A new heat transfer correlation for flow boiling in helically coiled tubes

Ji CuilianHan JitianLiu XiaopengShao LiChen Changnian

（1School of Energy and Power Engineering，Shandong University，Jinan 250061，China）

（2Municipal and Environmental Engineering Department，Shandong Urban Construction Vocational College，Jinan 250103，China）

A new heat transfer correlation for flow boiling in helically coiled tubes

Ji Cuilian1，2Han Jitian1Liu Xiaopeng2Shao Li1Chen Changnian1

（1School of Energy and Power Engineering，Shandong University，Jinan 250061，China）

（2Municipal and Environmental Engineering Department，Shandong Urban Construction Vocational College，Jinan 250103，China）

Based on the superposition principle of the nucleate boiling and convective heat transfer terms，a new correlation is developed for flow boiling heat transfer characteristics in helically coiled tubes．The effects of the geometric and system parameters on heat transfer characteristics in helically coiled tubes are investigated by collecting large amounts of experimental data and analyzing the heat transfermechanisms．The existing correlations are divided into two categories，and they are calculated w ith the experimental data．The Dnfactor is introduced to take into account the effect of a complex geometrical structure on flow boiling heat transfer．A new correlation is developed for predicting the flow boiling heat transfer coefficients in the helically coiled tubes，which is validated by the experimental data of R134a flow boiling heat transfer in them；and the average relative error and rootmean square error of the new correlation are calculated．The results show that the new correlation agrees well w ith the experimental data，indicating that the new correlation can be used for predicting flow boiling heat transfer characteristics in the helically coiled tubes．

helically coiled tube；flow boiling；heat transfer coefficient correlation；heat transfer

H elical-coiled tubes are extensively used in the nuclear，petrochem ical，refrigeration and heat pump systems，and many others，due to high efficiency in heat transfer and compactness in volume．Many researchers investigated flow boiling heat transfer characteristics in the helically coiled tubes by experiments，numerical simulations，theoretical exploration and mechanism analysis，obtained a variety of data of engineering applications，and developed a series of correlations for flow boiling heat transfer coefficients．Those correlations can be mainly classified into two categories．One is the empirical heat transfer coefficient correlations including the boiling number based on the experimental results．They do not have universal significance，andmay only be applied to operating statesw ith the same conditions［14］．The other category is based on themechanism of flow boiling heat transfer，which consists of an explicit convection item and boiling item．They are generally not dependent on the boiling number and_ have clear physicalmeaning and w ide applicable ranges［58］．Apparently，a certain progress has been achieved in the study of flow boiling heat transfer in the helically coiled tubes．However，the fundamental basis of the phenomena is very incomplete and the correlations of engineering applications are still lacking due to the complexity of flow boiling phenomena and the lim itation in the current research expertise．

Accordingly，it is important to develop new correlations for heat transfer coefficients of flow boiling heat transfer in the helically coiled tubes．Chen’s［5］correlation based on the mechanism of nucleate and convective heat transfer isw idely used to correlate flow boiling heat transfer coefficients in straight tubes．However，it cannot predict the flow boiling heat transfer characteristics in the helically coiled tubes and other complex geometrical tubes．Therefore，the main objective of this study is to develop a new heat transfer coefficient correlation for flow boiling in the helically coiled tubes based on the Chen’s superposition principle of nucleate and convective heat transfer．The Dnfactor is introduced to take into account the geometrical parameter effect of complex tubes on flow boiling heat transfer in the helically coiled tubes，and the regression method is used to obtain the index of the Dn．The prediction accuracy of the developed correlation is further evaluated by the experimental data of flow boiling heat transfer．

