Thermohydraulic characteristics of inline and staggered angular cut baffle inserts in the turbulent flow regime

Abstract

In the present work, heat transfer and pressure drop characteristics in flow through a tube with inline and staggered baffles having angular cut at the edge are reported for various operating conditions. An experimental test rig is designed and developed to investigate heat transfer and pressure drop behavior for different conditions. Effects of different geometrical parameters, i.e., pitch ratios, baffle arrangement and cutting angle of baffles on heat transfer rate and pressure drop characteristics, have been investigated for turbulent flow regime. Reynolds number ranging from 10,000 to 52,000 has been considered in the present study. The maximum heat transfer rate has been observed for staggered arrangement with pitch ratio of 0.1 and cutting angle of 60°, while minimum heat transfer rate has been observed for inline arrangement with pitch ratio of 0.2 and cutting angle of 30°. Empirical correlations for Nusselt number and friction factor have been developed as a function of geometrical and flow parameters. The deviations between experimental and predicted values of Nusselt number and friction factor for staggered arrangements have been observed as ± 10%, ± 4%, respectively, whereas for inline arrangement the deviation has been observed as ± 12%, ± 5%, respectively. Results from empirical correlations are well agreed with the experimental data.

Appendix: Uncertainty analysis

Here uncertainty analysis of friction factor and Nusselt number calculation has been presented.

Friction factor

$$f = \frac{1}{2}\left\{ {\frac{\Delta P}{{L_{{\text{p}}} }}} \right\}\left\{ {\frac{{\rho D^{3} }}{{\text{Re}^{2} \mu^{2} }}} \right\}$$

(20)

$$\frac{\Delta f}{f} = \frac{1}{f}\left[ {\left\{ {\frac{\partial f}{{\partial \left( {\Delta P} \right)}}\Delta \left( {\Delta P} \right)} \right\}^{2} + \left\{ {\frac{\partial f}{{\partial L_{\text{p}} }}\Delta L_{\text{p}} } \right\}^{2} + \left\{ {\frac{\partial f}{\partial D}\Delta D} \right\}^{2} + \left\{ {\frac{\partial f}{{\partial \left( {\text{Re} } \right)}}\Delta \text{Re} } \right\}^{2} } \right]^{0.5}$$

(21)

or

$$\frac{\Delta f}{f} = \left[ {\left\{ {\frac{{\Delta \left( {\Delta P} \right)}}{\Delta P}} \right\}^{2} + \left\{ {\frac{{\Delta L_{\text{p}} }}{{L_{\text{p}} }}} \right\}^{2} + \left\{ {\frac{3\Delta D}{D}} \right\}^{2} + \left\{ {\frac{{2\Delta \text{Re} }}{\text{Re}}} \right\}^{2} } \right]^{0.5}$$

(22)

$$\Delta P \propto h$$

(23)

$$\therefore \frac{{\Delta \left( {\Delta P} \right)}}{\Delta P} = \frac{\Delta h}{h}$$

(24)

$$\text{Re} = \frac{{4\dot{m}}}{\pi D\mu }$$

(25)

$$\frac{{\Delta \text{Re} }}{{\text{Re}}} = \left[ {\left( {\frac{{\Delta \dot{m}}}{{\dot{m}}}} \right)^{2} + \left( {\frac{\Delta D}{D}} \right)^{2} } \right]^{0.5}$$

(26)

The uncertainty in friction factor has been calculated from the above equations.

Nusselt number

$${\text{Nu}} = \frac{hD}{k}$$

(27)

$$\frac{{\Delta {\text{Nu}}}}{{\text{Nu}}} = \frac{1}{{\text{Nu}}}\left[ {\left\{ {\frac{\partial }{\partial h}({\text{Nu}})\Delta h} \right\}^{2} + \left\{ {\frac{\partial }{\partial D}\left( {\text{Nu}} \right)\Delta D} \right\}^{2} + \left\{ {\frac{\partial }{\partial k}\left( {\text{Nu}} \right)\Delta k} \right\}^{2} } \right]^{0.5}$$

or

$$\frac{{\Delta {\text{Nu}}}}{{\text{Nu}}} = \left\{ {\left( {\frac{\Delta h}{h}} \right)^{2} + \left( {\frac{\Delta D}{D}} \right)^{2} } \right\}^{0.5}$$

