Effect of tube pitch on heat transfer in shell-and-tube heat exchangers new simulation software

Transcription

1 Heat Mass Transfer (2006) 42: DOI 0.007/s ORIGINAL A. Karno Æ S. Ajib Effect of tube pitch on heat transfer in shell-and-tube heat exchangers new simulation software Received: 9 July 2004 / Accepted: 7 May 2005 / Published online: 25 November 2005 Ó Springer-Verlag 2005 Abstract A new program for simulation and optimization of the shell-and-tube heat exchangers is prepared to obtain useful results by employment of the computing technology fast and accurately. As an application of this program, the effects of transverse and longitudinal tube pitch in the in-line and staggered tube arrangements on the Nusselt numbers, heat transfer coefficients and thermal performance of the heat exchangers were investigated. The obtained values of the tube pitch were compared with literature values. Nomenclature A heat transfer area (m 2 ) c p specific heat at constant pressure (J/kg K) D i inside diameter of the shell (m) d diameter of tube (m) h heat transfer coefficient (W/m 2 K) k thermal conductivity (W/m K) _m mass flow rate (kg/s) Nu Nusselt number Pr Prandtl number _Q thermal performance (W) Re Reynolds number S baffle spacing (m) T temperature (K) DT temperature difference (K) U overall heat transfer coefficient (W/m 2 K) V volumetric flow rate (m 3 /s) w velocity (m/s) A. Karno (&) Æ S. Ajib Faculty of Mechanical Engineering, Department of Thermo and Magneto fluid-dynamics, Ilmenau University of Technology, PO Box: 00565, 98684, Ilmenau, Germany ali.karno@tu-ilmenau.de Tel.: Fax: Greek symbols t cinematic viscosity (m 2 /s) l absolute viscosity (N s/m 2 ) q density (kg/m 3 ) Subscripts c cold h hot i inlet, inside, inner lam laminar max maximum min minimum o outlet, outside, outer turb turbulence Introduction Although today a set of common types of heat exchangers (double-pipe, spiral, plate-and-frame, platefin, compact heat exchangers) are used in heat transfer applications, the shell-and-tube heat exchangers are still the most common type in use. They have larger heat transfer surface area-to-volume ratios than the most of common types of heat exchangers, and they are manufactured easily for a large variety of sizes and flow configurations. They can operate at high pressures, and their construction facilitates disassembly for periodic maintenance and cleaning. The shell-and-tube heat exchangers consist of a bundle of tubes enclosed within a cylindrical shell. One fluid flows through the tubes and a second fluid flows within the space between the tubes and the shell. Various forms of baffles, such as segmental, rod, disc and doughnut, and helical baffles, may be placed along the tube bundle to force the fluid between the tubes and shell to flow across the tubes, resulting in improved heat transfer performance. The heat transfer on the shell-side of the shell-and-tube heat exchangers is complicated

2 264 depending on baffle and tube characteristics such as baffle type, baffle geometry, tube size and tube pitch. For some types of shell-and-tube heat exchangers, Roetzel et al. [ 3] applied a set of design methods. A lot of analytical and experimental studies have been devoted in general to determine the pressure drop and the heat transfer coefficient on the shell-side [4 ]. Kottke and Li [2] investigated different baffle types such as segmental baffles and disc-and-doughnut baffles [3]. Significant number of papers address how to determine the effects of baffle spacing and baffle/shell leakage [4 7]. Karno and Ajib [8] have reported a program for design of the shell-and-tube heat exchangers. The input data in this program are the inlet and outlet fluid temperatures and the thermal performance. This program calculated the main dimensions of the heat exchangers, which gives the previous boundary conditions. In this paper, after a thorough analysis of the optimization methods used till now, new software for simulation and optimization of the shell-and-tube heat exchangers is prepared to obtain useful results by employment of the computing technology. This program determines the thermal efficiency, Reynolds numbers, Nusselt numbers, thermal performance and heat transfer coefficient curves in heat exchangers upon various input data of the flowing media, the assigned boundary conditions or the main dimensions of the heat exchanger without the effort of computation. As an application of this simulation software, the effects of transverse and longitudinal tube pitch in the in-line and staggered tube arrangements on the heat transfer are simulated and optimized. 2 Data and methods of analysis 2. Design data The shell-and-tube heat exchanger used in this work is shown in Fig.. It consists of a cylindrical shell with an inner diameter of 240 mm. The tube bundle contains 70 straight smooth tubes with an effective heat exchange length of 900 mm. The tubes have an inner diameter of 0 mm and an outer diameter of 2 mm. Thus the heat exchange surface (exterior of the tubes) amounts to 2,374 m 2. Eight segmental baffles with a diameter of 235 mm are placed along the tube bundle and thus the clearance between baffles and shell is 2.5 mm. The distance between baffles is 74 mm and the baffle cut is 60 mm. The thickness of baffles is 3 mm and the diameter of baffle hole is 2.5 mm and thus the clearance between the baffle holes and tubes is 0.25 mm. The inlet fluid temperature on the shell-side is 35 C and on the tube-side is 60 C. The volumetric flow rate in tube-side is 2.26 m 3 /h and in shell-side is 4.52 m 3 /h and thus the flows on both shell and tube sides are turbulence. These values can be varied according to the required work conditions. The imposed physical properties of water, which was used as a working fluid at different temperatures, are given in Table. 2.2 Mathematical modeling Starting from the basic equation for the heat transport, the thermal performance for the heat exchanger can be written as: _Q ¼ U A DT m; log ðþ The log-mean temperature difference DT m,log is calculated using the equation: DT m; log ¼ DT max DT min ln DT max DT min ð ¼ T hi T ci The thermal performance is, then, ðt hi T ci Þ ðt ho T co Þ _Q ¼ U A ln T hi T ci T ho T co Þ ðt ho T co Þ ln T hi T ci T ho T co ð2þ ð3þ Applying an energy balance to the adiabatic heat exchanger under steady-state conditions gives: _Q ¼ _m h c ph DT h ¼ _m c c pc DT c ð4þ Or with the temperature: Fig. The simulated shell-andtube heat exchanger

3 265 Table Physical properties of water [9] _Q ¼ _m h c ph ðt hi T ho Þ ¼ _m c c pc ðt co T ci Þ ð5þ From Eq. 5, the outlet temperature can be calculated as follows: _Q T ho ¼ T hi ð6þ _m h c ph _Q T co ¼ T ci þ ð7þ _m c c pc Substituting Eqs. 6 and 7 into Eq. 3 gives: 2 3 _Q ¼ T hi T ci ð8þ þ _m c c pc e UA þ _mccpc Substituting Eq. 8 into Eqs. 6 and 7 gives: T ho ¼ T hi 2 _m h c ph T hi T ci C7 4 A5 ð9þ þ _m c c pc T co ¼ T ci þ 2 _m c c pc 6 T hi T ci 4 þ _m c c pc 0 e UA þ _mccpc e UA þ _mccpc 3 C7 A5 ð0þ Equations 8, 9 and 0 calculate the thermal performance and the outlet temperatures in the heat exchangers as a function for the boundary conditions (inlet temperatures and inlet velocities), heat transfer surface and heat transfer coefficient, which can be computed from Eq. : U ¼ h i þ d i lnðd o =d i Þ k þ d i h o d o ðþ That is after the determination of the Nusselt numbers and the heat transfer coefficients inside the tubes as follows [20]: Nu i ¼ 0:027ðRe i Þ 0:8 ðpr i Þ 0:33 Or: h i d i k i T=35 C T=60 C Temperature q (kg/m 3 ) (kg/m 3 ) Density c p 4.77 (J/kg K) 4,84 (J/kg K) Specific heat capacity k (W/m K) (W/m K) Heat conductivity m 0.724Æ0 6 (m 2 /s) 0.475Æ0 6 (m 2 /s) Cinematic viscosity Pr 4,823 2,983 Prandtl number ð2þ ¼ 0:027 w 0:8 id i ðpr i Þ 0:33 ð3þ m i Rearranging: h i ¼ 0:027 w 0:8 id i ðpr i Þ 0:33 k i ð4þ m i d i The average Nusselt number on the shell-side can be calculated from the corresponding average value for cross-flow over a bundle of smooth tubes. Owing to the flow pattern and the leakage and bypass streams, it is less than that for ideal cross-flow [2]. The following equation applies: Nu 0; shell ¼ f W Nu 0; bundle ð5þ The factor f W is composed as follows: f W ¼ f G f L f B ð6þ where f G is a geometrical factor for the changes in the flow direction; f L is the leakage factor for the stream through the clearance between baffles and shell and the clearance between baffles holes and tubes; and f B is a factor for the bypass stream between the outer tubes and the shell. The average Nusselt number in cross-flow over a bundle of tubes can be calculated from [22] Nu 0; bundle ¼ f A Nu ; 0 ð7þ where, Nu,0 is the average Nusselt number in cross-flow over pipes, which can be calculated from [23] qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Nu ; 0 ¼ 0:3 þ Nu 2 ; lam þ Nu2 ; turb ð8þ where pffiffiffiffiffiffiffiffiffiffiffipffi Nu ; lam ¼ 0:664 Re o; w ½3ŠPro ð9þ and 0:8Pro 0:037 Re o; w Nu ; turb ¼ 0: ð20þ 2=3 þ 2:443 Re o; w Pr o Substituting Eqs. 6, 7, 8, 9 and 20 into Eq. 5 gives after rearranging: Nu o ¼ f G f L f B f A 0:3þ 0:44Re o ; wpro 2=3 þ0:0037 Re o ; w :6 2: Pro þ2:443 Re o ; w 0: Pr 2=3 o 2 0:5 ð2þ The arrangement factor f A depends on the longitudinal a=s /d o and the transverse b=s 2 /d o spacing ratios in the tube bundle. If the tubes are arranged in line, the factor f A is given by: f A; in line ¼ þ 0:7 b a 0:3 w :5 b a þ 0:7 2 ð22þ If the tubes are staggered,

4 266 f A; stag ¼ þ 2 ð23þ 3b where w is the void fraction, which can be calculated as follows: w ¼ p for b> 4a ð24þ w ¼ p for bh 4ab ð25þ The Reynolds number Re o, w can be determined from: Re o; w ¼ Re w o p 2 d o o w ¼ t o ð26þ w where w o is the velocity of the fluid: V w o ¼ _ o ð27þ D i S and the heat transfer coefficient in the shell-side: h o ¼ k o Nu o p 2 d o 2.3 The program ST-HEX ð28þ With the help of previous equations, a new software is prepared. The main task of this software is the simulation and optimization of shell-and-tube heat exchangers after the input of the main dimensions and the imposed boundary conditions. Figure 2 shows the main window of the program. The input data of this program are:. The main dimensions of the heat exchanger: inner and outer diameter of tube; number of tubes and tube length; transverse and longitudinal tube pitch and tube arrangements (aligned or staggered); inner diameter of shell and number of shells; inner diameter of nozzles; and number of baffles, baffle cut, baffle diameter, baffle thickness and diameter of baffle hole. 2. The boundary conditions (Fig. 3): the inlet fluid temperature on shell-side and tubeside; and the inlet fluid velocity on shell-side and tube-side. 3. The physical properties of fluids (Fig. 4): density; specific heat capacity; heat conductivity; cinematic viscosity; and Prandtl number. The output data are: the heat exchange surface; Reynolds number on shell-side and tube-side; Nusselt number on shell-side and tube-side; heat transfer coefficient on shell-side and tube-side; overall heat transfer coefficient; the outlet fluid temperature on shell-side and tube-side; the main logarithm temperature different; the thermal performance of the heat exchanger; and the thermal efficiency of the heat exchanger. Fig. 2 The main window of the program ST-HEX

5 267 Fig. 3 The input window of the boundary conditions Fig. 4 The input window of the fluids physical properties 3 Results and discussion The arrangement of tubes in shell-and-tube heat exchangers is categorized as either in-line or staggered. All the rows in an in-line arrangement are aligned, whereas alternating rows are offset by one-half of the tube spacing in a staggered tube arrangement, as shown as in Fig. 5. Aligned tubes form rectangles with the centers of their cross-section, whereas staggered tubes form isosceles triangles. Tube spacing parallel and perpendicular to the flow direction is defined as the longitudinal pitch, S, and transverse pitch, S 2, respectively. The dependence of the average heat transfer coefficient on the longitudinal tube pitch in aligned tube arrangement is represented in Fig. 6. Figure 6 shows that the average heat transfer coefficient increases 35% with increase in the longitudinal tube pitch from 2.6 to 4.4 mm, and it decreases with increase in the longitudinal tube pitch after 4.4 mm, which means the average heat transfer coefficient has a maximum value S =4.4 mm. This optimum value of the longitudinal tube pitch is unchangeable with the change in velocity of the fluid in shell-side as shown as in Fig. 7. Figure 7 shows that the Nusselt number on shell-side has a maximum value by a constant fluid velocity, when

6 268 Fig. 5 Tube arrangements in shell-and-tube heat exchangers Fig. 8 The average heat transfer coefficient of the heat exchanger depending upon the transverse tube pitch in aligned tube arrangements and for different tube materials Fig. 6 The average heat transfer coefficient depending upon the longitudinal tube pitch in aligned tube arrangements the longitudinal tube pitch has the value S =.2 d o =4.4 mm. The effects of the transverse tube pitch in aligned tube arrangement on the average heat transfer coefficient are represented in Figs. 8 and 9. Figure 8 shows that the average heat transfer coefficient has a maximum value, when the transverse tube pitch has the value S 2 =.5 d o =8 mm, and this value is unchangeable with the use of different tube materials. The average heat transfer coefficient increases.6 % by the use of copper instead of steel tubes because of the greater heat conductivity of copper, but the optimum transverse tube pitch will not be changed here. Figure 9 shows that the optimum value of transverse tube pitch in the aligned tube arrangement is changeable with the change of the longitudinal tube pitch value. The obtained values are given in Table 2. From Table 2 one can obtain an equation to determine the transverse tube pitch in aligned tube arrangement depending upon the longitudinal tube pitch as follows: S 2 ¼ :3S ð29þ The dependence of the average heat transfer coefficient of the longitudinal and transverse tube pitch in the staggered tube arrangement is represented in Figs. 0 and. The optimum value of the longitudinal tube pitch in staggered tube arrangements is S =.4 d o =6.8 mm, as shown as in Fig. 0, where the heat transfer coefficient Fig. 7 Nusselt number on shell-side depending upon the longitudinal tube pitch in aligned tube arrangements and for different fluid velocities Fig. 9 The average heat transfer coefficient of the heat exchanger depending upon the transverse tube pitch in aligned tube arrangements and for different transverse tube pitches

7 269 Table 2 The optimum values of the transverse tube pitch in aligned tube arrangement S (mm) S 2, optimum (mm) U (W/m 2 K) increases from 20%, when the longitudinal tube pitch increases from S =. d o =3.2 mm to S =.4 d o =6.8 mm, and decreases 5% when the longitudinal tube pitch increases from S =.4 d o =6.8 mm to S =2 d o =24 mm. Figure shows that the average heat transfer coefficient decreases 4% when the transverse tube pitch in staggered tube arrangements increases from S 2 = d o =2 mm to S =3 d o =36 mm, therefore the optimum value of the transverse tube pitch in staggered tube arrangements is S 2 = d o =2 mm, and it is unchangeable with the change of the longitudinal tube pitch, as shown as in Fig. 2. By this obtained values of tube pitch in staggered tube arrangement, the heat transfer coefficient in shellside is maximum, as shown as in Fig. 3. Fig. 2 The thermal performance of the heat exchanger depending upon the transverse tube pitch in staggered tube arrangements and for different transverse tube pitches Table 3 shows a comparison of the optimum obtained values of the tube pitch with data known from literature (when the outer diameter of tube is 2 mm). 4 Conclusions A new software for calculation, simulation and optimization of shell-and-tube heat exchangers has been developed. This ST-HEX program is able to predict the effects of baffle spacing, baffle cut, tube size, shell number, shell size, etc., on the average heat transfer coefficient, thermal performance and thermal efficiency Fig. 0 The average heat transfer coefficient depending upon the longitudinal tube pitch Fig. 3 The influence of the transverse and longitudinal tube pitch in staggered tube arrangements on the heat transfer coefficient in shell-side Table 3 Comparison of the optimum obtained values of the tube pitch with literature values (when the outer diameter of tube is 2 mm) Tube arrangement Tube pitch Obtained values (mm) Ref. [20] Fig. The average heat transfer coefficient depending upon the transverse tube pitch in staggered tube arrangements Aligned S S Staggered S S

8 270 of the shell-and-tube heat exchangers. Simulations were performed to analyze the effect of tube pitch on the heat transfer. Results have shown that the heat transfer coefficients can change when the longitudinal and transverse tube pitch are varied and the best values of these parameters are found. Good agreement is observed between the computed values and the literature values. References. Roetzel W, Spang B (993) Design of heat exchangers. In: VDIheat atlas. VDI-Verlag, Du sseldorf, pp Ca Roetzel W, Spang B (990) Effective mean temperature difference in segmentally baffled shell and tube heat exchangers. Proceedings of the Ninth International heat exchanger conference. Heat Transfer 5: Roetzel W, Lee D (994) Effect of baffle/shell leakage flow on heat transfer in shell-and-tube heat exchangers. Exp Thermal Fluid Sci 8: Gay B, Roberts PCO (970) Heat transfer on the shell-side of a cylindrical shell-and-tube heat exchanger fitted with segmental baffles II. Flow patterns and local velocities derived from the individual tube coefficients. Trans Inst Chem Eng 48:T3 T6 5. Gay B, Mackley NV, Jenkins JD (976) Shell-side heat transfer in baffled cylindrical shell-and-tube exchangers an electrochemical mass transfer modelling technique. Int J Heat Mass Transfer 9: Sun SY, Lu YD, Yan CQ (993) Optimization in calculation of shell-tube heat exchanger. Int Comm Heat Mass Transfer 20: Gaddis ES, Gnielinski V (997) Pressure drop on the shell-side of shell-and-tube heat exchangers with segmental baffles. Chem Eng Process 36: Prithiviraj M, Andrews MJ (998) Three-dimensional numerical simulation of shell-and-tube heat exchangers. Part I: Foundation and fluid mechanics. Numer Heat Transfer Part A 33: Prithiviraj M, Andrews MJ (998) Three-dimensional numerical simulation of shell-and-tube heat exchangers. Part II: Heat transfer. Numer Heat Transfer Part A 33: Ajib S, Nilius A, Karno A (2003) Thermodynamic properties of a tube bundle heat exchanger. Thermodynamics Cambridge, UK, 9 April. Ajib S, Karno A, Nilius A (2004) Thermodynamic properties of a low temperature driven absorption refrigeration machine. Proceedings of the Third International Conference on Heat transfer, Fluid Mechanics and Thermodynamics, 2 24 June, Cape Town, South Africa (Paper number AS2) 2. Kottke V, Li H (998) Local heat transfer in the first baffle compartment of the shell-and-tube heat exchangers for staggered tube arrangement. Exp Thermal Fluid Sci 6: Kottke V, Li H (999) Analysis of local shellside heat and mass transfer in the shell and tube heat exchanger with disc-anddoughnut baffles. Int J Heat Mass Transfer 42: Sparrow EM, Reifschneider LG (986) Effect of interbaffle spacing on heat transfer and pressure drop in a shell-and-tube heat exchanger. Int J Heat Mass Transfer 29: Shah RK, Pignotti A (997) Influence of a finite number of baffles on shell-and-tube heat exchanger performance. Heat Transfer Eng 8(): Kottke V, Li H (998) Effect of baffle spacing on pressure drop and local heat transfer in shell-and-tube heat exchangers for staggered tube arrangement. Int J Heat Mass Transfer 4(0): Kottke V, Li H (998) Effect of the leakage on pressure drop and local heat transfer in shell-and-tube heat exchangers for staggered tube arrangement. Int J Heat Mass Transfer 4(2): Karno A, Ajib S (2002) Auslegungsprogramm fu r Rohrbu ndelwärmetauscher. Deutsche Kälte- Klima- Tagung 2002, Magdeburg, November, Band II.2: Straub J (993) Properties of water. In: VDI-heat atlas. VDI- Verlag, Du sseldorf, pp Db Mukherjee R (998) Effectively design shell-and-tube heat exchangers. Chem Eng Prog February: Gaddis ES, Gnielinski V (993) Shell-side heat transfer in baffled shell-and-tube heat exchangers. In: VDI-heat atlas. VDI-Verlag, Du sseldorf, pp Gg Gnielinski V (993) Heat transfer in cross-flow around individual tube rows and through tube bundles. In: VDI-heat atlas. VDI-Verlag, Du sseldorf, pp Gf Gnielinski V (993) Heat transfer in cross-flow around individual tubes, wires and profiled cylinders. In: VDI-heat atlas. VDI-Verlag, Du sseldorf, pp Ge 4