**6. Conclusion**

336 Heat Exchangers – Basics Design Applications

Regression analysis was carried out using the entire set of two-phase heat transfer data. This

0424.0 7.0 

Fig. 17 shows the correlation along with the data points. The correlation is able to predict the

(32)

*s tp h h*

leads to a correlation,

data points within an error of 10%.

Fig. 16. Ratio htp/hs as a function of

Fig. 17. Correlation for estimation of htp/hs as a function of

It is observed that the use of constant values for the thermal and transport properties of the heat transport medium results in prediction of inaccurate heat transfer coefficients. Heat transfer characteristics of the heat exchanger with helical coil are also studied using the CFD code. The CFD predictions match reasonably well with the experimental results within experimental error limits. Based on the results a correlation was developed to calculate the inside heat transfer coefficient of the helical coil.

Necessary Python codes, which run in the framework of AnuVi visualisation package, have been developed for accurate estimation of Nusselt number at any point on the heat transfer surface. The research work also includes development of various C++ and MATLAB® codes.

Characteristics of non-isothermal fluid flow and heat transfer under turbulent flow of single phase water through helical coils have been presented in detail. Analysis has been carried out both for the constant wall temperature and constant wall heat flux boundary conditions. Fluid particles are found to undergo oscillatory motion inside the pipe and this causes fluctuations in heat transfer rates.

Nusselt numbers at various points along the length of the pipe was estimated. Nusselt number on the outer side of the coil is found to be the highest among all other points at a specified cross-section, while that at the inner side of the coil is the lowest. Velocity profiles for the two boundary conditions were found to be matching, while the temperature profiles are different.

A number of numerical experiments have been carried out to study influence of coil parameters, viz., pitch circle diameter, coil pitch and pipe diameter on heat transfer. The coil pitch is found to have significance only in the developing section of heat transfer. The torsional forces induced by the pitch causes oscillations in the Nusselt number. However, the average Nusselt number is not affected by the coil pitch. After establishing the parametric influence, a correlation has been developed for estimation of average Nusselt number. This correlation is compared with those available in the literature and the deviations are within reasonable limits. It is also observed that these correlations are applicable for either of the boundary conditions. For most of the engineering applications, the correlations are applicable for conjugate heat transfer as well.

In the fully developed section, ratio Nuloc/Nuav is almost independent of coil parameters and Dean number. Correlations have been developed for prediction of local values of Nusselt number as a function of the average Nusselt number and the angular position of the point along the circumference.

CFD simulations of heat transfer to air-water two-phase mixture flowing through a helically coiled heat exchanger has been carried out. Studies have been carried out by varying (i) coil pitch, (ii) pipe diameter (iii) pitch circle diameter. Their influence on heat transfer and pressure drop has been brought out.

Unlike the flow through a straight pipe, the centrifugal force caused due to the curvature of the pipe causes heavier fluid (water-phase) to flow along the outer side of the pipe. High velocity and high temperature are also observed along the outer side. The torsion caused by pitch of the coil makes the flow unsymmetrical about the horizontal plane of coil. As the

Helically Coiled Heat Exchangers 339

I express my sincere gratitude to Prof. Kannan N Iyer, Prof. S. M. Mahajani, Prof. J.C. Mandal and Prof. Vijayan P. K. for their meticulous guidance and extensive support during

Abdulla M. A., 1994, A four-region, moving-boundary model of a once through, helical coil

Akagawa, K., T. Sakaguchi, and M. Ueda. 1971, Study on a gas-liquid two-phase flow in helically coiled tubes. Bulletin of the JSME, Vol. 14 No. 72, pp 564-571. Akiyama, M., Cheng, K. C., 1792, Boundary vorticity method for laminar forced convection heat transfer in curved pipes, Int. J. Heat Mass Transfer, 15:1426-1431. Al-Hajeri M.H., A.M. Koluib, M. Mosaad, S. Al-Kulaib, 2007, Heat transfer performance

Awwad, A., R. C. Xin, Z. F. Dong, M. A. Ebadian, and H. M. Soliman., 1995, Measurement

helicoidal pipes. Int. J Multiphase Flow, Vol. 21, No. 4, pp 607-619.

during condensation of R-134a inside helicoidal tubes, Energy Conversion and

and correlation of the pressure drop in air-water two-phase flow in horizontal

team generator, Annals of Nuclear Energy, 21(9), 541-562

Lockhart-Martinelli parameter, dimensionless

φ Two-phase friction multiplier, dimensionless

Angular location along the periphery of pipe cross-section

Angle a cut plane makes with a plane passing through pipe inlet

 (temperature) difference, K δ Curvature ratio, dimensionless

 Non-dimensional pitch viscosity, kg m-1 s-1

 Density, kg m-3 τ Stress tensor, Pa

fi Internal fouling fo External fouling

k Phase, can be liquid (l) or gas (g)

pq from phase p to phase q

Management, 48, 2309–2315

s single-phase TP two-phase vm Virtual mass w wall

av Average b bulk

H helical i internal

lift lift LM Log Mean loc local m mixture o external ov Overall

**8. Acknowledgement** 

this research work.

**9. References** 

**Subscripts** 

pitch is increased, higher velocity and higher temperature regions are observed on the bottom half of the pipe.

Increase in pipe diameter, keeping the inlet velocity constant, causes higher heat transfer coefficient and lower pressure drop. This effect is due to the influence of secondary flows. As the PCD is increased, the centrifugal forces decreases and this causes reduction of heat transfer coefficient and pressure drop.

Estimation of inner heat transfer coefficient for the two-phase flow was carried out by changing the void fraction and flow velocity. Results indicate reduction in heat transfer coefficient with increase in void fraction.

The coil parameters, viz., PCD and pipe diameter and void fraction at inlet have significant effect on the heat transfer and pressure drop for two-phase flows through helical coils. However, the effect of pitch is negligible. It has been shown that the quantitative dependence of coil parameters on heat transfer is same for both single and two phase flows. Using the data generated from about 45 numerical experiments, a correlation to estimate two-phase heat transfer coefficient is developed.
