MAIN PAGE TABLE OF CONTENTS 4222 Analysis of Transfer Pumping Interfaces for Stratified Chilled Water Thermal Storage Systems—Part 1: Model Development William P. Bahnfleth, Ph.D., P.E. Christopher G. Kirchner, P.E. Member ASHRAE Associate Member ASHRAE ABSTRACT This paper describes methods for modeling the performance of transfer pumping interfaces used to connect open chilled water thermal energy storage tanks to closed chilled water systems. Indirect (heat exchanger) interfaces and direct interfaces are considered. Treatment of direct interfaces includes the use of energy recovery with centrifugal pumps serving as hydraulic turbines. Of the seven interface types considered, only three (constant-speed direct, constant-speed direct with energy recovery, and constant-speed indirect) have been previously discussed in the literature. Characteristics of interfaces with variable-speed pumping and a novel reversible direct interface with energy recovery are described quantitatively for the first time. Models of interface components are derived and assembled to simulate the performance of interfaces operating at both constant and variable speed. Representative examples of performance for moderate and large adverse static pressure differentials are presented and discussed. It is shown that the power vs. flow characteristics of the interface types investigated differ greatly and that these differences are affected by the value of the static pressure differential at the interface. The models presented in this paper are of practical value in the design of pumping interfaces for all types of open systems. INTRODUCTION Stratified chilled water thermal storage reduces peak cooling plant chiller capacity requirements, generates operating cost savings, and improves the operational flexibility of large district and campus chilled water systems. A critical feature of a chilled water thermal storage system is the interface between the storage tank, typically an open vessel, and the closed, pressurized chilled water system it serves. The location of the storage tank can create a significant adverse static pressure differential, which must be overcome by transfer pumps. The energy cost of pumping against a static pressure differential may substantially reduce thermal storage operating cost savings. Several options for interface design, with varying ranges of capital cost and energy consumption, are available to the design engineer. In order to select the best method for an application, modeling of interface performance is essential. This paper surveys transfer pumping interface types, some of which have not been documented previously, and describes practical techniques for modeling the performance of interfaces. Modeled power consumption characteristics of a variety of interface types are illustrated under low and high fixed head conditions. The use of these models in economic comparisons of interface alternatives is described in part 2 of this paper (Bahnfleth and Kirchner 1998). Transfer pumping interfaces are also found in other storage applications with open tanks including ice harvesters, containerized ice systems, and external melt ice-on-pipe systems. The analysis described in this paper is adaptable to these systems as well. TRANSFER PUMPING INTERFACE TYPES Transfer pumping interfaces control pressure, modulate flow rate, and regulate flow direction in chilled water storage systems. Interfaces can be divided into two classes: indirect and direct. These classifications indicate the method employed by the pumping interface to control pressure differential and transfer thermal energy between the open tank and the closed system. An indirect pumping (IP) interface physically isolates the water stored in the tank from the rest of the William P. Bahnfleth is an assistant professor in the Department of Architectural Engineering at Penn State University, University Park, Pa. Christopher G. Kirchner is a project mechanical engineer at SHG, Inc., Detroit, Mich. THIS PREPRINT IS FOR DISCUSSION PURPOSES ONLY, FOR INCLUSION IN ASHRAE TRANSACTIONS 1999, V. 105, Pt. 1. Not to be reprinted in whole or in part without written permission of the American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., 1791 Tullie Circle, NE, Atlanta, GA 30329. Opinions, findings, conclusions, or recommendations expressed in this paper are those of the author(s) and do not necessarily reflect the views of ASHRAE. Written questions and comments regarding this paper should be received at ASHRAE no later than February 13, 1999. BACK TO PAGE ONE chilled water system by use of a heat exchanger. A direct pumping (DP) interface permits the flow of water between the storage tank and chilled water system. Direct interfaces may be further classified on the basis of whether they incorporate hydraulic energy recovery. Direct interfaces with energy recovery may be unidirectional or reversible. Each of these types and subtypes is described below. Indirect Interface Indirect pumping in chilled water thermal energy storage (TES) systems provides hydraulic isolation from high staticpressure loads that occur in high-rise buildings and in district cooling systems with large variations in site elevation. A heat exchanger placed between tank and system creates independent hydraulic circuits, each with its own pumps, piping, and controls (Figure 1). This arrangement minimizes pressure disturbances, simplifies