavers, E. Sparrow, and R. Magnuson, "Experiments on hydrodynamically developing flow in rectangular ducts of arbitrary aspect ratio," International Journal of Heat and Mass Transfer, Vol. 13, No. 4, pp. 689-701, (1970).

[24] E. Sparrow and C. Anderson, "Effect of upstream flow processes on hydrodynamic development in a duct," J. Fluids Eng, Vol. 99, No. 3, pp. 556-560, (1977).

[25] B. Atkinson, M. Brocklebank, C. Card, and J. Smith, "Low Reynolds number developing flows," AIChE Journal, Vol. 15, No. 4, pp. 548-553, (1969).

[26] M. Brocklebank and J. Smith, "Laminar velocity profile development in straight pipes of circular cross section," Rheologica acta, Vol. 7, No. 3, pp. 286-289, (1968).

[27] N. S. Berman and V. A. Santos, "Laminar velocity profiles in developing flows using a laser doppler technique," AIChE Journal, Vol. 15, No. 3, pp. 323-327, (1969).

[28] A. Valencia and L. Hinojosa, "Numerical solutions of pulsating flow and heat transfer characteristics in a channel with a backward-facing step," Heat and mass transfer, Vol. 32, No. 3, pp. 143-148, (1997).

[29] F. Durst, S. Ray, B. Ünsal, and O. Bayoumi, "The development lengths of laminar pipe and channel flows," J. Fluids Eng, Vol. 127, No. 6, pp. 1154-1160, (2005).

[30] L. A. Davis Jr, Oscillating flow in a constricted tube, PhD thesis, Iowa State University, Ames, IA, (1973).

[31] White F., Viscous fluid flow, McGrawHill, New York, pp.125-129 - 287-289 (1991).

[32] M. Braza, P. Chassaing, and H. H. Minh, "Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder," Journal of fluid mechanics, Vol. 165, pp. 79-130, (1986).

[33] M. Coutanceau and J.-R. Defaye, "Circular cylinder wake configurations: A flow visualization survey," Applied Mechanics Reviews, Vol. 44, No. 6, pp. 255-305, (1991).

[34] C. H. Williamson, "Vortex dynamics in the cylinder wake," Annual review of fluid mechanics, Vol. 28, pp. 477-539, (1996).

[35] D. Boger, " Viscoelastic flows through contractions," Annual review of fluid mechanics, Vol. 19, pp. 157-182, (1987).

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