CFD analysis of unsteady and anisotropic turbulent flow in a circular-sectioned 90° bend pipe with and without ribs: A comparative computational study

Rachid Chiremsel; Ali Fourar; Fawaz Massouh; Zakarya Chiremsel

doi:10.15282/jmes.15.2.2021.03.0628

Authors

R. Chiremsel Department of Hydraulics, University of Batna 2, Research Laboratory in Applied Hydraulics, Constantine road N°53. Fesdis, Batna 05078, Algeria
A. Fourar Department of Hydraulics, University of Batna 2, Research Laboratory in Applied Hydraulics, Constantine road N°53 Fesdis, Batna 05078, Algeria
F. Massouh National Higher School of Arts and Crafts (ParisTech; ENSAM), Laboratory of Fluid Mechanics 75013, France
Z. Chiremsel Safety Department, University of Batna2, IHSI-LRPI, Constantine road N°53.Fesdis, Batna 05078, Algeria

DOI:

https://doi.org/10.15282/jmes.15.2.2021.03.0628

Keywords:

RSM, unsteady flow, anisotropy function, Dean number, invariant anisotropy map

Abstract

The Reynolds–averaged Navier–Stokes (RANS) equations were solved along with Reynolds stress model (RSM), to study the fully-developed unsteady and anisotropic single-phase turbulent flow in 90° bend pipe with circular cross-section. Two flow configurations are considered the first is without ribs and the second is with ribs attached to solid walls. The number of ribs is 14 ribs regularly placed along the straight pipe. The pitch ratios is 40 and the rib height e (mm) is 10% of the pipe diameter. Both bends have a curvature radius ratio, of 2.0. The solutions of these flows were obtained using the commercial CFD software Fluent at a Dean number range from 5000 to 40000. In order to validate the turbulence model, numerical simulations were compared with the existing experimental data. The results are found in good agreement with the literature data. After validation of the numerical strategy, the axial velocity distribution and the anisotropy of the Reynolds stresses at several downstream longitudinal locations were obtained in order to investigate the hydrodynamic developments of the analyzed flow. The results show that in the ribbed bend pipe, the maximum velocity value is approximately 47% higher than the corresponding upstream value but it is 9% higher in the case of the bend pipe without ribs. It was also found for both cases that the distribution of the mean axial velocity depends faintly on the Dean number. Finally, it can be seen that the analyzed flow in the bend pipe without ribs appears more anisotropic than in bend pipe with ribs.

References

S. A. Berger, L. Talbot, and L. S. Yao, “Flow in curved pipes,” Ann. Rev. Fluid Mech., vol. 15, no. 1, pp. 461–512, 1983, doi: 10.1146/annurev.fl.15.010183.002333.

A. K. Vester, R. Ӧrlü, and P. H. Alfredsson, “Turbulent flows in curved pipes: recent advances in experiments and simulations,” Appl. Mech. Rev., vol. 68, no. 5, pp. 1–25, 2016, doi: 10.1115/1.4034135.

J. L. Lumley, “Computational modeling of turbulent flows,” Adv. App. Mech., vol. 18, pp. 123–176, 1979, doi: 10.1016/S0065-2156(08)70266-7.

H. Ito, “Friction factors for turbulent flow in curved pipes,” J. Basic Eng., vol. 81, no. 2, pp. 123–132, 1959, doi: 10.1115/1.4008390.

W. H. Lyne, “Unsteady viscous flow in a curved pipe,” J. Fluid Mech., vol. 45, no. 1, pp. 13–31, 1971, doi: 0.1017/S0022112071002970.

B. R. Munson, “Experimental results for oscillating flow in a curved pipe,” Phys. Fluids., vol.18, no. 12, pp. 1607–1609, 1975, doi: 10.1063/1.861077.

J. A. C. Humphrey, J. H. Whitelaw, and G. Yee, “Turbulent flow in a square duct with strong curvature,” J. Fluid Mech., vol. 103, pp. 443–463, 1981, doi: 10.1017/S0022112081001419.

