Granryd, E.

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Purdue UniversityPurdue e-PubsInternational Refrigeration and Air ConditioningConference School of Mechanical Engineering1998Power for Fans and Pumps in Heat Exchangers ofRefrigerating PlantsE. GranrydRoyal Institute of TechnologyFollow this and additional works at: http://docs.lib.purdue.edu/iraccThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/Herrick/Events/orderlit.htmlGranryd, E., "Power for Fans and Pumps in Heat Exchangers of Refrigerating Plants" (1998). International Refrigeration and AirConditioning Conference. Paper 410.http://docs.lib.purdue.edu/iracc/410Power for fans and pumps in heat exchangers of refrigerating plants Eric Granryd, professor, Abstract Div. of Applied Thermodynamics and Refrigeration, Royal Institute of Technology, KTH, Stockholm, Sweden. The energy consumption to operate auxiliaries such as fans and pumps in heat exchangers have a significant influence on the total energy demand for operating a refrigerating system. With a starting point in a simple entropy analysis a more practical approach is adopted for common cases of air coil fans in evaporators or condensers. Examples are given to illustrate how the power for evaporator or condenser fans will affect the capacity and total energy demand of refrigerating systems. It is shown that the two different criteria: -maximum of capacity or -minimum of energy demand (equivalent to maximum system COP) will give different optima for the power to be used in fans or pumps. Simple relations are derived for optimum power in fans or pumps for the two different criteria applicable for many general cases in refrigerating systems. Introduction The energy needed to operate fans or pumps is important when considering the total energy demand to operate a refrigerating plant or a heat pump. It is not unusual that the electric power of such auxiliaries is in the order of25% or more of the power to operate the compressor in a system. The purpose of this paper is to illustrate and exemplify this issue. Simple relations will be derived for optimum power in fans or pumps to reach criteria like maximum capacity or maximum system COP. Let us exemplify with the application of an evaporator. As a starting point let us assume that we have a given plant where we can adjust the fan speed - in practice perhaps by means of an inverter control. It is obvious that by using a high fan speed the evaporator will operate with smaller temperature differences between the inlet air and the refrigerant evaporating temperature than if low speed is used. This will decrease the temperature lift of the cycle and thus decrease the compressor work. However we will have to pay for the fan power and what is of interest is the sum of the power for the compressor and the fan. It is obvious that there must exist a certain fan power that we can call optimal from the point of view of energy consumption. Two different approaches will be used: First a treatment minimizing the entropy generation and, secondly, a more practically oriented way of treatment will be demonstrated. This treatment will concentrate on refrigerating applications. Slightly different relations will be obtained for heat pump operation. Space limitations prevents a treatment for that case but the practical result for minimum energy demand are quite similar. Relations between pumping power and temperature difference The pumping power will influence the temperature difference for a case with given geometry. A reasonable assumption is that the overall heat transfer coefficient is proportional to V"u where Vis the fluid flow and nu is an exponent, which in most cases has a value in the range of 0,3 to 0,6. The pressure drop can be set proportional to V"P where for turbulent flow np = 1,8. The pumping power, Ep, will hence (assuming constant pump efficiency) be proportional to V(np+lJ. Based on a reasoning indicated we can write the overall temperature difference, 8, as where 8=:: C·(EPFnE: nE:: _!!!!____ which hence for most cases will be in the order ofO,l to 0,2 np+] C is a constant. 