Analysis of condenser shell side pressure drop based on the mechanical energy loss

Transcription

1 Article Calorifics December 01 Vol.57 No.36: doi: /s Analsis of condenser shell side pressure drop based on the mechanical energ loss ZENG Hui, MENG JiAn & LI ZhiXin * Ke Laborator of Thermal Science and Power Engineering of Ministr of Education, School of Aerospace, Tsinghua Universit, Beijing , China Received Ma 16, 01; accepted Jul 13, 01 The condenser performance is strongl affected b the tube arrangement. The steam pressure drop in the tube bundle influences the condenser back pressure, which is an important indicator of the condenser performance used to compare different condenser tube arrangements. The condenser shell side pressure drop is studied here using the mechanical energ loss of the steam flow in the condensers. The mechanical energ loss is due to the flow resistance of the tube bundle and the steam condensation. Three tpical tube arrangements are analzed numericall. The results show that a higher condenser shell side pressure drop for different tube arrangements alwas corresponds to a larger mechanical energ loss. The mechanical energ loss is mainl in the peripher of the tube bundle, indicating that the flow pattern and the mechanical energ losses are markedl determined b the tube bundle profile. The condenser shell side pressure drop can be reduced b reducing the total mechanical energ loss when the steam enters the tube bundle more uniforml. Thus, a well designed tube arrangement will reduce the mechanical energ loss, and also the shell side pressure drop. power plant condenser, tube arrangement, shell side pressure drop, mechanical energ loss Citation: Zeng H, Meng J A, Li Z X. Analsis of condenser shell side pressure drop based on the mechanical energ loss. Chin Sci Bull, 01, 57: , doi: /s *Corresponding author ( lizh@tsinghua.edu.cn) Condensers, normall comple shell-and-tube heat echangers, are the most important auiliar equipments in a power plant. The thermal efficienc of power unit strongl depends on the condenser back pressure. A condenser has a large number of cooling tubes. For eample, a condenser for a 300 MW unit has approimatel 0000 cooling tubes. The condenser performance is then highl dependent on the tube arrangement. The shell side pressure drop in the tube bundle is an important indicator of the condenser performance, which can be used to compare different condenser tube arrangements. Power plant condenser designs are traditionall based on recommendations from previous designs and eperimental results, often based on the standards developed b the Heat Echange Institute (HEI Standards) [1]. However, this method does not take a number of factors into account, including the tube arrangement. Numerical simulations of the fluid flow and heat transfer in condensers have been conducted b man researchers [ 10], with predictions agreeing well with eperimental data. The advantage of numerical simulations is that the can give more detailed information on the fluid flow and heat transfer in the condenser, which provides a more effective means for condenser design. However, there is still a lack of a good optimization method for the tube arrangement, which can improve the condenser performance b reducing the shell side pressure drop. Guo et al. [11] recentl introduced a new phsical quantit, entrans, for optimizing heat transfer processes, which describes the heat transfer abilit of a bod. The heat conduction equation is multiplied b the temperature to get an entrans balance equation, with (T) as the entrans dissipation rate. The entrans dissipation rate is a measure of the irreversibilit of a heat transfer process. Then, Guo et al. [11] proposed the etremum entrans dissipation principle The Author(s) 01. This article is published with open access at Springerlink.com csb.scichina.com