A. M. K. P. Taylor, J. H. Whitelaw, and M. Yianneskis, “Curved ducts with strong secondary motion: velocity measurements of developing laminar and turbulent flow,” J. Fluids Eng., vol. 104, no. 3, pp. 350–359, 1982, doi: 10.1115/1.3241850.

M. M. Enayet, M. M. Gibson, A. M. K. P. Taylor, and M. Yianneskis, “Laser-Doppler measurements of laminar and turbulent flow in a pipe bend,” Int. J. Heat & Fluid Flow., vol. 3, no. 4, pp. 213–219, 1982, doi: 10.1016/0142-727X(82)90024-8.

J. Azzola, J. A. C. Humphrey, H. Iacovides, and B. E. Launder, “Developing turbulent flow in a U-bend of circular cross-section: measurement and computation,” J. Fluids Eng., vol. 108, no. 2, pp. 214–221, 1986, doi: 10.1115/1.3242565.

P. Bovendeerd, A. Steenhoven, F. Vosse, and G. Vossers, “Steady entry flow in a curved pipe,” J. Fluid Mech., vol. 177, pp. 233–246, 1987, doi: 10.1017/S0022112087000934.

M. M. Ohadi and E. M. Sparrow, “Heat transfer in a straight tube situated downstream of a bend,” Int. J. Heat Mass Transfer., vol. 32, no. 2, pp. 201–212, 1989, doi: 10.1016/0017-9310(89)90168-3.

M. M. Ohadi, E. M. Sparrow, A. Walavalkar, and A. I. Ansari, “Pressure drop characteristics for turbulent flow in a straight circular tube situated downstream of a bend,” Int. J. Heat Mass Transfer., vol. 33, no. 4, pp. 583–591, 1990, doi: 10.1016/0017-9310(90)90157-P.

W. N. Al-Rafai, Y. D. Tridimas, and N. H. Woolley, “A study of turbulent flows in pipe bends,” J. Mech. Eng. Sci., vol. 204, pp. 399–408, 1990, doi: 10.1243/PIME_PROC_1990_204_120_02.

M. Anwer and R. M. C. So, “Swirling turbulent flow through a curved pipe,” Exp. Fluids., vol. 14, pp. 85–96, 1993, doi: 10.1007/BF00196992.

W. J. Kim and V. C. Patel, “Origin and decay of longitudinal vortices in developing flow in a curved rectangular duct(data bank contribution),” J. Fluids Eng., vol. 116, no. 1, pp. 45–52, 1994, doi: 10.1115/1.2910240.

A. Hilgenstock and R. Ernst, “Analysis of installation effects by means of computational fluid dynamics - CFD vs experiments,” Flow Meas. Instrum., vol. 7, pp. 161–171, 1996, doi: 10.1016/S0955-5986(97)88066-1.

G. Xiaofeng and B. M. Ted, “Simulations of flow in curved tubes,” Aerosol Sci Tech., vol. 26, no. 6, pp. 485–504, 1997, doi: 10.1080/02786829708965448.

S. E. Kim, D. Choudhury, and B. Patel, “Computations of complex turbulent flows using the commercial code Fluent,”in Modeling Complex Turbulent Flows., vol. 7, Springer, Dordrecht, 1997, pp. 259–276, doi: 10.1007/978-94-011-4724-8_15.

K. Sudo, M. Sumida, and H. Hibara, “Experimental investigation on turbulent flow in a circular-sectioned 90-degree bend,” Exp. Fluids., vol. 25, pp. 42–49, 1998, doi: 10.1007/s003480050206.

U. Kumar, S. N. Singh, and V. Seshadri, “Pressure losses in rough 90° bends of different radius of curvature,” in 26th National Conference on Fluid Mechanics and Fluid Power, I.I.T., Kharagpur, 15-17 December, 1999, pp. 337–342.

T. J. Hüttl and R. Friedrich, “Direct numerical simulation of turbulent flows in curved and helically coiled pipes,” Comput Fluids., vol. 30, no. 5, pp. 591–605, 2001, doi: 10.1016/S0045-7930(01)00008-1.

