ANALYTICAL CALCULATION FOR LAMINAR AIR FLOW MOMENTUM TRANSPORT IN UNDERGROUND MINE TUNNEL USING NEWTONIAN EQUATIONS OF MOTION

Arif Algifari, Adrian Adrian

Abstract


ABSTRAK

Dalam kasus tertentu terdapat terowongan percabangan tambang bawah tanah yang tidak teralirkan udara secara mekanis tetapi udara tetap mengalir secara alami teridentifikasi beraliran laminar. Studi ini memodelkan perpindahan momentum aliran laminar udara terowongan dengan dimensi rectangular atau Cartesian untuk memvisualisasikan profil distribusi kecepatan linier fluida dan profil tegangan geser fluida. Metode pemodelan menggunakan perhitungan analitik matematika dari persamaan gerak aliran fluida Newtonian untuk rejim laminar Navier-Stokes. Beberapa data yang dikumpulkan adalah dimensi terowongan, kecepatan linier udara, dan temperatur. Beberapa sifat fisik udara dikutip dari literatur. Hasil pengukuran kecepatan udara rata-rata diinputkan ke dalam model empiris untuk mendapatkan profil koordinat dua dimensi (x,z) untuk distribusi tegangan geser dan kecepatan udara yang mendekati keadaan sebenarnya untuk aliran laminar pada dimensi Cartesian. Hasil penelitian didapatkan pressure drop aliran sebesar 2,2 x 10-5 Pa, aliran mengandalkan perpindahan molekular bukan perpindahan secara konveksi paksa karena dilihat dari profil sebaran tegangan geser yang terlalu kecil dan laju alir sebesar 0,32 m3/s tidak memenuhi fungsi ventilasi tambang bawah.

 

Kata kunci: perpindahan momentum; aliran laminar; fluida newtonian; ventilasi tambang.

 

ABSTRACT

In certain case there is a mine tunnel branch that is not mechanically ventilated but air still flow naturally identified as laminar flow. This study modelled the momentum transport of the tunnel air laminar flow with rectangular or Cartesian dimensions to visualize the linear velocity distribution profile of the fluid and the fluid shear stress profile. The modelling method uses analytical mathematical calculations of the Newtonian fluid flow equations of motion for the laminar regime of Navier-Stokes. Some of the data collected are tunnel dimensions, air linear velocity, and temperature. Some physical properties of air are cited from literature. The results of the average air velocity measurement are input into the empirical model to obtain two-dimensional coordinate profiles (x,z) for the shear stress distribution and air velocity that are close to the actual situation for laminar flow in the Cartesian dimension. The results of the study obtained a pressure drop of the flow was 2,2 x 10-5 Pa, the flow using molecular transport instead of forced convection transport because seen from the shear stress distribution profile was too small and the flow rate was 0,32 m3/s did not fulfill the underground mine ventilation function.

 

Keywords: momentum transport; laminar flow; newtonian fluid; mine ventilation.


Keywords


momentum transport; laminar flow; newtonian fluid; mine ventilation.

Full Text:

PDF

References


Denis, B. (2020). An Overview of Numerical and Analytical Methods for solving Ordinary Differential Equations. (December). https://doi.org/10.13140/RG.2.2.11758.64329

Faruk, U., & Kamiran. (2017). Analisis Pengaruh Aliran Turbulen Terhadap Karakteristik Lapisan Batas pada Pelat Datar Panas. Jurnal Sains Dan Seni, 1(1), 57–60.

Franco, J. M., & Partal, P. (2008). Newtonian fluid. The IUPAC Compendium of Chemical Terminology, I. https://doi.org/10.1351/goldbook.n04138

Fukuchi, T., & Fukuchi, T. (2014). Numerical calculation of fully-developed laminar flows in arbitrary cross-sections using finite difference method Numerical calculation of fully-developed laminar flows in arbitrary cross-sections using finite difference method. 042109(2011). https://doi.org/10.1063/1.3652881

Imberger, J. (2013). Equations of Motion. In Environmental Fluid Dynamics. https://doi.org/10.1016/b978-0-12-088571-8.00002-4

Kanam, O. H., & Ahmed, M. O. (2021). A review on underground mine ventilation system. Journal of Mines, Metals and Fuels, 69(2), 62–70. https://doi.org/10.18311/jmmf/2021/27334

Khan, W., & Yovanovich, M. M. (2014). Analytical Modeling of Fluid Flow and Heat Transfer in Microchannel / Nanochannel Heat Sinks. (July 2008). https://doi.org/10.2514/1.35621

Laloui, L., & Rotta Loria, A. F. (2020). Heat and mass transfers in the context of energy geostructures. In Analysis and Design of Energy Geostructures. https://doi.org/10.1016/b978-0-12-816223-1.00003-5

Li, B., Zheng, L., Lin, P., Wang, Z., Liao, M., Li, B., … Wang, Z. (2016). Numerical Mathematics : Theory , Methods and Applications Applications : Terms of use : Click here A Mixed Analytical / Numerical Method for Velocity and Heat Transfer of Laminar Power-Law Fluids. 315–336. https://doi.org/10.4208/nmtma.2016.m1423

Lue, L. (2014). Momentum , Heat , and Mass Transfer. bookboon.

