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Optimization of ground heat exchanger parameters of ground source heat pump system for space heating applications T. Sivasakthivel*, K. Murugesan, P.K. Sahoo Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 May 2014 Received in revised form 27 September 2014 Accepted 16 October 2014 Available online xxx

In this paper Taguchi and utility methods have been employed to optimize eight important parameters (i.e. radius of U tube, borehole radius, heating load, grout conductivity, entering water temperature, distance between U tubes, U tube thermal conductivity and mass ﬂow rate) of GHX (ground heat exchanger) used for space heating applications. Length of GHX, COP (coefﬁcient of performance) and thermal resistance of GHX are considered as the objective functions. In Taguchi method lower the better concept is applied to obtain optimum values for the length of the GHX and its thermal resistance and for COP higher the better concept is used. In utility concept higher the better method has been employed. Based on the results obtained using Taguchi optimization, the optimum parameters and levels for GHX length, COP and GHX thermal resistances are found to be, A2B1C1D1E3F3G1I3, A2B2C1D3E3F3G1I2 and A1B2C1D2E1F1G3I1 respectively. Results obtained using the above optimized set of parameters show 15.17% reduction in the length of GHX, 2.5% increase in COP and 17.1% reduction in thermal resistance of GHX. The implementation of utility concept to obtain a single set of optimum parameters and levels resulted in 3.2% increase in GHX length, about 1.2% decrease in COP and 13.23% decrease in thermal resistance. © 2014 Elsevier Ltd. All rights reserved.

Keywords: Ground heat exchanger length Thermal resistance COP (coefﬁcient of performance) Taguchi optimization Ground source heat pump Utility concept

1. Introduction GSHP (Ground source heat pump) is one of the promising technologies for space heating and cooling applications [1,2]. A GSHP system extracts heat energy stored below the ground during the winter for heating applications. As the ground temperature at which heat is absorbed is higher than the ambient temperature, the coefﬁcient of performance of GSHP becomes higher than the system that would operate directly taking heat from the ambient which is very low during winter [3]. The efﬁciency of GSHP system depends on the ground heat exchanger loop that provides thermal connection between the heat pump and the ground. The ground loop used for GSHP applications can be either open loop or closed loop [4]. In an open loop system generally water bodies are used as a source for heating. In a closed loop system a GHX (ground heat exchanger) is used as a linking medium between the ground and heat pump. A GHX can be either a horizontal or a vertical loop system. In horizontal loop system HDPE (high density polyethylene) pipes are buried under the ground at a depth of 2e3 m. In

* Corresponding author. Tel.: þ91 9528468284. E-mail address: [email protected] (T. Sivasakthivel).

vertical systems boreholes are drilled at a depth of 30e300 m. Selection of loop for heat pump applications depends on the availability of water bodies, land etc. The horizontal loop system requires a vast area of land, whereas borehole systems require only a piece of land [5]. In general, there is a mindset among GSHP users that vertical borehole systems are more efﬁcient than the horizontal loop system because the variation in ambient temperature will have more inﬂuence on the horizontal loop system that is buried at shallow depth compared to the deep vertical boreholes. Nevertheless, in both the cases the performance of a GSHP system depends on many other parameters such as geological condition, heat exchanger material, carrier ﬂuid, diameter of the pipe, mass ﬂow rate of heat exchanger ﬂuid, distance between the pipes, trench type and borehole diameters [6]. Hence optimization of these parameters is important to reduce the initial cost and running cost of the GSHP system [7]. Bazkiaei et al. [8] proposed a method to optimize a horizontal GHX system by using homogenous and non-homogenous soil proﬁles. Based on their study, they concluded that the performance of GHX installed in soil with non-homogenous proﬁle has better extraction and dissipation rates compared to the soil with homogenous proﬁle. Zogou and Stamatelos [9] studied the design optimization of heat pump systems to examine the effect of

http://dx.doi.org/10.1016/j.energy.2014.10.045 0360-5442/© 2014 Elsevier Ltd. All rights reserved.

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Nomenclature GSHP ASHP HDPE RSM TRNSYS ANN S/N GHX HP COP U L CI DOF ANOVA TDOF NV Pi

ground source heat pump air source heat pump high density polyethylene response surface methodology transient system simulation artiﬁcial neural network single to noise ratio ground heat exchanger heat pump coefﬁcient of performance utility value levels conﬁdence interval degree of freedom analysis of variance total degree of freedom number of variables preference number

climatic conditions. They considered northern and southern parts of Europe for their analysis. Their study reveals that milder climates of the Mediterranean and subtropical climates are found to be favorable for a heat pump system. Spitler et al. [10] performed simulation and optimization for different components of a GSHP system. They considered the effect of heating and cooling loads of the buildings on the optimization of heat exchanger length when the GSHP system was operated for 20 years. Their optimization results enabled them to maintain the entering water temperature to the heat pump at the design value. Kjellsson et al. [11] optimized a solar assisted GSHP system with a vertical GHX installed in a dwelling. Their results reveal that using solar collector for hot water production in summer and recharging the ground in winter is the optimal combination. Park et al. [12,13] performed optimization of a hybrid GSHP with parallel conﬁguration of a GHX and compared with a non-hybrid GSHP system. They found that hybrid GSHP system was 21% more efﬁcient than the conventional GSHP system and also they optimized the hybrid GSHP using RSM (response surface methodology). Hackel et al. [14] investigated the optimization of a hybrid GSHP system using TRNSYS (transient system simulation) simulation studio and concluded that for cooling dominated buildings the hybrid system should be sized to meet the heating demand. Some researchers [15e17] carried out thermoeconomic optimization of horizontal and vertical ground coupled heat pump systems to reduce the cost of the system. Esen et al. [18] studied the performance of GSHP system and its economic beneﬁts compared to other conventional systems like electric heater, fuel oil, natural gas, liquid petrol gas, coal and oil. They found that during heating operation, the average COP (coefﬁcient of performance) of heat pump was 3.2 and GSHP is economically a good option compared to electric heater, fuel oil, coal, liquid petrol gas and oil but not as a good option compared to natural gas, because of plenty of availability of natural gas in Turkey. Gang and Wang [19] applied ANN (artiﬁcial neural network) to predict the exit temperature of GHX. Esen et al. [20e25] applied ANN, neuro-fuzzy and fuzzy logic methods to evaluate the performance of GSHP systems. Esen and Yuksel [26] studied the possibility of using various renewable energy sources for green house heating and they concluded that GSHP also can be used for green house heating. Park et al. [27] compared the cooling performance of an optimized hybrid GSHP system with conventional GSHP system. It was found

sys H N R Ve rbore hconv k rp,in rp,ext kpipe fe kgrout Ppump Pcomp Pfan p q h g

system center to center distance between the two pipes total number of experiments number of repetitions error in variance borehole radius convection coefﬁcient ground thermal conductivity inner radius of the U pipe outer radius of the U pipe thermal conductivity of the pipe error in degree of freedom thermal conductivity of the grout pump power consumption compressor power consumption fan power consumption ﬂuid density ﬂow Rate pump head acceleration due to gravity

