Chapter 4 Performance Evaluation Criteria for Two-Phase Heat Exchangers Prof. Min Zeng 1/50 1. Introduction 2. Operating Characteristics of Two-phase Heat Exchangers 3. Enhancement in Two-Phase Heat Exchange Systems 4. PEC for Two-Phase Heat Exchange Systems 5. PEC Calculation Method 6. Conclusions Outline 2/50 1
1. Introduction This chapter describes quantitative methods to define the performance benefits of enhanced heat transfer surfaces in a heat exchanger, for which at least one of the fluids is evaporating or condensing. Pressure drop of a two-phase fluid may reduce the mean temperature difference for heat exchange. This situation does not exist for heat exchange between single-phase fluids. This chapter shows how the performance evaluation criteria (PEC) previously defined for single-phase flow may be modified to account for the effect of pressure drop. 3/50 2. Operating Characteristics of Two-phase Heat Exchangers A two-phase heat exchanger is defined here as one for which at least one of the fluids undergoes a phase change. The heat exchangers of interest here are vaporizers and condensers. Use of two-phase heat exchangers include three general application areas: (1) Work-producing systems, such as a Rankine power cycle. 4/50 2
(2) Work-consuming systems, such as a vapor compression refrigeration system or a vacuum distillation process, which use a compressor to support the process. (3) Heat-actuated systems, such as an absorption refrigeration cycle, or a distillation process (as defined here, a turbine or compressor would not be in this system) 5/50 The quantitative relations given in Chapter 3 assume that the LMTD is not affected by the pressure drop if the total flow rate is held constant. This is not true for two-phase flow. In two-phase flow, thepressuredropcausesareductionofthe saturation temperature, causing reduced LMTD for fixed entering condenser temperature, or for fixed leaving evaporator temperature. This is illustrated in Figure 4.1. 6/50 3
Figure 4.1 Illustration of the effect of two-phase pressure drop on the LMTD 7/50 Hence, the previously proposed quantitative relations must be modified to account for the effect of two-phase pressure drop on the LMTD. The effect of a given pressure drop on the decrease of saturation temperature ( T sat ) depends on the value of dt/dp at the operating pressure. The Clausius-Clapeyron equation may be employed to establish the magnitude of dt/dp dt dp T( vv vl) (4.1) 8/50 4
Figure 4.2 dt/dp vs. p/p cr 9/50 Figure 4.2 shows dt/dp vs. p/p cr for several fluids. This figure shows that dt/dp increases as p/p cr decrease. Typical operating points for condensers and evaporators of refrigeration and power cycles are noted on Fig. 4.2. Examination of the figure shows that refrigerant evaporators and power cycle condensers will suffer the greatest LMTD reduction due to two-phase pressure drop. 10/50 5
For single-phase flow in heat exchangers, the pump or fan power requirement (P) is directly proportional to the fluid pressure drop for a fixed flow rate. This is why the pumping power is included as an objective function (or constraint) in Table 3.1. However, the same relationship between pumping power and pressure drop does not exist for two-phase heat exchanger applications. 11/50 3. Enhancement in Two-phase Heat Exchange Systems This section describes how enhanced heat transfer may be employed in the previously defined workproducing, work-consuming, and heat-actuated systems. 3.1 Work-consuming Systems The purpose of a refrigeration cycle is to cool air, water, or a process fluid. Mechanical power is consumed by the compressor, which pumps the evaporated refrigerant from the evaporator pressure to the condenser pressure. 12/50 6
Performance improvements that may be affected by the use of enhanced surfaces are as follows: (1) Reduced heat transfer surface area for fixed compressor power (P c ). (2) Increased evaporator heat duty for fixed compressor lift (pressure difference between condenser and evaporator). (3) Reduced compressor power for fixed evaporator heat duty. This would be affected by reducing the LMTD of the evaporator and/or condenser. This would increase the suction pressure to the compressor and reduce the inlet pressure to the condenser. 13/50 For the first case, one would seek reduced surface area in the evaporator and condenser for fixed compressor inlet and outlet conditions. The compressor power is not influenced by pressure drop in either the evaporator or condenser. However, pressure drop in either heat exchanger will reduce the LMTD, and reduce the net performance improvement. Figure 4.3 illustrates a refrigeration cycle for this case, and shows the effect of two-phase pressure drop on the LMTD. 14/50 7
Figure 4.3 Pressure vs. enthalpy diagram for a refrigeration cycle showing the effect of pressure drop on the LMTD in each heat exchanger 15/50 The second case would maintain constant heat transfer surface area and take advantage of the increased ka to obtain increased heat duty. Again, pressure drop would act to reduce the increase of evaporator heat duty. A larger compressor capacity would be required, because the refrigerant flow rate would increase in proportion to the heat transfer increase. The surface area is maintained constant for the third case and the ka increase is employed to reduce the LMTD. This allows the compressor lift to be reduced for the fixed evaporator heat duty. 16/50 8
