# Detailed measurement of heat/mass transfer and pressure drop in a rotating two-pass duct with transverse ribs

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## Abstract

The present study investigates the convective heat/mass transfer and pressure drop characteristics in a rotating two-pass duct with and without transverse ribs. The Reynolds number based on the hydraulic diameter is kept constant at 10,000 and the rotation number is varied from 0.0 to 0.2. When rib turbulators are installed, heat/mass transfer and friction loss are respectively augmented 2.5 times and 5.8 times higher than those of the smooth duct since the main flow is turbulated by reattaching and separating on the vicinity of the duct surfaces. Differences of heat/mass transfer and pressure coefficient between leading and trailing surfaces result from the rotation of duct, so that Sherwood number ratios and pressure coefficients are high on the trailing surface in the first-pass and on the leading surface in the second-pass. In the turning region, a pair of Dean vortices shown in the stationary case transform into one large asymmetric vortex cell, and subsequently heat/mass transfer and pressure drop characteristics also change. As the rotation number increases, the discrepancies of the heat/mass transfer and the pressure coefficient enlarge between the leading and trailing surfaces.

## Keywords

Secondary Flow Coriolis Force Pressure Coefficient Rotation Number Sherwood Number## List of symbols

*C*_{p}non-dimensional pressure coefficient, Eq. (3)

*D*_{h}hydraulic diameter (m)

*D*_{naph}mass diffusion coefficient of naphthalene vapor in air (m

^{2}s^{−1})*f*friction factor, Eq. (4)

*f*_{0}friction factor of a fully developed turbulent flow in a stationary smooth pipe

*h*heat transfer coefficient (W m

^{−2}K^{−1})*h*_{m}mass transfer coefficient (m s

^{−1})*H*passage height (m)

*k*_{c}thermal conductivity of coolant (W m

^{−1 }K^{−1})- Nu
Nusselt number,

*hD*_{h}/*k*_{c}*p*rib to rib pitch

*P*_{naph}naphthalene vapor pressure (N m

^{−2})- Pr
Prandtl number

*R*maximum radius of rotating arm (m)

- Re
Reynolds number,

*D*_{h}*u*_{b}/*ν*- Ro
Rotation number,

*D*_{h}*Ω*/*u*_{b}- Sc
Schmidt number,

*ν/D*_{naph}- Sh
Sherwood number,

*h*_{m}*D*_{h}/*D*_{naph}, Eq. (1)- Sh
_{0} Sherwood number of a fully developed turbulent flow in a stationary smooth pipe, Eq. (2)

- \( \,\overline{{{\text{Sh}}}} _{{\text{p}}} \, \)
picth-averaged Sh, \( \,{{\int_{x_{1} }^{x_{{1 + p}} } {{\int_{_{{ - W/2}} }^{_{{W/2}} } {{\text{Sh }}} }} }{\text{d}}y{\text{d}}x} \mathord{\left/ {\vphantom {{{\int_{x_{1} }^{x_{{1 + p}} } {{\int_{_{{ - W/2}} }^{_{{W/2}} } {{\text{Sh }}} }} }{\text{d}}y{\text{d}}x} {{\int_{x_{1} }^{x_{{1 + p}} } {{\int_{_{{ - W/2}} }^{_{{W/2}} } {{\text{d}}y{\text{d}}x} }} }}}} \right. \kern-\nulldelimiterspace} {{\int_{x_{1} }^{x_{{1 + p}} } {{\int_{_{{ - W/2}} }^{_{{W/2}} } {{\text{d}}y{\text{d}}x} }} }}\, \)

- \( \,\overline{{{\text{Sh}}}} _{{\text{R}}} \, \)
regional averaged Sh, \( \,{{\int_{x_{1} }^{x_{2} } {{\int_{_{{ - W/2}} }^{_{{W/2}} } {{\text{Sh }}} }} }{\text{d}}y{\text{d}}x} \mathord{\left/ {\vphantom {{{\int_{x_{1} }^{x_{2} } {{\int_{_{{ - W/2}} }^{_{{W/2}} } {{\text{Sh }}} }} }{\text{d}}y{\text{d}}x} {{\int_{x_{1} }^{x_{2} } {{\int_{_{{ - W/2}} }^{_{{W/2}} } {{\text{d}}y{\text{d}}x} }} }}}} \right. \kern-\nulldelimiterspace} {{\int_{x_{1} }^{x_{2} } {{\int_{_{{ - W/2}} }^{_{{W/2}} } {{\text{d}}y{\text{d}}x} }} }}\, \)

*u*_{b}passage averaged bulk velocity (m s

^{−1})*W*width of passage (m)

*x*coordinate and distance in the streamwise direction (m)

*y*coordinate and distance in the lateral direction (m)

*z*coordinate and distance in the vertical direction (m)

*μ*dynamic viscosity (kg m

^{−1}s^{−1})*ν*kinematic viscosity (m

^{2}s^{−1})*η*thermal performance, Eq. (5)

*Ω*angular velocity (rad s

^{−1})

## Notes

### Acknowledgments

This work was supported partially by the Electric Power Industry Technology Evaluation and Planning.

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