that hybrid GSHP system was 2e6.5% more efﬁcient than the conventional GSHP system. Balbay and Esen [28,29] studied GSHP based bridge and pavements heating to clear snow during winter in Turkey by using three different types of heat exchangers. It was found that the GSHP system was able to successfully remove the snow from the bridges and pavements. Pardo et al. [30] optimized the combination of GSHP, HVAC (heating, ventilating, and air conditioning) and ASHP (air source heat pump) to get better performance by studying different groupings of these systems. Luo et al. [31] carried out thermal performance study of a BHX (borehole heat exchanger) with three different borehole diameters. They concluded that boreholes with larger diameter are well suited to achieve better thermal performance. Esen et al. [32] carried out experimental study on a GSHP system coupled with horizontal ground heat exchanger. They evaluated the performance by calculating COP of the system and also created a numerical model to predict the temperature distribution in the vicinity of the heat exchanger and their numerical results compared close to their experimental data. Zhai et al. [33] optimized the required indoor temperature to reduce thermal imbalance in the ground. They concluded that indoor temperature in the range of 22e24 C is the best temperature for optimum performance of the system. Li and Lai [34] proposed a method to minimize entropy generation with an aim to optimize a single U tube heat exchanger. They concluded that the empirical value proposed for ﬂuid velocity was high compared to the optimum value. Alavy et al. [35] proposed an approach to optimize the design of a hybrid GSHP system. They applied the optimized design to ten different projects to reduce the initial investment cost, payback period and operating cost. Their optimized design was able to meet more than 80% of total annual load. Ramamoorthy et al. [36] proposed a procedure to optimize a GLHE (ground loop heat exchanger) that used cooling pond as heat rejection sink. The main objective of their study was to select an optimum GLHE length along with other supplemental heat rejection units. Khalajzadeh et al. [37] optimized various parameters of a vertical GHX by RSM. They considered depth of borehole, pipe diameter, inlet ﬂuid temperature and Reynolds number as parameters and studied their effect on the efﬁciency of heat transfer and effectiveness of heat exchanger. They concluded that the inlet ﬂuid temperature and pipe diameter were the most inﬂuential parameters. Fujii et al.

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[38] optimized the distance between two boreholes by considering ground water ﬂow for deep borehole heat exchangers. They concluded that for ground water ﬂow with Peclet number equal to or greater than 0.1, the aquifer was under exploitation. Comakli et al. [39] used Taguchi method to optimize two refrigerant mixtures in a heat pump. They concluded that the condenser air outlet temperature was the most effective parameter for the coefﬁcient of performance. Ramniwas et al. [40] optimized COP of a GSHP system by considering four important parameters of GSHP. They observed that the condenser outlet temperature played a major role in controlling the COP of the system for space heating applications. A detailed literature study indicates that only a few researchers [6,8e14,27,30,31,33e38] have attempted to optimize the GHX parameters to get better performance and reduce the cost of the GSHP system and most of them focused on thermo-economic optimization of GSHP systems [14e17,41]. To the best knowledge of the authors, not many works have been reported on optimization of design parameters of GHX to get optimum values for length of GHX, COP and thermal resistance of GHX. The main challenge in the optimization of parameters of GHX is that the parameters which are more inﬂuential for the optimization of length of GHX are not dominant for the optimization of COP and thermal resistance of GHX and vice versa. Hence ﬁnding the optimum parameters which will give the optimum values of length of GHX, COP and thermal resistance of GHX is a complex task. However, this multifaceted optimization can be obtained by the combined implementation of Taguchi and utility methods. Applications of Taguchi method combined with utility concept can be seen in a wide range of problems from manufacturing to concrete research [42e47]. In the present study Taguchi technique has been employed to optimize the parameters related to length of GHX, COP and thermal resistance of GHX independently. Then in order to get a single set of optimum parameters for all the three objective functions (length of GHX, COP and thermal resistance of GHX) the utility concept has been implemented. In the present analysis eight important control factors have been considered. The detailed discussion on the

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implementation of Taguchi method and utility concept is discussed in the following sections. 2. Methodology The GHX in a GSHP system plays a vital role in deciding the performance of the GSHP system. Fig. 1 shows cause and effect diagram with a list of important parameters that affect the performance and length of a GHX. These parameters can be categorized under different groups, namely, ground properties, borehole properties, heat exchanger ﬂuid properties and load. Experimental analysis is possible only when the optimization involves a few parameters. However, for the case of systems like GHX, the number of parameters to be considered will be closer to ten. Hence implementation of experimental method will be highly demanding; even if all the experiments are performed, it may be highly complex to analyze the ﬁnal results obtained for various combinations of parameters. Design of experiments based on Taguchi method is one of the best tools to carry out optimization analysis with a number of parameters even more than ten. This method involves an elegant procedure to determine optimum levels of the various parameters considered for optimization of a given objective function. It makes use of standard orthogonal arrays to arrange the parameters at various levels. Taguchi method is limited to optimize a single objective function. The main objective of the present work is to optimize the length of GHX, COP and thermal resistance of GHX of a GSHP (objective functions). Hence after optimizing the individual objective function using Taguchi method, utility concept will be employed to obtain optimum level of parameters for simultaneous optimization of all the three objective functions. The details of implementation of Taguchi method and utility concept are explained in the following sections. 2.1. Taguchi method Taguchi method is an experimental optimization technique that uses standard orthogonal arrays for laying out the matrix of

Fig. 1. Cause and effect diagram of GHX.

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experiments. By using this matrix it will help us to get maximum information from a minimum number of experiments and also the best level of each parameter can be found. The major steps followed in implementing the Taguchi method are presented in Fig. 2. Three type of signal to noise (S/N) ratios are available for date analyses that are: lower the better, higher the better and nominal the better. One of these characteristics can be selected based on the requirement in a given problem. ANOVA (analysis of variance) provides the information about the percentage contributions of individual parameters on the selected performance parameter. 2.2. Taguchi method e parameters and levels In the present analysis, eight control parameters are considered for optimization, seven parameters with three levels and one with two levels. Table 1 shows the eight control parameters and their levels. In Taguchi optimization, the total number of trial runs can be obtained using the following expression [47]:

NTaguchi ¼ 1 þ NV L 1

(1)

where NV is the number of variables, L is the number of levels and NTaguchi is the total number of trial runs. Eq. (1) is valid only for control parameters with equal levels. However, for eight control parameters with mixed levels, L18 orthogonal array is selected from the standard orthogonal arrays, L4, L8, L9, L12, L16, L18 etc. [48]. The layout of experimental trial runs for L18 array is depicted in Table 2. Computations were carried out to determine the performance parameters (length of GHX, thermal resistance of GHX and COP) by using the combination of control parameters with levels as given in the above layout for all the 18 trial runs. With these results the S/N ratios are evaluated for the performance parameters by following lower the better concept for the length of GHX and thermal