(28)

$$h = \frac{{q^{{\prime \prime }} }}{{T_{\text{wi}} - T_{\text{b}} }}$$

(29)

$$\frac{\Delta h}{h} = \frac{1}{h}\left[ {\left\{ {\frac{\partial h}{{\partial q^{{\prime \prime }} }}\Delta q^{{\prime \prime }} } \right\}^{2} + \left\{ {\frac{\partial h}{{\partial T_{\text{wi}} }}{\Delta} T_{\text{wi}} } \right\}^{2} + \left\{ {\frac{\partial h}{{\partial T_{\text{b}} }}{\Delta} T_{\text{b}} } \right\}^{2} } \right]^{0.5}$$

$$\frac{\Delta h}{h} = \left[ {\left\{ {\frac{{\Delta q^{{\prime \prime }} }}{{q^{{\prime \prime }} }}} \right\}^{2} + \left\{ {\frac{{\Delta {T_{\text{wi}}} }}{{T_{\text{wi}} - T_{\text{b}} }}} \right\}^{2} + \left\{ {\frac{{{\Delta} T_{\text{b}} }}{{T_{\text{wi}} - T_{\text{b}} }}} \right\}^{2} } \right]^{0.5}$$

(30)

$$q^{{\prime \prime }} = \frac{0.5}{{\pi DL_{\text{h}} }}\left[ {\left( {V^{2} /R} \right) + \dot{m}C_{\text{p}} \left( {T_{\text{bo}} - T_{\text{bi}} } \right)} \right]$$

(31)

$$\frac{{\Delta q^{{\prime \prime }} }}{{q^{{\prime \prime }} }} = \frac{1}{{q^{{\prime \prime }} }}\left[ \begin{array}{l} \left\{ {\frac{\partial }{\partial R}\left( {q^{{\prime \prime }} } \right)\Delta R} \right\}^{2} + \left\{ {\frac{\partial }{\partial V}\left( {q^{{\prime \prime }} } \right)\Delta V} \right\}^{2} + \left\{ {\frac{\partial }{{\partial \dot{m}}}\left( {q^{{\prime \prime }} } \right)\Delta \dot{m}} \right\}^{2} + \left\{ {\frac{\partial }{{\partial T_{\text{bo}} }}\left( {q^{{\prime \prime }} } \right)\Delta {T_{\text{bo}}} } \right\}^{2} \hfill \\ + \left\{ {\frac{\partial }{{\partial T_{\text{bi}} }}\left( {q^{{\prime \prime }} } \right){\Delta} T_{\text{bi}} } \right\}^{2} + \left\{ {\frac{\partial }{\partial D}\left( {q^{{\prime \prime }} } \right)\Delta D} \right\}^{2} + \left\{ {\frac{\partial }{{\partial L_{\text{h}} }}\left( {q^{{\prime \prime }} } \right)\Delta L_{\text{h}} } \right\}^{2} \hfill \\ \end{array} \right]^{0.5}$$

$$\frac{{\Delta q^{{\prime \prime }} }}{{q^{{\prime \prime }} }} = \left[ \begin{array}{l} \frac{1}{{\left( {1 + \dot{m}C_{\text{p}} R{\Delta} T_{\text{b}} /V^{2} } \right)^{2} }}\left( {\frac{\Delta R}{R}} \right)^{2} + \frac{4}{{\left( {1 + \dot{m}C_{\text{p}} R{\Delta} T_{\text{b}} /V^{2} } \right)^{2} }}\left( {\frac{\Delta V}{V}} \right)^{2} \hfill \\ + \frac{1}{{\left( {1 + \frac{{V^{2} }}{{R\dot{m}C_{\text{p}} {\Delta} T_{\text{b}} }}} \right)^{2} }}\left( {\frac{{\Delta \dot{m}}}{{\dot{m}}}} \right)^{2} + \frac{1}{{\left( {1 + \frac{{V^{2} }}{{R\dot{m}C_{\text{p}} {\Delta} T_{\text{b}} }}} \right)^{2} }}\left( {\frac{{{\Delta} T_{\text{bo}} }}{{{\Delta} T_{\text{b}} }}} \right)^{2} \hfill \\ + \frac{1}{{\left( {1 + \frac{{V^{2} }}{{R\dot{m}C_{\text{p}} {\Delta} T_{\text{b}} }}} \right)^{2} }}\left( {\frac{{{\Delta} T_{\text{bi}} }}{{{\Delta} T_{\text{b}} }}} \right)^{2} + \left( {\frac{\Delta D}{D}} \right)^{2} + \left( {\frac{{\Delta L_{\text{h}} }}{{L_{\text{h}} }}} \right)^{2} \hfill \\ \end{array} \right]^{0.5}$$

(32)

where ${\Delta} T_{\text{b}} = T_{\text{bo}} - T_{\text{bi}}$.