1 Assessment of Existing Correlations

A bank of experimental data was collected for flow boiling heat transfer in tubes，including 1 152 data_ po_ints from different sources and nine different fluids［13，916］．The predictive capability of those correlations is determ ined as illustrated in Fig．1 by testing the correlations in Refs．［1- 4］against the data available in Refs．［11-13］．In Fig．1，hTPis the flow boiling heat transfer coefficient，and hlis the liquid phase heat transfer coefficient．As shown in Fig．1，the prediction values of correlation in Ref．［1］are slightly higher than the experimental ones，while the prediction ones of correlation in Ref．［4］are lower than the experimental data．The differences are partially attributed to the experimental conditions，which mainly include the test section geometry parameters，system parameters and test fluids．Correlation in Ref．［4］is obtained by fitting the experimental data in the circular tubes．The heat transfer coefficients in the circular tubes are lower than those in the helically coiled tubes．

Fig.1 Comparison of correlations in Refs．［1- 4］

Using the experimental data in Refs．［1- 2，9］，the comparison of prediction accuracy of correlations in Refs．［5- 8］is shown in Fig．2．The predicting values of correlation in Ref．［6］are close to the experimental values while the ones of correlation in Ref．［5］deviate from the experimental data，which is primarily attributed to the effect of geometric parameters of the helically coiled tubes on the heat transfer characteristics．The secondary flow generated by the centrifugal forces in the helically coiled tubes enhances the heat transfer in comparison w ith that in straight tubes．Therefore，the correlation based on the straight tubes needs to be modified for applying to the prediction of flow boiling heat transfer in the helically coiled tubes．

Fig.2 Comparison of correlations in Refs．［5- 8］

It is evident from the above discussion that the existing correlations cannot well predict the boiling heat transfer characteristics for the helically coiled tubes．Therefore，a new correlation is developed for flow boiling heat transfer characteristics in the helically coiled tubes using Chen’s［5］methodology for correlating flow boiling heat transfer．

2 Correlation Development

Follow ing Chen’s［5］superposition method of nucleate boiling and convective heat transfer，the flow boiling heat transfer coefficient correlation for flow boiling heat transfer coefficients in the helically coiled tubes can be expressed as

where（Fhl）nis the forced convective contribution；F is the forced convective heat transfer enhancement factor；（Shpool）nis the nucleate boiling contribution．

The value of F is always greater than 1 because the fluid velocities in two-phase flows are much higher than those in single-phase liquid-only flows．According to the forced convection heat transfer mechanism，superheated liquid vapor layers in flow boiling are thinner than those in pool boiling．Therefore，the suppression factor S is always less than 1．S is assumed to be a function of the two-phase flow m ixture Reynolds number Rem．The follow ing formula proposed by Liu et al．［6］is used to calculate F and S：

where Pr is the Prandtl Number；x is the vapor quality；ρlis the liquid density，kg／m3；ρvis the vapor density，kg／m3；Relis the Reynolds number．

There are many available methods to calculate hlin the literature．The follow ing correlation w ith high precision is used to calculate the average heat transfer coefficient in the helically coiled tubes：

where diis the inner diameter，mm；D is the helical diameter，mm．The flow boiling heat transfer phenomenon in the helically coiled tubes ismore complex than that in straight tubes due to the secondary flow resulting from the centrifugal force［14］．Therefore，the Dnfactor is introduced to take into account the comprehensive influence of the geometric parameters of the helically coiled tube on flow boiling heat transfer，which include the tube diameter，helical tube diameter，and helical pitch．

where vmis the two-phase mixture velocity；μlis the viscosity；G is themass flux．

The correlation for pool boiling is an appropriate choice for hpoolsince it is verified that the correlation provides good prediction for experimental heat transfer coefficientsin a variety of channels［17］．Introducing the two-phase Dean number Dninto the correlation，the pool boiling heat transfer coefficient used for correlating flow boiling heat transfer coefficients in the helically coiled tubes is as follows：

where q is the heat flux，kW／m2；M is the molecular mass of the fluid，kg／kmol；c1，c2and c3are the constants determ ined by experiments．Through themultivariate nonlinear regression analysis on the experimental data，the values of c1，c2and c3are obtained，being 0.125，0.723，and 0.078，respectively．

The index n is equal to 2 in Eq．（1）．Therefore，the flow boiling heat transfer coefficient can be calculated using Eq．（1）togetherw ith Eqs．（2）to（7）．The correlation is verified by experimental data in Refs．［15- 16， 18］．The predictive capability of the new correlation is illustrated in Fig．3．It can be seen that the prediction values of the new correlation are in good agreementw ith the experimental data．

Fig.3 Comparison of prediction values and experimental data

As shown in Fig．4，the statistical results indicate that the maximum deviation is 23.6%，w ith 93.2%of the experimental data distributing in±20%error range of the new correlation．

Fig.4 Prediction errors of new correlation

The developed correlation for flow boiling heat transfer coefficients in the helically coiled tubes can be summarized as follows：

Parameter ranges in the correlation are as follows：500 mm＜L＜7 070 mm；3.0 mm＜di＜15.0 mm；100 mm＜D＜400 mm；35 mm＜Pt＜120 mm；100 kg／（m2· s）＜G＜400 kg／（m2·s）；5 kW／m2＜q＜20 kW／m2；0.1＜x＜0.9；0.8＜Pr＜10；500＜Rem＜2×105；0.2 MPa＜P＜1.2 MPa．Here，L is the heating length；Ptis the pitch；P is the system pressure．

In order to quantitatively determ ine the predictive accuracy of the new correlation，their mean relative error（MRE）and rootmean square error（RMSE）are calculated，respectively．

The results demonstrate that good predictive accuracy is achieved by the developed correlation，w ith the MRE and RMSE being 8.23%and 0.532，respectively．

3 Conclusion

Based on large amounts of experimental data available in the literature，a new heat transfer coefficient correlation is developed for flow boiling in horizontal helically coiled tubes by superposing the nucleate boiling contribution and the convective heat transfer one．The Dnfactor is introduced to take into account the effect of geometrical parameters on flow boiling heat transfer in helically coiled tubes，and the regressionmethod is used to obtain the index of the Dn．The experimental data verifies that the developed correlation has good prediction accuracy．

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一種新的螺旋管內(nèi)流動沸騰傳熱關(guān)聯(lián)式

冀翠蓮1，2韓吉田1劉曉鵬2邵 莉1陳常念1

（1山東大學(xué)能源與動力工程學(xué)院，濟(jì)南250061）
（2山東城市建設(shè)職業(yè)學(xué)院市政與環(huán)境工程系，濟(jì)南250103）

為了改善螺旋管內(nèi)流動沸騰換熱特性的預(yù)測方法，利用核態(tài)沸騰項和對流換熱項的疊加原理建立了新的預(yù)測關(guān)聯(lián)式．基于收集的大量實驗數(shù)據(jù)和流動沸騰換熱機(jī)理，分析螺旋管幾何參數(shù)和實驗參數(shù)對流動沸騰傳熱的影響，將已經(jīng)建立的關(guān)聯(lián)式分為2類，并用大量實驗數(shù)據(jù)對其進(jìn)行計算．為了考慮復(fù)雜管道對傳熱特性的影響，在新建立的螺旋管內(nèi)流動沸騰傳熱預(yù)測關(guān)聯(lián)式中引入了Dn因子．采用以R134a為介質(zhì)的螺旋管內(nèi)流動沸騰傳熱實驗數(shù)據(jù)進(jìn)行了驗證，并計算新關(guān)聯(lián)式的平均相對誤差和均方根誤差．結(jié)果表明，新的預(yù)測關(guān)聯(lián)式與實驗值吻合較好，可以用于螺旋管流動沸騰傳熱特性的預(yù)測分析．

螺旋管；流動沸騰；傳熱系數(shù)關(guān)聯(lián)式；傳熱

TK121

10．3969／j．issn．1003－7985．2015．03．014

2014-12-29．

Biography：Ji Cuilian（1975—），female，master，associate professor，jicuilian75＠163．com．

The National Natural Science Foundation of China（No．50776055，51076084）．

：Ji Cuilian，Han Jitian，Liu Xiaopeng，et al．A new heat transfer correlation for flow boiling in helically coiled tubes［J］．Journal of Southeast University（English Edition），2015，31（3）：380- 383．

10．3969／j．issn．1003－7985．2015．03．014