Abstract
Two dimensional unsteady Navier-Stokes and the energy equations are solved using finite element method for the case of flow past five row deep in-line bundle of circular cylinders with pitch to diameter ratios (PDR) of 1.5 and 2.0. Numerical solutions of governing equations have been obtained using Euler's explicit algorithm. Analysis have been made for Reynolds number of 100 and Prandtl number of 0.71. The effect of Richardson number (Ri=Gr/Re 2) on the flow and heat transfer have been investigated forRi=−1.0, −0.5, 0.0, +0.5 and +1.0. Streamlines, isovorticity lines, pressure and temperature contours, local and average Nusselt numbers, pressure and shear stress distribution around the cylinders are presented. Results obtained for forced convection (Ri=0.0) agree well with the available experimental and numerical results. There is considerable effect of buoyancy over tube bundles both in buoyancy aiding and opposing flows.
Zusammenfassung
Die zweidimensionalen instationären Navier-Stokes-und Energiegleichungen werden mittels der Finitelement-Methode für den Fall von 5 fluchtend übereinander liegenden Kreiszylindern gelöst. Die numerischen Lösungen der Grundgleichungen erfolgten über den expliziten Euler-Algorithmus, und zwar für eine Reynolds-Zahl von 100, eine Prandtl-Zahl von 0.71 und Richardson-Zahlen (Ri=Gr/Re 2) vonRi=−1.0; −0.5; 0.0; +0.5 und +1.0, jeweils für die beiden Verhältnisse Abstand/Durchmesser von 1.5 und 2.0. Stromlinien, Kurven gleicher Zirkulation, Druck- und Temperaturkonturen, lokale und mittlere Nusselt-Zahlen, Druck-und Scherspannungsverteilungen um die Zylinder werden dargestellt. Die für Zwangskonvektion (Ri=0) erhaltenen Ergebnisse stimmen gut mit zugänglichen experimentellen und numerischen Befunden überein. Auftriebseffekte sind sowohl bei förderlicher wie hemmender Anströmung von Bedeutung.
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Abbreviations
- C p :
-
specific heat
- D :
-
diameter of the cylinder
- Gr :
-
Grashof number (βg(T w −T in)D 3/v 2)
- h :
-
heat transfer coefficient
- k :
-
thermal conductivity
- Nu :
-
Nusselt number (hD/k)
- P :
-
Nondimensional pressure (p/ρU 2av )
- Pe :
-
Peclect number (Re Pr)
- Pr :
-
Prandtl number (μC p/k)
- Re :
-
Reynolds number (U av D/v)
- Ri :
-
Richardson number (Gr/Re 2)
- St :
-
Strouhal number (fvs D/U)
- T :
-
temperature
- T in :
-
inlet temperature
- T w :
-
wall temperature
- T b :
-
bulk temperature at minimum cross section
- U :
-
nondimensional axial velocity (u/U av)
- V :
-
nondimensional normal velocity (v/U av)
- X :
-
nondimensional axial coordinate (x/D)
- Y :
-
nondimensional normal coordinate (y/D)
- τ :
-
nondimensional time (D/U av)
- 0:
-
nondimensional temperature (T−T in)/(T w−T in)
- v :
-
kinematic viscosity
- ρ :
-
density
- in:
-
inlet
- w:
-
wall
- av:
-
average
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Krishne Gowda, Y.T., Aswatha Narayana, P.A. & Seetharamu, K.N. Numerical investigation of mixed convection heat transfer past an in-line bundle of cylinders. Heat and Mass Transfer 31, 347–352 (1996). https://doi.org/10.1007/BF02184049
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DOI: https://doi.org/10.1007/BF02184049