0
Research Papers: Flows in Complex Systems

# Computational Fluid Dynamic Modeling to Determine the Resistance Coefficient of a Saturated Steam Flow in 90 Degree Elbows for High Reynolds Number

[+] Author and Article Information
Juan C. López-López

Instituto de Ingeniería,
Circuito Escolar s/n,
Delegación Coyoacán,
CDMX, C.P. 04510, México;
Gerencia de Geotermia,
Energías limpias,
Ave. Reforma 113,
Col. Palmira,
Cuernavaca, Mor. 62490, México
e-mail: jlopezl@iingen.unam.mx

Martín Salinas-Vázquez

Instituto de Ingeniería,
Circuito Escolar s/n,
Delegación Coyoacán,
CDMX, C.P. 04510, México
e-mail: msalinasv@iingen.unam.mx

Mahendra P. Verma

Gerencia de Geotermia,
Energías limpias,
Ave. Reforma 113,
Col. Palmira,
Cuernavaca, Mor. 62490, México
e-mail: mahendra@ineel.mx

William Vicente

Instituto de Ingeniería,
Circuito Escolar s/n,
Delegación Coyoacán,
CDMX, C.P. 04510, México
e-mail: wvicenter@iingen.unam.mx

Iván F. Galindo-García

Gerencia de Simulación,
Energías limpias,
Ave. Reforma 113,
Col. Palmira,
Cuernavaca, Mor. 62490, México
e-mail: igalindo@inel.mx

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 5, 2018; final manuscript received April 5, 2019; published online May 8, 2019. Assoc. Editor: Praveen Ramaprabhu.

J. Fluids Eng 141(11), 111103 (May 08, 2019) (11 pages) Paper No: FE-18-1744; doi: 10.1115/1.4043495 History: Received November 05, 2018; Revised April 05, 2019

## Abstract

The pressure drop in 90 deg elbows under the operating conditions of geothermal power plants in Mexico is studied using the computational fluid dynamics model. The elbow resistance coefficient was calculated for a steam flow with high Reynolds numbers (1.66–5.81 × $106$) and different curvature ratios (1, 1.5, and 2). The simulations were carried out with the commercial software ANSYScfx, which considered the Reynolds-averaged Navier–Stokes (RANS) compressible equations and the renormalization group (RNG) k–$ε$ turbulence model. First, the methodology was validated by comparing the numerical results (velocity and pressure) with published data of airflow (25 °C, 0.1 MPa) with high Reynolds numbers. Then, scenarios with different diameters (0.3–1.0 m) and conditions of the working fluid (0.8–1.2 MPa) were simulated to obtain velocity, pressure, density, and temperature profiles along the pipeline. The temperature and density gradients combined with the compressible effects achieved in the 90 deg elbows modified the flow separation, pressure drop, and resistance coefficient. Based on the resistance coefficient, factors were generated for a new equation, which was integrated into Geosteam.Net to calculate the pressure drop in a pipeline at the Los Azufres geothermal power plant. The difference with the data measured by a pressure transducer was 7.59%, while the equations developed for water or air showed differences between 11.23% and 45.22%.

<>

## References

Crawford, N. M. , Cunningham, G. , and Spence, S. W. T. , 2007, “ An Experimental Investigation Into the Pressure Drop for Turbulent Flow in 90° Elbow Bends,” Proc. Inst. Mech. Eng., Part E, 221(2), pp. 77–88.
Al-Tameemi, W. M. , and Ricco, P. , 2018, “ Pressure-Loss Coefficient of 90 Deg Sharp-Angled Miter Elbows,” ASME. J. Fluids Eng., 140(6), p. 061102.
Kalpakli Vester, A. , Örlü, R. , and Alfredsson, P. , 2016, “ Turbulent Flows in Curved Pipes: Recent Advances in Experiments and Simulations,” ASME Appl. Mech. Rev., 68(5), p. 050802.
Verma, M. P. , 2013, “ Steam Transport Simulation in a Geothermal Pipeline Network Constrained by Internally Consistent Thermodynamic Properties of Water,” Rev. Mex. Cienc. Geol., 30(1), pp. 210–221.
Ellenberger, J. P. , 2010, Piping and Pipeline Calculations Manual: Construction, Design Fabrication, and Examination, Elsevier, Burlington, MA.
García-Gutiérez, A. , Hernández, A. F. , Martínez, J. I. , Ceceñas, M. , Ovando, R. , and Canchola, I. , 2015, “ Hydraulic Model and Steam Flow Numerical Simulation of the Cerro Prieto Geothermal Field, Mexico, Pipeline Network,” Appl. Therm. Eng., 75, pp. 1229–1243.
Crane, 1988, Flow of Fluids Through Valves, Fittings, and Pipes, Crane, New York.
Idelchik, I. E. , 1986, Handbook of Hydraulic Resistance, 2nd ed., Hemisphere, Washington, DC.
Martínez-Estrella, J. I. , García-Gutiérrez, A. , Hernández-Ochoa, A. F. , Verma, M. P. , Mendoza-Covarrubias, A. , and Ruiz-Lemus, A. , 2010, “ Simulación Numérica de la Operación de la Red de Transporte de Vapor Del Campo Geotérmico de Los Azufres, Mich,” Geotermia, 23(2), pp. 2–12.
García-Gutiérrez, A. , Martínez-Estrella, J. I. , Hernández-Ochoa, A. F. , Verma, M. P. , Mendoza-Covarrubias, A. , and Ruiz-Lemus, A. , 2010, “ Development of a Numerical Hydraulic Model of the Los Azufres Steam Pipeline Network,” Geothermics, 32(3), pp. 313–325.
Hooper, W. , 1981, “ The Two-K Method Predicts Head Losses in Pipe Fittings,” Chem. Eng., 88, pp. 96–100.
Rennels, D. C. , and Hudson, H. M. , 2012, Pipe Flow: A Practical and Comprehensive Guide, Wiley, Hoboken, NJ.
Enayet, M. M. , Gibson, M. M. , Taylor, A. M. K. P. , and Yianneskis, M. , 1982, “ Laser- Doppler Measurements of Laminar and Turbulent Flow in a Pipe Bend,” Int. J. Heat Fluid Flow, 3(4), pp. 213–219.
Ono, A. , Kimura, N. , Kamide, H. , and Tobita, A. , 2011, “ Influence of Elbow Curvature on Flow Structure at Elbow Outlet Under High Reynolds Number Condition,” Nucl. Eng. Des., 241(11), pp. 4409–4419.
Takamura, H. , Ebara, S. , Hashizume, H. , Aizawa, K. , and Yamano, H. , 2012, “ Flow Visualization and Frequency Characteristics of Velocity Fluctuations of Complex Turbulent Flow in a Short Elbow Piping Under High Reynolds Number Condition,” ASME J. Fluid Eng., 134(10), p. 101201.
Hüttl, T. J. , and Friedrich, R. , 2001, “ Direct Numerical Simulation of Turbulent Flows in Curved and Helically Coiled Pipes,” Comput. Fluids, 30(5), pp. 591–605.
Noorani, A. , El Khoury, G. K. , and Schlatter, P. , 2013, “ Evolution of Turbulence Characteristics From Straight to Curved Pipes,” Int. J. Heat Fluid Flow, 41, pp. 16–26.
Tanaka, M. A. , Ohshima, H. , and Monji, H. , 2009, “ Numerical Investigation of Flow Structure in Pipe Elbow With Large Eddy Simulation Approach,” ASME Paper No. PVP2009-77598.
Rütten, F. , Schröder, W. , and Meinke, M. , 2005, “ Large-Eddy Simulation of Low Frequency Oscillations of the Dean Vortices in Turbulent Pipe Bend Flows,” Phys. Fluids, 17(3), p. 035107.