195 (1) If we consider different operating conditions for a given geometry we can express the constant C based on the temperature difference Bo and pumping power Epo in a reference case ( "o "); thus C = Bo · { Epo FE . Entropy generation in forced flow heat exchange processes A thermodynamic approach for the analysis of the heat exchange in a heat exchanger can be used minimizing the entropy generation. (E.g. Bejan, 1996, give thorough discussion on methods. De Jong et al 1997 show an application.) A simple treatment can be made as follows: The "entropy generation" due to the temperature differences in a heat exchanger where the heat flow Q is transferred between two media of temperatures Ta and Tb is Q Q Q L1Shx =--- = --· (Ta- Tb} Ta Tb Ta·Tb which also can be written .JS~ =' SL.(} T2 where Tis the average temperature;=( ../Ta · Tb) and 8 (= Ta- Tb) is the temperature difference. However in a system with forced convection the pumping power will be dissipated (at o; temperature T) by friction and other irreversibilities so that, in total, the entropy generation is: Q Er &tot =' - • (} +- (2) T2 T Figure 1 shows the relation between the entropy generation and the pumping power for three examples with different reference temperature differences B0 • (The relation between (} and Er as given by equation 1 is used.) Q (/,) 6,E-04 5,E-04 Ill Figure 1. Entropy generation (.dStor /Q) for heat exchange for three cases with reference temperature differ-ences fJo = 5; 10 and 20 K. (For all cases nE =0, 15). a t:' ~ ~ 0,) t: 0,) 0> >.. Q, e ...... &i 4,E-04 i'--... 3,E-04 2,E-04 ._ 1,E-04 O,E+OO 0,001 Dt= 20"C ~Ill ~ ~ .... ~ ., 1'1 I ll 15"C / ~lll ,.,.. ..... / ..,..,.. ~ 0,01 0,1 Pumping power, E p/Q It is obvious that a certain pumping power will result in a minimum entropy generation. Given the assumptions made it can be shown that the following value of the pumping power will result in this minimum entropy generation: Er (} (Q )AS min=' nE. T (3) Notice that the larger the temperature difference is, the larger fan power should be used to minimize entropy generation. Example: Let us assume that the temperature difference in the operating point considered is (} =' l0°C, T = 273K and exponent nE= 0,15 then we fmd that Ep (Q)LlSmm:;: 0,15 · JO /273 := 0,005 This means that a fan power of only about 5 Watts per kW heat transferred should be spent!! Can we trust the results form the entropy approach also for practical applications? Let us also a more practical approach: 196 A practical approach Let us consider a complete refrigerating systemas shown in figure 2 (compare Granryd, 1973) We can assume that system exists, with given components. Let us also assume that we have a possibility to adjust the fan speed to any level we desire without other changes in the plant. In figure 3 a number of parameters are exemplified versus the air velocity in the evaporator fan coil for a given system. It is obvious that there is a certain velocity resulting in a maximum net cooling capacity of the plant and still another velocity that will give minimum energy demand. Which speed should we choose? It is obvious that we can have different criteria in mind: • Maximum cooling capacity with a given set of components • Lowest total energy demand for a given cooling load duty. (Jt;~' ~ ~ git d 10 P-p.t1 8t ~~ 8 +--rt---+---+---+----..::ot.-+--P------l ~ ~~ ~ ~ ~ s 6 +-----+-----+-::._..,.~--+~++---+ -10 Ecampr &:.:.:: -15 0 1 2 3 4 5 6 Q2N"'Q2-Ep2 Figure 2. Refrigerating system and schematic temperatures in evaporator and condenser Figure 3. Influence of air velocity in evaporator (Data: Wo = 2,5 m/s; Q2o= 10 kW; Ejo=0,5 kW; t100m= 0°C; t2o= -J0°C; t1= 30°C; !cq:::: 0,055; nE= 0,]5) Net cooling capacity. To derive the net useful cooling capacity Q2N we must, from the compressor cooling capacity Q2, deduct the fan power, Ep, which will be dissipated in the cooled space: Qm=Q2-EP (4) Often the cooling capacity for a vapor compression system can be set Q2 = Q2o • {1- kq • (!2- f2o}} (5) where o(Qz) . d" . h . h "thth . /cq = --- a parameter m 1catmg ow capac1ty c anges w1 e evaporanng temperature. o(tz) Often kq is in the order of 0,05 (5% increase in cooling capacity per degree increasing evaporating temperature), somewhat depending on the type of compressor and operating temperatures. Inserting t2= tRoom-B with B as given by eq. (1) we will (with Q2o and Epo denote the cooling capacity and fan power in the reference case in which we have temperature difference B 0 ) have: (6) 197 The net cooling capacity compared to that for the reference case (Q2IIQ2No) is exemplified in Figure 4 as a ftmction if the fan power in the evaporator. Three reference cases are shown with different temperature differences in the evaporator. Changes in the cooling capacity will for a practical case with given net cooling load be compensated by changes in the relative running time of the compressor (provided that we have an on·offtype capacity modulation). ~ ~ 1,0 0,8 ~ 0,6 0 .. ~ 0 0,4 "" -.E UJ 0,2 I I ... !