2 Zeng H, et al. Chin Sci Bull December (01) Vol.57 No for optimizing heat transfer processes where the etremum entrans dissipation corresponds to the optimal heat transfer performance when a thermodnamic ccle is not involved. This new principle has been applied to optimizing heat conduction [11 19], convective heat transfer [0 3], thermal radiation [4] processes and the heat transfer in heat echanger [5 33], with all the studies confirming that the optimal results can be obtained based on the etremum entrans dissipation principle. Chen et al. [34 36] analzed the heat, mass and momentum transfer to etend the entrans concept to convective mass transfer and fluid flow processes. The mass entrans and momentum entrans dissipations were defined for optimizing convective mass transfer and fluid flow processes. The momentum entrans dissipation is equivalent to the mechanical energ loss during a fluid flow process. In order to improve the condenser performance, this stud analzes the condenser shell side pressure drop based on the mechanical energ loss for the steam flow. Three tpical tube arrangements are taken into consideration to stud the impact of the tube arrangement on the condenser shell side pressure drop. 1 Phsical model Figure 1 shows the entire cross section of a condenser with the cap-shaped tube arrangement. The shell side of the condenser can be divided into two distinct flow regions, one is the tube bundle region where the cooling tubes are densel positioned, and the other is the free flow region. The steam ehaust from the turbine enters the condenser from the top and flows through the tube bundle to condense. The noncondensable gases (mainl air) and the non-condensed steam are etracted b the vents in the centre of each tube bundle. Baffles guide the steam flow. Some tube arrangements have an independent tube bundle in front of the vent, which is called air cooling region. As in previous studies, the shell side of the condenser is modeled as a porous medium. An isotropic porosit,, is defined as the ratio of the volume occupied b the fluid to the total volume. In the present work, = f =1 in the free flow region, and in the tube bundle region, where the tubes are laid out in an equilateral triangular pattern, = t, it is set to D o 1, 3 Pt t where D o is the tube outer diameter and P t is the tube pitch. The comple shell side flow in the condenser is simplified as a two dimensional gas (a miture of steam and air) flow through a porous medium. The two-dimensional steadstate governing equations for mass, momentum, and the air mass fraction in the Cartesian coordinate sstem are as follows [6]. Mass conservation equation for the steam and air miture: u v m; (1) () Momentum conservation equations for the steam and air miture: uu vu u u P t t mu Fu, (3) uv vv v v P t t mv Fv ; (4) Conservation of air mass fraction: a a Ya Y D D D D uy vy a t t, (5) where m is the steam condensate rate per unit volume, F u and F v are the flow resistance force components in the and directions due to the tube bundle, is the dnamic viscosit, D is the diffusivit of air in the vapor, t is the turbulent dnamic viscosit, D t is the turbulent diffusivit of air in the vapor, and Y a is the air mass fraction. Mechanical energ loss for the condenser shell side flow Figure 1 Condenser cross-section. The epression of the mechanical energ loss can be derived

3 470 Zeng H, et al. Chin Sci Bull December (01) Vol.57 No.36 from the governing equations. The porosities in both the tube bundle region and the free flow region are uniform and change onl at the interface between the two regions, so the mechanical energ dissipation caused b the porosit variation is neglected. Multipling eqs. (3) and (4) b the velocit components u and v respectivel gives u uu u vu u u P u t u t u mu Fu u, (6) v uv v vv v v P v t v t v mv Fv v. (7) Combining eqs. (6) and (7) and make some transformations, and substituting eq. () into it ields 1 1 Pu u u v v u v Pv P 1 m u v m F u u Fv v, (8) where is the viscous dissipation function, which is epressed as u v u v t. (9) Integrating eq. (8) over the whole flow region and using Gauss rule gives 1 u v ui vj n da Pui vj n da A A P 1 m u v m F u u Fv v d V. V (10) Eq. (10) is the mechanical energ conservation equation for the condenser shell side flow. The left side of eq. (10) is the mechanical energ transport through the boundar, and the right side is the mechanical energ loss during the fluid flow. Since most of the steam will condense in the condenser, the mechanical energ transport through the vents can be neglected. Thus, the mechanical energ conservation equation can be simplified to 1 Pi Ui Qi P 1 m u v m F u u Fv v d V, V (11) where U i and Q i are the inlet velocit and mass flow rate determined b the condenser operating conditions. P i is the inlet pressure. The absolute pressure in eq. (11) can be changed to a relative pressure with the vent pressure, P o, as the reference: P P P. (1) o The relative inlet pressure, P i, is then equal to the shell side pressure drop, P. Then eq. (11) can be written as 1 U i P Qi P 1 m u v m F u u Fv v d V. V (13) The phsical meanings of each term in the mechanical energ conservation equation, eq. (13), are 1 UQ, i i the kinetic energ input through the inlet; P Qi, the potential energ input through the inlet; P m d V V, the potential energ loss due to the steam condensation in the tube bundle region; 1 u v m dv V, the kinetic energ loss due to the steam condensation in the tube bundle region; Fu u Fv v dv, the mechanical energ loss due V to the flow resistance in the tube bundle region; V dv, the mechanical energ loss due to viscous dissipation in the free flow region. Because there is steam condensation during the fluid flow process, the total mechanical energ loss consists of not onl the mechanical energ loss due to the flow resistance, but also the mechanical energ loss due to the steam condensation. Based on eq. (13), the total mechanical energ input, E i, and the total mechanical energ loss rate, e, can be defined as 1 P Ei Ui Q, (14)