system design, reduces pump motor size, and eliminates the need for pressure accommodation between the storage tank and chilled water system. It also eliminates the pump energy consumption that would be needed to overcome the static pressure differential between the tank and system. The design temperature differential between the cool inlet and warm outlet temperatures of the interface heat exchanger is typically no less than 2°F (1.1°C). This temperature differential imposes thermodynamic penalties on the storage system and chilled water system that detract from the energy savings created by hydraulic separation and may significantly increase capital cost relative to a system having a direct interface. Direct Interface As illustrated in Figure 2, direct pumping allows chilled water from the thermal storage tank to be pumped directly into the chilled water supply system while return water flows from the system to the tank. Transfer pumps boost the pressure of water leaving the tank to match the system level, and pressuresustaining valves (PSVs) throttle away excess pressure of water flowing into the tank. A direct interface maximizes the temperature differential across the storage tank by utilizing the lowest supply and highest return temperatures possible. This results in higher storage density and smaller tank size than are possible when an indirect interface is used. The first cost of a direct interface is less than that of an indirect interface because it requires less equipment, fewer controls, and fewer reversing valves. However, when the static pressure differential becomes large, the economic impact of factors such as pump size, PSV size, PSV reliability, and pumping energy can become significant (Gatley and Mackie 1995). In extreme cases, the energy required to pump against a static differential may account for 20% or more of the cost to produce and deliver a unit of thermal energy from storage (Bahnfleth 1995). Figure 1 Indirect pumping interface. BACK TO PAGE ONE Figure 2 Direct pumping interface. Direct Interface with Energy Recovery Direct pumping with hydraulic turbine energy recovery (DPT) is an alternative to indirect pumping for high static pressure applications. In a DPT interface, an energy recovery turbine (ERT) in the return line to the tank is connected to a transfer pump through a double extended motor shaft (Figure 3). The turbine operates in series with a pressure-sustaining valve to absorb excess system pressure as water flows back to the tank, converting energy associated with static pressure differential into shaft power that directly reduces pump motor input power. This allows the storage tank to be connected directly to the chilled water system without paying the full energy penalty of an adverse static pressure differential. As flow through the turbine decreases from its design value, the fraction of the available energy recovered decreases. When it can no longer absorb energy from the system, a clutch disengages the turbine to prevent it from becoming an additional load on the motor. In typical applications, a turbine recovers 35% to 50% of the peak pump motor power (Bahnfleth 1995; Taylor 1989). Although relatively uncommon, DPT interfaces have been successfully applied in several high-rise buildings and district energy installations (Bahnfleth 1995; Taylor 1989; Tackett 1988) Reversible Direct Interface with Energy Recovery Reversible direct pumping with hydraulic turbine energy recovery (RDPT) is a special case of the DPT interface. Instead of reversing flow through the tank by changing the position of the flow control valves, the reversible interface changes flow direction by reversing the rotation of the pump/turbine set (Figure 4). The charge mode pump becomes the discharge mode turbine and vice versa. A voltage inverter changes the direction of rotation of the motor driving the set to reverse the flow direction. A variable-speed RDPT transfer pumping system is currently in use at a semiconductor manufacturing facility (Fiorino 1994). The turbines in this system unload each motor by approximately 40%. In an RDPT interface, each pump/turbine must be identical. Selection for pump performance takes precedence over turbine performance with the consequence that turbine performance is less than ideal. Interface Pump, Turbine, and System Curves Transfer pumps must overcome the sum of the static pressure differential and frictional resistance to flow imposed on them. In an indirect interface, the transfer pumps on both sides of the heat exchanger work only against frictional resistances. In a direct interface, transfer pumps must overcome adverse static pressure differential plus the frictional resistance of the path from the outlet diffuser to the point of connection with the chilled water system. The path from the other point of connection to the inlet diffuser is not part of the system for the direct interface transfer pump. However, for interfaces with energy recovery, this return path is the system for the hydraulic turbine and affects the pressure available to it. Figure 5 shows typical shapes of pump and turbine characteristic curves and system curves for a direct interface. The pump curve is taken from a manufacturer’s data. The turbine characteristic was generated using performance prediction methods described in the following section. Pump and turbine system curves in a direct interface with energy