-"" 5"C .... !_ I "" 10"C ,.~ llrt 15"C(. I 10" I 5"C< I Evap. L 10" -Temp. t2"'-. 15"C i I -~""' V"""'i-'~"" ~ ~ v,_ -1_ Q2NIQ2N / A / V/ltot/Q2~ vJi ~~-"' / 1/ L-o~ I -~ __. ... -0,0 0,001 0,010 0,100 Ef2/Q2o ~ ' ~ I 1\ \ ~ -.... -5 (.) -15 ° C\1 -25-1,000 Figure 4. Influence of evaporator fan power on net cooling capacity, Q1IIQ2No, and total energy, E10/Qm. (Example with tl = 30 "C; !Room= 0 °C; kq = 0,055; nE = 0,15; TJcr = 0,5. Also the evaporator temperature, tz, is indicated in the lower part of the diagram.) , Total energy demand For many operating conditions the plant is oversized and the user does not need maximum cooling capacity for the cooling duty. The plant may thus be operated on·off or with reduced capacity. The user wants naturally to operate his plant as efficiently as possible, saving energy and money. Let us examine how the pumping power influences the energy demand. The power to operate the plant is basically the power for the compressor and for the pumps or fans. We can, with reference to figure 2, write the total energy demand (denoting the compressor cycle performance COP2 = Q/Ecompr): Eror = [ C~~1 + Epz + Epl] (7) or, which is more interesting, the total energy demand in relation to net cooling capacity, QzN: Eror Qz [ 1 Epz Epl Q1] Q2N = QzN. COPz + Qz +0· Qz (8) The compressor COP2 of the system is influenced by the evaporating and condensing temperatures. Let us express this relation by introducing a total Carnot efficiency of the system, by which: where Tz (9) TJCt =total cycle Carnot efficiency (including refrigerant cycle as well as compressor efficiencies) T 2 = evaporating temperature = Tsource • 8 z Tl = condensing temperature = T.mk + e I 198 T.rource is the temperature in the heat source (or the room to be cooled) Tsmk is the temperature of the heat sink (ambient temperature or cooling water) (} 2 and (} 1 are the temperature differences in evaporator and COndenser. Figure 4 exemplifies the influence of the fan power on the net cooling capacity Q2NIQ2No as well as the total energy demand , £ 10/QJN, of a plant. Notice that the minimum of E10/Q2N (corresponding to maximum of an overall COP of the system) is achieved with considerably lower fan power than what is needed to reach maximum cooling capacity! As is seen the curves are quite flat around the optima It might in practice for simplicity be beneficial to choose a fan power somewhere between the two criteria. Simple relations can however be derived for the two optima as follows: Evaporator fan power for maximum net cooling capacity From the equations (6) and (1) it can be shown that the following very simple relation give the optimum evaporator fan power to reach maximum net cooling capacity (Ep2/ Q2)Qma< = nE2·kq ·Bz"" = C2Qmax·B2 •. (10) where 82 •· is the temperature difference prevailing for the given plant in conditions for the criteria Qmax· Example: With typical values nE2 ~ 0,15 and kq ~ 0,05 the result is: ( EpJ/ Q2}Qmw::::: 0,15 · 0,05 · (}/' := 0,0075 ·Bz"" and for design temperature differences: 82"" ~ this means: 5 0,038 10 0,075 It is thus beneficial to spend larger fan power the larger the temperature differences in the evaporator. Commercial evaporators are often equipped with fans in the order of 5 to 8 % of the nominal capacity. This seem to coincide quite well with the criteria for maximum capacity for cases where the temperature differences are about 10 °C. Fan power for minimum energy demand Evaporator side Based on the equations (1) and (8) to (9) it can be shown that the minimum energy demand for a given net cooling capacity will be obtained if the