Experimental study of the effect of disk obstacle rotating with Different angular ratios on heat transfer and pressure drop in a pipe with turbulent flow

Abstract

This article presents the effects of a circular disk obstacle with different angle ratios on heat transfer and pressure drop under a turbulent flow inside the tube with a constant temperature wall. Remarkable investigations have suggested the use of various obstacles for heat transfer enhancement in heat exchangers. The used geometry for almost all studies has been fixed obstacles. However, the use of the rotary obstacle is an innovative issue to the author’s best knowledge. The obstacle rotation influences heat transfer rate through the effective displacement of the fluid particles. Thus, this investigation studies the effect of disk obstacle rotation from 50 to 200 rpm at different angle ratios and pitch ratios 1 and 2 on heat transfer and pressure drop in shell and tube heat exchanger of water–air type in the Reynolds number between 10,000 and 25,000. The results showed that rotating obstacles have less pressure drop than that of the fixed obstacle under similar shape and configuration. Compared to the smooth pipe, the Nusselt number, friction coefficient, and thermal performance coefficient increased by 300%, 69.38%, and 131%, respectively. The maximum heat performance coefficient 1.62 times relative to the fixed obstacle in similar condition was recorded.

Appendix: The detailed calculations and analysis of the uncertainty

The method introduced by Kline and Mcclintock was used to compute the uncertainties of the experimental values [64]. In the Kline and Mcclintock [64] equation, the magnitude of the uncertainty is expressed as R(u_R), where R = R(× 1, × 2,…, x_n) and x_n is a variable that affects the results of R.

$$u_{\text{R}} = \left[ {\sum\limits_{{\text{i}} = 1}^{n} {\left( {\frac{\partial R}{{\partial x_{\text{i}} }}u_{{x_{\text{i}} }} } \right)^{2} } } \right]^{0.5}$$

(17)

Reynolds number uncertainty

The Reynolds number is obtained from relation 17 and its uncertainty from relation 18.

$$\text{Re} = \frac{\rho VD}{\mu }$$

(18)

$$u_{\text{Re}} = \left( \begin{aligned} \left( {\frac{{\partial \text{Re} }}{\partial \rho }} \right)^{2} u_{\rho }^{2} + \left( {\frac{{\partial \text{Re} }}{\partial V}} \right)^{2} u_{\text{V}}^{2} + \hfill \\ \left( {\frac{{\partial \text{Re} }}{\partial D}} \right)^{2} u_{\text{D}}^{2} + \left( {\frac{{\partial \text{Re} }}{\partial \mu }} \right)^{2} u_{\mu }^{2} \hfill \\ \end{aligned} \right)^{0.5}$$

(19)

According to the above equations, the relative uncertainty of Nusselt number is calculated to be 5.3%.

Nusselt number uncertainty

The heat transfer is obtained from relation 20 and its uncertainty from relation 21.

$$Q = mc\Delta T$$

(20)

$$u_{\text{Q}} = \left( {\left( {\frac{\partial Q}{\partial m}} \right)^{2} u_{\text{m}}^{2} + \left( {\frac{\partial Q}{\partial \Delta T}} \right)^{2} u_{\Delta T}^{2} } \right)^{0.5}$$

(21)

$$\frac{\partial Q}{\partial m} = C\Delta T$$

(22)

$$\frac{\partial Q}{\partial \Delta T} = mc$$

(23)

The effective temperature difference between two fluids is obtained from relation 24 and its uncertainty from relation 25.

$${\text{LMTD}} = T_{\text{w}} - \frac{{T_{\text{i}} + T_{\text{o}} }}{2}$$

(24)

$$u_{\text{TD}} = \left( \begin{aligned} \left( {\frac{{\partial {\text{TD}}}}{{\partial T_{\text{w}} }}} \right)^{2} u_{{T_{\text{w}} }}^{2} + \left( {\frac{{\partial {\text{TD}}}}{{\partial T_{\text{o}} }}} \right)^{2} u_{{T_{\text{o}} }}^{2} + \hfill \\ \left( {\frac{{\partial {\text{TD}}}}{{\partial T_{\text{i}} }}} \right)^{2} u_{{T_{\text{i}} }}^{2} \hfill \\ \end{aligned} \right)^{0.5}$$