recovery typically mirror one another because static pressure is identical and frictional pressure drop is similar. The pump pressure differential required increases as flow increases, while the turbine available pressure differential decreases. Pump and turbine pressure-flow characteristics also have a qualitatively BACK TO PAGE ONE Figure 3 Direct pumping interface with hydraulic energy recovery turbine. Figure 4 Reversible direct pumping interface. BACK TO PAGE ONE Figure 5 Typical pump, turbine, and system curves for a direct interface. mirror-image relationship. The pump pressure differential falls with increasing flow, while the turbine pressure differential absorbed increases. When a turbine operates at constant speed, it will generally consume less pressure differential than is available from the system, as shown in Figure 5. This excess system head must be throttled away by a PSV, as also indicated in the figure. This is analogous to the behavior of a constantspeed pump under variable-flow conditions, for which excess pump head must be wasted by a control valve. Sharma 1985; Stepanoff 1957). The pump affinity laws are valid for centrifugal pumps operating as turbines and can be used to predict performance once a point on the turbine curve is known (Garay 1993; Ingersoll 1976). The literature describes several methods for estimating the BEP performance of centrifugal pumps operating as turbines on the basis of pump performance characteristics (Buse 1981; Sharma 1985; Stepanoff 1957). Two distinct approaches have been used, which for convenience will be identified as the “best efficiency point method” and the “specific speed method.” TURBINE PERFORMANCE OF REVERSE RUNNING CENTRIFUGAL PUMPS Best Efficiency Point Method Specially built hydraulic turbines are prohibitively expensive for thermal storage applications. However, standard centrifugal pumps running backwards have acceptable turbine characteristics and are substantially less expensive. Reverse running pumps have been used successfully as ERTs in cool storage DPT and RDPT interfaces serving high-rise buildings and district energy systems (Bahnfleth 1995; Fiorino 1994; Tackett 1988; Taylor 1989). The fundamental assumption of the best efficiency point method is that the BEP efficiencies of a centrifugal pump operating as a turbine (ηt,BEP) and as a pump (ηp,BEP) are equal (Sharma 1985; Stepanoff 1957). Taking this assumption as a starting point, Sharma developed the following relations for converting pump BEP volume flow rate (Qp,BEP) and pressure (Hp,BEP) to the corresponding values of turbine BEP flow rate (Qt,BEP) and pressure (Ht,BEP): The concept of using reverse-running centrifugal pumps as turbines is well documented in the literature (Buse 1981; Garay 1993; Nelik and Cooper 1984; Sharma 1985; Stepanoff 1957). Testing has shown that a properly selected centrifugal pump, when acting as a turbine, has a peak hydraulic efficiency within a few percentage points of its best performance as a pump (Buse 1981; Ingersoll Rand 1976). This difference is typically 2% to 3% at the best efficiency point (BEP). For practical purposes, turbine and pump peak efficiency can be considered equal, according to several sources (Garay 1993; Q t , BEP = H t , BEP = Q p , BEP η p , BEP 0 .8 H p , BEP η p , BEP 1 .2 ≡ C q ⋅ Q p , BEP (1) ≡ C h ⋅ H p , BEP (2) where Cq and Ch are conversion factors relating turbine BEP flow and pressure to pump BEP values of the same parameters. BACK TO PAGE ONE Specific Speed Method An alternative approach to the BEP method is based on conversion factors that are functions of turbine specific speed (Buse 1981). Turbine specific speed is a similarity parameter combining turbine BEP speed, flow rate, and pressure: Ns = N BEP × QBEP H BEP 0.75 (3) where Ns is specific speed, NBEP is BEP speed, QBEP is BEP flow rate, and H B E P is BEP pressure. BEP speed is expressed in rpm. In the I-P system, flow has units of gpm and pressure is given in feet of head. In the SI system, flow is given in m 3 /s and pressure is given in meters of head. Consequently, the numerical value of Ns in I-P units is 51.65 times the value in SI units. Buse presents data on values of conversion factors Cq, Ch, and Ce, which relate, respectively, turbine BEP flow rate (Qt,BEP), pressure (Ht,BEP), and efficiency (ηt,BEP) to pump BEP values. Given a desired turbine selection point (flow rate and pressure), these conversion factors permit rapid calculation of required pump characteristics: Q p , BEP = Qt , BEP H p , BEP = H t , BEP Cq Ch η t , BEP = η p , BEP ⋅ C e (4) (5) (6) According to Buse, Cq and Ch vary from 2.2 to 1.1 and Ce varies from 0.92 to 0.99 over a specific speed range of 500 to 2800 (9.7 to 54.2). Considering these values, it is evident that (1) peak turbine efficiency is less than pump peak efficiency and occurs at a higher flow rate, and (2) the pressure drop in turbine duty is greater than the pressure developed by the pump. Consequently, the maximum BHP is higher in turbine duty. Comparison of BEP Performance Models Williams (1994) compared the BEP performance predictions of eight pump-to-turbine prediction methods to the measured turbine performance of 35 different types of pumps. Predicted and measured BEP values for turbine flow rate and head were compared via a prediction coefficient having values varying between zero and one when the sum of square errors in predicted flow and head is within acceptable tolerances. Prediction coefficient values greater than one indicate unacceptably large errors and a value of zero indicates a perfect prediction. Sharma’s best efficiency point method yielded the lowest average prediction coefficient for all of the pumps tested, and only 20% of tested pumps had prediction coefficients greater than one. In contrast, 81% of predictions using the least accurate method had prediction coefficients greater than one. Based on Williams’ results, Sharma’s best efficiency point method is the best available procedure for preliminary determination of turbine BEP performance from peak pump efficiency and has acceptable accuracy for that purpose. However, both Williams (1994) and Buse (1981) emphasize that testing should be undertaken to determine actual turbine performance once a preliminary selection has been made. The specific speed method has been utilized in the design of several successful DPT and RPDT systems for chilled water TES applications (Bahnfleth 1995; Tackett 1988; Taylor 1989). It has proved reasonably reliable for the selection and performance prediction of centrifugal pumps used as turbines when the manufacturer’s conversion factors are used. However, manufacturers frequently consider conversion factors proprietary, which makes the independent application and testing of this method difficult. For this reason, the specific speed method was not tested by Williams. Turbine Performance Curves The best efficiency point and specific speed methods predict turbine performance only at the best efficiency point. Other means must be employed to predict turbine behavior at other operating points. Buse (1981) published representative curves showing constant-speed turbine pressure and efficiency ratio variation as a function of percentage of turbine BEP flow rate for a range of specific speeds. The shape of the performance curve for a turbine can be developed from these curves given the turbine specific speed and BEP performance estimated by the BEP or specific speed method (Buse 1981). Typical constant-speed pressure and efficiency characteristics for a centrifugal pump (from manufacturer’s data) and the corresponding turbine performance curves generated using Sharma’s best efficiency point method and Buse’s curves are shown in Figure 6. The best efficiency point for the pump is 2070 gpm (131 L/s) with a head of 217 ft (67 m) of water, at which it attains a hydraulic efficiency of 90%. The corresponding BEP for the pump operating as a turbine determined by using the best efficiency point method is 2252 gpm (142 L/s) and 246 ft (75 m) of water, at which efficiency is also assumed to be 90%. These curves can be generalized to the variable-speed case through the application of affinity laws, as is described in the next section. TRANSFER PUMPING INTERFACE COMPONENT MODELS Heat Exchanger A simple heat exchanger model can be developed using LMTD analysis. Pure counterflow has been assumed in the example presented here; other flow arrangements can be modeled using correction functions available in the literature. BACK TO PAGE ONE Figure 6 Predicted turbine performance of a centrifugal pump: BEP method. In the LMTD formulation, the load, q, on the heat exchanger, is given by q = U ⋅ A ⋅ LMTD (7) where U is the overall heat transfer coefficient, A is the heat exchange area of the heat exchanger, and LMTD is the log mean temperature difference. The LMTD is defined as follows: ( T hi – T co ) – ( T ho – T ci ) LMTD = ----------------------------------------------------------T hi – T co ln --------------------- T ho – T ci (8) where Tci and Tco are the cold fluid inlet and outlet temperatures, respectively, and Thi and Tho are the hot fluid inlet and outlet temperatures. Inlet and outlet temperatures on the storage tank side of the heat exchanger and inlet temperature on the system side were assumed to be known and constant. In practice, this could be achieved by controlling flow rate to regulate the leaving temperature. On the system side of the heat exchanger, the inlet temperature was assumed to be known and constant for both charge and discharge modes. The charge and discharge outlet temperatures on the system side of the heat exchanger do not remain constant under varying loads and must, therefore, be calculated. Design temperatures representative of conditions in actual chilled water storage systems with indirect interfaces are shown in Figure 7. Of particular significance is the design heat exchanger temperature differential of 2°F (1.1°C), which reduces the maximum temperature differential across the storage tank by 4°F (2.2°C) over a complete cycle. This reduces storage density by nearly 20% for the assumed system charge and return temperatures and commensurately increases the size of the tank and peak flow rate for a given capacity. The unknown system-side charge and discharge outlet temperatures can be expressed in terms of the fraction of full design load (φ). As a consequence of Equation 7, φ= q U ⋅ LMTD = q d U d ⋅ LMTD d (9) where qd, Ud, and LMTDd are the load, overall heat transfer coefficient, and log mean temperature difference at design conditions, respectively. In general, the overall heat transfer coefficient decreases as flow decreases because of reductions in convective heat transfer coefficients. In some instances, however, it is an acceptable approximation to assume that U is