pumping power is chosen to satisfy the following relation: where ( Ep2 / QlN }E min S: C2E min• (}/ (11) 82 • is the temperature difference prevailing for the given plant in conditions for the criteria Emm· C2E mm =: [nE2 · rpl · T!] TI-T2·(1-TJCt) T2 lp2 is a factor which for practical cases can be set to := 1,25 (strictly a function of T1, T2; TJCt and kq, The interested reader is referred to Granryd, 1973) T1 and T2 are the condensing and evaporating temperatures, expressed in absolute temperature (K) 7Jc1 ~the total Carnot efficiency of the cycle Condenser side Minimum total energy demand for a given net cooling capacity is similarly achieved if the fan power is chosen to (12) where (},· is the condenser temperature difference for the given plant in conditions for the criteria Emin CJE mm =:: [nEJ· rpl ] TI- T2. (1-TJC!) lp1 is a factor (in analogy to lp2 ) which for practical cases can be set:= 1,05 199 Example: Let us use the following temperatures and data which can be representative for a typical practical example: Temperatures: T1 = 303K (= 30°C) T2 = 263K (= -l0°C); and data: kg= 0,055 1/K ne1 = 0,15 ne2 = 0,15 TJct = 0,5 The result is, for the different criteria: Minimum energy demand: Maximum net cooling capacity Evaporator side Condenser side: C/Emln;: 0,001 (lfOC) Assuming temperature differences in the evaporator and condenser in the order of I 0°C the result is (by equations 10, 11 and 12 respectively): (Ep/QJJEmin =: 0,012 or 1,2% (Ep/QJEmin=> O,Olor 1%. Discussion and some conclusions Many commercially sold evaporators have often, as mentioned, fan power installed in the range of 5 to 8% of the nominal capacity at a temperature difference of I 0 °C. This corresponds for many cases quite closely to the criterion of maximum cooling capacity but it is 6 to 8 times higher than what strictly would correspond to a maximum of system COP. The ratio of fan power for maximum capacity to that for maximum system COP corresponds roughly to what is achieved if the full fan speed (used in conditions where max. capacity is needed) would be cut in half to save energy in conditions when the capacity is large enough for the demand. For advanced fan speed control e.g. by inverters the relations derived here may be beneficial to use for an intelligent microprocessor control of the fan (or pump) speed at different conditions to reach optimal control for different criteria and in different operating conditions. As is seen from figure 4 the curves are quite flat around the optima and it might in practice for simplicity be beneficial to make a compromise between the two criteria and choose the fan power somewhere in between. Slightly different relations will be obtained for heat pump operation but the fmal result for minimum energy demand will be quite similar. Summary Relations for the fan power resulting in maximum net cooling capacity and minimum energy requirement for a given net cooling load can be summarized by the following relations: For maximum net cooling capacity the fan power in the evaporator should be chosen as: ( Ep2 I Q2 N )Q max = C2Q max· e·· and minimum energy demand for given net cooling capacity the fan power should be chosen as:: ( Ep I Q)e min = Ce min' e· where 8" and e· are temperature differences (in operating point with optimal fan power). C2g max:; 0,005 ~ 0,01 l/°C Ce min = 0,001 - 0,002 l/°C which is roughly applicable for both evaporators as well as condensers. References: Bejan, A.: "Entropy generation minimization", Textbook, CRC Press, 1996 DeJong, N.C.; Gentry, M.C.; Jacobi, A.M.: An entropy-Based Air-Side Heat Exchanger Perfomance Evaluation Method: Application to a Condenser., HVAC&R Research vol3, No 3 1997. Granryd, E.: "lnverkan av fl~effekt vid tOra.ngare och kondensor pa en kylanlaggnings kyleffekt och totala energibehov" (Influence of fan power in evaporators and condensers on the total capacity and energy requirement of a refrigeranting plant); Scandinavian Refrigeration, No 4, p124- 132, 1973 (in Swedish). 200 

Power for Fans and Pumps in Heat Exchangers of Refrigerating Plants

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Power for Fans and Pumps in Heat Exchangers of Refrigerating Plants

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