4 Zeng H, et al. Chin Sci Bull December (01) Vol.57 No where d, e e V (15) V P 1 e m u v m F u u Fv v (16) is the mechanical energ loss rate. In eq. (13), U i and Q i are fied values for the given operating conditions, indicating that the condenser shell side pressure drop can be measured b the mechanical energ loss. The mechanical energ loss is related to the tube arrangement, so it provides a wa to stud the impact of the tube arrangement on the condenser shell side pressure drop. 3 Numerical analses of tpical tube arrangements Three tpical tube arrangements are considered to stud the impact of the tube arrangement on the condenser shell side pressure drop. Figure shows the tube arrangements where tpe A is a cap-shaped tube arrangement, tpe B is a doublepeak-shaped tube arrangement, and tpe C is a lozengeshaped tube arrangement. Since all condensers are smmetric across their center planes, Figure onl shows half of each tube bundle. Each condenser has double tube-passes, so each tube bundle is formed b two parts with equal numbers of tubes. The cooling water enters into the lower tube bundle and then eits from the upper tube bundle. The condenser shell side flow is comple, so the flow parameters distribution has no analtical solution. Thus, numerical method is used to analze the three tpical tube arrangements based on the mechanical energ loss. The condenser geometries and operating parameters are listed in Table 1. The geometr and boundar conditions are smmetric, so onl the left half of the condenser was simulated. The steam condensate rate per unit volume, m, and the flow resistance forces, F u and F v, in eqs. () (5) were taken from Zhang and Bokil [6]. The RNG k-ε model [37] was used to model the turbulence through the turbulent viscosit, μ t, and the turbulent diffusivit of air, D t, in the vapor. The boundar conditions for the computational domain are Steam inlet: The velocit and air mass fraction are given at the inlet boundar; Vent: The pressures at all the vents are all the same; Walls: The shell walls and baffles of the condenser were assumed to be non-slip and impermeable; Smmetr plane: Along the center smmetr line the derivatives with respect to the cross-stream direction of all field variables were set to zero ecept for the cross flow velocit which is set to zero. The simulations were performed using the commercial Figure Three tpical tube arrangements. (a) Cap-shaped tube arrangement; (b) double-peak-shaped tube arrangement; (c) Lozenge-shaped tube arrangement. Table 1 Condenser geometric and operating parameters Geometric parameters Operating parameters Tube material TP 304L Inlet steam mass rate t/h Tube number 374 Inlet steam drness fraction 0.9 Tube length m Air in-leakage mass fraction Outer tube diameter 5 mm Venting pressure 4900 Pa Inner tube diameter 4 mm Cooling water flow rate t/h Tube pitch 3 mm Inlet cooling water temperature 0 C Tube cleanliness factor 0.9