T. Kawamura, T. Nakao, and M. Takahashi, “Reynolds number effect on turbulence downstream from elbow pipe,” Trans. Jpn. Soc. Mech. Eng. B., vol. 68, no. 667, pp. 645–651, 2002, doi: 10.1299/kikaib.68.645.

T. H. Chang and H. S. Lee, “An experimental study on swirling flow in a 90 degree circular tube by using particle image velocimetry,” J. Vis., vol. 6, pp. 343–352, 2003, doi: 10.1007/BF03181741.

P. L. Spedding, E. Benard, and G. M. McNally, “Fluid flow through 90 degree bends,” Dev. Chem. Eng. Mineral Process., vol. 12, no. 1-2, pp. 107–128, 2004, doi: 10.1002/apj.5500120109.

J. Pruvost, J. Legrand, and P. Legentilhomme, “Numerical investigation of bend and torus flows, part I: effect of swirl motion on flow structure in U-bend,” Chem. Eng. Sci., vol. 59, no. 16, pp. 3345–3357, 2004, doi: 10.1016/j.ces.2004.03.040.

M. Raisee, H. Alemi, and H. Iacovides, “Prediction of developing turbulent flow in 90°-curved ducts using linear and non-linear low-Re k-ε models,” Int. J. Numer. Meth. Fluids., vol. 51, no. 12, pp. 1379–1405, 2006, doi: 10.1002/fld.1169.

N. M. Crawford, G. Cunningham, and S. W. T. Spence, “An experimental investigation into the pressure drop for turbulent flow in 90° elbow bends,” Proc Inst Mech Eng E, J Process Mech Eng., vol. 221, no. 2, pp. 77–88, 2007, doi: 10.1243/0954408JPME84.

T. Shiraishi, H. Watakabe, H. Sago, M. Konomura, A. Ymaguchi, and T. Fujii, “Resistance and fluctuating pressures of a large elbow in high Reynolds numbers,” J. Fluid Mech., vol. 128, no. 5, pp. 1063–1073, 2006, doi: 10.1115/1.2236126.

T. Shiraishi, H. Watakabe, H. Sago, and H. Yamano, “Pressure fluctuation characteristics of the short radius elbow pipe for FBR in the postcritical Reynolds regime,” J. Fluid Sci. Technol., vol. 4, no. 2, pp. 430–441, 2009, doi: 10.1299/jfst.4.430.

J. Mojtaba, C. Cathy, and P. Hassan, “Secondary flow velocity field in laminar pulsating flow through curved pipes-PIV measurements,” Proc. ASME Fluids Eng. Div. Summer Meet., 78141, pp. 1577–1584, 2009, doi: 10.1115/FEDSM2009-78141.

A. Ono, N. Kimura, H. Kamide, and A. Tobita, “Influence of elbow curvature on flow structure at elbow outlet under high Reynolds number condition,” Nucl. Eng. Des., vol. 241, no. 11, pp. 4409–4419, 2011, doi: 10.1016/j.nucengdes.2010.09.026.

A. Noorani, G. K. El Khoury, and P. Schlatter, “Evolution of turbulence characteristics from straight to curved pipes,” Int. J. Heat & Fluid Flow., vol. 41, pp. 16–26, 2013, doi: 10.1016/j.ijheatfluidflow.2013.03.005.

C. Min and Z. Zhiguo, “Numerical simulation of turbulent driven secondary flow in a 90° bend pipe,” Adv Mat Res., vol. 765-767, pp. 514–519, 2013, doi: 10.4028/www.scientific.net/AMR.765-767.514.

L. Niu and H. S. Dou, “Stability study of flow in a 90° bend based on the energy gradient theory,” in 6th International Conference on Pumps and Fans with Compressors and Wind Turbines, IOP Conf. Ser: Mater. Sci. Eng., vol. 52, no. 2, pp. 1–6, 2013, 10.1088/1757-899X/52/2/022006.