A vacuum distillation process may occur at a sufficiently low temperature that a refrigeration system is required to provide condenser coolant (an evaporating liquid) at the required low condensing temperature. Use of an enhanced heat transfer surface in the distillation reflux condenser may allow the compressor of the refrigeration system to operate at a higher suction pressure, and thereby save compressor power. 17/50 3.2 Work-producing Systems Next, consider the case of a Rankine power cycle. The boiler feed pump raises the pressure of the working fluid from the condenser pressure to the boiler pressure. This pumping power is calculated by P ( pb pc) Wv (4.2) l The pressure drop in the boiler is negligible compared to the pressure difference between the boiler and the condenser (p b -p c ). Hence, the mechanical energy consumed by frictional pressure drop in the boiler is of negligible concern. 18/50 9
However, pressure drop in the boiler or condenser will decrease the thermodynamic efficiency of the power cycle, because of the effect of dt/dp on the LMTD. Performance improvements that may be affected by the use of enhanced surfaces are twofold: (1) Reduced boiler and/or condenser surface area for constant turbine output (P t ). (2) Increased turbine output for fixed boiler heat input, or fixed condenser heat rejection. This would increase the boiler pressure or reduce the condensing temperature. 19/50 The first case maintains fixed boiler exit pressure and/or fixed condenser inlet pressure. Increased pressure drop in either heat exchanger will reduce the LMTD, and hence reduce the performance improvement. Based on the information presented in Fig. 4.2, one sees that the pressure drop in the boiler will have a very small effect on the boiler performance improvement. However, the same pressure drop in the condenser may significantly reduce the LMTD. 20/50 10
The second case maintains constant heat transfer surface area, and it employs the increased ka to allow reduction of the LMTD. If the LMTD in the condenser is reduced, the turbine can expand to a lower back pressure and produce more work. It is unlikely that the LMTD reduction in the boiler would have a significant effect on the turbine power output. 21/50 3.3 Heat-actuated Systems These systems may have a pump to transport liquids, but they do not use compressors or turbines in the process operations. A good example of a heat-actuated system is the absorption refrigeration cycle. This cycle has four heat exchangers that involve condensation or boiling processes (evaporator, concentrator, condenser, and absorber). A pump is used to transport the working fluid between the absorber and the concentrator, but a compressor is not employed. 22/50 11
In the LiBr-water absorption cycle, water is the refrigerant. Heat, in the form of steam or combustion products, is added in the concentrator to boil off water and concentrate the LiBr-water solution. If the LMTD in any of the four heat exchangers can be reduced, the thermodynamic irreversibility of the heat exchanger processes will be reduced. 23/50 A second example of a heat-actuated system is the oil refining process. A number of cascaded process condensers may be employed in a refinery crude train. The heat rejected by one condenser may provide heat input to an evaporator. Energy, in the form of combustion products, is employed to provide heat input to the top crude. Energy consumption will be decreased if the LMTD to each cascaded heat exchanger is reduced. This is probably more important than using the higher performance of the enhanced surface to reduce the capital cost of the heat exchanger. 24/50 12
A third example is distillation processes, in which heat rejection occurs to cooling water. Heat, in the form of steam, is added to a reboiler and heat is rejected in a water-cooled condenser. Enhanced surfaces may be employed for the same purposes as in the first two examples. Mechanical energy (e.g., compressors or turbines) is not used in the above examples. Performance improvements may be affected by use of enhanced surfaces for three different purposes. 25/50 (1) Reduced heat transfer surface area for fixed operating temperatures. (2) Increased heat exchange capacity for fixed amount of heat exchange surface area. (3) Reduced LMTD for fixed amount of heat exchange surface area, which will increase the thermodynamic efficiency of the process or cycle. Pressure drop of either two-phase stream will act to reduce the LMTD. The smaller LMTD will decrease the surface area reduction possible, or will decrease the efficiency improvement. 26/50 13