Eguchi, Y. , Murakami, T. , Tanaka, M. , and Yamano, H. , 2011, “ A Finite Element LES for high-Re Flow in a Short-Elbow Pipe With Undisturbed Inlet Velocity,” Nucl. Eng. Des., 241(11), pp. 4368–4378.
Tan, L. , Zhu, B. , Wang, Y. , Cao, S. , and Liang, K. , 2014, “ Turbulent Flow Simulation Using Large Eddy Simulation Combined With Characteristic-Based Split Scheme,” Comput. Fluids, 94, pp. 161–172.
Kim, J. , Yadav, M. , and Kim, S. , 2014, “ Characteristics of Secondary Flow Induced by 90-Degree Elbow in Turbulent Pipe Flow,” Eng. Appl. Comput. Fluid Mech., 8(2), pp. 229–239.
Crawford, N. , Spence, S. , Simpson, A. , and Cunningham, G. , 2009, “ A Numerical Investigation of the Flow Structures and Losses for Turbulent Flow in 90° Elbow Bends,” Proc. Inst. Mech. Eng., Part E, 223(1), pp. 27–44.
Dutta, P. , and Nandi, N. , 2015, “ Effect of Reynolds Number and Curvature Ratio on Single Phase Turbulent Flow in Pipe Bends,” Mech. Mech. Eng., 19(1), pp. 5–16.
Dutta, P. , Saha, S. K. , Nandi, N. , and Pal, N. , 2016, “ Numerical Study on Flow Separation in 90° Pipe Bend Under High Reynolds Number by k-ε Modelling,” Eng. Sci. Technol., Int. J., 19(2), pp. 904–910.
Wang, Y. , Dong, Q. , and Wang, P. , 2015, “ Numerical Investigation on Fluid Flow in a 90-Degree Curved Pipe With Large Curvature Ratio,” Math. Probl. Eng., 2015, pp. 1–12.
Wang, S. , Ren, C. , Sun, Y. , Yang, X. , and Tu, J. , 2016, “ A Study on the Instantaneous Turbulent Flow Field in a 90-Degree Elbow Pipe With Circular Section,” Sci. Technol. Nucl. Install., 2016, pp. 1–8.
Dutta, P. , and Nandi, N. , 2015, “ Study on Pressure Drop Characteristics of Single Phase Turbulent Flow in Pipe Bend for High Reynolds Number,” ARPN J. Eng. Appl. Sci., 10(5), pp. 2221–2226.
Wang, S. , Ren, C. , Gui, N. , Sun, Y. , Tu, J. , Yang, X. , and Jiang, S. , 2017, “ Experimental and Numerical Study on the Circumferential Pressure Distribution on the Wall of a 90° Elbow Pipe With Circular Section,” Ann. Nucl. Energy, 109, pp. 419–430.
Dutta, P. , and Nandi, N. , 2016, “ Effect of Bend Curvature on Velocity & Pressure Distribution From Straight to a 90° Pipe bend-A Numerical Study,” Rest J. Emerging Trends Modell. Manuf., 2, pp. 103–108.
Dutta, P. , and Nandi, N. , 2018, “ Numerical Study on Turbulent Separation Reattachment Flow in Pipe Bends With Different Small Curvature Ratio,” J. Inst. Eng. (epub).
Verma, M. P. , and Torres-Encarnación, J. A. , 2018, “ GeoSteam.Net: Steam Transport Simulator for Geothermal Pipeline Network,” 43rd Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, CA, Feb. 12–14, pp. 1–6.
Fernández, J. M. , 2012, Técnicas Numéricas en Ingeniería de Fluidos, Editorial Reverté, Barcelona, Spain.
Wagner, W. , Cooper, J. R. , Dittmann, A. , Kijima, J. , Kretzschmar, H.-J. , Kruse, A. , Mareš, R. , Oguchi, K. , Sato, H. , Stöcker, I. , Šifner, O. , Takaishi, Y. , Tanishita, I. , Trübenbach, J. , and Willkommen, T. , 2000, “ The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam,” ASME J. Eng. Gas Turbines Power, 122(1), pp. 150–182.
Yakhot, V. , and Orszag, S. A. , 1986, “ Renormalization Group Analysis of Turbulence I: Basic Theory,” J. Sci. Comput., 1(1), pp. 3–51.
ANSYS, 2013, ANSYS CFX-Solver Theory Guide, Release 15, ANSYS, Canonsburg, PA.
Sudo, K. , Sumida, M. , and Hibara, H. , 1998, “ Experimental Investigation on Turbulent Flow in a Circular-Sectioned 90° Bend,” Exp. Fluids, 25(1), pp. 42–49.
Ito, H. , 1960, “ Pressure Losses in Smooth Pipe Bends,” ASME J. Basic Eng., Ser. D, 82(1), pp. 131–140.