L. H. O. Hellström, M. B. Zlatinov, G. Cao, and A. J. Smits, “Turbulent pipe flow downstream of a 90° bend,” J. Fluid Mech., vol. 735, pp. 1–12, 2013, doi: 10.1017/jfm.2013.534.

K. Jongtae, Y. Mohan, and K. Seungjin, “Characteristics of secondary flow induced by 90-degree elbow in turbulent pipe flow,” Eng. Appl. Comput. Fluid Mech., vol. 8, no. 2, pp. 229–239, 2014, doi: 10.1080/19942060.2014.11015509.

P. Dutta and N. Nandi, “Effect of Reynolds number and curvature ratio on single phase turbulent flow in pipe bends,” Mech. Mech. Eng., vol. 19, no. 1, pp. 5–16, 2015.

W. Yan, D. Quanlin, and W. Pengfei, “Numerical investigation on fluid flow in a 90-degree curved pipe with large curvature ratio,” Math. Probl. Eng., vol. 2015, no. 2, pp. 1–12, 2015, doi: 10.1155/2015/548262.

R. Röhrig, S. Jakirlic´, and C. Tropea, “Comparative computational study of turbulent flow in a 90° pipe elbow,” Int. J. Heat & Fluid Flow., vol. 55, pp. 120–131, 2015, doi: 10.1016/j.ijheatfluidflow.2015.07.011.

P. Dutta, S. K. Saha, N. Nandi, and N. Pal, “Numerical study on flow separation in 90° pipe bend under high Reynolds number by k-ε modeling,” Eng. Sci. Technol. Int J., vol. 19, no. 2, pp. 904–910, 2016, doi: 10.1016/j.jestch.2015.12.005.

Z. Wang, R. Örlü, P. Schlatter, and Y. M. Chung, “Direct numerical simulation of a turbulent 90° bend pipe flow,” Int. J. Heat & Fluid Flow., vol. 73, pp. 199–208, 2018, doi: 10.1016/j.ijheatfluidflow.2018.08.003.

J. L. Lumley and G. Newman, “The return to isotropy of homogeneous turbulence,” J. Fluid Mech., vol. 82, no. 1, pp. 161–178, 1977, doi: 10.1017/S0022112077000585.

S. Nayak, N. Kumar, S. M. A. Khader, and R. Pai, “Effect of dome size on flow dynamics in saccular aneurysms– A numerical study,” J. Mech. Eng. Sci., vol. 14, no. 3, pp. 7181–7190, 2020, doi: 10.15282/jmes.14.3.2020.19.0564.

D. Ramírez, A. R. Clemente, and E. Chica, “Design and numerical analysis of an efficient H-Darrieus vertical-axis hydrokinetic turbine,” J. Mech. Eng. Sci., vol. 13, no. 4, pp. 6036–6058, 2019, doi: 10.15282/jmes.13.4.2019.21.0477.

P. Pasymi, Y.W. Budhi, A. Irawan, and Y. Bindar, “Three dimensional cyclonic turbulent flow structures at various geometries, inlet-outlet orientations and operating conditions,” J. Mech. Eng. Sci., vol. 12, no. 4, pp. 4300–4328, 2018, doi: 10.15282/jmes.12.4.2018.23.0369.

G. Honoré, “Numerical analysis of anisotropic turbulent flows using nonlinear turbulence models,” Mechanical PhD thesis, Polytechnic of Lille. 2008.

B. E. Launder, “Second-moment closure: present... and future?,” Int J Heat Fluid Fl., vol. 10, no. 4, pp. 282–300, 1989, doi: 10.1016/0142-727X(89)90017-9.

Y. G. Lai, R. M. C. So, M. Anwer, and B. C. Hwang, “Calculations of a curved pipe flow using Reynolds stress closure,” Proc. Inst. Mech. Eng. Pt. C J. Mech. Eng. Sci., vol. 205, no. 4, pp. 231–244, 1991, doi: 10.1243/PIME_PROC_1991_205_115_02.