constant. In an indirect transfer pumping interface, heat exchanger performance determines flow rate, which governs pumping power. In the present study, temperature differential is specified on one side of the heat exchanger; therefore, flow variation due to variation in U will affect only the other side. Additionally, the indirect interfaces considered in this study were assumed to have four heat exchangers in parallel, and these heat exchangers were staged to maintain the highest possible velocity for any operating configuration. Although the maximum error in flow on one side of the heat exchanger could exceed 10%, the average error in total pumping power BACK TO PAGE ONE Figure 7 Heat exchanger parameters: (a) discharge cycle, and (b) charge cycle. for both sides of the heat exchanger was estimated to be less than 5%. On this basis, it was assumed that U was constant. For constant U, it follows from Equation 9 that the LMTD under an arbitrary loading is φ (LMTDd). Forms of Equation 9 particular to the charge and discharge modes can be solved for their respective system-side outlet temperatures. For the charge mode, (10) ( T ho – T ci ) – ( ( T co – T hi ) – ( T ci – T ho ) ) T co = T hi – EXP ln ------------------------------------------------------------------------------------------------φ ⋅ ( LMTD d ) and for discharge mode, (11) ( T hi – T co ) – ( ( T hi – T co ) – ( T ho – T ci ) ) T ho = T ci – EXP ln ------------------------------------------------------------------------------------------------φ ⋅ ( LMTD d ) Equation 10 is implicit in the unknown Tco and Equation 11 is similarly implicit in Tho with all other quantities being known for a specified value of the part-load fraction. These equations are easily solved by successive substitution or other iterative techniques. Figure 8 shows outlet charge and discharge temperatures as a function of the load fraction (φ) obtained by solving Equations 10 and 11 for the design condi tions shown in Figure 7. If all temperatures other than the system-side outlet are assumed constant, it is convenient to use polynomial approximations of the functions shown in Figure 8 in place of repeated iterative solutions of Equations 10 and 11 in the indirect interface model. For example, for charging, Tco = W1φ 3 + W 2φ 2 + W 3φ + W 4 (12) where the Wi are constant regression coefficients. Equation 12 can be evaluated explicitly; therefore, its use reduces computational time. This is an advantage when the interface model is used in hourly annual simulation requiring solutions for thousands of operating points. After the system-side outlet temperature has been determined, the system-side flow rates needed for calculation of pumping energy can be obtained. The charge cycle flow rate, Qs,c, is Q s ,c = q ρ c p (T co − T ci ) (13) where cp and ρ are the fluid specific heat and density. Similarly, for discharge, BACK TO PAGE ONE Figure 8 Heat exchanger system-side outlet temperature. Q s ,d = q ρ c p (T hi − T ho ) . Variable-Speed Pump and Turbine (14) Constant-Speed Pump and Turbine The pressure and efficiency characteristics of centrifugal pumps and centrifugal pumps operating as turbines are functions of their respective specific speeds (Ns). Pressure (H) and efficiency (η) data for pump performance as functions of flow rate (Q) are easily obtained from manufacturer’s literature and selection software. Some pump manufacturers can furnish limited turbine performance information upon special request, but this information is not easily available. Application of methods for estimating turbine performance, such as those described previously, are generally more useful for conducting preliminary studies. Typical constant-speed pressure and efficiency characteristics, based on the horizontal split case centrifugal pumps of a major manufacturer, are shown in Figures 9a and 9b, respectively. For each specific speed, these characteristics were modeled by second-order polynomial regressions. The regression coefficients themselves were then modeled as secondorder functions of specific speed. Thus, the model for H(Q, Ns) for either a pump or turbine has the form H = C 1Q 2 + C 2 Q + C 3 (15) 2 (16) where E n = F1, n N s + F2, n N s + F 3, n . The specific speed (Ns) utilized in equations Cn and En refers to pump or turbine specific speed as appropriate. H = C 1Q 2 N N + C 3 + C 2 Q N 0 N0 2 (17) A derivation of Equation 17 is given in the appendix. When Equation 17 is used to model a variable-speed pump operating to provide system flow, Qsys, at system pressure, Hsys, the required speed can be determined by means of the quadratic formula: (18) [( ) − C Q + C − 4C C ⋅ Q 2 Sys 1 3 N = 2C 3 2 2 2 Sys + 4C 3 H Sys ] 0.5 ⋅ N0 The variable-speed efficiency map for a pump or turbine is developed by applying affinity relations to the constantspeed efficiency model (Equation 16) in a manner similar to that used in the derivation of Equation 17: 2 2 where C n = D 1, n Ns + D 2, n N s + D 3, n . Similarly, pump or turbine efficiency may be expressed as η = E 1Q 2 + E 2 Q + E 3 Performance models for variable-speed pumps and turbines can be developed by applying pump affinity laws to constant-speed head and efficiency characteristics (Equations 15 and 16). For a pump or turbine with pressure characteristic H0 defined as a function of flow Q0 for operation at reference speed N0, the characteristic at an arbitrary speed N is N N Q 2 + E 2 η = E 1 N0 N0 Q + E 3 . (19) When energy recovery is employed in a direct pumping interface, the turbine typically is connected to the pump through a double extended motor shaft. Therefore, pump and turbine must operate at the same speed. Because the speed of the pump and turbine set is determined by the requirements of BACK TO PAGE ONE Figure 9 Effect of specific speed on constant-speed pump performance characteristics: (a) pressure vs. flow rate, (b) efficiency vs. flow rate. Ns is given in IP units: flow in gpm, head in ft, speed in rpm. the pump, it is the pump system characteristics that control motor speed and the motor acts as a governor for the turbine. Q ⋅ H ⋅η t W& t = K (21) The shaft power input required by a pump is W& p Q⋅H , = K ⋅η p and the shaft power output of a turbine is (20) where ηp and ηt are pump and turbine efficiencies, respectively, and K is a constant required for consistency of units. In I-P units, K has a value of 3960 for water at 68°F (20°C) when shaft power is given in horsepower, flow in gallons per minute, and pressure in feet of water. In the SI system, K is BACK TO PAGE ONE 1000 when power is expressed in kW, flow in L/s, and pressure in kPa. Because the variation in water density is negligible over the range of temperatures found in chilled water systems, these common engineering expressions may be used in place of variable property forms with little error. Electric Motor and Variable-Speed Drive Models The power required to drive a centrifugal pump in the absence of energy recovery can be expressed in terms of pump, motor, and drive efficiencies. Motor power is given by W& m = W& p (22) ηm where ηm is the motor efficiency. The efficiency of an electric motor varies as a function of the fraction of its full-load power rating. A generic high-efficiency motor performance curve from the literature (ASHRAE 1996), approximated by a piece-wise continuous polynomial, was used in this investigation. · The total electric power input, W total , required to operate a variable-speed pump is given by W& W& total = m ηd (23) where ηd is the efficiency of the variable-speed drive controlling the pump motor. If the pump has no variable-speed drive, ηd is equal to one. In the present study, a generic high-performance variable-speed drive efficiency curve vs. fraction of full speed was obtained from the literature (ASHRAE 1996) and approximated as a quadratic function of the ratio of operating speed to full speed. The shaft power produced by an energy recovery turbine is deducted directly from the output that must be produced by the pump motor to which it is connected. The total power required by an interface with energy recovery is, therefore, W& total = W& p − W& t η m ⋅ηd = Q (H p − H tη pη t ), Kη pη mη d (24) where Hp and Ht are the pump and turbine heads, respectively. Because motor efficiency depends upon the fraction of nameplate power being consumed, this reduction in motor power alters the motor efficiency; however, because pump speed is determined solely by pumping requirements, drive efficiency is not affected by the addition of the turbine. TYPICAL PERFORMANCE CHARACTERISTICS Seven interface energy consumption models were developed from the component models described above. These included indirect interfaces (Figure 1) operated at both constant (IC) and variable (IV) speed, direct interfaces without energy recovery (Figure 2) operated at constant (DC) and variable (DV) speed, direct interfaces with energy recovery (Figure 3) operated at constant (DCT) and variable (DVT) speed, and a reversible, variable-speed direct interface with energy recovery (RDVT, Figure 4). These interface types and their acronyms are summarized for reference in Table 1. TABLE 1 Summary of Interface Types Description Acronym Indirect, Constant Speed IC Indirect, Variable Speed IV Direct, Constant Speed DC Direct, Variable Speed DV Direct with Energy Recovery, Constant Speed DCT Direct with Energy Recovery, Variable Speed Reversible Direct with Energy Recovery, Variable Speed DVT RDVT To illustrate the differing performance characteristics of various interface types, total power required as a function of flow rate was calculated for two levels of adverse static pressure differential between the chilled water system and thermal storage tank (see Kirchner [1997] for full details regarding component selection, interface design, and model coefficients). Frictional head in each case was determined by takeoff from the piping layout particular to the interface. The lower fixed-head value, 130 ft (40 m), is relatively small but has potential for application of energy recovery in a direct interface. The higher value, 260 ft (79 m), represents the static differential of a twenty-story-tall building and may be sufficiently large to justify the use of an indirect interface. Actual thermal storage interfaces typically have two to three pump sets, so three parallel sets were assumed in this example. Pumps were selected with best efficiency points at 2,070 gpm (131 L/s) for direct interfaces and 2,530 gpm (159 L/s) for the indirect interfaces. Peak efficiencies varied from 80% to 88%. Motor nameplate and variable-speed drive, full-speed efficiencies were assumed to be 95%. Chilled water supply and return temperatures and nominal heat exchanger performance were as shown in Figure 7. Figures 10 and 11 show electric power required by the seven interface types