The above discussion shows that the different operating conditions of two-phase exchangers used in refrigeration and power cycles establish a need for a different set of PEC than those of Table 3.1, which are established for single-phase flow. There are three basic differences: (1) The LMTD is affected by the two-phase pressure drop. (2) The mechanical power of interest in workproducing/consuming cycles is not a pump or fan; rather it is a turbine or compressor. The power consumed by the circulation pump of a power cycle 27/50 is negligible compared to that produced by the turbine. Hence, the effect of the heat exchanger performance on the work produced by the turbine or on the work input to the compressor is the key point of concern. (3) In heat-actuated systems, the heat exchanger size or the thermodynamic efficiency of the system is influenced by the LMTD in the heat exchangers. Hence, the effect of the two-phase fluid pressure drop on the LMTD is the point of concern. 28/50 14
4. PEC for Two-phase Heat Exchange Systems Having defined the performance improvements that may be affected in two-phase heat exchange systems, it is now possible to prepare a table similar to Table 3.1. Table 4.1 shows PEC corresponding to the FG, FN, and VG cases for the previously discussed two-phase heat exchanger applications. 29/50 Table 4.1 Performance Evaluation Criteria for Two-Phase Heat Exchange System Fixed Parameters Case Geometry W P w Φ ΔT i Objective FG-1a N, L a ⅹ Φ FG-1b N, L ⅹ ⅹ ⅹ Δt * i FG-3 N, L ⅹ ⅹ ⅹ P w b FN-1 N ⅹ ⅹ ⅹ L FN-2 N ⅹ ⅹ ⅹ L FN-3 N ⅹ ⅹ P b w VG-1 ⅹ ⅹ ⅹ NL VG-2a N,L ⅹ ⅹ Φ VG-2b NL ⅹ ⅹ ΔT i VG-3 NL ⅹ ⅹ P w b Δt i * is defined as the temperature difference between the leaving boiling fluid and the entering process fluid for vaporizers. For condensers, it is the difference between the entering vapor temperature and the entering coolant temperature. b Replace by for heat-actuated systems. 30/50 15
Table 4.1 is laid out using the same cases as listed in Table 3.1. However there are several key differences between Tables 3.1 and 4.1. (1) The pumping power variable (P) oftable3.1is not used in Table 4.1. This is replaced in workconsuming (or work-producing) systems by the variable P w, which means work performed by (or on) the system. For heat-actuated systems, one may wish to constrain or reduce the pressure drop, because of its effect on the LMTD. The variable p applies for heat-actuated systems. 31/50 (2) The condensers and evaporators considered here are for complete evaporation or condensation. In this case, the heat duty is given by q=w x. Because x will be a constant for the evaporator or condenser, q W. Hence, W and q are not independent variables, as they are treated in Table 3.1. (3) Several of the cases in Table 3.1 do not apply for the present considerations. Hence, they do not appear in Table 4.1. 32/50 16
(4) Because the variable P w applies to workproducing or work-consuming systems and p applies to heat-actuated systems, separate tables should apply to these two systems types. To avoid this complication, Table 4.1 is prepared using an asterisk code (*) to differentiate between the two system types. Table 4.1 is equally applicable for vaporization or condensation inside tubes or on the outside of tubes in a bundle. 33/50 5. PEC Calculation Method An algebraic calculation must be performed to determine the value of the objective function for the case of interest in Table 4.1. Before any PEC calculations can be made, it is necessary to know the heat transfer coefficient and friction factor (or p characteristics) of the enhanced tube as a function of the flow and geometry conditions. The heat transfer and friction characteristics for vaporization or condensation on enhanced surfaces depend on the following variables: 34/50 17
(1) Geometry: The tube diameter and the specific geometric features of the enhanced surface. (2) The operating pressure (or saturation temperature). (3) The mass velocity (G), the vapor quality (x), and the heat flux (q) or the wall-to-fluid temperature difference (T w -T s ). The data may be measured as a function of the local vapor quality, or as average values over a given inlet and exit vapor quality. With the basic heat transfer and friction correlations in hand, for the particular enhanced geometry of interest, one is prepared to perform the PEC analysis. 35/50 5.1 PEC Example 4.1 Consider Case FN-2 for a refrigeration evaporator with tube-side vaporization. Assume that an evaporator design for vaporization in smooth tubes has been completed. Figure 4.4 illustrates the operating conditions for the smooth-tube design. Figure 4.4 Illustration of operating conditions for an air-cooled refrigerant evaporator with tube side vaporization 36/50 18
Air enters the evaporator at flow rate W a1 and T a1 and is cooled to T a2. The total heat duty of the evaporator is tot. Assume that the plain tube design has N refrigerant circuits in parallel. The heat duty per circuit is given by c = tot /N and the refrigerant mass flow rate per circuit is given by W rc =W r /N r. The refrigerant mass velocity is given by G=W rc /A c where A c is the flow cross section area for the circuit. The enhanced tube design operates at the conditions shown on Figure 4.4, except for the entering refrigerant temperature (T r1 ), which is a dependent variable. 37/50 The objective is to reduce the evaporator size (circuit length) for fixed compressor suction pressure, which fixes T r2. It is assumed that the frontal area of the finned tube heat exchanger is held constant, and that the evaporator length reduction is accomplished by removing tube rows in the airflow direction. If the pressure drop in the enhanced evaporator tube is greater than that of the plain tube, the LMTD will be reduced, as is qualitatively illustrated by the dashed line of Figure 4.4. 38/50 19