5 47 Zeng H, et al. Chin Sci Bull December (01) Vol.57 No.36 software FLUENT 6.. The discretization used the SIMPLEC algorithm with the QUICK scheme. Non-uniform quadrilateral grids were generated using Gambit.0, with fine elements in the tube bundle region and coarse elements in the eternal free flow region. As an eample, the grids near the boundar between the tube bundle region and the free flow region of condenser for tube arrangement A are shown in Figure 3. Calculation results with different element numbers of condenser for tube arrangement A are listed in Table to test the grid independence. The results showed that the element number of about is sufficientl fine to result in a grid-independent solution. 3.1 Mechanical energ loss for tube arrangement A Tube arrangement A is a cap-shaped tube arrangement. The tubes are arranged as a continuousl closed band, and which is curved to form steam inlet channels. According to the simulation result, the total mechanical energ input, E i, is 85 kw and the total mechanical energ loss, e, is 746 kw. The total mechanical energ loss is onl 10% less than the total mechanical energ input, showing that e can be used to approimatel measure the shell side pressure drop. The difference between e and E i is the mechanical energ loss due to the change of porosit when the steam enters the tube bundle region from the free flow region. Figure 4 shows the flow streamlines in the condenser for tube arrangement A. The steam enters the condenser at the top with a uniform downward velocit, flows around the tube bundle and enters into the tube bundle from all around the peripher. Because of the steam condensation in the tube bundle, the steam velocit decreases rapidl as the steam flows through tube bundle towards the vent. The side wall causes the flow resistance in the left channel to be larger than that in the right channel where the smmetr plane has no effect on the flow resistance. The steam flowing through the right main channel turns into the bottom channel and then flows upward into the left main channel until reaching the middle part of the lower tube bundle. The steam enters the tube bundle intensivel in the top part of the upper tube bundle, in the bottom part of the lower tube bundle and in the left part of the lower tube bundle. Some vortices develop near the right channel where the pressure is lower. Not much of the steam flow through the right channel enters the tube bundle, indicating that this part of tube bundle is not effectivel used. The mechanical energ losses in the condenser for tube arrangement A is shown in Figure 5. The viscous dissipation in the free flow region is not so high where the maimum viscous dissipation in the free flow region is about 1000 W/m 3, and the viscous dissipation in most of the free flow region is lower than 50 W/m 3. As the steam enters the tube bundle to condense with a rapidl decreasing velocit and pressure, the mechanical energ loss decreases from 0000 W/m 3 to less than 50 W/m 3 near the vent. The region with mechanical energ losses higher than 0000 W/m 3 is where the steam enters into the tube bundle. Besides the region near the vents, along the right side of the tube bundle in the right channel, there are also some regions with mechanical energ losses lower than 50 W/m 3. The pressure distribution of condenser for tube arrangement A is shown in Figure 6. The pressure plotted in the figure is the relative pressure with the vent pressure as reference. Figure 6 shows that the pressure drops rapidl in the Figure 3 Grids near the boundar between the tube bundle region and the free flow region. Table Grid independence test results Element number P (Pa) Figure 4 Streamlines of condenser for tube arrangement A.

6 Zeng H, et al. Chin Sci Bull December (01) Vol.57 No Figure 5 Mechanical energ losses of condenser for tube arrangement A (W/m 3 ). tube bundles, each bundle is shaped as two connected peaks. The steam channels are taper-shaped. Figure 7 shows the flow streamlines of the condenser for tube arrangement B. The steam first flows downward through the middle and right channels, then enters into the bottom main channel and finall flows upward through the left main channel to the top-left corner of the tube bundle. The steam flow through the tapered channels uniforml enters the tube bundle at different positions all along the bundle. There are some small vortices in the lower tube bundle and in the middle and right channels. The mechanical energ losses in the condenser for tube arrangement B are shown in Figure 8. The double-peakshaped tube arrangement reduces the maimum mechanical energ loss compared to tube arrangement A. There are onl small regions with mechanical energ losses higher than W/m 3 and the mechanical energ losses in most of the tube bundle are between W/m 3. There are some small regions with mechanical energ losses lower than 50 W/m 3 in the peripher of the lower tube bundle, showing that the mechanical energ loss distribution there is not reasonable. The distribution of the mechanical energ loss of the condenser for tube arrangement B is much more uniform than for tube arrangement A. The maimum mechanical energ loss is lower and the regions in the peripher of the tube bundle with low mechanical energ losses are smaller. Thus, the total mechanical energ loss is 370 kw and the shell side pressure is 130 Pa of the condenser for tube arrangement B, which are both lower than of the condenser for tube arrangement A. 3.3 Mechanical energ losses for tube arrangement C Tube arrangement C is a lozenge-shaped tube arrangement Figure 6 Pressure distribution of condenser for tube arrangement A. regions with high mechanical energ losses. That means high mechanical energ loss corresponds to large pressure drop in the condenser. The mechanical energ loss distribution in the condenser for tube arrangement A is not uniform. The total mechanical energ loss is quite large so the condenser shell side pressure drop is quite high. The shell side pressure drop of the condenser for tube arrangement A is 98 Pa. 3. Mechanical energ loss for tube arrangement B Tube arrangement B is a double-peak-shaped tube arrangement with each half of the condenser having two identical Figure 7 Streamlines of condenser for tube arrangement B.