(25)

$$\frac{{\partial {\text{TD}}}}{{\partial T_{\text{w}} }} = 1$$

(26)

$$\frac{{\partial {\text{TD}}}}{{\partial T_{\text{o}} }} = \frac{{\partial {\text{TD}}}}{{\partial T_{\text{i}} }} = - \frac{1}{2}$$

(27)

The overall heat transfer coefficient is obtained from relation 28 and its uncertainty from relation 29.

$$U = \frac{Q}{{A \cdot {\text{TD}}}}$$

(28)

$$u_{\text{u}} = \left( \begin{aligned} \left( {\frac{\partial U}{\partial Q}} \right)^{2} u_{{T_{Q} }}^{2} + \left( {\frac{\partial U}{\partial A}} \right)^{2} u_{{T_{A} }}^{2} + \hfill \\ \left( {\frac{U}{\text{TD}}} \right)^{2} u_{\text{TD}}^{2} \hfill \\ \end{aligned} \right)^{0.5}$$

(29)

$$\frac{\partial U}{\partial Q} = \frac{1}{{A \cdot {\text{TD}}}}$$

(30)

$$\frac{\partial U}{\partial A} = - \frac{Q}{{A^{2} \cdot {\text{TD}}}}$$

(31)

$$\frac{\partial U}{{\partial {\text{TD}}}} = - \frac{Q}{{A \cdot {\text{TD}}^{2} }}$$

(32)

The heat transfer coefficient is obtained from relation 33 and its uncertainty from relation 34.

$$h = \left( {\frac{1}{U} - \frac{1}{{h_{\text{w}} }}} \right)^{ - 1}$$

(33)

$$u_{\text{h}} = \frac{\partial h}{\partial U}u_{\text{u}}$$

(34)

$$\frac{\partial h}{\partial U} = \frac{1}{{U^{2} }}\left( {\frac{1}{U} - \frac{1}{{h_{\text{w}} }}} \right)^{ - 2}$$

(35)

The Nusselt number is obtained from relation 36 and its uncertainty from relation 37.

$${\text{Nu}} = \frac{{h_{\text{i}} D}}{k}$$

(36)

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

(37)

$$\frac{{\partial {\text{Nu}}}}{\partial h} = \frac{D}{K}$$

(38)

$$\frac{{\partial {\text{Nu}}}}{\partial h} = \frac{h}{K}$$

(39)

According to the above equations, the relative uncertainty of Nusselt number is calculated to be 7.3%.

Coefficient friction uncertainty

The coefficient friction is obtained from relation 40 and its uncertainty from relation 41.

$$f = \frac{\Delta P}{{\frac{1}{2}\frac{L}{D}\rho V^{2} }}$$

(40)

$$u_{\text{f}} = \left( \begin{aligned} \left( {\frac{\partial f}{\partial \Delta P}} \right)^{2} u_{\Delta P}^{2} + \left( {\frac{\partial f}{\partial D}} \right)^{2} u_{\text{D}}^{2} + \hfill \\ \left( {\frac{\partial f}{\partial L}} \right)^{2} u_{\text{L}}^{2} + \left( {\frac{\partial f}{\partial V}} \right)^{2} u_{\text{V}}^{2} + \hfill \\ \left( {\frac{\partial f}{\partial \rho }} \right)^{2} u_{\rho }^{2} \hfill \\ \end{aligned} \right)^{0.5}$$

(41)

$$\frac{\partial f}{\partial \Delta P} = \frac{2D}{{\rho LV^{2} }}$$

(42)

$$\frac{\partial f}{\partial L} = - \frac{2D\Delta P}{{\rho L^{2} V^{2} }}$$

(43)

$$\frac{\partial f}{\partial V} = - \frac{4D\Delta P}{{\rho L^{{}} V^{3} }}$$

(44)

$$\frac{\partial f}{\partial \rho } = - \frac{2D\Delta P}{{\rho^{2} L^{{}} V^{2} }}$$

(45)

According to the above equation, the relative uncertainty of friction factor is calculated to be 7%.