Polyacrylamide 수용액의 Dean 불안정성에 관한 연구

김연숙; 김종엽

HWAHAK KONGHAK, Vol.34, No.4, 462-470, August, 1996

Export Citation

Polyacrylamide 수용액의 Dean 불안정성에 관한 연구

Dean's Instability of Aqueous Solutions of Polyacrylamide

김연숙, 김종엽

초록

마찰감소유체의 하나인 polyacrylamide 수용액의 Dean 불안정성에 관하여 종횡비가 1:35인 장치로 Dean 수 100 이하에서 실험적인 연구를 수행하였다. 뉴튼유체에 대하여는 임계 Dean 수 39, 임계 파수 3.95로 이론적인 해석결과와 일치하였으며, Dean 수가 임계수보다 커짐에 따라 압력손실이 증가하는 경향과 이때 파수가 3.95로부터 갑자기 5.2로 증가하는 현상은 이론적으로만 발표된 비선형해석의 결과와 잘 일치되었다. 폴리아크릴아마이드수용액의 경우 임계 Dean 수는 100ppm 이하에서 용액의 농도에 따라 DNc=39-0.078c(DNc:임계 Dean 수;c:농도)와 같이 변하였으며, 임계 Dean 수에서의 파수는 3-3.5로서 뉴튼유체의 경우보다 작게 나타났지만, Dean 수가 커지면 5.0으로 증가되어 뉴튼유체의 경우와 같았다. 추적자를 넣고 유동을 관찰한 결과 기본적인 굽은 유로에서는 Poiseuille 유동뿐만 아니라 Dean불안정성에 의하여 생성되는 와류도 용액의 탄성에 의하여 더욱 불안정하여지는 것을 알 수 있었다.

Experimental studies on the Dean’s instability of aqueous solution of polyacrylamide were performed for the flow in a curved channel with the aspect into of 1:35. The range of Dean number investigated was up to 100. The critical Dean number, were number and pressure drop vs. Dean number were examined for distilled water to validate the experimental set-up and found to be in agreement with the values reported in the literatures. The nonlinear characteristics after the onset of instability were also in good agreement with the recent report. Thi critical Dean number decreased with polymer concentration according to the relation Dn_c=39-0.078c(Dn_c : critical Dean number; c : concentration) when c was smaller than 100 ppm. The wave number at the onset was smaller and in the range of 3-3.5. But it in- creased to the same value of 5.0 after the onset as in the case of Newtonian fluid. The present study reveals that both the base flow in the curved channel and Dean vortices be- come more unstable due to elasticity.

Keywords:Drag Reduction;Turbulent Burst;Elasticity

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[1] Larson RG, Rheol. Acta, 31, 213 (1992)

[2] Gampert B, "The Influence of Polymer Additives on Velocity and Temperature Fields," IUTAM Symposium, Essen (1984)

[3] Gampert B, Germany, Springer-Verlag, Berlin (1985)

[4] Gyr A, "Structure of Turbulence and Drag Reduction," IUTAM Symposium, Zurch (1989)

[5] Gyr A, Switzerland, Springer-Verlag, Berlin (1990)

[6] Sellin RHJ, Moses RT, "Drag Reduction in Fluid Flows(Techniques for Friction Control)," Ellis Horwood, Chichester (1989)

[7] Drazin PG, Reid WH, "Hydrodynamic Stability," Camb. Univ. Press, Cambridge (1981)

[8] Reid WH, Proc. Roy. Soc. Lond., A244, 186 (1958)

[9] Gibson RD, Cook AE, Q. J. Appl. Math., 27, 149 (1974)

[10] Sparrow EM, Z. Angew. Math. Phys., 15, 638 (1964)

[11] Brewster DB, Grosberg P, Nissan AH, Proc. Roy. Soc. Lond., A251, 76 (1959)

[12] Kelleher MD, Flentie DL, McKee RJ, Trans. ASME, 102, 92 (1980)

[13] Ligrani PM, Niver RD, Phys. Fluids, 31, 3605 (1988)

[14] Finlay WH, Keller JB, Ferziger JH, J. Fluid Mech., 194, 417 (1988)

[15] Matsson OE, Alfredsson PH, Phys. Fluids A, 4, 1666 (1992)

[16] Guo Y, Finlay WH, J. Fluid Mech., 264, 1 (1994)

[17] Bottaro A, J. Fluid Mech., 251, 627 (1993)

[18] Joo YL, Ph.D. Dissertation, Stanford University, Stanford (1993)

[19] Joo YL, Shaqfeh ESG, Phys. Fluids, A3, 1691 (1991)

[20] Joo YL, Shaqfeh ESG, Phys. Fluids, A4, 524 (1992)

[21] Joo YL, Shaqfeh ESG, Phys. Fluids, A4, 2415 (1992)

[22] Larson RG, Shaqfeh ESG, Muller SJ, J. Fluid Mech., 218, 573 (1990)

[23] Muller SJ, Larson RG, Shaqfeh ESG, Rheol. Acta, 28, 499 (1989)

[24] Happel J, Brenner H, "Low Reynolds Number Hydrodynamics," Martinus Nijhoff, Dordrecht (1983)

[25] Zimm BH, Crothers DM, Proc. Nat'l Acad. Sci., 48, 905 (1962)

[26] Renardy M, J. Non-Newton. Fluid Mech., 59(1), 93 (1995)

[27] Renardy M, Abstracts of the 67th Annual Meeting of the Society of Rheology, Sacramento (1995)