A Numerical Approach for Modeling of Turbulent Newtonian Fluid Flow in Eccentric Annulus
Türbülanslı akımlar, yalnızca doğada değil mühendislik uygulamalarında da görülen karmaşık bir yapıdadır. Navier-Stokes denklemlerinin türbülanslı çözümlerinin karmaşık ve zor olmasından dolayı sayısal yöntemler sıklıkla kullanılır. İki farklı sayısal teknik vasıtasıyla boru dönmesi hesaba katılmış Navier-Stokes denklemleri çözülmüştür. Geliştirilen sayısal yöntemin etkinliği Newton-Raphson method kullanılarak elde edilen sonuçlarla karşılaştırılmıştır. Geliştirilen sayısal metot her ne kadar işlevsel olarak ağır olsa da, hidrolikteki linear olmayan zor problemlerin çözümünü sağlamaya yol açabilir. İç içe geçmiş borular arasından geçen tam gelişmiş türbülanslı akımın içteki borunun dönmesi etkili olduğu basınç farklarının tayini için geliştirilmiş sayısal metot ile birlikte bir mekanistik model geliştirilmiştir. Sayısal hesaplamalar MATLAB’ta geliştirilen kodlarla yapılmıştır. Yapılan sayısal hesaplamalar İzmir Katip Çelebi Üniversitesi’nde yapılan deneylerin sonuçlarıyla teyit edilmiştir. Elde edilen sonuçlar, hesaplamalı akışkanlar modelinin basınç gradyanını %14’den daha az bir hata ile tahmin ettiğini göstermiştir.
A Numerical Approach for Modeling of Turbulent Newtonian Fluid Flow in Eccentric Annulus
Turbulent flow is a complicated process that frequently appears not only in nature but also in engineering applications. Numerical methods frequently are used to solve turbulent flow problems due to the trouble in solving Navier-Stokes equations. Navier-Stokes equations including inner pipe rotation effect are solved via two different numerical techniques. The efficiency of the proposed numerical technique is compared with the obtained solutions of Newton-Raphson method. The proposed method is computationally expensive, however, it may allow tackling the non-linearity of challenging problems in hydraulics. A mechanistic model including proposed numerical method is also developed in order to predict pressure gradient for fully developed turbulent flow through fully eccentric horizontal annulus including pipe rotation. The computational frameworks are developed in MATLAB. Mathematical model is confirmed by the experimental study, which is conducted in Izmir Katip Celebi University. Results show that computational fluid model is a capable of estimating frictional pressure gradient with an error of less than 14 %.
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- Referans1
Deissler, R. G. (1954). Analysis of turbulent heat transfer, mass transfer, and friction in smooth tubes at high Prandtl and Schmidt numbers.
- Referans2
Deissler, R. G., & Taylor, M. F. (1955). Analysis of fully developed turbulent heat transfer and flow in an annulus with various eccentricities. NACA Tech. Note 3451.
- Referans3
Wolffe, R. A., & Clump, C. W. (1963). The maximum velocity locus for axial turbulent flow in an eccentric annulus. AIChE Journal, 9(3), 424-425.
- Referans4
Heyda, J. F. (1959). A Green's function solution for the case of laminar incompressible flow between non-concentric circular cylinders. Journal of the Franklin Institute, 267(1), 25-34.
- Referans5
Jonsson, V. K., & Sparrow, E. M. (1965). Results of laminar flow analysis and turbulent flow experiments for eccentric annular ducts. AIChE Journal, 11(6), 1143-1145.
- Referans6
Jonsson, V. K., & Sparrow, E. M. (1966). Experiments on turbulent-flow phenomena in eccentric annular ducts. Journal of Fluid Mechanics, 25(01), 65-86.
- Referans7
Rehme, K. (1973). Simple method of predicting friction factors of turbulent flow in non-circular channels. International Journal of Heat and Mass Transfer, 16(5), 933-950.
- Referans8
Kacker, S. C. (1973). Some aspects of fully developed turbulent flow in non-circular ducts. Journal of Fluid Mechanics, 57(03), 583-602.
- Referans9
Usui, H., & Tsuruta, K. (1980). Analysis of fully developed turbulent flow in an eccentric annulus. Journal of Chemical Engineering of Japan, 13(6), 445-450.
- Referans10
Tosun, I. (1984). Axial laminar flow in an eccentric annulus: an approximate solution. AIChE journal, 30(5), 877-878.
- Referans11
Özgen, C., & Tosun, I. (1987). Application of geometric inversion to the eccentric annulus system. AIChE journal, 33(11), 1903-1907.
- Referans12
Uner, D., Ozgen, C., & Tosun, I. (1988). An approximate solution for non-Newtonian flow in eccentric annuli. Industrial & engineering chemistry research, 27(4), 698-701.
- Referans13
Ogino, F., Sakano, T., & Mizushina, T. (1987). Momentum and heat transfers from fully developed turbulent flow in an eccentric annulus to inner and outer tube walls. Heat and Mass Transfer, 21(2), 87-93.
- Referans14
Haciislamoglu, M., & Langlinais, J. (1990). Non-Newtonian flow in eccentric annuli. Transactions of the ASME. Journal of Energy Resources Technology, 112(3), 163-169.
- Referans15
Nouri, J. M., Umur, H., & Whitelaw, J. H. (1993). Flow of Newtonian and non-Newtonian fluids in concentric and eccentric annuli. Journal of Fluid Mechanics, 253, 617-641.
- Referans16
Nouri, J. M., & Whitelaw, J. H. (1994). Flow of Newtonian and non-Newtonian fluids in a concentric annulus with rotation of the inner cylinder. Transactions-American Society Of Mechanical Engineers Journal Of Fluids Engineering, 116, 821-821.
- Referans17
Erge, O., Ozbayoglu, M. E., Miska, S. Z., Yu, M., Takach, N., Saasen, A., & May, R. (2014). Effect of drillstring deflection and rotary speed on annular frictional pressure losses. Journal of Energy Resources Technology, 136(4), 042909.
- Referans18
Mossa, M. (2006). Resistance coefficient in a smooth concentric annular pipe. Journal of Hydraulic Research, 44(6), 832-840.
- Referans19
Erge, O., Vajargah, A. K., Ozbayoglu, M. E., & van Oort, E. (2016, March). Improved ECD Prediction and Management in Horizontal and Extended Reach Wells with Eccentric Drillstrings. In IADC/SPE Drilling Conference and Exhibition. Society of Petroleum Engineers.
- Referans20
Rushd, S., Shazed, A. R., Faiz, T., Kelessidis, V., Hassan, I. G., & Rahman, A. (2017, March). CFD Simulation of Pressure Losses in Eccentric Horizontal Wells. In SPE Middle East Oil & Gas Show and Conference. Society of Petroleum Engineers.
- Referans21
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot (2002) Transport phenomena. John Wiley & Sons.
- Referans22
Iyoho, Aniekan W., and Jamal J. Azar. (1981) An accurate slot-flow model for non-Newtonian fluid flow through eccentric annuli, Society of Petroleum Engineers Journal 21.05: 565-572.
- Referans23
Ulker, E., Sorgun, M., Solmus, I., & Karadeniz, Z. H. (2017). Determination of Newtonian Fluid Flow Behavior Including Temperature Effects in Fully Eccentric Annulus. Journal of Energy Resources Technology, 139(4),04200.