Zhang Jianqin Li Shaopeng

(Institute of High Energy Physics，Chinese Academy of Science，Beijing 100049，China)

Numerical studies of an eccentric tube-in-tube helically coiled heat exchanger for 20MPa helium purification system

Zhang Jianqin Li Shaopeng

(Institute of High Energy Physics，Chinese Academy of Science，Beijing 100049，China)

The tube-in-tube helically coiled(TTHC)heat exchangers with different eccentricity ratios were numerically studied for turbulent flow. The working fluid was helium at the pressure of 20 MPa. The inner and annulus Nusselt numbers were compared between the concentric and eccentric TTHC heat exchangers. The results show that with the eccentricity increasing，the annulus Nusselt number increases substantially. According to the numerical data，new empirical correlations of Nusselt number as a function of Reynolds number and eccentricity for the inner tube and the annulus were presented. The TTHC heat exchanger of the purifier was designed under the given conditions.

tube-in-tube heat exchanger；eccentricity；helical；numerical；heat transfer

1 Introduction

Helium purification system is an important sub-system which meets the high helium purity standard of the cryogenic system in the accelerator driven sub-critical system of the Institute of High Energy Physics，Chinese Academy of Science(IHEP-ADS). The purifier includes dewar，high pressure heat exchanger，condenser，liquid air separator and adsorption cylinders. The high pressure heat exchanger is used to transfer the heat of helium between the temperature of 300 K and 78K. Because of the pressure of 20 MPa and the compact structure，tube-in-tube helically coiled(TTHC)heat exchanger is a good choice.

Helically coiled heat exchangers are superior to straight tubes，for which have compact structures and higher heat transfer coefficients. It is known that centrifugal forces caused by the pipe curvature will result in a secondary flow，which enhances heat transfer rates. A number of studies focused on the fluid flow and heat transfer characteristics in helical pipes[1-3]. Mori and Nakayama[4]theoretically and experimentally studied the flow and heat transfer in a curved tube both in laminar and turbulent regions，and provided empirical correlations. Furthermore，Rennie and Raghavan[5]conducted experimental study of a TTHC heat exchanger with different curvature ratios. Numerical methods were used to study the helical tubes with computational fluid dynamics(CFD)simulation[6]. Rennie and Raghavan[7]and Later Kumar[8]numerically studied the laminar and the turbulent flow and heat transfer of a TTHC heat exchanger. The literature above-mentioned mainly focused on the concentric TTHC heat exchangers，while in many practical situations，they are eccentric，coiled without sharing the same vertical or horizontal center line. Louw and Meyer[9]experimentally compared the annular contact TTHC heat exchanger with a concentric one. Besides, natural convection and turbulent forced convection flow in vertical eccentric annulus were investigated experimentally[10-13]. However，the eccentric TTHC heat exchanger hasn’t been studied systematically.

2 Materials and methods

A sectional view of a vertical eccentric TTHC heat exchanger is show in Figure 1a. The eccentricity of the inner tube ranges from the concentric case(E=0)to the annular contact case(E=1)，which is 0，0.4，0.8，0.96 and 1 respectively. Considering the manufacturing condition，the case ofE=1 is welded with copper，which is shown in Figure 1b. Except for the different eccentricity ratios，the geometries of the eccentric TTHC heat exchangers are same. The outside diameter of the inner tube is 8mm with a wall thickness of 1 mm，while the outside diameter of the outer tube is 18mm with a wall thickness of 2.5 mm.

Fig.1 Sectional views of a TTHC heat exchanger

The transport and thermal properties of helium were dependent on the temperature. Fluent was used in the simulation. The geometrical and flow parameters for the inner and outer tubes are given in table 1.The working fluid in the inner tube and the annulus was helium,which were counter flow and heat was transferred through the copper wall. The total number of simulations performed for each type of TTHC heat exchanger was 21(11 inner tube flow rates and 10 annulus flow rates).

Table 1 Geometrical and flow parameters for inner and outer tubes

3 Results and discussion

3.1 Temperature profiles

The temperature profiles at the exit of the inner tube and the annulus forE=0 andE=0.96 of TTHC heat exchangers are given in Figure 2. The mass flow rate in the inner tube is 2 g/s，and the mass flow rate in the annulus is 10 g/s. In the Figure 2a，the outlet temperature profiles of the inner tube for different eccentricities are similar. The right side is the inner side of the coil，and has a higher temperature compared to the outer side. The average outlet temperature for the inner tube of the concentric heat exchanger is higher than that of the eccentric one. In the Figure 2b，the right side is the inner side of the coil. With the center offset increasing，the high temperature region moves from the outer side to the inner side. Moreover，the secondary flow enhanced the heat transfer in the annulus region withEincreasing.

Fig.2 Temperature profiles in inner tube/annulus for different eccentricities

3.2 Inner tube and annulus heat transfer coefficient

Heat transfer coefficients for the inner sidehiand the annulus tube sideho，were calculated with traditional Wilson plots[3,5]. Wilson plots allow the heat transfer coefficients to be calculated based on the overall heat transfer coefficient，without the requirement of wall temperature. The outer Reynolds number of the annulus was calculated by equivalent diameter. New empirical models were developed with Sieder-Tate type[14-15]equation，which was used to fit the inner and annulus Nusselt number with a coiled effect term δ0.1[4]and was the function of eccentricity. The differences between the empirical data and numerical data are less than 2%. The equations are：

(1)

(2)

Where the values of the coefficientsCi，Coandti，toare given in Table 2，for 14 000

Table 2 Values of coefficients for inner and annulus Nusselt number equation in concentric and eccentric TTHC heat exchangers

The empirical constants(Ci，ti，Co，to)are related toE，and the relations are as follows：

Ci=2.807E21.219+0.268

(3)

ti=-0.399E2+0.173E+0.634

(4)

Co=0.45E+0.441

(5)

to=-0.325E2.436+0.498

(6)

Figure 3 illustrates that the inner Nusselt number decreases by approximately 11.8%，14.4%，17.7% and 15.6% forE=0.4，E=0.8，E=0.96 andE=1 compared withE=0. The reason is probably that the eccentricity causes the temperature non-uniformity of the wall，and heat transfer turns worse in the lowering wall temperature region compared with the concentric one. Figure 3 also shows that the experimental data of Schmidt[16]has a good agreement with the concentric TTHC heat exchanger.

Fig.3 Nusselt number vs. inner Reynolds number， average annulus Reynolds number is 7000

Figure 4 shows the Nusselt number increases with the annulus Reynolds number increasing. It can be seen from the figure that the annulus Nusselt number increases with E increasing，especially at the large Reynolds number. The Nusselt numbers in the cases ofE=0.4，E=0.8，E=0.96，andE=1 are approximately 10.8%，27.8%，34.7% and 41.2% separately higher than those in the case ofE=0. With the eccentricity ratio increasing，the flow non-uniformity is enhanced with secondary flow and the heat transfer is improved the in the annulus.

Fig.4 Nusselt number vs. annulus Reynolds number， average inner Reynolds number is 28000

The relationship between the overall heat transfer coefficient and the inner/annulus heat transfer coefficient was as follows：

(7)

Compared with the inner and annulus heat transfer coefficients，the conduction resistance termRcis negligible. It is obvious in the Figure 3 and Figure 4 that the Nusselt number in the annulus is less than the inner tube at the same mass flow rate. So an increase of eccentricity is good for the increase of the overall heat transfer coefficient.

3.3 Friction factors

The inner and annulus friction factors were as follows：

(8)

Where ΔPis the pressure drop of the inner tube and the annulus，Lis the length of the heat exchanger，Deis the equivalent diameter of the inner tube and the annulus andu0，rare the average velocity and the density of the inner tube and the annulus，respectively.

Figure 5 shows the numerical data in the inner tube and the annulus for the concentric and eccentric TTHC heat exchangers and the experimental data of Schmidt[16]. Figure 5a presents that the inner friction factors of the concentric and eccentric TTHC heat exchangers are almost same at the same Reynolds number，and have a good agreement with Schmidt’s experimental data. Figure 5b presents that the annulus friction factor has a decrease of 13% and 25% forE=0.96 andE=1 separately compared with the value ofE<0.96.

Fig.5 Friction factor versus inner Reynolds number and annulus Reynolds number

3.4 Design of the heat exchanger

According to the analysis in 3.2，the case ofE=1 TTHC heat exchanger is preferred to design the heat exchanger in the purifier，especially in the high Reynolds number region. The design parameter of the heat exchanger is shown in Table 3. The diameter of the inner tube is 8 mm with a thickness of 1 mm，and the diameter of the outer tube is 16 mm with a thickness of 2.5 mm. The coil diameter is 300 mm. In order to decrease the flow resistance,the heat exchanger is divided into 5 branches. The inner and annulus heat transfer coefficients are calculated with Equations(1)and(2). The length of the tube is 16.3 m. The pressure drop of the inner tube and the annulus are 1 306 Pa and 1 885 Pa separately.

Table 3 Parameters of helically coiled tube-in-tube heat exchanger

4 Conclusions

Numerical studies of different eccentricity ratios of TTHC heat exchangers were performed with helium in the inner tube and the annulus. With the eccentricity increasing，the inner Nusselt number decreases slowly，while the annulus Nusselt number increases rapidly. In the case ofE=1，the inner Nusselt number decreases by approximately 15.6% and the annulus Nusselt number increases by approximately 41.2% compared with the case ofE=0. Eccentricity is good for the heat transfer of the annulus in an eccentric TTHC heat exchanger，especially in the large Reynolds number region. New empirical correlations of the Nusselt number versus the Reynolds number and eccentricity in the inner tube and the annulus were presented. The friction factors of the inner tube and annulus were studied for the concentric and eccentric TTHC heat exchangers. The heat exchanger of the purification system was designed with the case ofE=1 TTHC heat exchanger. In order to examine the reliability of CFD results，an experiment for an eccentric TTHC heat exchanger should be conducted in the future.

Reference

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2016-09-28；

2016-11-01

張建琴，女，29歲，博士、工程師。Zhang Jianqin，female，29 years old，doctor and engineer of Institute of High Energy Physics，Chinese Academy of Science.

TB611

A

1000-6516(2016)06-0062-06

螺旋式偏心套管換熱器的數(shù)值模擬

張建琴 李少鵬

(中國科學院高能物理研究所 北京 l00049)

采用數(shù)值模擬的方法研究了不同偏心度螺旋套管換熱器在紊流區(qū)域的換熱和流動特性。為了使計算結果更貼近實際情況，模擬計算中采用的是氦氣在壓力為20 MPa條件下的溫度依賴的變物性參數(shù)。通過數(shù)值計算結果，比較了同心和偏心螺旋套管換熱器內(nèi)管和外管的換熱系數(shù)，其中外管的換熱系數(shù)隨著偏心度的增加而大幅增加。根據(jù)計算結果提出了套管換熱器內(nèi)管和外管換熱系數(shù)隨偏心度和雷諾數(shù)的變化關系式。最后在給定的條件下設計了純化器中的偏心套管換熱器。

螺旋式套管換熱器 偏心 換熱 數(shù)值計算