Table 1 The parameters and their levels. Label

A

B C D E F G I

Parameters

Levels

Thermal conductivity of heat exchanger pipe material (W.m1.K1) Mass ﬂow rate of ﬂuid per kW of load (kg.s1.kW1) Heating load (kW) Borehole radius (m) Inner radius of U tube heat exchanger (m) Grout thermal conductivity (W.m1.K1) Entering water temperature ( C) Center to center distance between U tubes (m)

1

2

3

0.10

0.42

e

0.04

0.05

0.06

7 0.0635 0.0127 0.73 4 0.05

8.75 0.0762 0.0159 2.10 8 0.06

10.5 0.0889 0.0191 2.59 12 0.07

resistance of GHX and higher the better concept for COP. Table 3 shows the S/N ratio values for the length of GHX, COP and thermal resistance of GHX for L18 orthogonal array used in Taguchi method. This analysis will enable us to determine the optimum control parameters and their levels for the optimum value of length of GHX, COP and thermal resistance of GHX individually. 2.3. Utility concept From the Taguchi method, three different set of control parameters have been obtained to achieve optimum length of GHX, COP and thermal resistance of GHX. However, it is necessary to determine a single set of control parameters which will provide the beneﬁts of optimization of the three performance parameters to get optimum performance of the GSHP. This can be achieved using utility concept. In the optimization of GSHP system utility concept calculates the utility value of individual performance parameters to get a single performance index. These utility values are combined together to get a collective utility value. In this paper the collective values refer to the combination of utility values of length of GHX, COP and thermal resistance of GHX. In the case of utility analysis, the overall utility function (U) can be written as [48]:

UðZ1 ; Z2 :::Zn Þ ¼ f ðU1 ðZ1 Þ; U2 ðZ2 Þ; ::: ; Un ðZn ÞÞ

(2)

where U (Z1, Z2, … .., Zn) is the overall utility of ‘n’ performance parameters. It is assumed that all the performance parameters (i.e. Table 2 Experimental plan of L18 (2*1and 3*7).

Fig. 2. Flowchart of Taguchi method.

Taguchi trial number

Parameters A

B

C

D

E

F

G

I

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42

0.04 0.04 0.04 0.05 0.05 0.05 0.06 0.06 0.06 0.04 0.04 0.04 0.05 0.05 0.05 0.06 0.06 0.06

7.00 8.75 10.50 7.00 8.75 10.50 7.00 8.75 10.50 7.00 8.75 10.50 7.00 8.75 10.50 7.00 8.75 10.50

0.0635 0.0762 0.0889 0.0635 0.0762 0.0889 0.0762 0.0889 0.0635 0.0889 0.0635 0.0762 0.0762 0.0889 0.0635 0.0889 0.0635 0.0762

0.0127 0.0159 0.0191 0.0159 0.0191 0.0127 0.0127 0.0159 0.0191 0.0191 0.0127 0.0159 0.0191 0.0127 0.0159 0.0159 0.0191 0.0127

0.73 2.10 2.59 2.10 2.59 0.73 2.59 0.73 2.10 2.10 2.59 0.73 0.73 2.10 2.59 2.59 0.73 2.10

4 8 12 12 4 8 8 12 4 8 12 4 12 4 8 4 8 12

0.05 0.06 0.07 0.07 0.05 0.06 0.07 0.05 0.06 0.05 0.06 0.07 0.06 0.07 0.05 0.06 0.07 0.05

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T. Sivasakthivel et al. / Energy xxx (2014) 1e14 Table 3 Taguchi signal to noise ratio for GHX length, COP and effective GHX thermal resistance. Taguchi trial number

GHX length (m)

S/N value (dB)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

163.6 167 233.3 186.2 120.3 350.2 154 391.9 148.3 84.1 145.7 153.8 184 92.7 127 66.6 139.2 214.3

44.2757 44.4543 47.3583 45.3996 41.6053 50.8863 43.7504 51.8635 43.4228 38.4959 43.2692 43.7391 45.2964 39.3416 42.0761 36.4695 42.8728 46.6204

COP

3.3311 3.4826 3.3407 3.0535 3.5650 2.6161 3.0599 2.1970 3.3905 3.7199 3.5889 3.7439 3.0636 3.7491 3.7160 3.6355 3.2913 2.9843

S/N value (dB)

10.4518 10.8381 10.4767 9.6960 11.0412 8.3531 9.7141 6.8366 10.6053 11.4106 11.0992 11.4665 9.7246 11.4785 11.4015 11.2113 10.3473 9.4968

Effective GHX thermal resistance (m.K.W1)

S/N value (dB)

0.352 0.204 0.170 0.185 0.171 0.406 0.226 0.374 0.162 0.106 0.091 0.196 0.191 0.121 0.082 0.097 0.131 0.122

9.0691 13.8074 15.3910 14.6566 15.3401 7.8295 12.9178 8.5426 15.8097 19.4939 20.8192 14.1549 14.3793 18.3443 21.7237 20.2646 17.6546 18.2728

n X

Ui ðZi Þ

5

Wi ¼ 1

(7)

i

That is; Wi ¼ WGHX length þ WCOP þ Wthermal resistance

(8)

where WGHx length, WCOP, Wthermal resistance are the weights assigned to length of GHX, COP and thermal resistance of GHX respectively. In this research work the following weighting factors are assigned, WGHx length ¼ WCOP ¼ 0.35 and Wthermal resistance ¼ 0.3. These weighting factors have been assumed for the fact that use of long GHX pipe gives rise to increase in entering water temperature, which in turn results in increase in the COP of GSHP system. Thus length of GHX and COP are linked to respectively the initial and running costs of GSHP and hence both these parameters are given equal weightage, slightly higher than the thermal resistance. Hence selecting optimum weighting factor will result in optimum COP, optimum thermal resistance and optimum GHX length and the overall utility based on weighting factor can be written as [47]

U¼

n X

Wi Pi

(9)

i¼1

length of GHX, COP and thermal resistance of GHX) are independent of each other and the overall utility is a linear function of sum of individual utilities and it can be written as

UðZ1 ; Z2 ; :::::::Z n Þ ¼

n X

(3)

Once the Taguchi optimization is applied to optimize the length of GHX, COP and thermal resistance of GHX, the resulting optimized values are used to construct the preference scale along with the weighting factors in order to calculate the overall utility values for multi objective optimization. Fig. 3 presents the generalized steps involved in optimization using Taguchi based utility concept. 2.4. GHX length and calculation of performance parameters

i¼1

The performance parameters can be ordered and weighted based on their importance. The general form of weighting for a performance parameter is given as.

UðZ1 ; Z2 ; :::::::Z n Þ ¼

n X

Wi Ui ðZi Þ

A typical vertical GHX is shown in Fig. 4. The GHX consists of a single U tube heat exchanger ﬁlled with grout. Estimating the length of GHX to meet the required heating or cooling demand is an

(4)

i¼1

In Eq. (4) Wi is the weight assigned to the performance parameters of GHX length, COP and thermal resistance of GHX. The sum of weights assigned to all the performance parameters must be equal to 1. In utility concept higher the better formulation is used to analyze signal to noise ratio values. The individual preference scale needs to be constructed along with the weighting factors in order to calculate the overall utility function for the performance parameters of GHX length, COP and thermal resistance of GHX. The preference number is calculated by constructing the preference scale between 0 and 9 [48]. The general form of the preference number is:

Pi ¼ A log

Zi Zi0

(5)

The value of constant ‘A’ can be chosen arbitrarily such that Pi ¼ 9 at Zi ¼ Z*, where Z* ¼ optimum value of Zi. Hence

A¼

9 * log ZZ 0

(6)

i

where Zi is the optimum performance value of length of GHX, COP and thermal resistance of GHX, Zi0 is the minimum acceptable performance value of GHX length, COP and thermal resistance of GHX. The following conditions need to be satisﬁed in order to assign a weighting factor for calculating different performance parameters.

Fig. 3. Steps in utility optimization.

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Fig. 4. Schematic diagram of (a) vertical U tube ground heat exchanger (b) AeA cross section of view.

important step in GSHP installation. Different methodologies have been proposed in the literature to calculate the length of GHX. In this paper a methodology proposed by ASHRAE [49,50] has been used. Using the thermal resistance circuit concept for heat conduction, the length of GHX can be calculated as.

L¼

qh Rb þ qy R10y þ qm R1m þ qh R6h Tm Tg þ Tp

(10)

In the above equation, L is length of the heat exchanger, Tm is mean ﬂuid temperature of GHX, Tg is the undisturbed ground temperature and it is estimated by circulating the normal tap water in the GHX for half an hour, Tp is the temperature penalty associated with GHX, for single GHX, Tp ¼ 0, qh, qm, and qy are peak hourly ground load, peak monthly ground load and average yearly ground load on GHX respectively, R6 h, R1 m and R10 y are the ground thermal resistance for six hours, 1 month and 1 year respectively, Rb is the effective thermal resistance of GHX and it mainly depends on the thermal resistance of pipe, grout resistance and convective resistance. The effective thermal resistance of GHX can be calculated using the following equation [49,50]:

Rb ¼ Rg þ

Rp þ Rconv 2

(11)

The grout resistance (Rg), pipe resistance (Rp) and convective resistance inside the pipe (Rconv) used in the above equation can be calculated by the following equations.

1 2prp; in hconv

(12)

ln rp; ext rp; in Rp ¼ 2pkpipe

(13)

Rconv ¼

2 1 4ln rbore þ ln rbore Rg ¼ 4pkgrout rp; ext H 0 13 4 rbore kgrout k @ ln þ 4 A5 kgrout þ k 4 rbore H2

(14)

This model assumes constant ground temperature and thermal properties of soil is assumed to be uniform throughout the depth of the ground and the effect of variations of these properties on length of BHE can be found in Ref. [50]. The main focus of the present model is to predict the optimum heat exchanger length from different design parameters. The performance of a GSHP can be evaluated by calculating the COP as follows [51]:

COPHP ¼

Qghx þ Pcomp: Qcond: or COPHP ¼ Pcomp: Pcomp:

(15)

COPsys ¼

Qcond: Pcomp þ Ppump þ Pfan

(16)

Various power input to the GSHP system can be calculated by calculating electric power supply to compressor, fan and pump.

Pcomp: & fan ¼ VI cos f Ppump: ¼ VI cos f ðorÞ Ppump: ¼

(17) qrgh h

(18)

3. Results and discussions Designing a GSHP in a particular location requires knowledge of important parameters like thermal conductivity of soil, type of soil, water movement, grout thermal conductivity, type of heat exchanger, entering water temperature, borehole radius, diameter of the heat exchanger, heat exchanger material and distance between the two U tube pipes. Some of the above parameters are controllable and others are not. In this research, the parameters which will affect the performance of the GSHP and the length of GHX are considered. Computational experimental plan of L18 array is presented in Table 2. The main aim of this study is to determine the parameters that inﬂuence the length of GHX and thermal resistance of GHX and COP of GSHP system and then to establish a single set of control parameters which will provide optimum performance of GSHP including the beneﬁts of optimization of the performance parameters.

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3.1. Taguchi e signal to noise ratio analysis In Taguchi method once required trial runs are completed, the next step is to convert the trial run results into signal to noise (S/N) ratio. The term signal represents the preferable effect on the output (i.e. length of GHX, COP and thermal resistance of GHX) and the term noise represents the unwanted effects on the heat exchanger length, COP and thermal resistance. To analyze the Taguchi model, three types of S/N ratios, smaller the better, larger the better and nominal the best can be employed. In this study, the length of GHX and thermal resistance are analyzed by selecting smaller the better concept because for a given load the length of GHX and thermal resistance should be kept minimum so that the initial investment of the GSHP will be reduced. However, for the case of COP higher the better concept is employed. The procedure to calculate the S/N ratios is discussed as follows [47]: For smaller the better concept, n 1X y2 n i¼1 i

Smaller the better S=NðdBÞ ¼ 10*log10

! (19)

where, Yi is the response, ‘n’ is the trial number, ‘i’ is the number of repetitions in a trial. For larger the better concept,

Larger the better S=NðdBÞ ¼ 10*log10

n 1X 1 2 n y i¼1 i

! (20)

For nominal the best concept,

0

1

1 Bn ðSm

Ve ÞC A Ve

Nominal the best S=NðdBÞ ¼ 10*log10 @

where Sm

n 1 X ¼ y n i¼1 i

!2 and Ve ¼

Fig. 5. Inlet ﬂuid temperature for Taguchi L18 array.

(21)

n 1 X ðy yÞ2 n 1 i¼1 i

In general the performance of the system where the smaller the better or larger the better concept is employed, is analyzed using the mean S/N ratio of the system. 3.1.1. Length of ground heat exchanger The S/N ratio of the Taguchi L18 array for GHX length is presented in Table 3. The average value of S/N ratios for the eight control parameters are listed in Table 4. The average S/N ratio is considered as the index of the output. In this study average S/N ratio is calculated using the smaller the better concept. The effect of each parameter on average S/N ratio is given in Table 4 and the difference between the maximum and minimum values of the S/N ratio for GHX length are also shown in the above table. Using this data the control parameters can be ranked. For the case of GHX length, the following order of control parameters indicates their ranking from 1 to 8: entering water temperature (G), grout thermal

conductivity (F), thermal conductivity of heat exchanger pipe material (A), heating load (C), inner radius of U tube heat exchanger (E), borehole radius (D), mass ﬂow rate of ﬂuid per kW of load (B), center to center distance between U tubes (I). From Table 3 the minimum and maximum lengths of the heat exchanger are found to be 66.6 m and 391.9 m respectively. Fig. 5 shows the inlet ﬂuid temperature of GHX for Taguchi L18 array. The inlet ﬂuid temperature at 3rd and 11th trial runs is 10 C. Fig. 6 shows the S/N ratio graphs for GHX length. The optimum levels of the control parameters for the GHX length can be easily obtained from Fig. 6 and the same can be veriﬁed from the data shown in Table 4. The most inﬂuencing parameters for GHX length are: thermal conductivity of heat exchanger pipe material, heating load, inner radius of U tube heat exchanger, grout thermal conductivity and entering water temperature. Based on the S/N ratio values shown in Table 4 and Fig. 6, the optimum parameterselevel combination for GHX length is A2B1C1D1E3F3G1I3 i.e. thermal conductivity of heat exchanger pipe material is 0.42 W.m1.K1, mass ﬂow rate of ﬂuid per kW of load is 0.04 kg.s1.kW1, heating load is 7 kW, borehole radius is 0.0635 m, inner radius of U tube heat exchanger is 0.0191 m, grout thermal conductivity is 2.59 W.m1.K1, entering water temperature is 4 C and center to center distance between U tubes is 0.07 m.

3.1.2. Coefﬁcient of performance The S/N ratio values computed for the optimization of COP using the Taguchi L18 trial runs are presented in Table 3. The minimum and maximum COPs are found to be 2.19 and 3.75 respectively. The average values of S/N ratios for the eight parameters are presented in Table 5 and also it presents the effect of each parameter on the average S/N ratio. Fig. 7 shows the S/N ratio graphs for different parameters of COP. Table 5 and Fig. 7 help to identify the optimum levels of the considered parameters. It is clear from Fig. 7 and Table 5 that all the eight parameters in some way inﬂuence the COP value. Based on the S/N ratio, the optimum parameterselevel combination for COP is A2B2C1D3E3F3G1I2. i.e. thermal

Table 4 Taguchi response table for GHX length. Level

A

B

C

D

E

F

G

I

1 2 3 Delta (S/Nmax e S/Nmin) Rank Optimum

45.89 42.02

43.60 44.10 44.17 0.57 7 B1

42.28 43.90 45.68 3.40 4 C1

43.55 44.24 44.07 0.69 6 D1

44.69 44.00 43.18 1.52 5 E3

46.49 42.96 42.42 4.07 2 F3

41.48 43.76 46.63 5.16 1 G1

44.16 43.97 43.74 0.41 8 I3

3.87 3 A2

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Fig. 6. Taguchi e S/N ratio analysis for GHX length.

conductivity of heat exchanger pipe material is 0.42 W.m1.K1, mass ﬂow rate of ﬂuid per kW of load is 0.05 kg.s1.kW1, heating load is 7 kW, borehole radius is 0.0889 m, inner radius of U tube heat exchanger is 0.0191 m, grout thermal conductivity is 2.59 W.m1.K1, entering water temperature is 4 C and center to center distance between U tubes is 0.06 m Table 5 also gives the difference of the S/N ratio for COP to rank the parameters. The orders of the inﬂuencing parameters based on the ranks are: heating load (C), entering water temperature (G), thermal conductivity of heat exchanger pipe material (A), mass ﬂow rate of heat exchanger ﬂuid (B), grout thermal conductivity (F), inner radius of U tube heat exchanger (E), center to center distance between U tubes (I) and borehole radius (D). In general whenever the entering water temperature increases COP will also increase for space heating application. 3.1.3. GHX thermal resistance Thermal resistance of GHX depends on the resistance of the heat exchanger pipe, grout resistance and convective resistance. Table 3 shows the values of the GHX thermal resistance along with the S/N ratio for Taguchi L18 array. The minimum and maximum thermal resistances of the GHX from 18 trial runs are found to be 0.082 m.K.W1 and 0.406 m.K.W1 respectively. Fig. 8 shows the pipe and grout thermal resistance for Taguchi L18 array. From the above ﬁgure the minimum pipe resistance is found to be 0.052 m.K.W1 for trial number 17 and its maximum pipe resistances is 0.34 m.K.W1. The minimum grout thermal resistance is found to be 0.04 m.K.W1 at trial number 4. The average value of

Table 5 Taguchi response table for COP. Level

A

D

E

F

G

I

1 2 3 Delta (S/Nmax e S/Nmin) Rank Optimum

11.59 11.87 12.50 12.31 12.21 11.91 11.77 11.44 0.73 0.44 1.05

B

11.95 11.92 11.98 0.06

12.04 11.76 12.05 0.30

11.69 12.05 12.12 0.43

12.35 12.15 11.36 0.99

11.82 12.03 12.01 0.21

3 A2

8 D3

6 E3

5 F3

2 G1

7 I2

4 B2

C

1 C1

S/N ratios of the GHX thermal resistance is listed in Table 6. The effect of each parameter on the average S/N ratio and the difference of the S/N ratio (S/Nmax e S/Nmin) for the GHX thermal resistance are also given in the above table. Based on this difference the control parameters can be ranked as follows: grout thermal conductivity (F), thermal conductivity of GHX pipe material (A), borehole radius (D), inner radius of U tube heat exchanger (E), heating load (C), entering water temperature (G), mass ﬂow rate of ﬂuid per kW of load (B) and center to center distance between U tubes (I). Using the data shown in Fig. 9 and Table 6 the optimum levels of the control parameters can be identiﬁed. It is clear from Fig. 9 that only ﬁve parameters have inﬂuence on the thermal resistance of GHX. The most inﬂuencing parameters are grout thermal conductivity, borehole radius, thermal conductivity of heat exchanger pipe material and inner radius of U tube heat exchanger. The optimum parameters and levels for optimum thermal resistance of GHX is found to be A1B2C1D2E1F1G3I1 i.e. thermal conductivity of heat exchanger pipe material is 0.10 W.m1.K1, mass ﬂow rate of ﬂuid per kW of load is 0.05 kg.s1.kW1, heating load is 7 kW, borehole radius is 0.0762 m, inner radius of U tube heat exchanger is 0.0127 m, grout thermal conductivity is 0.73 W.m1.K1, entering water temperature is 12 C and center to center distance between U tubes is 0.05 m. 3.2. Taguchi-ANOVA analysis ANOVA uses statistical techniques to determine the important parameters that affect the length of GHX, thermal resistance and COP. It also helps to ﬁnd out the corresponding importance of individual factor in terms of percentage allowance to the comprehensive response of all the control factors. In the present research ANOVA analysis has been carried out with a conﬁdence level of 95%. ANOVA table contains degrees of freedom, SS (Sum of squares), MS (Mean of squares), F ratio, P value and percentage contribution, these factors are computed for all the control parameters. Among these data, the F ratio is used to identify the parameters which have signiﬁcant effect on the GHX length and resistance. The following formulas have been used to calculate the SS (sum of squares), MS (mean of squares), CF (correction factor) and DOF (degree of freedom):

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9

Fig. 7. Taguchi e S/N ratio analysis for COP.

SS ¼

1 ðsum of S=N ratio level IÞ2 þ ðsum of S=N ratio level IIÞ2 2

þ ðsum of S=N ratio level IIIÞ2 C:F (22)

Correction factor ðC:FÞ ¼

2 sumof NS N

(23)

where, N ¼ total number of trials (N ¼ 18)

Degree of Freedom ¼ Level 1 Mean of squares ¼

SS DOF

(24) (25)

3.2.1. Length of ground heat exchanger ANOVA analysis for the length of GHX is presented in Table 7 for Taguchi L18 array. The degree of freedom for ANOVA analysis has been selected on the basis of ‘Level 1’ concept. From Table 7 it is

clear that only ﬁve parameters have considerable effect on the GHX length and their contributions are, entering water temperature (G): 31.86%, thermal conductivity of heat exchanger pipe material (A): 26.79%, grout thermal conductivity (F): 23.29%, heating load (C): 13.81% and inner radius of U tube heat exchanger (E): 2.74% and the contribution of other three parameters, borehole radius, mass ﬂow rate of ﬂuid per kW of load and center to center distance between U tubes is 1.5%. This can be veriﬁed by analyzing the F value given in Table 7 which clearly reveals that the entering water temperature, thermal conductivity of heat exchanger pipe material, grout thermal conductivity and heating load are the most signiﬁcant factors (F value > 10) affecting both the S/N ratio and the length of GHX. From the data of length of GHX shown for 18 trial runs in Table 2, the minimum length of the heat exchanger is found to be 66.6 m. However, by the use of Taguchi optimization, the length of GHX is found to be reduced to 56.5 m. 3.2.2. Coefﬁcient of performance ANOVA analysis for COP of a GSHP is presented in Table 8. The order in which the control parameters affect the performance of GSHP can be listed as, heating load (C), entering water temperature (G), thermal conductivity of heat exchanger pipe material (A), Mass ﬂow rate of ﬂuid per kW of load (B), grout thermal conductivity (F) and inner radius of U tube heat exchanger (E). Parameter D (borehole radius) and I (center to center distance between U tubes) are found to be insigniﬁcant. The percentage contribution from the signiﬁcant parameters are, C: 30.12%, G: 29.62%, A: 21.54%, B: 6.79%, F: 5.8% and E: 4.23%. The percentage contribution from the insigniﬁcant parameters (D and I) are 0.10% Table 6 Taguchi response table for effective GHX thermal resistance.

Fig. 8. Pipe and grout resistances for Taguchi L18 array.

Level

A

D

E

F

G

I

1 2 3 Delta (S/Nmax e S/Nmin) Rank Optimum

12.60 15.46 15.13 18.35 15.38 15.75 15.38 15.53 5.75 0.20 0.62

B

16.62 14.81 14.98 1.81

14.54 15.52 16.34 1.80

11.94 16.73 17.74 5.80

15.50 15.57 15.34 0.23

15.41 15.48 15.52 0.11

2 A1

3 D2

4 E1

1 F1

6 G3

8 I1

7 B2

C

5 C1

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Fig. 9. Taguchi e S/N ratio analysis for GHX thermal resistance.

and 1.69% respectively. Hence whenever the GHX is installed in any kind of climatic conditions, heating load, entering water temperature and thermal conductivity of GHX pipe material and grout play a major role. Entering water temperature depends on the soil properties, so before installing any high capacity GSHP system, a TRT (Thermal Response Test) needs to be carried out in order to ﬁnd out the soil thermal conductivity and undisturbed ground temperature. Before applying Taguchi optimization technique, the maximum COP obtained from L18 array was found to be 3.749, whereas, with the optimization, the COP has increased by 2.46%

resistance from L18 array is found to be 0.082 m.K.W1 but it is reduced to 0.068 m.K.W1 after Taguchi optimization. By comparing the average S/N ratio of GHX length and GHX thermal resistance the effect of controllable parameter is observed to be high in the case of thermal resistance of GHX but in the case of length of the GHX, the uncontrollable parameters are dominant. It is also noted that the percentage contribution and the control parameters that inﬂuence the optimum values of GHX length and thermal resistance are different. In GHX length, the entering water temperature plays a predominant role; however, it doesn't exhibit any impact on thermal resistance.

3.2.3. GHX thermal resistance ANOVA analysis for GHX thermal resistance is presented in Table 9. The important parameters that affect the thermal resistance and their percentage contributions are, thermal conductivity of heat exchanger pipe material (A): 51.62%, grout thermal conductivity (F): 40.04%, borehole radius (D): 4.17%, inner radius of U tube heat exchanger (E): 3.49%, heating load (C): 0.41%, entering water temperature (G): 0.15%, mass ﬂow rate of ﬂuid per kW of load (B): 0.10% and center to center distance between U tubes (I): 0.02%. The main reason for grouting thermal conductivity affects more than any other parameters is that it enhances the heat transfer rate between heat exchanger and the ground. The minimum thermal

3.3. Utility e signal to noise ratio analysis

Table 7 Taguchi ANOVA for GHX length.

Table 8 Taguchi ANOVA for COP.

Source

Degree of freedom (DF)

Sum of squares (SS)

Mean of squares (MS)

F ratio

P value

A B C D E F G I Error Total

1 2 2 2 2 2 2 2 2 17

67.417 1.158 34.760 1.552 6.907 58.627 80.201 0.512 0.564 251.696

67.4165 0.05789 17.3799 0.7758 3.4536 29.3134 40.1003 0.2558 0.2819

239.12 2.05 61.64 2.75 12.25 103.97 142.23 0.91

0.004 0.328 0.016 0.267 0.075 0.010 0.007 0.524

% contribution

26.785 0.466 13.81 0.6166 2.744 23.292 31.864 0.423 100

From the Taguchi analysis three different sets of parameters and levels were obtained for optimum values of GHX length, COP and thermal resistance of GHX. However, when the GSHP is employed for different operations, it is essential to estimate the optimum parameters for GHX length, COP and thermal resistance and also to determine a single level of optimum parameters and levels for all the three objective functions. This can be achieved with the help of utility concept, which is widely used in manufacturing techniques. In a given application, there may be three possibilities of requirements, reduced GHX length, or high COP or least thermal

Source

Degree of freedom (DF)

Sum of squares (SS)

Mean of squares (MS)

F ratio

P value

A B C D E F G I Error Total

1 2 2 2 2 2 2 2 2 17

2.3853 0.6295 3.3435 0.0116 0.3359 0.6460 3.2815 0.1544 0.2844 11.0722

2.38535 0.31477 1.67176 0.00581 0.16796 0.32299 1.64075 0.07720 0.14220

16.77 2.21 11.76 0.04 1.18 2.27 11.54 0.54

0.055 0.311 0.078 0.961 0.458 0.306 0.080 0.648

% contribution

21.543 6.785 30.197 0.104 4.231 5.824 29.622 1.694 100

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T. Sivasakthivel et al. / Energy xxx (2014) 1e14 Table 9 Taguchi ANOVA for effective GHX thermal resistance. Source

Degree of freedom (DF)

Sum of squares (SS)

Mean of squares (MS)

F ratio

P value

A B C D E F G I Error Total

1 2 2 2 2 2 2 2 2 17

148.744 0.120 1.189 12.017 9.755 115.365 0.162 0.040 0.715 288.127

148.744 0.060 0.595 6.008 4.888 57.683 0.081 0.020 0.358

415.86 0.17 1.66 16.80 13.66 161.27 0.23 0.06

0.002 0.857 0.376 0.056 0.068 0.006 0.816 0.947

% contribution

51.624 0.101 0.412 4.17 3.485 40.039 0.153 0.016 100

resistance. In GSHP installation, the length of GHX and COP are important parameters that will decide the initial cost and running cost respectively and hence in the present analysis, GHX length and COP are considered as the main important objectives and thermal resistance is treated as second level objective. This principle has been taken care by assigning the weighting factor for GHX length and COP as 0.35 each and 0.3 for thermal resistance of GHX. Using Eqs. (2)e(9), the utility values of GHX length, COP and thermal resistance of GHX have been computed for the eight control parameters at different levels and then they are combined to form the overall utility value for L18 trial runs and their corresponding S/N values are calculated based on the higher the better concept, as presented in Table 10. Table 11 shows the average S/N ratios of the eight control parameters, A, B, C, D, E, F, G and I at different levels for utility concept. The maximum value of the average S/N value indicates the optimum value of the operating parameters. Hence, from Table 11, the best combinations of the parameters to get the optimum GHX length, optimum COP and optimum thermal resistance are found to be A2B2C1D1E3F3G1I3 i.e. thermal conductivity of heat exchanger pipe material: 0.42 W.m1.K1, mass ﬂow rate of ﬂuid per kW of load: 0.05 kg.s1.kW1, heating load: 7 kW, borehole radius: 0.0635 m, inner radius of U tube heat exchanger: 0.0191 m, grout thermal conductivity: 2.59 W.m1.K1, entering water temperature: 4 C and center to center distance between U tubes: 0.07 m. This is also conﬁrmed by the plots of S/N values for all the eight parameters shown in Fig. 10. From Table 11 and Fig. 10 it is clear that all the eight control parameters have some effect on the performance of the GSHP system. Table 11 also gives the difference (S/

Table 10 Utility value and its S/N ratio. Utility trial number

Utility value

S/N value (dB)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

3.849434 4.147751 3.213921 4.395791 5.626995 2.093685 4.725092 0.852717 4.580631 7.305757 5.801079 4.490037 4.602013 6.925738 6.113138 7.903256 5.60993 4.156274

11.7079 12.3563 10.1407 12.8607 15.0055 6.4182 13.4882 1.3839 13.2185 17.2733 15.2702 13.0450 13.2590 16.8093 15.7253 17.9561 14.9791 12.3741

11

Nmax e S/Nmin) of the S/N ratio to rank the parameters. Based on the ranking, the inﬂuencing parameters are ordered as: grout thermal conductivity (F), thermal conductivity of heat exchanger pipe material (A), entering water temperature (G), borehole radius (D), heating load (C), inner radius of U tube heat exchanger (E), center to center distance between U tubes (I) and mass ﬂow rate of ﬂuid (B). 3.4. Utility e ANOVA analysis The computed values for ANOVA of utility concept based on 95% conﬁdence interval and 5% signiﬁcance are presented in Table 12. ANOVA also helps to identify the signiﬁcance of each control factors on the performance parameters. The data for ANOVA analysis can be evaluated by calculating the percentage contribution of each control factor. The percentage contributions of each parameters are as follows, thermal conductivity of heat exchanger pipe material (A): 30.18%, grout thermal conductivity (F): 26.31%, entering water temperature (G): 16.52%, heating load (C): 8.08%, borehole radius (D): 7.28%, inner radius of U tube heat exchanger (E): 5.41%, center to center distance between U tubes (I): 3.38%, mass ﬂow rate of ﬂuid per kW of load (B): 2.84%. These data can also be veriﬁed by analyzing the F value given in ANOVA table. It is clear from the observations of Table 12 that for optimum GHX length, COP and GHX thermal resistance, thermal conductivity of heat exchanger pipe material, grout thermal conductivity, entering water temperature, heating load and inner radius of U tube heat exchanger need to be selected very carefully and all of these parameters in unison contribute around 94%. Based on the Taguchi optimization, the optimum levels of control parameters for the three objective functions are, length of GHX: A2B1C1D1E3F3G1I3, COP: A2B2C1D3E3F3G1I2 and thermal resistance of GHX: A1B2C1D2E1F1G3I1. By comparing the levels of various control parameters for the three optimum parameters with those of the levels obtained from utility concept (A2B2C1D1E3F3G1I3), it can be noted none of the control parameters are found to appear for all the three performance parameters (objective functions). This conﬁrms the present methodology adopted for optimization of GSHP based on Taguchi method and utility concept has predicted the results without error. 3.5. Utility e weighting factor sensitivity analysis In utility analysis selection of right kind of weighting factors decides the optimum length of GHX, optimum COP and optimum GHX thermal resistance. The results discussed in the present work are based on the weighting factors assigned as, WGHx length ¼ WCOP ¼ 0.35 and Wthermal resistance ¼ 0.3. For the length of GHX and COP equal weighting factors are assigned for the reason that whenever the entering water temperature increases COP of GSHP system also increases, therefore it results in an increase in the length of the GHX, and also the length of GHX and COP are linked respectively to the initial and running costs of GSHP. Hence in order to avoid too much increase in length or too much decrease in COP, equal weightage are considered to both GHX length and COP. However, it is essential to understand the inﬂuence of the selection of weights for the three performance parameters. A sensitivity analysis for the weighting factors are carried out by considering four cases, in which for any given parameter the weight has been varied from a minimum value of 0.1 to a maximum value of 0.5, however, keeping equal weights for COP and GHX length. Table 13 presents the results for the sensitivity analysis of different combinations of weight factors for optimum length of GHX, optimum COP and optimum GHX thermal resistance. The percentage variations of the above parameters between two consecutive cases are indicated by the side of the respective values of the parameters. The upside

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Table 11 Utility response table of S/N ratios. Level

A

B

C

D

E

F

G

I

1 2 3 Delta (S/Nmax e S/Nmin) Rank Optimum

10.424 15.188

13.299 13.346 11.772 1.574 8 B2

14.424 12.173 11.820 2.604 5 C1

13.960 13.255 11.202 2.758 4 D1

12.678 11.760 13.979 2.219 6 E3

9.671 14.149 14.598 4.927 1 F3

14.624 13.373 10.420 4.204 3 G1

11.784 13.080 13.554 1.770 7 I3

4.764 2 A2

Fig. 10. Utility e S/N ratio analysis.

and downside arrow marks are used to indicate the increase and decrease in the values of the parameters with the variation of the weights. Values in bold letters indicate the weights used for the results discussed in this paper. It is observed from the table that whenever the weighting factor assigned to the length of GHX is increased from 0.250 to 0.450, GHX length decreases approximately by 9%. In the case of COP, for the increase of weighting factor from 0.250 to 0.450 the increase in COP is not uniform, however it is more sensitive to the weighting factor range of 0.250e350 and the optimum value lies in between 0.350 and 0.450. It is observed that thermal resistance of GHX is more sensitive when the weighting factor was decreased from 0.300 to 0.100 compared to the decrease from 0.500 to 0.333, but it exhibits very narrow variation for the Table 12 Utility ANOVA. Source

Degree of freedom (DF)

Sum of squares (SS)

Mean of squares (MS)

F ratio

P value

A B C D E F G I Error Total

1 2 2 2 2 2 2 2 2 17

102.146 9.624 23.947 24.633 14.925 89.051 55.911 10.076 8.105 338.418

102.146 4.812 11.974 12.317 7.462 44.525 27.956 5.038 4.053

25.20 1.19 2.95 3.04 1.84 10.99 6.90 1.24

0.037 0.457 0.253 0.248 0.352 0.083 0.127 0.446

% contribution

30.183 2.843 8.076 7.278 5.41 26.313 16.521 3.376 100

change of weighting factor from 0.333 to 0.300, so the optimum weighting factors range from 0.333 to 0.300. From the detailed sensitivity analysis it is found that the best optimum weighting factors to get optimum performances are WGHx length ¼ WCOP ¼ 0.35 and Wthermal resistance ¼ 0.3. Thus the selection of right kind of weighting factors will yield the required optimum values for the parameters. 3.6. Selection of optimal levels, conﬁrmation tests and comparison with other studies In Taguchi method the response of the predicted values is not the same as the trial run values and the predicted values are less in the case of results obtained using the smaller the better concept and large in the case of larger the better concept. Hence a conﬁrmation test is required to validate the results of optimization. The CI (conﬁdence interval) can be calculated to estimate the range of performance parameters. In this study, 95% of conﬁdence interval is considered. The CI is evaluated using the following formula:

" CI ¼

Fða;1;fe Þ Ve

#!1 2 1 1 N þ and Neff ¼ Neff R 1 þ TDOF

(26)

where Fða;1;fe Þ is the F value from the F table from statistical table in the suitable conﬁdence interval and at a degree of freedom of 1. Table 14 presents the optimum levels of control parameters predicted using the Taguchi method and utility concept and it also

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13

Table 13 Utility - sensitivity analysis of weighting factors. Cases

Weighting factors WGHx

1 2 3 4

length

0.250 0.333 0.350 0.450

Optimum values WCOP

Wthermal

0.250 0.333 0.350 0.450

0.500 0.333 0.300 0.100

resistance

GHX length (m)

COP

70.7 64.4 58.3 53.1

2.942 3.427 3.796 3.876

presents the predicted optimum values, conﬁdence intervals and conﬁrmation results for GHX length, COP and thermal resistance of GHX for Taguchi optimization. From the Taguchi optimization technique, the predicted optimum values for GHX length, COP and thermal resistance are 59.20 m, 3.76 and 0.074 m.K.W1 respectively and Taguchi conﬁrmation results show that GHX length is 4.56% less than the predicted value, in the case of COP it is 2.2% higher than the predicted value and thermal resistance of GHX is 8.11% less than the predicted value. At the end of the utility optimization, the optimum GHX length, COP and thermal resistance are predicted as 58.3 m, 3.796 and 0.059 m.K.W1 respectively. When comparing the results from the present research to already published research works it was found that varying thermal conductivity of soil [8] plays a critical role in deciding the length of the GHX and to evaluate this parameter accurately thermal response test has to be carried out. Borehole heat exchanger diameter is another important parameter to get high thermal performance [31]. Larger diameter boreholes are better but it increases the initial investment. High Grout thermal conductivity will result in less GHX and better COP [33]. Thermal interaction between two legs of the U tube plays a signiﬁcant role in deicing thermal efﬁciency of GHX in order to avoid thermal interaction between two legs centre to centre distances between two legs needs to be at higher side [6]. Applying GSHP system for an average load will result in better payback period compared to meeting the whole peak demand by a GSHP system [35]. 4. Conclusions This study presents the application of Taguchi and utility method in determining the optimum GHX parameters for GSHP applications. Based on this study, the following conclusions are drawn: ✓ Minimum length of the GHX from Taguchi L18 array is 66.6 m and maximum is 391.9 m and the corresponding loads are 7 kW and 8.75 kW. For 10.5 kW load the minimum length of the GHX is found to be 127 m. From this, it is clear that it's not only the heating load which dictates the length of the GHX.

8.91%Y 9.47%Y 8.91%Y

Thermal resistance (m.K.W1) 16.48%[ 10.76%[ 2.12%[

0.042 0.056 0.059 0.097

33.33%[ 5.36%[ 64.41%[

✓ In Taguchi optimization for length of the GHX the most inﬂuential parameters are entering water temperature, thermal conductivity of heat exchanger pipe material, grout thermal conductivity and heating load. Entering water temperature depends on the ground formation, so TRT (Thermal Response Test) needs to be carried out for high capacity installation. ✓ The important parameters that affect the COP of the GSHP system is heating load, entering water temperature, thermal conductivity of heat exchanger pipe material and mass ﬂow rate of ﬂuid per kW of load. COP of the GSHP system for Taguchi L18 array varies from 2.20 to 3.75. ✓ Parameters which affect the GHX thermal resistance are grout thermal conductivity, thermal conductivity of heat exchanger pipe material, borehole radius and pipe diameter. The minimum and maximum thermal resistances are found to be 0.082 m.K.W1 and 0.406 m.K.W1 respectively. ✓ Selecting a right kind of weighting factor for given objective functions decides the efﬁciency of the optimization, hence researchers have to give due importance while selecting the weighting factors for different kind of objective functions. ✓ Optimum parameters and levels for Taguchi optimization are, length of GHX: A2B1C1D1E3F3G1I3, COP: A2B2C1D3E3F3G1I2 and thermal resistance of GHX: A1B2C1D2E1F1G3I1. Utility optimum parameters and levels are: A2B2C1D1E3F3G1I3. ✓ From Taguchi optimization analysis, the optimum GHX length, COP and thermal resistance are computed as 56.5 m, 3.84 and 0.068 m.K.W1 respectively. Application of the utility concept has resulted in 3.2% increase in the length of the GHX, 1.18% decrease in COP and 13.23% decrease in thermal resistance of the GHX. Acknowledgments The ﬁrst author is thankful to the Ministry of Human Resources and Development, Government of India, for providing the fellowship for pursuing PhD at Indian Institute of Technology Roorkee, Roorkee, India. References

Table 14 Optimum parameters and conﬁrmation results. Performance Optimum Parameters parameters

GHX length COP Thermal resistance of GHX Utility

Conﬁrmation Predicted 95% of optimum predicted results conﬁdence value intervals

A2B1C1D1E3F3G1I3 59.20 A2B2C1D3E3F3G1I2 3.76 A1B2C1D2E1F1G3I1 0.074

A2B2C1D1E3F3G1I3

±4.56 ±1.02 ±0.08

56.5 m 3.8414 0.068 m.K.W1

Length: 58.3 m COP: 3.796 Thermal resistance: 0.059 m.K.W1

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