7 474 Zeng H, et al. Chin Sci Bull December (01) Vol.57 No.36 Figure 8 Mechanical energ losses of condenser for tube arrangement B (W/m 3 ). with each half of the condenser having two tube bundles, which are similar but not the same. The tube bundle is approimatel lozenge-shaped with tubes removed in the tube bundle peripher to form tin secondar branch channels. Figure 9 shows the flow streamlines in the condenser for tube arrangement C. The steam flows downward in the right main channel, but in the left main channel the steam onl flows half wa and then turns into the horizontal main channel, and then flows to the right main channel. The two steam flows mingle and flow around the lower tube bundle until reaching the left-top corner. There are two large vortices with one in the lower-left part of the upper tube bundle and the other in the lower-right part of the lower tube bundle, forming a large area of the tube bundle region where the steam does not flow to the vent and the new steam cannot enter. The mechanical energ losses in the condenser for tube arrangement C are shown in Figure 10. The regions in the center of each bundle are connected with the vortices to form large areas with mechanical energ loss lower than 50 W/m 3. The region with mechanical energ losses higher than 0000 W/m 3 is larger than in the condensers for tube arrangements A and B. The mechanical energ loss distribution in the condenser for tube arrangement C is reasonable in part of tube bundle region, but the regions with low mechanical energ losses are too large, as well as the regions are with high mechanical energ losses. The total mechanical energ loss is 801 kw and the shell side pressure is 314 Pa of the condenser for tube arrangement C, which is higher than for tube arrangement A. Among the three tube arrangements, condenser for tube arrangement B has the most uniform distribution of the mechanical energ loss, i.e. the regions with high and low mechanical energ losses are both small, so the total mechanical energ loss and the shell side pressure drop are both lower than for the other two tube arrangements. The mechanical energ loss distributions for tube arrangements A and C are not so reasonable with regions of low mechanical energ losses in the main condensation tube bundle, so the regions with high mechanical energ losses are ver large. The mechanical energ losses are concentrated in the peripher of the tube bundle, indicating that the flow pattern and the mechanical energ losses are markedl determined b the profile of the tube bundle. Figure 9 Streamlines of condenser for tube arrangement C. Figure 10 Mechanical energ losses of the condenser for tube arrangement C (W/m 3 ).

8 Zeng H, et al. Chin Sci Bull December (01) Vol.57 No Conclusions (1) A theoretical analsis of the condenser shell side flow was used to develop a simplified epression for the mechanical energ loss rate. The mechanical energ loss consists of the mechanical energ dissipation due to the resistance of the tube bundle and that due to steam condensation. A well designed tube arrangement can reduce the mechanical energ loss and also the shell side pressure drop. () Three tpical tube arrangements were analzed numericall. The results show that a higher condenser shell side pressure drop alwas corresponds to a larger total mechanical energ loss. The mechanical energ loss is concentrated in the peripher of the tube bundle, indicating that the flow pattern and the mechanical energ loss are markedl determined b the tube bundle profile. 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