A COMMENT ON UNSTEADY–PERIODIC FLOW FRICTION FACTOR: AN ANALYSIS ON EXPERIMENTAL DATA GATHERED IN PULSATILE PIPE FLOWS

Year 2020, , 16 - 27, 06.01.2020

Melda Carpinlioğlu

https://doi.org/10.18186/thermal.670986

Cited By: 2

Abstract

In 1940’s, Schultz- Grunow proposed that time-average value of friction factor, λ_u,ta was similar to its corresponding steady state value, λ for the presence of gradual and slow oscillations in pulsatile flows. A recent approach was available for low frequency pulsatile flows through narrow channels in transitional and turbulent regimes by Zhuang et al, in 2016 and 2017. In this analysis; extensive experimental data of λ_u,ta in fully laminar and turbulent sinusoidal flow are processed in the measured time-average Reynolds number range of 1390 ≤ Re_ta ≤ 60000 disregarding the transitional regime. The ranges of dimensionless frequency-Womersley number, √(ω') and oscillation amplitude, A_1 are 2.72 ≤ √(ω') ≤ 28 and 0.05 ≤ A_1≤ 0.96 respectively. A multiplication element is defined as Mel = Re_ta×√(ω^'). A modified friction multiplier, λ_(Mel ) which is similar to the conceptual parameter of Zhuang et al’s friction factor ratio C ( λ_Mel = λ_(u,ta)/λ ) is also referred. The correlation of λ_Mel = λ_Mel (Mel) is dependent on flow regime and the magnitude of Re_ta for the range of √(ω^') > 1.32. The proposal of Schultz-Grunow is verified irrespective of the oscillations in turbulent regime since the magnitude of λ_Mel = 1 is observed for turbulent flow cases with Re_(ta ) ≥ 35000. In laminar regime the magnitude of Re_(ta ) is governing the fact. The magnitude of λ_Mel varies in 0.589 ≤ λ_Mel ≤ 28.125 for Re_(ta ) ≤ 5000 while λ_Mel = 1 is obtained for Re_(ta ) > 5000. The graphical representation of λ_Mel = λ_Mel (Mel) can be considered as a counterpart of Moody Diagram in pulsatile fields for a significant practice.

Keywords

Time-Average Friction Factor, Time-Average Reynolds Number, Womersley Number, Multiplication Element, Modified Friction Multiplier = C

