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

Martín Salinas-Vázquez

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

Mahendra P. Verma

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

William Vicente

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

Iván F. Galindo-García

Gerencia de Simulación,
Instituto Nacional de Electricidad y
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

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%.

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Figures

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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.

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Fig. 2

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

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Fig. 3

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

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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].

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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

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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.

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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.

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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]

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Fig. 9

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

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Fig. 10

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

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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

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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

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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.

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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

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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

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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

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