## Figures

Fig. 1

Schematic diagram of the 90 deg elbow. Cross sections in the upstream and downstream pipes are defined by z′/D and z/D, respectively. In elbows, three regions (inner, bottom, and outer) were analyzed at different angles from the inlet elbow.

Fig. 2

Computational grid distribution: (a) longitudinal section and (b) cross section

Fig. 3

Pressure coefficient from z′/D = −1 to z/D = 5. Comparison of present simulation (RNG) and experimental data (SUDO) [37].

Fig. 4

Normalized velocity profiles (w/winlet) from z′/D = −1 to z/D = 5. Comparison of present simulation (RNG) and experimental data (SUDO) [37].

Fig. 5

Velocity contours and secondary flow (dean vortices generated from 30 deg): (a) z′/D = −1, (b) elbow inlet (θ = 0 deg), (c) θ = 30 deg, (d) θ = 60 deg, (e) elbow outlet (θ = 90 deg), (f) z/D = 1, (g) z/D = 2, (h) z/D = 5, and (i) z/D = 10

Fig. 6

Normalized velocity profile (w/winlet) along the elbow. Comparison of present simulation (RNG) and numerical results [24] for C = 1: (a) Re = 1 × 105 and (b) Re = 10 × 105.

Fig. 7

Normalized velocity profile (w/winlet) along the elbow. Comparison of present simulation (RNG) and numerical results [24] for C = 2: (a) Re = 1 × 105 and (b) Re = 10 × 105.

Fig. 8

Velocity contour along the pipeline and normalized velocity profiles (w/winlet) at the elbow outlet: (a) Re = 10 × 105 with C = 2 and (b) comparison of several turbulence model made in this work and published data [25]

Fig. 9

Pressure coefficient in the elbow (C = 1) for air and steam flow with Re = 5.81 × 106

Fig. 10

Normalized velocity at different angles of the elbow for incompressible and compressible flow at Re = 5.81 × 106

Fig. 11

Results of present simulation for Pref = 0.8 MPa, C = 1, and D = 0.3 m (Re = 5.81 × 106): (a) velocity contour and (b) static pressure contour

Fig. 12

Normalized velocity profiles (w/winlet) at different angles along the elbow: (a) Re = 1.74 × 106 with C = 1, 1.5, and 2 and (b) Re = 5.81 × 106 with C = 1, 1.5, and 2

Fig. 13

Pressure distribution (p/Pref) along the pipeline for different Reynolds numbers and elbows with C = 1. The total pressure drop (Δp) for each elbow was considered from the elbow inlet to z/D = 6, where the same hydraulic gradient for the straight pipe is reached.

Fig. 14

Pressure distribution (p/Pref = 0.8 MPa) along the pipeline for the different reference pressures and curvature ratios: (a) p = 0.8, 1.0, and 1.2 MPa with C = 1 and (b) C = 1, 1.5, and 2 with p = 0.8 MPa

Fig. 15

Results of present simulation for Pref = 0.8 MPa, C = 1, and D = 0.3 m (Re = 5.81 × 106): (a) temperature contour and (b) density contour

Fig. 16

Pressure drop measured in a segment of the Los Azufres pipeline network [9] and the results obtained with GeoSteam.Net [32] using different equations to represent the 90 deg elbows

## Errata

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections