Abstract
The present work is an experimental and a numerical investigation of the turbulent fluid flow and heat transfer in an annular channel between two concentric cylinders with heated stationary outer cylinder (constant heat flux) and adiabatic rotating inner cylinder. Numerically, the governing equations are discretized in a finite volume fashion using a non-staggered (collocated) arrangement of the variables. The solutions were obtained using the SIMPLE algorithm with upwind scheme. A computer program in FORTRAN 90 was build to solve a set of partial differential equations that govern the fluid flow and heat transfer in annular channels. The experimental results are obtained for an inlet air velocity range of 2–6 m/s, for a wall heat flux range of 600–1200 W/m2 and a rotational speed range of inner cylinder of 0–1500 rpm with a gap width of 1.5 cm. Finally, the relationships between the average Nusselt number and the effective Reynolds number for experimental and numerical results were proposed and compared with those in the existing literature.
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Abbreviations
- d :
-
Air gap thickness or gap width (m): \({{d} = {r}_{{\rm o}}- {r}_{{\rm i}}}\)
- \({{D}_{{\rm h}}}\) :
-
Hydraulic diameter (m): \({{D}_{{\rm h}} = 2({r}_{{\rm o}}- {r}_{{\rm i}})}\)
- \({{r}_{{\rm o}}}\) :
-
Radius of outer cylinder (m)
- \({{r}_{{\rm i}}}\) :
-
Radius of inner cylinder (m)
- \({{u}_{{\rm in}}}\) :
-
Inlet air velocity (m/s)
- N :
-
Rotation speed of inner cylinder (rpm)
- L :
-
Length (m)
- \({{k}_{{\rm a}}}\) :
-
Air thermal conductivity \({({\rm W/m}^{2} \,^{\circ} {C})}\)
- \({{q}_{{\rm w}}}\) :
-
Wall heat flux (W/m2)
- \({\overline {{T}_{\rm s}}}\) :
-
Average surface temperature of outer cylinder \({(^{\circ} {\rm C})}\)
- \({\overline{{T}_{\rm a}}}\) :
-
Average air temperature \({(^{\circ} {\rm C})}\)
- P :
-
Pressure (N/m2)
- k :
-
Turbulent kinetic energy (m2/s2)
- \({\overline{{Nu}}}\) :
-
Average Nusselt number: \({\overline{{Nu}} = {q}_{{\rm w}}{D}_{{\rm h}} /(\overline {{T}_{{\rm w}} }-\overline{{T}_{{\rm a}} } ) {k}_{{\rm a}}}\)
- Pr :
-
Prandtl number: \({\Pr = \mu{C}_{{\rm p}} / {k}_{{\rm a}}}\)
- \({{Re}_{{\rm a}}}\) :
-
Axial Reynolds number: \({{Re}_{{\rm a}}=\rho \,\,{u}_{{\rm in}}{D}_{{\rm h}}/ \mu}\)
- \({{Re}_{{\rm r}}}\) :
-
Rotational Reynolds number: \({{Re}_{{\rm r}}=\rho\,\, {r}_{{\rm i}} \varOmega {D}_{{\rm h} }/ \mu}\)
- \({{u}_{{\rm eff }}}\) :
-
Effective velocity (m/s): \({{u}_{{\rm eff}} = [ {u}_{{\rm in}}^{2 }+ ({r}_{{\rm i}} \varOmega / 2)^{2 }]^{0.5}}\)
- \({{Re}_{{\rm eff}}}\) :
-
Effective Reynolds number: \({{Re}_{{\rm eff}}=\rho\,\,{u}_{{\rm eff}} {D}_{{\rm h}}/ \mu}\)
- μ :
-
Dynamic viscosity (N s/m2)
- \({\mu_{{\rm t}}}\) :
-
Turbulent viscosity (N s/m2)
- \({\varOmega}\) :
-
Angular velocity of inner cylinder (rad/s): \({\varOmega {=} 2 \pi {\rm N} / 60}\)
- \({\rho}\) :
-
Density (kg/m3)
- \({\varepsilon}\) :
-
Turbulent energy dissipation rate (m2/ s2)
- \({\varGamma}\) :
-
General exchange coefficient
- a:
-
Axial
- r:
-
Rotational
- eff:
-
Effective
- w:
-
Wall
- in:
-
Inlet
- t:
-
Turbulent
- o:
-
Outer
- i:
-
Inner
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Jalil, J.M., Hanfash, AJ.O. & Abdul-Mutaleb, M.R. Experimental and Numerical Study of Axial Turbulent Fluid Flow and Heat Transfer in a Rotating Annulus. Arab J Sci Eng 41, 1857–1865 (2016). https://doi.org/10.1007/s13369-015-1909-1
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DOI: https://doi.org/10.1007/s13369-015-1909-1