Maria Ulfah Handayani, Zahrani Dalimunthe, Rika Sari Indah, J. R. (2016). Penentuan Aliran Fluida Dengan Menggunakan Metode Persamaan Navierstokes Dan Bantuan Persamaan Diferensial. Prosiding Seminar Nasional Inovasi Dan Teknologi Informasi SNITI- 3, (March).

Nasution, A., Komar, S., Abro, A., Pertambangan, J. T., Teknik, F., & Sriwijaya, U. (2014). ANALISIS SISTEM EXHAUST UNTUK KEBUTUHAN SUPPLY UDARA PENAMBANGAN PADA TAMBANG BAWAH TANAH OMBILIN 1 ( SAWAHLUWUNG ) PT . BUKIT ASAM ( PERSERO ) TBK UPO ANALYSIS OF EXHAUST SYSTEM FOR AIR SUPPLY NEEDS MINING IN UNDERGROUND MINING OMBILIN 1 ( SAWAHLUWUNG ) . 1, 0–8.

Obracaj, D., Korzec, M., & Deszcz, P. (2021). Study on methane distribution in the face zone of the fully mechanized roadway with overlap auxiliary ventilation system. Energies, 14(19). https://doi.org/10.3390/en14196379

Patnaik, S., & Pandey, S. C. (2019). Case Study Research. Methodological Issues in Management Research: Advances, Challenges, and the Way Ahead, (August), 163–179. https://doi.org/10.1108/978-1-78973-973-220191011

Prakash, O. (2014). Estimation of Air Density and its importance in Barometric Pressure Measurements Estimation of Air Density and its importance in Barometric Pressure Measurements. (February 2012).

R. Byron Bird, Stewart, W. E., & Edwin N. Lightfoot. (2002). Transport Phenomena. USA: John Willay & Sons, Inc.

Rapp, B. E. (2017). The Circular Flow Tube. Microfluidics: Modelling, Mechanics and Mathematics, 309–313. https://doi.org/10.1016/b978-1-4557-3141-1.50014-9

Sasmito, A. P., Birgersson, E., Ly, H. C., & Mujumdar, A. S. (2013). Some approaches to improve ventilation system in underground coal mines environment - A computational fluid dynamic study. Tunnelling and Underground Space Technology, 34, 82–95. https://doi.org/10.1016/j.tust.2012.09.006

Tiwow, V. A., Fisika, J., & Makassar, U. N. (2015). ANALISIS ALIRAN FLUIDA NEWTONIAN PADA PIPA TIDAK HORIZONTAL V. JURNAL SAINS DAN PENDIDIKAN FISIKA (JSPF), 2015(April), 104–108.

Utami, D. H., & Azhar, I. (2017). Tranfer Massa dan Panas. In Tekkim.

Wicaksono, A. F., Subekti, S., & Indriyanto, K. (2021). Analisis Pengaruh Penyumbatan Aliran Fluida Pada Pipa Dengan Metode Fast Fourier Transform. Jurnal Dinamika Vokasional Teknik Mesin, 6(1), 77–83. Retrieved from https://journal.uny.ac.id/index.php/dynamika/issue/view/2049

Widiatmojo, A., Widodo, N. P., & Sasaki, K. (2021). Metode Gas Tracer Untuk Evaluasi Efisiensi Ventilasi Tambang Bawah Tanah. Indonesian Mining Professionals Journal, 3(1), 1–8. https://doi.org/10.36986/impj.v3i1.28

Zołek-Tryznowska, Z. (2015). Rheology of Printing Inks. Printing on Polymers: Fundamentals and Applications, 87–99. https://doi.org/10.1016/B978-0-323-37468-2.00006-3




DOI: https://doi.org/10.31764/orbita.v9i2.17053

Refbacks



Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

______________________________________________________

ORBITA: Jurnal Pendidikan dan Ilmu Fisika

p-ISSN 2460-9587 || e-ISSN 2614-7017

 Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

 

EDITORIAL OFFICE: