ASHRAE LV-11-C005-2011 Capacity Control of Air Coils for Heating and Cooling Transfer Functions Drive Power and System Design.pdf

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1、g51g72g85g3g41g68g75g79g72g81g3g76g86g3g68g3g83g85g82g73g72g86g86g82g85g3g76g81g3g87g75g72g3g39g72g83g68g85g87g80g72g81g87g3g82g73g3g40g81g72g85g74g92g3g68g81g71g3g40g81g89g76g85g82g81g80g72g81g87g15g3g38g75g68g79g80g72g85g86g3g56g81g76g89g72g85g86g76g87g92g3g82g73g3g55g72g70g75g81g82g79g82g74g92g15

2、g3g42g82g87g75g72g81g69g88g85g74g15g3g54g90g72g71g72g81g17g3g3g38g68g85g82g79g76g81g72g3g3g48g68g85g78g88g86g86g82g81g3g3g76g86g3g68g3g85g72g86g72g68g85g70g75g3g86g87g88g71g72g81g87g3g76g81g3g87g75g72g3g86g68g80g72g3g71g72g83g68g85g87g80g72g81g87g17g3 g3 g3g38g68g83g68g70g76g87g92g3g38g82g81g87g85g8

3、2g79g3g82g73g3g36g76g85g3g38g82g76g79g86g3g73g82g85g3g43g72g68g87g76g81g74g3g68g81g71g3g38g82g82g79g76g81g74g29g3g3g55g85g68g81g86g73g72g85g3g41g88g81g70g87g76g82g81g86g15g3g39g85g76g89g72g3g3g3g3g3g51g82g90g72g85g3g68g81g71g3g54g92g86g87g72g80g3g39g72g86g76g74g81g3g3g51g72g85g3g41g68g75g79g112g81g3

4、g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3g3 g38g68g85g82g79g76g81g72g3g48g68g85g78g88g86g86g82g81g3g3 g3 g3Member ASHRAE Research Student g36g37g54g55g53g36g38g55g3Liquid-to-air coils used as air heating system coils and air system cooling coils for air-con

5、ditioning, refrigeration etc. rarely use their design capacity. The capacity must therefore be reduced accordingly, traditionally by means of on-off operation or by means of control valves. Draw-backs of traditional control are excessive pressure drop and drive power to pumps due to high flows as we

6、ll as the need for balancing valves and control valves with authority. There are, however, possibilities to substantially reduce the drive energy of pumps and fans for air coils, e.g. by replacing valve and damper control by direct control of decentralized pumps and fans. This may achieve better con

7、trol at a lower cost while using substantially less drive energy. This paper includes basic analysis of heat transfer and control methods to study how coil design affects the transfer function of an air coil on capacity turn-down. The analysis indicates that direct flow control, using variable-speed

8、 pumps, may require only a fraction of the drive power needed by traditional valve control. Furthermore, system designs for low flow rate and pressure drop also provide opportunities for new types of laminar-flow coil designs. Results show that the transfer functions of alternative control methods f

9、or the capacity and outlet temperatures of air coils can be written as simple functions of the controlling variable (supply temperature, inlet temperature or coil liquid flow rate). The transfer functions may be tailored to specific needs by changing design parameters such as the design values of ai

10、r and liquid flow rate and the heat transfer characteristics and heat transfer areas of the respective air and liquid sides. Also, the paper provides an example of alternative system design and control strategy. g20g3g3g44g49g55g53g50g39g56g38g55g44g50g49g3There is an abundance of liquid-to-air coil

11、s used as air heaters or air coolers for air conditioning, refrigeration etc. They are sometimes designed for variable air flow, as in VAV air-conditioning systems, and sometimes with constant air flow as in supermarket display cabinets. In other applications, such as hydronic radiators for heating

12、or chilled beams for cooling, the air-side relies on natural convection for heat transfer. The design capacity of an air coil is rarely used and must therefore be reduced accordingly, traditionally by means of on-off operation or control valves. Shunt groups are often used with constant liquid flow

13、in the coil irrespective of demand. Traditional control will result in excessive pressure drop due to high flows and the need for balancing valves and control valves with authority. The result is excessive drive power to the pumps, which is further aggravated by the traditionally low efficiency of s

14、mall pumps. In this paper we will look at alternative ways of control of the coil capacity and how these affect the transfer function (controlled variable/controlling variable), pressure drop and pumping power of the system. The aim of the discussion is to show the advantages of direct flow control

15、by means of decentralized pumps1, 7. The advantages are quantified by an example with fan-coil units for heating and cooling as analyzed in a report by Fahln5. LV-11-C00540 ASHRAE Transactions2011. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Publ

16、ished in ASHRAE Transactions, Volume 117, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAES prior written permission.g3g21 g38g36g51g36g38g44g55g60g3g38g50g49g55g53g50g47g3g50g41g3g36g44g53g3g38g50g4

17、4g47g54g3The thermal capacity of an air coil can be calculated by means of the g72-NTU method and specified inlet air and liquid (brine) temperatures to the coil (ta1and tb1). The general expression will be: g11g1211min abattCQ g16g152g152g32g6g6g72W (1) g21g17g20g3g38g82g81g87g85g82g79g3g83g85g76g8

18、1g70g76g83g79g72g86g3Applying logarithmic differentiation2to equation (1), the sensitivity of the thermal capacity to changes in the respective parameters can be estimated, g11g12g11g121111minminababaattttCCQQg16g16g39g14g39g14g39g32g39g6g6g6g6g72g72- (2) where ),(tuNRg72g72 g32 is the effectiveness

19、 of the coil, maxmin/ CCRg6g6g32 is the ratio of the minimum and maximum heat capacity flow rates, and min/ CAUNtug6g152g32 . In high-flow systems baCCg6g6g100 , and then apaacVC,ming152g152g32 g85g6g6. This type of sensitivity analysis is helpful in formulating linearized transfer functions in cont

20、rol system design. It is straightforward also to differentiate ),(baCCg6g6g72g72 g32 . Equation (2) also indicates the main possibilities of capacity control: g3 Primary side (liquid) supply temperature: sbt,(with no mixing arrangement, sbbtt,1g32; see 3.1 and 3.2) g3 Primary side (liquid) inlet tem

21、perature: 1bt (with mixing, 2,1)/1()/(baccvsbaccvbtVVtVVt g152g16g14g152g32g6g6g6g6) g3 Primary side (liquid) flow rate: bpbbbcVC,g152g152g32 g85g6g6(sbbtt,1g32= constant) g3 Secondary side (air) flow rate: apaaacVC,g152g152g32 g85g6g6(1at = constant) g21g17g21g3g3 g39g72g86g76g74g81g68g87g76g82g81g

22、86g3g68g81g71g3g68g86g86g88g80g83g87g76g82g81g86g3The discussion presumes a liquid-to-air coil for heating or cooling of air. This means that thermal capacity is positive when the air temperature is raised and negative when reduced. Also, losses from the coil are neglected, i.e. baQQg6g6g16g32 . Ind

23、ex “a” is used for air and “b” for the liquid as many of the original applications described by Fahln3, 4, 6were on refrigeration with a single-phase brine (= b). In the analysis of transfer functions, Fahln3has motivated the use of arithmetic instead of logarithmic mean temperature differences (g84

24、 is used for temperature difference between two media and tg39 for temperature change of one medium). Figure 1 illustrates the system of designations. Mean temperature differences: Possible simplifications gmmg84g84 g124if 215 g84g84 g152g31and ammg84g84 g124 if 213 g84g84 g152g31 with 2/)(21g84g84g

25、84 g14g32am, 21g84g84g84 g152g32gmand g11g122121/ln/)( g84g84g84g84g84 g16g32lmg55g72g80g83g72g85g68g87g88g85g72g3g55g3g43g72g68g87g3g87g85g68g81g86g73g72g85g3g68g85g72g68g3g36g3g39Tg69g3g39Tg68g3g84g20g3g84g21g3g84g80g3g68g3g69g3g20g3g20g3g21g3g21g3g51g85g76g80g68g85g92g3g54g72g70g82g81g71g68g85g92

26、g3Figure 1 Definitions and designations of temperatures (t for celsius and T for kelvin), temperature changes of one medium (g39 t or g39 T), temperature differences between two media (g84 ), type of media (a = air, b = brine, liquid) and location (1 = inlet, 2 = outlet). 2011 ASHRAE 41To compare al

27、ternative solutions Fahln3has introduced a non-dimensional controlling variable and a non-dimensional controlled variable (the controlled variable is usually a temperature or capacity): Controlling variable: %)100(%)(valuedesignxvalueactualxbg32; Controlled variable: %)100(%)(capacitydesignycapacity

28、actualyag32; Fahln has also introduced a base load for the pump consisting of the pressure drop of the basic pipe work and the coil. This is the minimum pressure drop of the system used as a benchmark. Additional pressure drops for control purposes will increase the drive power in relation to the be

29、nchmark. g22g3 g55g53g36g49g54g41g40g53g3g41g56g49g38g55g44g50g49g54g3g50g41g3g36g44g53g3g38g50g44g47g54g3Due to varying loads etc. the demand situation will differ between the various rooms of a building. The supply temperature should be modulated to make the deciding terminal unit operate at its d

30、esign flow. All other units will then operate at reduced capacity with the given supply temperature. Variable capacity can be achieved by means of temperature control (supply or mixing) and/or flow control as indicated in 2.1. g22g17g20g3 g54g88g83g83g79g92g3g87g72g80g83g72g85g68g87g88g85g72g3g70g82

31、g81g87g85g82g79g3From an efficiency perspective, supply temperature should never be higher than required for heating or lower than required for cooling. In heating systems, it is common to have an outdoor temperature related feed-forward control. This, however, is less common in cooling applications

32、 where a fixed temperature, required only at the design load, is often used. From equation (2) we see that the third term provides the relative change of capacity as a function of the relative change in temperature difference. Hence, according to Fahln3, the transfer function becomes: baxy g32 - wit

33、h dasbasbbttttx)()(1,1,g16g16g32- and daaaQQy,g6g6g32- (1) Supply temperature control is linear and direct. It should always be included as a primary control method of heating as well as cooling coils. Also, there is no pressure drop penalty involved in supply temperature control. g22g17g21g3 g51g85

34、g76g80g68g85g92g15g3g79g76g84g88g76g71g16g86g76g71g72g3g76g81g79g72g87g3g87g72g80g83g72g85g68g87g88g85g72g3g70g82g81g87g85g82g79g3Figure 2 illustrates the principle of controlling capacity by means of a variable liquid-side inlet temperature to the coil. This can be achieved by the illustrated arran

35、gement, i.e. a three-way valve and constant supply flow, or by using a two-way valve and variable supply flow. Trschel and Fahln3provide expressions for how capacity varies with the flow rate through the control valve CV. As the coil flow is constant, the brine-side temperature efficiency bg75 will

36、be a constant from the coil design. The supply temperature (tb,s) and liquid flow through the coil are also constant. Variable inlet temperature Transfer function: g11g12g11g12bbbbaxxxyg14g16g152g321g75Pumping power: g184g184g185g183g168g168g169g167g39g39g152g16g14g39g39g14g39g39g152g16g152g16g32bas

37、ebvbasebvbaseacdbasetotppppppWW21,)1(111g69g69g69g6g6g38g43g57g3g51g20 g51g21g3g37g57g20g3g16aVg6g39g83g36g38g3g39g83g37g57g21g3g39g83g37g57g20g39g83g51g21g3g38g571bVg6g3g37g57g21g3tb1tb2tb,rtb,ssbV,g6g36g38g3g54g88g83g83g79g92g3g86g92g86g87g72g80g3Figure 2 Capacity control by means of a variable in

38、let temperature (tb1). The transfer function shows that although capacity is a linear function of the inlet temperature, it is certainly not a linear function of flow rate. However, the control valve flow is the controlling variable and the lower bg75 is the more non-42 ASHRAE Transactionslinear wil

39、l be the transfer function. The pumping power of this particular configuration will remain constant irrespective of the thermal heat transfer and it will be much larger than the required base power (pipe system plus coil). Assuming a control authority g69= 0.5, we see that the drive power at the des

40、ign condition will be typically more than twice the base value (depending on how much balancing that is required). g22g17g22g3 g51g85g76g80g68g85g92g15g3g79g76g84g88g76g71g16g86g76g71g72g3g73g79g82g90g3g85g68g87g72g3g70g82g81g87g85g82g79g3Fahln3has derived a relation between the controlling variable

41、 xb(liquid flow ratio) and the controlled variable ya(coil capacity ratio). The transfer function )(baaxyy g32 can be shaped to conform to desired characteristics by means of the overall size, the ratio between the liquid and air side heat transfer capacity and the air and liquid flow rates accordin

42、g to: g11g12g11g126565)(1)(dbdbbbddbaKxKxFxxKKxFyg14g152g152g14g152g14g14g152g32- with mbddmbbxKKxxFg152g14g14g152g321111)(and dbbbVVx,g6g6g32- (4) The design constants Kd1to Kd6in the relations above are given by (m is the flow related heat transfer exponent):Design heat transfer capacity Ratio of

43、heat transfer capacity on the liquid side to that of the air side: dadadbdbdAAK,1g152g152g32g68g68-; Design air flow rate (a = air) Air temperature change, i.e. required flow rate, at the design condition: dadtK,2g39g32K; Design liquid flow rate (b = brine) Liquid temperature change, i.e. required f

44、low rate, at the design condition: dbdtK,3g39g16g32K; Design heat exchanger size Mean temperature difference, i.e. required heat exchanger size, at the design condition: damdK,4g84g32K; Facilitating constants Constants introduced to simplify the relation for ya: 425dddKKK g32- and 436dddKKK g32-. Fl

45、ow control can be realized by means of on-off operation (not discussed in this paper) or continuous variation using either a) a central pump (CP) and valve control (see figure 3) or b) a decentralized pump (DP) with continuous VSD control (see figure 4). Continuous flow control will have a non-linea

46、r transfer function. However, just as in the case with inlet temperature control, it is possible to tune the characteristics by means of suitable coil design. With a), see figure 3, the current practice is to operate the pump P1 with VSD control of the supply pressure. If this is kept constant at th

47、e design level, then pumping power will decrease linearly with flow rate but faster in relation to a capacity reduction (c.f. figure 5). With g69= 0.5 the design pump power will be more than twice the benchmark value. (a) Flow control using a two-way valve Transfer function: g11g12g11g126565)(1)(dbd

48、bbbddbaKxKxFxxKKxFyg14g152g152g14g152g14g14g152g32Pumping power (constant pressure control): g184g184g185g183g168g168g169g167g184g184g185g183g168g168g169g167g39g39g14g152g184g184g185g183g168g168g169g167g16g152g32dbasebvbdbasetotppxWW111,g69g6g6g38g57g3g37g57g3g51g20g16aVg6g39g83g36g38g3g39g83g38g57g

49、3g39g83g51g201bVg6g3tb,rtb,stb1tb2g39g83g37g57g3g36g38g3g54g88g83g83g79g92g3g86g92g86g87g72g80g3Figure 3 Capacity control by means of a variable coil flow using a two-way valve. 2011 ASHRAE 43In the case of b), decentralized pump control (DP-VSD), see figure 4, pumping power will equal the benchmark value at the design capacity. With reduced flow and reduced capacity, power will drop very quickly (c.f. figure 5). Note that no balancing or control valves are required in this case. (b) Flow control using a decentralized VSD pu