W. J. Richard, “Modeling strategies for unsteady turbulent flows in the lower plenum of the VHTR,” Nucl. Eng. Des., vol. 238, no. 3, pp. 482–491, 2008, doi: 10.1016/j.nucengdes.2007.02.049.

L. Belhoucine, M. Deville, A. R. Elazehari, and M. O. Bensalah, “Explicit algebraic Reynolds stress model of incompressible turbulent flow in rotating square duct,” Comput Fluids., vol. 33, no. 2, pp. 179–199, 2004, doi: 10.1016/S0045-7930(03)00055-0.

F. S. Lien and M. A. Leschziner, “Assessment of turbulence-transport models including non-linear RNG eddy-viscosity formulation and second-moment closure for flow over a backward-facing step,” Comput Fluids., vol. 23, no. 8, pp. 983–1004, 1994, doi: 10.1016/0045-7930(94)90001-9.

M. M. Gibson and B. E. Launder, “Ground effects on pressure fluctuations in the atmospheric boundary layer,” J. Fluid Mech., vol. 86, no. 3, pp. 491–511, 1978, doi: 10.1017/S0022112078001251.

S. Fu, B. E. Launder, and M. A. Leschziner, “Modeling strongly swirling recirculating jet flow with Reynolds-stress transport closures,” in 6th International Symposium on Turbulent Shear Flows, Toulouse, France, 7-9 September, 1987, pp.17-6-1–17-6-6.

S. Sarkar and L. Balakrishnan, “Application of a Reynolds stress turbulence model to the compressible shear layer,” AIAA Journal., vol. 29, no. 5, pp. 743–752, 1991, doi: 10.2514/3.10649.

M. R. Nematollahi and M. Nazifi, “Enhancement of heat transfer in a typical pressurized water reactor by different mixing vanes on spacer grids,” Energy Convers. Manag., vol. 49, no. 7, pp. 1981–1988, 2008, doi: 10.1016/j.enconman.2007.12.016.

A. R. Al-Obaidi, “Influence of guide vanes on the flow fields and performance of axial pump under unsteady flow conditions: Numerical study,” J. Mech. Eng. Sci., vol. 14, no. 2, pp. 6570–6593, 2019, doi: 10.15282/jmes.14.2.2020.04.0516.

H. K. Versteeg and W. Malalasekera, An introduction to computational fluid dynamics-the finite volume method. Harlow: Pearson Education Limited, 2007.

H. M. Quamrul, “CFD Analysis of single and multiphase flow characteristics in elbow,” Sci. Res., vol. 4, no. 4, pp. 210–214, 2012, doi: 10.4236/eng.2012.44028.

A. Sherikar and P. J. Disimile, “RANS study of very high Reynolds- number plane turbulent Couette flow,” J. Mech. Eng. Sci., vol. 14, no. 2, pp. 6663–6678, 2020, doi: 10.15282/jmes.14.2.2020.10.0522.

ANSYS Meshing User's Guide, ANSYS Inc., Southpointe 2600 ANSYS Drive Canonsburg, PA 15317, 2018.

K. S. Choi and J. L. Lumley, “The return to isotropy of homogenous turbulence,” J. Fluid Mech., vol. 436, pp. 59–84, 2001, doi: 10.1017/S002211200100386X.

H. S. Shafi and R. A. Antonia, “Anisotropy of the Reynolds stresses in a turbulent boundary layer on a rough wall,” Exp. Fluids., vol. 18, pp. 213–215, 1995, doi: 10.1007/BF00230269.

R. A. Antonia and P. Å. Krogstad, “Turbulence structure in boundary layers over different types of surface roughness,” Fluid Dyn. Res., vol. 28, no. 2, pp. 139–157, 2001, doi: 10.1016/S0169-5983(00)00025-3.

R. Smalley, S. Leonardi, R. Antonia, L. Djenidi, and P. Orlandi, “Reynolds stress anisotropy of turbulent rough wall layers,” Exp. Fluids., vol. 33, pp. 31–37, 2002, doi: 10.1007/s00348-002-0466-z.