Experimental and numerical investigation of energy saving potential of centralized and decentralized pumping systems

Applied Energy 251 (2019) 113359

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Experimental and numerical investigation of energy saving potential of centralized and decentralized pumping systems

T

Mingzhe Liua, , Ryozo Ookab, Wonjun Choib, Shintaro Ikedac ⁎

a

Graduate School of Engineering, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan Institute of Industrial Science, University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505, Japan c Tokyo University of Science, 6-3-1, Niijuku, Katsushika-ku, Tokyo 125-8585, Japan b

HIGHLIGHTS

experiments on three pumping configurations were carried out. • Reduced-scale decentralized pumping system offers better energy-saving potential. • ASignificant energy-savings can be achieved under variable water volume control. • A three-dimensional model for reproducing pipe pressure loss is presented. • The proposed model numerical is validated by experimental data and its accuracy is evaluated. • ARTICLE INFO

ABSTRACT

Keywords: Pumping system Pump control strategy Energy saving potential Pressure loss Computational fluid dynamics (CFD) Equivalent length method

In energy distribution systems, thermal energy is usually transferred by a heat carrier fluid via pumps. Improper design and unreasonable control of pumping systems result in inefficient operation which accounts for a significant part of electricity consumption in the industry. The need to save energy has been sharpened the focus on improving energy efficiency in pumping systems. The application of a decentralized pumping system with the variable-frequency drive can be considered a technological improvement that has potential in saving energy compared to the conventional centralized pumping system. In this paper, a reduced-scale experimental apparatus and computational fluid dynamic model are used to investigate the energy saving potential of decentralized and centralized pumping systems. The energy-saving potential of decentralized configuration and two types of centralized configurations are then compared. The results showed that the decentralized pumping system consumes less power than centralized pumping systems under the same conditions. When the flow rate is reduced to 80%, the power consumption of the decentralized configuration decreases by 47% while the consumption for a centralized configuration with constant pressure control decreases by only 19%. The decentralized pumping system can offer higher energy-saving potential under variable flow rate conditions, which is expected to extend to other fluid delivery systems for improving efficiency. Moreover, the computational fluid dynamic simulation results correspond well with experimental results. The maximum discrepancies of the developed model for prediction of gauge pressure and system total pressure loss are 7.2% and 9% respectively, which confirms the accuracy and applicability of this model.

1. Introduction Growth in energy demand around the world is increasing at an alarming rate, resulting in energy insufficiency and environmental problems such as global warming will [1]. Energy use in buildings accounts for a significant portion of society’s total energy use. Although the portion varies by country and region, it is thought to constitute 35% to 40% of global energy use [2]. Heating ventilation and air ⁎

conditioning (HVAC) systems are generally responsible for a large portion of the total building operation energy use in modern cities [3,4]. By optimizing the efficiency of HVAC systems, the overall energy efficiency of buildings can be improved, and substantial reductions in energy use can be achieved [5,6]. Although easy to overlook, the pumping system has a significant impact on the overall energy efficiency of HVAC systems [1]. An essential criterion for the optimal operation of an energy system is the minimization of the costs of the

Corresponding author. E-mail addresses: [email protected] (M. Liu), [email protected] (R. Ooka), [email protected] (W. Choi), [email protected] (S. Ikeda).

https://doi.org/10.1016/j.apenergy.2019.113359 Received 13 January 2019; Received in revised form 4 May 2019; Accepted 16 May 2019 Available online 24 May 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

A f g H k ks L p Ppi Ppo Pt Pb1

Pb2

Pm

R Rb1 Rb2 Rb1 Rm

b2

V Vb1 Vb2 Vm Xi Y

the upper limit of the measuring range pressure loss per unit length (kPa/m) gravitational acceleration (m/s2) total head loss through system (m) turbulent kinetic energy (m2/s2) equivalent sand-grain roughness height (m) total length of the piping system (m) pressure loss of entire hydronic system (kPa) pump inlet pressure (kPa) pump outlet pressure (kPa) theoretical power requirement of pump (W) total pressure loss of entire hydronic system for pump in branch pipe 1 (kPa) total pressure loss of entire hydronic system for pump in branch pipe 2 (kPa) total pressure loss of entire hydronic system for main pump (kPa) virtual resistance (kPa) virtual resistance in branch pipe 1 (kPa) virtual resistance in branch pipe 2 (kPa) virtual resistance between branch pipes 1 and 2 (kPa) virtual resistance in main return pipe (kPa)

volumetric flow rate (L/min) Volumetric flow rate in branch pipe 1 (L/min) volumetric flow rate in branch pipe 2 (L/min) volumetric flow rate in main pipe (L/min) the i-th independent measured parameter function of a series of measured independent variables

Subscripts

b1 b2 b1, 2 i m str fit

branch pipe 1 branch pipe 2 between branch pipes 1 and 2 the i-th item main pipe straight pipe pipe fittings

Greek letters

R

operating fluid transport system, as the energy used by the pumps to transport thermal energy into rooms is responsible for a significant portion of the total HVAC energy use [7,8]. Moreover, because it facilitates matching low-grade energy sources with demand, the pumping system plays a vital role in achieving low exergy building systems [9]. Therefore, applying an appropriate pump arrangement and control strategy for a pumping system is a key solution in reducing the energy utilization of building operation and whole industries, such as the energy industry and the chemical industry. The rationality of system design often plays a crucial role in the energy efficiency of a system. Therefore, significant efforts have been made to improve the performance of hydronic systems by optimizing the system design such as proper component selection and pipeline dimensioning. A design method for the chilled water pumping system, which uses a single large-diameter pipe instead of many individual pipes, was proposed by Zhao et al. [10]. The energy savings effect was investigated by simulation and results showed that this design method would be useful for a variable speed pumping system with long pipe lengths. Chen et al. [11] proposed an optimal design method for a chiller system based on an analysis of the heat transfer processes by the thermal resistance-based method. The fluid flow processes were optimized based on the characteristics of the variable speed pumps and fans and the pipeline pressure drop. Tol and Svendsen [12] proposed a new method for designing a low-energy district heating system that focuses on different pipe dimensioning methods, substation types and network layouts. By analyzing the effects of these factors, the authors presented an optimization method that can provide an energy saving of 14% that was validated by simulation in random scenarios. Cheng et al. [13] proposed an optimal design method of chilled water pump systems that ensures the minimum annual total cost considering uncertainties of inputs and system reliability. This method is realized by optimizing the pump pressure head, the total pump flow capacity and the number of chilled water pumps. The results of a case study showed that the total cost of an optimized pump system could be reduced significantly compared with the conventional design. To reduce unnecessary pressure head and significant energy consumption caused by throttling, Li and Wang developed a new approach consisting of probabilistic optimal design concerning uncertainties and on-site adaptive commissioning [14]. Through case studies, it is indicated that both the optimal design

accuracy grade (%) uncertainty relative uncertainty (%) turbulent dissipation rate (m2/s3) fluid density (kg/m3)

method and commissioning are applicable and can achieve significant energy savings over the conventional design. Ensuring that a system functions at the optimal level require not only good design and fault detection but also system optimization of an operation strategy or control method for each component [15,16]. Olszewski [17] analyzed the methodology for optimization of a pumping system with a set of parallel centrifugal pumps and developed an optimization method based on a genetic algorithm. The applicability was verified by experiment and results indicated that the strategy of minimizing power consumption was more energy efficient than flow rate balancing or maximization of overall efficiency. To improve the efficiency of the chilled water pump system, Gao et al. [18] proposed a robust pump speed control strategy for practical applications that can avoid low delta-T syndrome. By eliminating the deficit flow problem and providing a reliable temperature set-point, 39% of the total chilled water pump energy can be saved in a year when compared to the conventional control strategies. Using a genetic algorithm, Olszewski and Arafeh [19] analyzed the energy efficient control method of a multi-pump system that has four various parallel pumps to explore the potential of self-learning control for the complex pumping station. The results demonstrated the self-learning applicability in controlling pumping stations in a parallel configuration and determined the basic hardware structure of self-learning pumping systems. Ma et al. [5] proposed a model-based supervisory and optimal control strategy for central chiller plants using simplified models of major components and the genetic algorithm. The results, based on a simulation for an actual central chiller plant in a super high-rise building, showed that this strategy can optimize the overall system performance through optimizing the temperature set-points only. To avoid energy waste and high peak demand during the morning start period, Tang et al. [20] proposed an optimal control strategy for chiller, secondary pumps and fans. The test results showed that about 50% of energy consumption for precooling is saved since the proposed control strategy can effectively shorten the precooling time. A class of theoretical models based on parallel hydraulic pump characteristics and on-line control optimization methods for variable-flow hydraulic pumps in central air-conditioning systems was developed by Tianyi et al. [21] that could perform on-line decision-making to determine the optimal number of operating hydraulic pumps based on calculated operational zones. A 2

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Group Search Optimizer-based optimal operation strategy for an integrated energy-based district heating system was developed by Jiang et al. [22] to minimize fossil fuel consumption by optimizing the boiler set-point temperature and pump water flow rate. Xue et al. [23] proposed a fast chiller power demand response control strategy for commercial buildings which can respond to the request of the electrical grid rapidly. Simulation results show that by taking proper control measures, fast and significant power demand reductions of the building HVAC systems can be achieved, and imbalanced chilled water flow distribution and air temperature unevenness can also be eliminated. Wang et al. [24] proposed the thermal resistance-based optimization method for heat exchanger networks and offered two direct optimal control strategies of variable speed pumps and valves for heat exchanger networks. Based on a series of experiments with a variable water volume control, authors demonstrated the universality of two direct optimal control strategies. Tianyi et al. [25] defined the most unfavorable thermodynamic loop and proposed a most unfavorable loop-based variable differential pressure control strategy for central air conditioning water system variable volume adjustment. Tests showed that the proposed strategy could save 47% to 58% water pump power consumption compared with the conventional control strategy while ensuring a better overall cooling energy supply. Xuefeng et al. [26]

proposed an analytical model of a parallel pump set based on the adjustment characteristics of the bypass loop. By analyzing the operating characteristics of the pump set under different control strategies, it was found that there is a direct correlation between the pump set energysaving effect and the supply-return water differential pressure. The literature reviewed above mainly focused on centralized pumping systems, in which pumps are usually set centrally in one place in parallel and cannot fundamentally deal with the throttling loss for the flow rate adjustment. However, valves used to regulate and balance the flow rate account for approximately 30% of the total pumping energy used by pumps and fans in a typical centralized pumping system [10]. Therefore, reducing the energy wasted by these valves would improve the efficiency of a pumping system. Moreover, traditional centralized systems can be characterized as having a higher energy input than required, as it is typically throttled or mixed until the necessary supply is produced [7]. Mixing and throttling result in a high exergy loss and should be avoided in low exergy systems. Introducing a decentralized pumping system would be a good alternative in this regard. In a decentralized pumping system, some variable-speed pumps are installed at installed at user's location to replace the throttling control; the unnecessary energy waste due to control valves in pumping systems can be eliminated. Therefore, decentralized pumping systems

Fig. 1. (a) Schematic of experimental apparatus that can implement different pumping systems, (b) and (c) photos of experimental apparatus. 3

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switching the gate valves installed in the bypass. The experimental system consisted of two branches and a bypass which was connected in parallel with the branches. The size of the entire piping system was 4.5 × 2.4 m (length × width, as shown in Fig. 1). The entire piping system was made from stainless steel. The main pipe had an inner diameter of 26.58 mm; the branch and bypass pipes had the same inner diameter of 20.22 mm. Water was used as the heat carrier fluid. Valves Rb1 and Rb2 were arranged in each branch pipe to model the pressure loss caused by HVAC components such as heat exchangers and fan coil units in real piping systems. Because the actual length of a piping system is typically much longer than that in a reduced-scale experimental setup, valves Rb1 b2 and Rm were arranged in the branch pipe 1 and main return pipe respectively, in order to model the pressure loss over a long pipeline. To prevent reverse-flow between the two branch pipes, a check valve was installed in between branch pipes 1 and 2. The system was equipped with three variable speed pumps. One pump, regarded as the main pump, is installed in the main pipeline for the centralized pumping system. Two other pumps, regarded as the branch pump, are installed in the branch pipe with motorized two-way control valves for the decentralized pumping system. The two-way valves were manually or automatically able to regulate the flow rate in the branch flow paths. The main pump and branch pumps had a hydraulic head of 78 kPa and 59 kPa, respectively.

Table 1 Specification of measuring devices used in experiments. Device

Accuracy

Pressure sensor Flow rate sensors Data Logger

± 1.0% of the full scale ± 1.6% of the full scale ± 0.05% of reading ± 2 digits

offer significant potential for both energy savings and reduction in energy/exergy demand for building operations. Nowadays, energy saving efforts require the development of new technical and scientific expertise, both in the field of building and the entire energy supply system [27]. However, most previous studies have focused on the optimization and comparison of the centralized pumping systems with different controls; there are few experimental comparisons between typical centralized and decentralized pumping systems, and the data necessary for analysis is not available. The present work attempts to fill this gap. By investigating and comparing the energy saving potential of centralized and decentralized pumping systems, this study hopes to offer fundamental knowledge leading towards the application of decentralized pumping configuration. Meanwhile, the results of this study can also help to provide new ideas and insights for the energy efficient design and optimization of fluid and energy delivery systems in both buildings and other fields. Therefore, this work fits alongside the most recent energy-related trends, which surrounds the optimal use of energy resources and optimization of energy systems. The purpose of this paper is to investigate the energy-saving potential of centralized and decentralized pumping systems. Both experiment and computational fluid dynamics method are conducted in this work. In the experiment, the flow rate and system total pressure loss are measured to calculate the theoretical power requirement for both systems under various flow rate conditions. Then comparisons are made in terms of the theoretical power requirement and overall energysaving potential. Meanwhile, a three-dimensional computational fluid dynamics (CFD) model has been developed for predicting the pressure in pumping systems, which is also used to calculate the theoretical power requirement. In addition, the CFD results are compared to experimental results to confirm its accuracy and applicability.

2.2. Measurement and control system Diaphragm-type pressure sensors and electromagnetic flow meters were installed to measure the gauge pressures and flow rate with high accuracy. As shown in Fig. 1, a total of twelve pressure sensors were installed at the inlet and outlet of the main pump, the outlet of two branch pumps, before and after the virtual resistances, and the branch inlet. Three electromagnetic flow meters were installed at each branch pipe and the main pipe. A data logger was used to record the analog output from the pressure and flow rate sensors. The specifications of the sensors used are listed in Table 1. 2.3. Assumed pumping systems and power requirement In the experiments, three different variable water volume systems—two different control strategies for the centralized pumping system and the decentralized pumping system—were compared, as shown in Fig. 2. Fig. 2(a) depicts the centralized pumping system with constant pressure (CP) control, which is typically used for water supply and pressure holding in circulation systems. For this system, the discharge pressure of the pump was maintained at a constant value during operation, regardless of changes in flow rate due to heating or cooling load changes. In general, although adjustment according to changes in the load mainly depends on pump speed regulation and two-way valves, the pump discharge pressure is constant. As a result, the rotation

2. Experimental system 2.1. Experimental apparatus In this study, a reduced-scale hydronic system was built to carry out experiments comparing the performance of centralized and decentralized pumping systems under the same flow rate conditions. Fig. 1 shows a schematic and photos of the experimental system. To ensure the consistency of unrelated variables in experiments in which different pumping control strategies were adopted, the experimental apparatus was designed to be switched between different configurations by

Fig. 2. Three different configurations of pumping system: (a) Centralized pumping system with constant pressure control, (b) Centralized pumping system with constant terminal flow rate Control, (c) Decentralized pumping system. 4

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speed of the pump cannot be too significantly reduced; therefore, the energy savings that can be achieved are very limited. Specifically, even if the flow rate decreases, it is necessary to operate the pump to maintain a constant pressure, and thus this unnecessary pump head results in inefficiency. Fig. 2(b) depicts the centralized pumping system with constant terminal flow rate (CTF) control. In this control strategy, the rotational speed of the pump was regulated by inverters in accordance with the necessary heating or cooling load. Unlike CP control, it is not necessary to maintain a high pressure at a small flow rate, so the rotational speed of the pump can be reduced as the flow rate decreases, offering improved energy efficiency. Finally, Fig. 2(c) depicts the decentralized pumping system. In this configuration, variable speed pumps were installed at each branch pipe; speed can be adjusted according to the load change of each user. The flow rates of all pumps in three control strategies can be controlled by the proportional–integral–derivative controller. There were no balancing or control valves to regulate the flow rate in the branch pipe. Because the energy use of each pump is affected by its mechanical characteristics, a direct comparison between different types of pumps is not valid. Therefore, to avoid the effects of the different performance characteristics of the pumps and to enable the comparison of the energy savings potential of three different pumping system configurations, the theoretical power requirement of the pump Pt , was used as the evaluation index. The theoretical power requirement represents the kinetic energy loss in the form of a pressure loss in the pipe. This index is typically used to analyze and calculate the hydraulic performance of pipelines. The theoretical power requirement of the pump depends directly on the flow rate V , water density , total head loss H , and gravitational acceleration g , as expressed in Eq. (1). It should be noted that the denominator in Eq. (1) is for the conversion of the flow rate, V , in units from L/min to m3/s. The denominator in Eq. (2) is for the conversion of pressure units from kPa to m. Ppi and Ppo is the pump inlet and outlet pressure, respectively.

Pt =

gVH 60 × 1000

H = (Ppo

3. Experimental results 3.1. Case settings The five cases described in Table 3 were investigated to compare the performance of decentralized and two typical centralized pumping systems under various flow rate conditions. The branch pipe closest to the main pump was labeled Branch Pipe 2, and the other was labeled Branch Pipe 1, as shown in Fig. 1. Cases 1 and 2 represent a centralized pumping system with CP control and a decentralized pumping system, respectively, at the rated flow rates condition. Cases 3 and 4 represent centralized pumping systems with CP control and CTF control, respectively, at partial flow rates condition (80% of the rated flow). Case 5 represents a decentralized pumping system with the same flow rates as in Cases 3 and 4. In all cases, the flow rate in each branch pipe was assumed to be half of the total flow rate. The two-way electronic valve was only used in the centralized pumping system to regulate the flow rate and control the balance between the branch pipes. The effective length of the virtual resistance in the main return pipe was assumed to be 4.7 m, and between branches 1 and 2 it was assumed to be 15 m. For CP control in Cases 1 and 2, the setting discharge pressure was set to the value at the rated flow rate (rated load condition), which was 21.5 kPa in this experiment. In the centralized pumping systems, only the main pump was operated, so the two branch pumps were turned off, while in the decentralized pumping systems the circumstance is reversed. At the rated flow rate, the virtual resistances Rb1(b2) , Rb1 b2 , and Rm were set to 5, 1.5, and 4.5 kPa, respectively. These values were reduced to 3, 1.1, and 3.3 kPa, respectively, when the flow rate was decreased to 80% of the rated flow. 3.2. Experimental results and discussion Table 4 provides the experimental results from Cases 1–5. When the system was in stable operation, the data was collected over a 6-min period with a sampling interval of 5 s, and the average values over the 6-min period were taken as the results. The theoretical power of the main pump was calculated as the total value in the centralized pumping system. In the decentralized pumping system, the theoretical power was calculated as the total output of the two pumps installed in the branch pipes. The total pressure loss of each system represents the pressure difference between the inlet and outlet of the pump. Finally, the mean pressure and flow rate were used to calculate the theoretical power for comparison. As shown in Table 4, when the flow rate was set to a rated flow rate of 26 L/min in the case of the centralized pumping system with CP Control (Case 1), the total flow rate and total pressure loss in the system were 25.9 L/min and 16.8 kPa, respectively. As only the main pump was running to provide the power for water circulation, the theoretical power of the main pump was the total theoretical power, which was 7.13 W in this case. For the decentralized pumping system under the same conditions (Case 2), the flow rates in branch pipes 1 and 2 were 13.1 and 12.9 L/min, respectively. Because there was no valve to adjust the flow rate in each branch pipe, the total pressure losses in branch pipes 1 and 2 were 14.8 and 14.4 kPa, respectively. Therefore, the theoretical power of each pump was 3.12 W and 3.09 W, and the total

(1) (2)

Ppi )/9.8

Based on the three different configurations mentioned above, the five different cases listed in Table 2 were established to compare energy use via the theoretical pump power requirement. 2.4. Uncertainty analysis The reliability of the measured data as well as the results obtained by the experiment are an essential element in the experiment. Therefore, uncertainty analysis is needed to prove the reliability of the experiments. In this experiment, uncertainty analysis for both measured and calculated parameters is carried out. The basic root-sum-square (RSS) method introduced by Robert J. Moffat [28] is used to evaluate the relative uncertainty of the calculated parameters. This calculation method was also used in many studies [29–31]. It was found that the relative uncertainty of the theoretical power requirement was from 5.27% to 8.76%, which is an acceptable uncertainty range. The calculation procedure and relative uncertainties regarding their typical values of the main parameters are given in Appendix A.

Table 2 Case setting for comparing the energy use of typical centralized and decentralized pumping systems under variable flow conditions. Case Case Case Case Case Case

1 2 3 4 5

System configuration

Control strategy

Description

Centralized Decentralized Centralized Centralized Decentralized

CP control Inverter control CP control CTF control Inverter control

Basic comparison for the energy use of decentralized and centralized systems at a rated flow rate condition. Case1 is regarded as the reference case. Comparison for the energy use of two different control strategies for the centralized system and decentralized system at a partial flow rate (partial load condition).

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Table 3 Experimental conditions of five experimental cases, under the same flow rate conditions. Case

System configuration

1 2 3 4 5

Control strategy

Centralized Decentralized Centralized Centralized Decentralized

CP control Inverter control CP control CTF control Inverter control

Design flow rate (L/min)

Vm (L/ min)

Vb1 (L/ min)

Vb2 (L/ min)

Rb1 (kPa)

Rb2 (kPa)

1 2 3 4 5

25.9 26.0 21.6 21.9 21.8

12.8 12.9 10.8 10.8 10.5

13.1 13.1 10.8 11.1 11.3

4.2 4.2 2.8 2.8 2.6

4.6 4.6 2.7 2.9 3.1

Pm (kPa) 16.8 N/A* 16.4 11.1 N/A*

Rb1

Vm

Vb1

Vb2

26 26 21 21 21

13 13 10.5 10.5 10.5

13 13 10.5 10.5 10.5

Pb1 (kPa)

Pb2 (kPa)

N/A* 14.8 N/A* N/A* 9

N/A* 14.4 N/A* N/A* 9.6

5 5 3 3 3

Rb2 5 5 3 3 3

Rb1 1.5 1.5 1.1 1.1 1.1

b2

Rm 4.5 4.5 3.3 3.3 3.3

decentralized pumping system helps to improve the energy efficiency in buildings, which can significantly reduce the overall energy demand and eventually reduce the global environmental impact. In addition, based on the results of this study, this kind of decentralized configuration can also be extended to other fluid delivery systems for efficient energy supply. For example, the decentralized configuration can be adopted in the HVAC duct system to achieve variable air volume operation while avoiding energy waste at the damper. Also, the decentralized configuration can be used in cooling water systems to improve the efficiency of a chilled water plant and district heating/cooling system. These applications can help realize the optimal use of energy resources and optimization of fluid and energy delivery in whole industries, such as the energy industry and the chemical industry. To prove the reliability of the experimental results, a calculation for the pressure and theoretical power requirements of each case was also completed using the equivalent length method [32,33]. The calculated and measured theoretical power requirements in each pumping system were then compared, with results for the centralized and decentralized pumping systems as shown in Fig. 4. In the calculation, the pressure loss in the piping system was determined by the following equations:

Table 4 Measured flow rate and total pressure drop from the experiment in 5 scenarios. Case

Design virtual resistance (kPa)

* Because the pressure difference between inlet and outlet of the pump in the main pipe Pm was used to calculated theoretical power, there is no need to measure the Pb1 and Pb2 in Case 1, Case 3, and Case 4. This is the opposite in Case 2 and Case 5.

theoretical power was 6.21 W, 13% less than in Case 1. Cases 3–5 in Table 4 show the operating data from the centralized pumping system with CP Control (Case 3), CTF Control (Case 4), and the decentralized pumping system (Case 5), in which the flow rate was reduced to 80% of the rated flow rate. In the case of CP Control (Case 3), the total flow rate was 21.6 L/min, while the total pressure loss pressure remained almost unchanged around an average of 16.4 kPa. Therefore, the total theoretical power requirement was 5.79 W. As there is no need to maintain a constant discharge pressure when the flow rate is reduced, CTF control (Case 4) did not produce much additional pressure loss when reducing the flow rate. Consequently, the rotational speed of the pump in Case 4 was less than that in Case 3, leading to a lower theoretical power of 3.98 W. In the decentralized pumping system (Case 5), the adjustment of the flow rate was achieved by adjusting the speed of the pump instead of throttling. As a result, the total theoretical power was 3.3 W (1.6 W + 1.7 W), which was the lowest of all cases. At that point, the motor speeds of the pumps in branch pipes 1 and 2 were also at their minimums. A comparison of the theoretical power required by the different cases is shown in Fig. 3. Under the same flow rate conditions, the theoretical power requirement of the centralized pumping system is higher than that of the decentralized pumping system due to additional energy for throttling. Compared to the rated flow rate operation, the theoretical power of the centralized pumping system decreased by 19% under constant pressure control at the partial (80%) flow rate. In the decentralized pumping system, the theoretical power decreased by 47% when the flow rate was decreased to 80% of the rated flow rate, which shows that the energy saving effect is more remarkable when system is operating at the partial load than at the rated load. This is of particular interest for buildings with frequent load changes, such as office buildings. The pumping system is generally designed according to the maximum heat/cold load, but most pumping systems operate at partial load inefficiently for most of the time. In the decentralized pumping system, the flow rate is adjusted by changing the pump speed rather than throttling to cope with load changes, there is no need to input extra energy for throttling and balancing. Therefore, the use of a

(3)

p = fL L = Lstr + Lfit

(4)

In Eq. (3), pressure loss per unit length f and the total length of the piping system L were used to calculate the total pressure loss throughout the piping system. The pressure loss per unit length was given for different diameters, based on the SHASE-S206-2009 regulations and explanations for water supply and drainage sanitation equipment [34]. The given values in this calculation for different flow rates and diameters are as shown below.

fmainpipe = fbranchpipe =

0.30 kPa/ m , V = 26 L / min ; 0.22 kPa/ m , V = 21 L / min 0.32 kPa /m , V = 13 L/ min 0.24 kPa /m , V = 11 L/ min

Fig. 3. Comparison of theoretical power requirement under different scenarios.

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Fig. 4. Comparison of theoretical power between experiment and equivalent length equation: (a) centralized pumping system; (b) decentralized pumping system.

The total length of the piping system was determined as the sum of two parts: the length of the straight pipe (Lstr ) and the equivalent length of piping fittings and valves (Lfit ). The length of the straight pipe is the sum of all straight pipes in the piping system, which determines the amount of friction pressure losses. For the equivalent length of piping fittings and valves, minor losses in the system caused by 90° elbows and similar were converted to their equivalent length Lfit representing the same pressure loss per unit length as a straight pipe. As shown in Table 5, the value for different diameters was given based on the ASHRAE Handbook - Fundamentals [35] and the Society of Heating, Air-Conditioning, and Sanitary Engineers of Japan’s Plumbing Code: Chapter 7 Piping design [36]. The total pipe length was used to calculate the total pressure loss in the system. A comparison of the results in Fig. 4 shows that the theoretical power requirements of each pump are similar at different flow rates. Also, the value calculated using the equivalent pipe length method was 10–20% greater than the experimental results in each system. A maximum deviation of approximately 29% occurred in Case 5 (the decentralized pumping system operating at 80% of the rated flow rate). Because the measuring range of flow rate sensor and pressure sensor is much larger than the actual measured value in Case 5, this is considered to be the cause of a significant error. Table A1 shows that the maximum error occurs in Case 5, which validated our judgment.

pressure characteristics in the piping system. Finally, the developed model was then validated by comparing the numerical simulation results to the experimental data. Two cases were established to evaluate the accuracy of using CFD to predict pressure in piping systems. Case A represents the centralized pumping system with constant pressure control, and Case B represents the decentralized pumping system. The arrangement of the model in Cases A and B correspond to the flow path and conditions of Cases 1 and 2 in the experiment. 4.2. Numerical model and computational parameters 4.2.1. Computational geometry and grid For the CFD simulation, the commercial software STAR-CCM+ was used. As mentioned above, the three-dimensional numerical model of the flow path had to be consistent with the actual experimental conditions, so the diameter of the main pipe was set to 26.58 mm, and the diameter of the branch and bypass pipes was set to 20.22 mm to match the inner diameter of the pipes in the experiment. Fig. 5 is a schematic diagram of the numerical model of the flow path used in the CFD simulations. In Fig. 5, valves are represented by a rectangle and pressure measuring sections are indicated by a red dot. Fig. 6 shows the valve part in the numerical model. To facilitate the overall calculation without changing the role of the virtual resistance, the valve model created in the CFD simulation was simplified as a gate valve instead of a globe valve. Because the gate valve was used to provide virtual resistance in the experiment, only the gate part was created in the numerical model. This part provided shut-off and throttling effects. Additionally, the pressure measuring sections were in almost the same positions as the pressure sensors installed in the experiment, and the average cross-section pressure was used to define the value of each measuring section in the CFD simulations. Compared with the tetrahedral mesh often used in machine analysis, the use of an appropriate polyhedral mesh has been found to improve the accuracy of the analysis and reduce the total calculation time [38]. Therefore, in this study, a polyhedral mesh was adopted in the central part of the whole flow path. As shown in Fig. 7, three prism layers were positioned along the inner walls, and the mesh was refined in geometrically important areas.

4. CFD simulations of pressure in a hydronic system 4.1. Description of CFD simulations Although experiments are the most effective and reliable method for verification, model experiments are not always efficient in terms of the considerable time and resources required to build an entire hydronic system. Computational fluid dynamics (CFD) were initially introduced for industrial applications such as pumps and other mechanical designs, and are now used to study the building environment and energy efficiency issues [37]. Based on the apparatus used in the experiment, a three-dimensional numerical model of the piping system was created in which the scale was the same as the experimental apparatus. The piping system was then simulated using a commercial CFD software package to predict the Table 5 Equivalent lengths for valves and fittings used in the calculation [m]. Diameter

90° Elbow

Tee (Confluence)

Tee (Diversion)

