TORCHE

This is a collection of Python scripts for pressure drop and heat transfer calculations for crossflow tube bundles for both inline and staggered configurations.

Author(s): Jonah Haefner* and Lane Carasik^

Contributing and previous work done by: Julien Clayton

*Texas A&M University Thermal-hydraulics Research Group

^Virginia Commonwealth University Fluids in Advanced Systems and Technology (FAST) Research Group

These models are simple to use pressure drop and Nusselt Number calculators based off the work of Zukauskas et al. and Gnielinski and Gaddis. It is intended that future versions will include additional crossflow models in tube bundles, across helical coils, and across packed bends.

TORCHE is discussed in greater detail in the following conference proceedings:

1. J. B. Haefner, L. B. Carasik, Y. A. Hassan, "Development and Verification of MATLAB Functions for Pressure Drop Estimation in Crossflow Tube Bundles." Transactions of the American Nuclear Society (Vol. 115(1), pp. 1535-1537). Las Vegas, Nevada
2. J. B. Haefner, L. B. Carasik, Y. A. Hassan, "TORCHE - Toolbox for Reactor Cross-Flow Heat Exchangers." Transactions of the American Nuclear Society (Vol. 116(1), pp. 1387-1390). San Francisco, California

Pressure Drop Correlations and Models

There is currently only two crossflow pressure drop models implemented. These are models developed by Zukauskas-Ulinskas and Gnielinski-Gaddis where the former is based off curve fits from old figures while the latter is a generalized set of equations based on inline or staggered geometries.

Zukauskas Model

Notes:

• These are only considered valid for the specific pitch to diameter ratios listed.
• The Reynolds number is based on the maximum velocity in the narrowest area between tubes. Validity: (need to recheck ranges)
• Number of rows of tubes: Nr >= 1
• Reynolds number: 10 ≤ Re ≤ 10e6
• For in-line tube arrangement: a x b = 1.25 x 1.25; 1.5 x 1.5; 2.0 x 2.0.
• For staggered tube arrangement: a x b = 1.25 x ----; 1.5 x ----; 2.0 x ----.

References:

1. A. ZUKAUSKAS, R. ULINSKAS, Heat Transfer in Banks of Tubes in Crossflow, Hemisphere Publishing, United States (1988).

Gnielinski-Gaddis Model

Notes:

• Not limited to specific pitch-diameter ratios within limits after a high enough Reynolds numbers.
• The Reynolds number is based on the maximum velocity in the narrowest area between tubes. Validity:
• The available experimental measurements used to develop the above equations covered the following ranges: Reynolds number: 1 ≤ Re ≤ 3 /* 10E5 and number of tube rows: nR ≥ 5.
• Number of rows of tubes: Nr >= 5
• Reynolds number: 1 ≤ a ≤ 3*10e5
• In the range Re < 10E3: For in-line tube arrangement: a x b = 1.25 x 1.25; 1.5 x 1.5; 2.0 x 2.0. For staggered tube arrangement: a x b = 1.25 x 1.0825; 1.5 x 1.299; 1.768 x 0.884.
• In the range Re ≥ 10E3: For in-line tube arrangement: 1.25 ≤ a ≤ 3.0; 1.2 ≤ b ≤ 3.0. For staggered tube arrangement: 1.25 ≤ a ≤ 3.0; 0.6 ≤ b ≤ 3.0; c ≥ 1.25.

References:

1. VDI. VDI Heat Atlas. Berlin, Heidelberg: VDI-Buch-Springer, 2010. Chapter L1
2. Gaddis, E., Gnielinski, V., 1985, "Pressure drop in cross flow across tube bundles," Int. Chem. Eng., vol. 25(1), pp. 1-15

Heat Transfer Correlations and Models

There is currently only two crossflow heat transfer models implemented. These are models developed by Zukauskas-Ulinskas and Martin-Gnielinski where the former is based off curve fits from old figures while the latter is a generalized set of equations based on inline or staggered geometries.

Zukauskas Model

NOTE:

• Currently only applicable for staggered geometry
• The Reynolds number is based on the maximum velocity in the narrowest area between tubes. Validity: (need to recheck ranges)
• Number of rows of tubes: Nr >= 2
• Reynolds number: 100 ≤ Re ≤ 3x10e5 For in-line tube arrangement: 1.25 ≤ a ≤ 3.0; 1.2 ≤ b ≤ 3.0. For staggered tube arrangement: 1.008 ≤ a ≤ 2.0; 1.008 ≤ b ≤ 2.0

? 10 < Re < 2e6 ? 0.7 < Pr < 500

References:

1. Zhukauskas, A., R. Ulinskas., 1988, "Heat Transfer in Tube Banks in Crossflow," Hemisphere Publishing Corporation. New York, NY. 1988.
2. Zukauskas, A., 1972, "Heat Transfer from Tubes in Cross Flow," Adv. in Heat Trans, vol. 8, Academic Press, New York.

Martin-Gnielinski Model

Gnielinski and Martin Model Based off Leveque Analogy

NOTE:

• The Reynolds number is based on the maximum velocity in the narrowest area between tubes. Validity: (need to recheck ranges)
• Number of rows of tubes: Nr >= 2
• Reynolds number: 100 ≤ Re ≤ 3x10e5 For in-line tube arrangement: 1.25 ≤ a ≤ 3.0; 1.2 ≤ b ≤ 3.0. For staggered tube arrangement: 1.25 ≤ a ≤ 2.0; 1.25 ≤ b ≤ 2.0

References:

1. Martin, H., 2002, “The Generalized Lévêque Equation and its practical use for the prediction of heat and mass transfer rates from pressure drop,” Chem. Eng. Sci., vol. 57, pp. 3217-3223.