The evaporator is designed to operate between entering vapor quality x 1 and 1.0 exit vapor quality. Assume that a correlation exists to calculate the circuit average refrigerant heat transfer coefficient (h i ) at the given operating pressure. This is given by hi fcn( G, q) (4.3) Similarly, the pressure gradient is assumed to be known in the form p fcn( G, L) (4.4) 39/50 The PEC calculation proceeds as follows: (1) Guess the required circuit length and calculate the circuit averaged heat flux from the required heat load ( c )as c q (4.5) dl i (2) Calculate the refrigerant-side h and p using the known refrigerant mass velocity (G), heat flux (q), and the assumed circuit length (L) using Eqs. 4.3 and 4.4. 40/50 20
(3) Calculate the ka value of the enhanced tube exchanger from 1 1 w 1 (4.6) ka hiai waw hoao (4) From the calculated refrigerant pressure drop, calculate the entering refrigerant temperature (T r1 ). Then calculate the LMTD for the heat exchanger. (5) Calculate the available heat transfer rate ( av ) by ka LMTD (4.7) av 41/50 (6) If av > c (the required value), one assumes a shorter circuit length and repeats steps 1 through 5. The procedure is repeated until av = c. The material savings offered by the enhanced surface are L/L p,wherel p is the evaporator circuit length of the plain tube design. It is possible that the enhanced tube design would provide better performance characteristics if it were designed to operate at a different flow rate per circuit than used for the plain tube design. This question must be resolved by performing a parametric study of the enhanced tube design as a function of the number of circuits. 42/50 21
5.2 PEC Example 4.2 Assume the same plain tube heat exchanger design employed in PEC Example 4.1. For the present problem, the enhanced evaporator tube will be used to increase the compressor suction pressure, and hence reduce the compressor power. This calculation involves case FN-3 of Table 4.1. The enhanced tube operating conditions are the same as for PEC Example 4.1, except now the refrigerant temperature leaving the evaporator (T r2 ) is not fixed. 43/50 One may be tempted to fix the entering evaporator temperature (T r1 ) to the value of the plain tube design. However, this has little meaning, because the entering temperature inherently adjusts to meet the compressor suction pressure and the evaporator circuit pressure drop. A more direct approach is to specify the desired compressor suction pressure, which fixes T r2 and to calculate the circuit length of the enhanced tube that gives the required heat duty and the desired T r2. 44/50 22
The recommended approach for this problem is then to specify the desired T r2 and proceed to calculate the required evaporator circuit length. This calculation would proceed following the same procedures outlined for PEC Example 4.1. For a specified T r2 one calculates the circuit length (L) required to satisfy the specified evaporator load. One may repeat the calculations for several specified values of T r2 and plot a graph as indicated by Figure 4.5. This graph provides information to evaluate the trade-offs between evaporator cost and compressor power. 45/50 Figure 4.5 Illustration of the effects of enhanced evaporator tubes on the evaporator performance. 46/50 23
6. Conclusions PEC are defined for application to heat exchangers, for which at least one of the fluids is a two-phase fluid. Because pressure drop of the two-phase fluid may affect the mean temperature difference in the heat exchanger, the PEC equations must account for the effect of this situation. An assessment of two-phase heat exchanger applications shows that the reducing pumping power objective function used for single-phase flow is not generally applicable to the two-phase flow situation. 47/50 Three generic applications for two-phase heat exchangers are defined and provide a basis for establishing relevant objective functions and operating constraints. The 10 PEC cases defined for two-phase heat exchangers are closely related to the 12 single-phase PEC cases. 48/50 24
A new objective function is defined for two-phase exchangers and relates to the work done on or by the system in which the two-phase heat exchanger is installed. This objective function replaces the reduced pumping power objective function for single-phase flow. Two examples using the twophase PEC are presented. 49/50 Thank you for your attention! Prof. Min Zeng Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi'an Jiaotong University Xi'an, Shaanxi, 710049, P.R. China Email: zengmin@mail.xjtu.edu.cn http://gr.xjtu.edu.cn/web/zengmin Tel : +86-29-82665581 50/50 25