Gate valve

Globe valve

Check valve

20.22 mm 26.58 mm

0.6 m 0.8 m

1.2 m 1.5 m

0.24 m 0.27 m

0.3 m 0.4 m

7.2 m 9.6 m

2.4 m 3.2 m

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meshes with different straight pipe mesh sizes—mesh 1 (1,217,000), mesh 2 (1,555,000), and mesh 3 (1,985,000)—were employed at Cases A and B. The total system pressure loss was selected as the index to judge the mesh independence. The results showed that there was no significant difference between the total pressure losses from mesh 1 to 3, with the relative error being less than 1%. Accordingly, mesh 1 is chosen for the following simulation. Detailed calculation results are given in Appendix B. 4.2.3. Solver settings The type of flow was determined before applying the turbulence model. For the flow rates in both analyzed cases, the Reynolds number was approximately 20000, indicating fully developed turbulent flow. All simulations were conducted under isothermal conditions and the object fluid was assumed incompressible. The turbulence model used in this simulation was the realizable k − [39]. The same model was used in a simulation to predict the loss coefficients of the elbows under the same conditions and showed a fast calculation speed and good accuracy [40]. Therefore, the realizable k was adopted. A two-layer model was applied with an enhanced wall treatment in the solver to resolve for the near wall flow field. In this two-layer model, the whole domain was subdivided into a viscosity-affected region and a fully-turbulent region by a wall-distance-based turbulent Reynolds number. The one-equation model of Wolfstein [41] was employed to model the viscosity-affected near wall region, while the fully turbulent region was modeled by the realizable k turbulence model. Additionally, an all y+ wall treatment [42] was used to capture the boundary layer near the surface of the wall, where if the mesh was coarse enough ( y+ > 30), the wall law was equivalent to a logarithmic profile. If not coarse enough, the wall law was equivalent to the low y+ treatment where the boundary layer was fully resolved. Finally, the semi-implicit method for pressure-linked equations (SIMPLE) was used for pressure-velocity coupling, and a second-order upwind scheme was used for the convection terms in the governing equations.

Fig. 5. Schematic view of the numerical model showing the measurement positions and valves.

4.2.4. Boundary conditions As the object of this study was to observe the flow path in the piping system rather than the pump, the connection with the pump outlet in the piping system was set as the inflow boundary condition (inlet condition). Similarly, the connection with the pump inlet in the piping system was set as the outflow boundary condition (outlet condition). As shown in Fig. 5, the main inlet was set as the inlet boundary and the main outlet was set as the outlet boundary in Case A. In Case B, the Se1 inlet and Se2 inlet in Fig. 5 were set as the inlet boundaries and the Se1

Different mesh sizes were used in straight pipe sections and specific parts such as elbows and tee joints to improve the calculation speed. The reference mesh size in straight pipe sections was 0.01 m and was 0.003 m in elbow and tee joints. In total, the numerical model consisted of approximately 1,217,000 grid cells. 4.2.2. Verification of mesh independence To check the mesh independence of numerical results, three sets of

Fig. 6. Schematics of the numerical model: (a) combination of concentric reducer and equal tee used to replace reducing tee; (b) simple gate valve model.

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Fig. 7. Views of the computational grid (polyhedral mesh and prism layer mesh) on some of the domain surface: (a) elbow; (b) inlet & outlet.

outlet and Se2 outlet were set as the outlet boundaries. The experimentally measured pressures and velocity were used to define the boundary conditions. Two cases were conducted: (1) a centralized configuration, which was Case 1 in the experiments; and (2) a decentralized configuration, which was Case B in the experiments. In both cases, the flow rate was set to 26 L/min in the main pipe and 13 L/min in each branch pipe and the virtual resistances were set at the same values. However, the inlet velocity of the two cases is not the same because of the different inlet diameters. At the pipe inner walls, the standard wall functions given by Launder and Spalding [43] were used. The intensity of the turbulence was calculated based on the Reynolds number and the hydraulic diameter; the value of the turbulence length scale l was calculated based on the relevant hydraulic diameter [44,45]. Notably, roughness effects are a critical issue in diverse engineering applications, as even small surface imperfections can lead to significant disturbances in the velocity field and change the flow behavior. According to the pipe used in the experiments and referring to [36], the equivalent sand-grain roughness height of commercial steel pipe and wrought iron pipe was set to 0.00005 m to indicate rough wall condition. Details of the boundary conditions and remaining assumptions are presented in Table 6.

was less than the measured result. Table 7 indicates that the results are generally in good agreement, with minimal differences, all less than 10%. In Case A, the maximum discrepancy between the CFD results and experimental results was 6.1% at point 12, just before the reducing tee. In modeling the pipe tee, a variable diameter tee was replaced by a combination of a concentric reducer and equal tee. This structural change may have caused the relatively high discrepancy at this point. Therefore, the variable diameter tee should be studied in more detail. The other points exhibited a discrepancy of 5% or less. In Case B, the maximum discrepancy between the simulated and measured values was 7.2% at point 7, which is before the virtual resistance arranged in the main return pipe. For other points, the CFD results and experimental results are in good agreement, with discrepancies of less than 5%. Table 8 and Fig. 9 show the comparison between numerically simulated and experimentally measured pressure losses in Cases A and B. The pressure losses were calculated as the difference between the average pressure at each measuring point cross-section. The pressure loss at the virtual resistance in branch pipe 1 (or branch pipe 2), named Rb1 (or Rb2 ), is the pressure loss between points 1 and 2 (or points 6 and 5). The direction is from point 1 to point 2, which is the same as the fluid flow ensuring that the pressure loss is always positive. Similarly, pressure loss Rb1 b2 (or Rm ), which denotes the virtual resistance in branch 1 (or the main return pipe), is the pressure loss between points 3 and 4 (or points 7 and 8). The pressure loss of the whole system ( Pm for Case A; Pb1 and Pb2 for Case B) is defined as the pressure loss between the system inlet and outlet. The numerically determined total pressure loss throughout the system was 15.7 kPa, which was slightly less than the experimental value of 16.8 kPa (Table 8). The discrepancy between the simulated and measured values in Case A was a maximum of 21.4% between points 3 and 4. At the other points, the CFD results and experimental results were in good agreement, with discrepancies of less than 10%. For

4.3. CFD simulation results The results are validated against the experimental data. To facilitate direct comparison, the base pressure was set to 1 atm in the simulations, which means the results can be considered as relative pressures (gauge pressure). Table 7 and Fig. 8 show the comparison between numerically simulated and experimentally measured gauge pressures in Cases A and B. The numbers indicate the same locations shown in Fig. 5, and negative values indicate that the numerically simulated gauge pressure Table 6 Summary of boundary and initial conditions. Type of flow Fluid density Inlet boundary condition Outlet boundary condition Wall boundary

Case Case Case Case

A B A B

Incompressible flow (water) 998 kg/m3 Main inlet: 0.78 m/s (velocity inlet); Turbulence intensity: 0.05; Turbulence length scale: 0.001 Se1 & Se2 branch inlets: 0.67 m/s (velocity inlet); Turbulence intensity: 0.05; Turbulence length scale: 0.001 Main outlet: 4.6 kPa (pressure outlet) Se1 outlet: 4 kPa (pressure outlet); Se2 outlet: 3.5 kPa (pressure outlet) Generalized logarithmic law; Rough wall surface (ks = 0.00005 m)

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Table 7 Comparison of gauge pressure between CFD and experiment (discrepancy of CFD model against experimental results is given in parentheses. Measurement point+

1 2 3 4 5 6 7 8 9 10 11 12

Case A

10-1 10-2

Case B

Experiment [kPa]

CFD [kPa]

Experiment [kPa]

CFD [kPa]

18.3 14.2 14.0 12.6 12.3 16.9 11.0 6.5 4.6 N/A1

17.7 (−3.3%) 13.5 (−5.0%) 13.3 (−5.0%) 12.2 (−3.2%) 12.0 (−2.4%) 16.7 (−1.2%) 11.2 (+1.8%) 6.3 (−3.0%) 4.6* (0%) N/A1

12 21.3

11.7 (−2.5%) 20 (−6.1%)

18.6 14.3 14.1 12.2 12.3 16.9 11.1 6.8 N/A2 4 3.5 12.1 3.7

18.9 (+1.6%) 14.6 (+2.1%) 14.4 (+2.1%) 12.8 (+4.9%) 12.6 (+2.4%) 17.0 (+1.0%) 11.9 (+7.2%) 7.1 (+4.4%) N/A2 4* (0%) 3.5* (0%) 12.3(+1.7%) 3.6 (−2.7%)

+

Regarding measurement points, please refer toFig. 5. * Measured value in the experiment was used as the boundary condition in CFD. 1 The bypass channels in two branches were used in Case A. 2 The bypass channel in the main channel was used in Case B.

Rb1,2 , there was little difference between the absolute calculated and experimental values; the discrepancy did not exceed 0.9 kPa (Table 8). In this CFD simulation, the absolute value of the pressure loss was small, and so even differences of 0.9 kPa or less resulted in large discrepancies of up to 21.4%. However, the pressure loss of the entire piping system, excluding the virtual resistance part, was measured as 8.4 kPa in the experiment and calculated to be 7.2 kPa in the simulations, giving a discrepancy of 14.3% (larger than when the virtual resistance was included). In Case B, there were two branch pumps, and the total pressure loss of the system in each branch pipe was labeled Pb1 and Pb2 . The numerically determined values of Rb1, Rb2 , Rb1 b2 , and Rm were 4.3, 4.4, 1.6, and 4.8 kPa respectively, which were not significantly different from the experimental values. The total pressure losses Pb1 and Pb2 were 16.3 and 14.5 kPa, respectively. The simulated value of Pb2 was almost the same as the experimental value, whereas Pb1 was 9% higher than in the experiment. The maximum discrepancy in the prediction of the pressure losses in Case B was 15.8% between points 3 and 4. As for Case A, excluding the virtual resistance part, the total pressure loss of the piping system in branch 1 and branch 2 was 4.3 and 3.6 kPa, respectively, in the experiment and 5.4 and 3.7 kPa respectively, in the simulation, resulting in a discrepancy of 20.4% and 2.7%, respectively. Table 9 provides a comparison of pressure loss throughout the

Table 8 Comparison of pressure loss between CFD and experiment [kPa] (discrepancy given in parentheses). Pressure difference

Rb1 Rb2 Rb1 Rm Pm Pb1 Pb2 1 2

b2

Case A

Case B

Experiment

CFD

Experiment

CFD

4.1 4.6 1.4 4.5 16.8 N/A1 N/A1

4.2 (+2.4%) 4.7 (+2.2%) 1.1 (−21.4%) 4.9 (+8.9%) 15.7 (−6.5%) N/A1 N/A1

4.3 4.6 1.9 4.3 N/A2 14.8 14.4

4.3 (0%) 4.4 (−4.3%) 1.6 (−15.8%) 4.8 (+11.6%) N/A2 16.1 (+9.0%) 14.5 (+1.0%)

The bypass channels in two branches were used in Case A. The bypass channel in the main channel was used in Case B.

system as determined by the equivalent length method, CFD simulation, and experiment. Based on the results, the CFD simulation provides higher accuracy for the predicted pressure loss throughout the piping system. As the studied system has a relatively short total pipe length, the pressure loss discrepancy in the pipe will be less than the total discrepancy of the system including the virtual resistance part. However, there is a possibility that the discrepancy of the entire system may

Fig. 8. Comparison of gauge pressures between CFD and experiment: (a) Cases A; (b): Case B.

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Fig. 9. Comparison of pressure losses between CFD and experiment: (a) Case A; (b) Case B.

Table 9 Comparison of pressure loss through the system among equivalent length method, CFD calculation, and experiment [kPa] (discrepancy given in parentheses). Case A Experiment

Pm 16.8

Case B CFD

Pm 15.7 (−6.5%)

Equivalent*

Pm 18.7 (+11.3%)

Experiment

Equivalent*

CFD

Pb1

Pb2

14.8

14.4

Pb1 16.1 (+9.0%)

Pb2 14.5 (+1.0%)

Pb1 18.4 (+24.3%)

Pb2 16.4 (+13.8%)

* Results obtained the using the equivalent length method will be presented inSection 3.2.

decentralized pumping system consumes less power compared with the centralized pumping system under the same conditions. When the flow rate is reduced to 80% of the rated flow rate, the power consumption of the decentralized pumping system decreases by 47%, which is the highest of all configurations. Different from the conventional centralized pumping system, the flow rate adjustment in decentralized pumping system is controlled by pumps with inverters instead of throttling; hence unnecessary energy waste due to control valves can be eliminated. This demonstrates that the decentralized pumping system has great potential in energy efficiency and can offer better energysaving performance than conventional centralized pumping systems under variable water volume control. In addition, the results can also help provide new ideas and insights for the energy efficient design and optimization of fluid and energy delivery systems in building and other fields, such as duct and cooling water systems. Moreover, the computational fluid dynamic simulation results correspond well with experimental results. The maximum discrepancies of the developed model for prediction of gauge pressure and system total pressure loss are 7.2% and 9% respectively. The results turn out that this model is feasible for predicting the pressure in pumping systems and could be used with confidence for more complicated hydronic systems; hence this model is expected to be used in relevant studies that have no access to a laboratory or full-scale facilities.

increase when applied on the scale of actual buildings, where the pipe length can become very long. Therefore, a more detailed study on the equivalent sand-grain roughness height in straight pipe sections is still required. Based on the experimental and CFD results, the relationships between the flow path of the piping system and the pressure inside the pipe for Case A (constant pressure control) and Case B (decentralized system with inverter control) are presented in Fig. 10. The horizontal axis represents the flow path and is proportional to the actual pipe length, and the vertical axis represents the pipe internal water pressure. In both figures, the discharge port of the pump is defined as the start of the flow path (the origin of the horizontal axis), and the suction port of the pump is defined as the end of the flow path. The inlet of the central pump (point 9) is the reference point in Case A, and the inlet (point 10) of the decentralized pump installed in branch pipe 2 is the reference point in Case B. As shown in Fig. 10, the CFD results exhibit almost the same tendency as the experimental values concerning the gauge pressure in the pipe system under all cases, which proves that this CFD model can be used to predict the pressure in a hydronic system effectively. The results also prove this method could be used with confidence in studies that have no access to a laboratory or full-scale facilities. 5. Conclusions

Acknowledgement

In this paper, a set of experiments and computational fluid dynamic simulation were conducted to investigate the energy-saving performance of decentralized and centralized pumping systems under various flow rate conditions. Then the decentralized and typical centralized pumping systems were compared in terms of their energy use for water delivery and their overall energy-saving potential. Based on the theoretical power requirements of the pumps, the results indicate that the

This work was supported by the New Energy and Industrial Technology Development Organization of Japan (Grant No: 141015390). The authors are also deeply grateful to Masao Masuda from Takasago Thermal Engineering Co., Ltd. (Japan) for his help on this research.

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Fig. 10. Pipe internal water pressure distribution for system flow path: (a) Case A: centralized pumping system with CP Control; (b) Case B: decentralized pumping system.

Appendix A In this experiment, the measured parameters include the flow rate (Vm, Vb1, Vb2 ) and each gauge pressure. The calculated parameters include the theoretical power requirement of pump Pt and head loss ( Pm , Pb1, Pb2 ), which can be calculated by Eqs. (1) and (2). The uncertainties Xi and relative uncertainties RXi for the measured parameters could be obtained from the following equations [29–31]:

Xi = A

i

(A1)

RXi =

Xi Xi

(A2)

where

i

is the accuracy grade according to the manufacturer, A is the upper limit of the measuring range, and Xi is the value of the measurement 12

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Table A1 Uncertainties of the main parameters in the experiment. Parameters

Typical value

Unit

Relative uncertainty

Flow rate in main pipe (Case 1) Flow rate in main pipe (Case 3) Flow rate in main pipe (Case 4) Flow rate in branch pipe 1 (Case 2) Flow rate in branch pipe 1 (Case 5) Flow rate in branch pipe 2 (Case 2) Flow rate in branch pipe 2 (Case 5) Total pressure loss of the whole system for main pump (Case 1) Total pressure loss of the whole system for main pump (Case 3) Total pressure loss of the whole system for main pump (Case 4) Pressure loss of whole system for pump in branch pipe 1 (Case 2) Pressure loss of whole system for pump in branch pipe 1 (Case 2) Pressure loss of whole system for pump in branch pipe 2 (Case 5) Pressure loss of whole system for pump in branch pipe 2 (Case 5) Theoretical power requirement of main pump (Case 1) Theoretical power requirement of main pump (Case 3) Theoretical power requirement of main pump (Case 4) Theoretical power requirement of pump in branch pipe 1 (Case 2) Theoretical power requirement of pump in branch pipe 1 (Case 5) Theoretical power requirement of pump in branch pipe 2 (Case 2) Theoretical power requirement of pump in branch pipe 2 (Case 5)

25.9 21.6 21.9 12.9 10.5 13.1 11.3 16.8 16.4 11.1 14.8 9 14.4 9.6 7.13 5.79 3.98 3.12 1.60 3.09 1.70

L/min L/min L/min L/min L/min L/min L/min kPa kPa kPa kPa kPa kPa kPa W W W W W W W

3.08% 3.70% 3.65% 3.10% 3.81% 3.05% 3.54% 2.98% 3.05% 4.50% 3.38% 5.56% 3.47% 5.21% 5.27% 5.73% 7.38% 5.74% 8.76% 5.83% 8.20%

parameters. The basic root-sum-square (RSS) method introduced by Robert J. Moffat [28] is used to evaluate the relative uncertainty of the calculated parameters. The RSS method is briefly described as follows: If a parameter Y is a function of a series of measured independent variables Y = Y (X1 , X2 , X3 , Xn ) , the relative uncertainty RY for the Y can be acquired from:

RY =

n 1

(

Y Xi

Xi )2 (A3)

Y

Taking into account an uncertainty value of ± 0.5% in the thermophysical properties and gravity, based on Eqs. (A2) and (A3), the relative uncertainties for all parameters can be obtained. The relative uncertainties regarding their typical values of the main parameters are listed in Table A1. Appendix B To check the mesh independence of numerical results, three sets of meshes with different straight pipe mesh sizes—mesh 1 (1,217,000), mesh 2 (1,555,000), and mesh 3 (1,985,000)—were employed at Case A and B. The total system pressure loss H is selected as the index to judge the mesh independence for it representing the performance of a piping system, which is an important index to determine the energy consumption. A dimensionless quantity H/H1 is used to represent the variation with mesh size, where H1 is the result of Mesh 1. Fig. B1 and Table B1 show the influence of mesh size on the calculation results and variation of total system pressure loss, respectively. Evidently, there was no significant difference between the total pressure losses from mesh 1 to 3, with the relative error being less than 1%. Accordingly, the mesh with approximately 1,217,000 can give reasonable computation results.

Fig. B1. Verification of mesh independence.

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Table B1 Results of dimensionless quantity H/H1 for different number of mesh. Number of cells

mesh 1 (1,217,000) mesh 2 (1,555,000) mesh 3 (1,985,000)

H/H1 Case A ( Pm )

Case B ( Pb1)

Case B ( Pb2 )

1 1.00412 1.00749

1 1.00098 1.00965

1 1.00307 1.00969

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