References

• [1] V. L. Streeter, E. B. Wylie, K. W. Bedford. Fluid Mechanics 9th edition McGraw Hill International Editions pp: 288-294; 1998.
• [2] H. Blasius. Das AhnlichkeitsgesetzbeiReibungsvorgangen in Flüssigkeiten, Ver. Dtsch.Ing. Forschungsh, 131; 1913.
• [3] L. F. Moody. Friction factors for pipe flow, Trans. ASME; 1944.
• [4] J. Nikuradse Strömungsgesetze in rauhenRohren. Ver. Dtsch. Ing. Forschungsh, 361; 1933.
• [5] F. Schultz-Grunow, PulsierenderDurchflussdurchRohre. Forschg. Ing.-Wes,11:170-187; 1940.
• [6] H. Schlichting Boundary Layer Theory, McGraw Hill Inc.,7th Edition, New York; 1987.
• [7] M. O. Carpinlioglu. An Experimental Investigation on Pulsatile Pipe Flows MF 97-04 Project Report, BAP, University of Gaziantep Turkey, No: 14, 2000.
• [8] M. O. Carpinlioglu. An Experimental Investigation on Laminar to Turbulent Transition in Time Dependent Pipe Flows MF 09-09 Project Report, BAP, University of Gaziantep Turkey, No: 268, 2012.
• [9] M. Y. Gundogdu, M. O. Carpinlioglu. Present State of Art on Pulsatile Flow Theory Part I: Laminar and Transitional Flow Regimes. JSME International Journal 1999;42(3):384-397.doi:10.1299/jsmeb.42.384
• [10] M. Y. Gundogdu, M .O. Carpinlioglu. Present State of Art on Pulsatile Flow Theory. Part 2 Turbulent Flow Regime. JSME International Journal 1999;42(3):398-410.doi:10.1299/jsmeb.42-398
• [11] M. O. Carpinlioglu, M. Y. Gundogdu. Presentation of a test system in terms of generated pulsatile flow characteristics. Flow Measurement and Instrumentation 2001;12(3):181-190.doi: 10.1016/S0955-5986(01) 00019-X
• [12] M. O. Carpinlioglu, M. Y. Gundogdu. A Critical Review on Pulsatile Pipe Flow Studies Directing Towards Future Research Topics. Journal of Flow Measurement and Instrumentation 2001;12(3):163-174. doi:10.1016/S0955-5986(01)00020-6
• [13] M. Y. Gundogdu. An Experimental Investigation on Pulsatile Pipe Flows. Ph.D Thesis, University of Gaziantep, Department of Mechanical Engineering, Gaziantep Turkey, 2000.
• [14] E. Ozahi. Analysis of Laminar-to Turbulent Transition in Time Dependent Pipe Flows. Ph.D Thesis, University of Gaziantep, Department of Mechanical Engineering, Gaziantep Turkey, 2011.
• [15] M. Ohmi, M. Iguchi, T. Usui. Flow Pattern and Frictional Losses in Pulsating Pipe Flow Part 5: Wall Shear Stress and Flow Pattern in a Laminar Flow Bulletin of JSME 1981;24(187 ),75.
• [16] M. Ohmi, M. Iguchi. Flow Pattern and Frictional Losses in Pulsating Pipe Flow Part 6: Frictional Losses in a Laminar Flow Bulletin of JSME 1981;24(196),1756.
• [17] M. O. Carpinlioglu, E. Ozahi. An experimental test system for the generation, control and analysis of sinusoidal pulsatile pipe flows (An application case for time dependent flow measurements). Journal of Flow Measurement and Instrumentation 2013;32:27-34.doi: 10.1016/j.flowmeasinst.2013.04.002
• [18] F. Durst, U. Heim, B. Unsal, G. Kullik. Mass flow rate control system for time-dependent laminar and turbulent flow investigations. Measurement Science and Technology 2003;14:893-902.
• [19] M. O. Carpinlioglu. An Approach for Transition Correlation of Laminar Pulsatile Pipe Flows via Frictional Field Characteristics. Journal of Flow Measurement and Instrumentation 2003;14(6):233-242.doi: 10.1016/ S0955-5986(03)00032-3
• [20] M. O. Carpinlioglu, E. Ozahi. An Updated Portrait on Transition to Turbulence in Laminar Pipe Flows with Periodic Time-Dependence (A Correlation Study). Journal of Flow Turbulence and Combustion 2012;89(4):691-711. doi: 10.1007/s10494-012-9420-1
• [21] E. Ozahi, M. O. Carpinlioglu. Definition of sub-classes in sinusoidal pulsatile air flow at onset of transition to turbulence in view of velocity and frictional field analyses. Measurement 2015; 64:94-104 .doi:10.1016/j.measurement.2014.12.034
• [22] E. Ozahi, M. O. Carpinlioglu . Determination of Transition Onset in Laminar Pulsatile Pipe Flows. Journal of Thermal Science and Technology 2013;33(2):125-133.
• [23] M. O. Carpinlioglu. An overview on pulsatile flow dynamics. Journal of Thermal Engineering 2015;1(3/6):496-504. doi:10.18186/jte.59285
• [24] E. Ozahi, M. O. Carpinlioglu. Devised application of Labview for an automatic test system based on generation, control and processing of pulsatile pipe flows. Journal of Thermal Science and Technology 2015;35(2):75-88.
• [25] M. Ohmi, M. Iguchi. Flow pattern and frictional losses in pulsating pipe flow Part 4: General representation of turbulent frictional losses. Bulletin of the JSME 1981;24(187):67-74.
• [26] E. Ozahi, M. O. Carpinlioglu. A Non-dimensional Parameter Describing Interactive Influence of Oscillation Frequency and Velocity Amplitude Ratio for Use in Pulsatile Flows. Measurement 2017;99:36-43. doi:10.1016/j.measurement.2016.12.018
• [27] N. Zhuang, S. Tan, H. Yuan. The friction characteristics of low frequency transitional pulsatile flows in narrow channel. Experimental Thermal and Fluid Science 2016;76:352-364. doi:10.1016/j.expthermflusci.2016.03.030
• [28] N. Zhuang. S. Tan, H.Yuan B. Yang. Flow resistance of low-frequency pulsatile turbulent flow. International Journal of Heat and Fluid Flow 2017;65:21-32.doi:10.1016/j.ijheatfluidflow.2017.03.005
• [29] M. O. Carpinlioglu. The status of art and possible future predictions on laminar-turbulent transition (transition control via sinusoidal oscillations). 22nd International Society of Air-Breathing Engines, ISABE 2015 Conference Phoenix Arizona, US: 25-30 October 2015.
• [30] P. Qi, X. Li, S. Qiao, S. Tan, Y. Chen. Experimental study on the resistance characteristics of the rod bundle channel with spacer grid under low frequency pulsating flows. Annals of Nuclear Energy 2019;131:80-92.doi:10.1016/j.anucene.2019.03.027