as a function of flow rate for the lower and higher fixed head cases, respectively. Transitions between operation with one pump and two pumps and between two pumps and three pumps are indicated by the discontinuities in the power vs. flow curves. An important difference between direct and indirect interface performance, apparent in both Figure 10 and Figure 11, is that the maximum flow rate for indirect alternatives is approximately 20% higher than for direct alternatives due to the reduced temperature differential associated with the use of the heat exchanger. Nevertheless, both constant- and variable-speed indirect interfaces consume substantially less pumping power than direct interfaces in the 260 ft (79 m) case (Figure 11). This is because the heat BACK TO PAGE ONE Figure 10 Interface power vs. flow rate, 130 ft (40 m) of static pressure: (a) alternatives without energy recovery, (b) alternatives with energy recovery (IV and DC also shown for comparison—see Table 1 for acronym definitions). BACK TO PAGE ONE Figure 11 Interface pumping power vs. flow rate, 260 ft (79 m) of static pressure: (a) alternatives without energy recovery, (b) alternatives with energy recovery (IV and DC also shown for comparison—see Table 1 for acronym definitions). BACK TO PAGE ONE exchanger eliminates the head associated with moving flow across the interface against the static pressure differential by separating the system into two hydraulically independent zones. This is not the case for the 130 ft (40 m) example, as indicated by Figure 10. The variable-speed indirect system requires less power than the direct interfaces at virtually all flow rates, but the constant-speed indirect system requires total power comparable to direct interfaces without energy recovery. Turbines in DCT and DVT interfaces recover approximately half of the pumping power required at the peak flow rate of each system configuration (i.e., with one, two, or three sets fully loaded). Figures 10b and 11b indicate that the turbine in the DCT interface reduces the peak pumping power by approximately 40% at 130 ft (40 m) of fixed head and by 54% at 260 ft (79 m) of fixed head relative to the DC system. The higher recovery rate in the 260 ft (79 m) case is due to the larger component of static pressure in the system curve. Generally speaking, direct interfaces consume more power than direct interfaces with energy recovery and still more than indirect interfaces. However, because pumping power required to overcome friction cannot be recovered, the percentage of total pumping power reclaimed decreases as the design ratio of static head to total pumping head decreases. At low static head, the differences in performance between the three interface types are small, but they increase greatly as static head increases. Turbine power output in the RDVT case and the corresponding peak demand reduction are significantly less than for either the DCT or DVT systems as a result of the suboptimal turbine performance of the full-size pump. Net power consumption for the RDVT and DCT interfaces is similar. However, RDVT energy recovery falls off more rapidly with decreasing flow rate. At the peak flow rate of 6,846 gpm (440 L/s), the turbine reduces peak electrical demand by 43%, relative to the DV system. However, when the flow rate is reduced by 26% to 5,052 gpm (320 L/s), the reduction in power is only 25%. Therefore, the turbine in the RDVT system recovers a very small amount of energy at low flow and tends to operate more like a DV system near the changeover points. By comparison, the DVT system operating with an optimum turbine for the same conditions reduces peak demand by 54% at full flow and by 45% at the reduced flow rate. Typical turbine performance characteristics are shown in Figure 12 for an interface with three parallel pump and turbine sets operating in a system with a static pressure of 260 ft (79 m) of water. The turbine system curve is shown in Figure 12a. It is typical of system characteristics well suited to the application of energy recovery turbines because of its large fixedhead component. Figure 12a shows that the variable-speed turbine (DVT) has a lower operating pressure for a given flow rate than either of the other alternatives. The reversible pump/ turbine, which is not optimized for turbine performance, requires the greatest pressure and operates over a more restricted range of flow rate. Power recovered by turbines as a function of flow rate is shown in Figure 12b. The suboptimal reversible turbine (RDVT) recovers less power than either of the other alternatives. The difference in power recovered by the optimized DVT and DCT turbines is small. Note that the maximum power of a given DCT interface configuration does not occur at its peak flow rate (Figures 10 and 11). This is because power recovered by the turbine in a DCT interface decreases more rapidly than does the power required by the pump as flow decreases. This is not the case for variable-speed operation. In this case, peak power demand occurs at full flow rate but remains relatively constant as flow decreases. Figure 12b show that recovered power for constantand variable-speed turbines is quite similar; therefore, the difference between the DCT and DVT cases in Figures 10b and 11b are due primarily to the effect of speed variation on pumping power. CONCLUSIONS Empirical models suitable for simulating transfer pumping interface performance have been derived and utilized to illustrate the energy consumption characteristics of a variety of chilled water thermal storage interface types. These models can be employed to evaluate the performance of interface alternatives in the preliminary stages of system design. Performance models and selection methods for the application of centrifugal pumps as hydraulic turbines can be developed using published information and pump/turbine affinity laws. Such models are suitable for preliminary design only. For final design, a pump manufacturer should be consulted for specific equipment selections and performance data. Despite statements in the published literature (Taylor 1989), the present study identified no technical considerations precluding the use of energy recovery turbines with variablespeed pumping. It is not necessary to sacrifice the advantages of one to obtain the other. Variable-speed operation reduces the amount of energy recovered by the turbine slightly because turbine head is reduced relative to constant-speed operation; however, it substantially improves the performance of the pump in such an interface. The various interface alternatives discussed have greatly varying power consumption characteristics. They also differ substantially in construction cost, as may be inferred from the relative complexity and equipment quantities indicated in Figures 1 through 4. As a result, significant trade-offs exist between capital and operating costs. In order to determine the best alternative for an application, economic analysis relating annual operating cost to capital cost must be performed. The second part of this paper will demonstrate the application of detailed interface models in a parametric study of interface energy consumption, energy cost, simple payback, and lifecycle cost as a function of adverse static pressure differential. BACK TO PAGE ONE Figure 12 Typical energy recovery turbine performance, 260 ft (79 m) of static pressure: (a) pressure vs. flow rate, (b) output shaft power vs. flow rate (see Table 1 for acronym definitions). ACKNOWLEDGMENTS tional District Energy Association. 86th Annual Conference. The authors wish to extend their appreciation to Mr. Steve Gavlick of the PACO Pump Corporation for his assistance in making the pump selections needed in this research. Partial support of this work through an ASHRAE Graduate Grant-inAid is also gratefully acknowledged. Bahnfleth, W.P., and C.G. Kirchner. 1998. Analysis of transfer pumping interfaces for stratified chilled water thermal storage systems—Part 2: Parametric study. ASHRAE Transactions 105(1). REFERENCES Buse, F. 1981. Using centrifugal pumps as hydraulic turbines. Chemical Engineering, Jan. 26, pp. 113-117. ASHRAE. 1996. 1996 ASHRAE handbook—HVAC systems and equipment. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. Bahnfleth, W.P. 1995. Hydraulic issues in the design of chilled water storage systems. Proceedings, Interna Fiorino, D. 1994. District cooling re-invented. ASHRAE Journal, 36(5): pp. 20-28. May. Garay, P.N. 1993. Standard pumps used as hydraulic turbines for power production. Pump Application Deskbook, pp. 377 - 396. New Jersey: Fairmount Press. BACK TO PAGE ONE Gatley, D.P., and I. Mackie 1995. Cool storage open hydronic systems design guide. EPRI, TR-104906. Electric Power Research Institute. Ingersoll Rand. 1976. Hydraulic turbines. Cameron Pump Manual, M-7006.10. New Jersey: Ingersoll-Rand Company. Kirchner, C.G. 1997. Analysis and modeling of transfer pumping for stratified chilled water thermal storage systems. M.S. thesis, Department of Architectural Engineering, The Pennsylvania State University. Nelik, L., and P. Cooper 1984. Performance of multi-stage radial-inflow hydraulic power recovery turbines. ASME Winter Meeting Conference Paper. New York: American Society of Mechanical Engineers. Sharma, K.R. 1985. Small hydroelectric projects—Use of centrifugal pumps as turbines. Kirloskar Electric Company, Bangalore, India. Stepanoff, A.J. 1957. Centrifugal and axial flow pumps, pp. 276 - 277. New York: John Wiley and Sons. Tackett, R.K. 1988. The use of direct pumping and hydraulic turbines in thermal storage systems. ASHRAE Transactions 94(1): 1989 - 2007. Taylor, R.M. 1989. Chilled water storage tank requires special consideration when designing a piping distribution system. IDHCA Cooling Conference. Williams, A.A. 1994. The turbine performance of centrifugal pumps: A comparison of prediction methods. Journal of Power and Energy, Part A, pp. 59 - 66. DERIVATION OF VARIABLE-SPEED PUMP CHARACTERISTIC (A2) where H is head. A quadratic approximation to the pump characteristic at the reference speed N0 may be written in the form H 0 = C 1 Q 02 + C 2 Q 0 + C 3 (A3) where C1, C2, and C3 are regression coefficients. From Equation A2, N H = H 0 N0 2 (A4) Therefore, substituting for H0 from Equation A3, ( H = C 1Q 2 0 + C 2Q 0 + C 3 N ⋅ N0 ) 2 (A5) From Equation A1, N Q0 = Q ⋅ 0 N (A6) Substituting from Equation A6 for Q0 in Equation A5 gives (A7) which simplifies to Equation 17: According to affinity laws for homologous pumps, N 2 H ------ = ------ N0 H0 2 N0 N 2 2 N0 H = C 1 Q ------ + C 2 Q ------ + C3 ⋅ ------ , N 0 N N APPENDIX A Q N = Q0 N 0 where Q is head, N is speed, and the subscript 0 denotes a reference or nominal condition. (A1) N N + C 3 H = C 1 Q 2 + C 2 Q N0 N0 2 (A8) Equation 19 may be derived by a similar procedure.