Influence of ground surface boundary conditions on horizontal ground source heat pump systems

Applied Thermal Engineering 152 (2019) 160–168

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Influence of ground surface boundary conditions on horizontal ground source heat pump systems

T

⁎

Chaofeng Lia,b, Jinfeng Maob, , Xue Penga, Wei Maoa, Zheli Xinga, Bo Wangc a

Academy of Military Science PLA China, Beijing 100036, China Army Engineering University of PLA, Nanjing 210007, China c Rocket Force University of Engineering, Xi’an 710025, China b

H I GH L IG H T S

of shading on horizontal GSHP systems is studied. • Effect fluid temperature and its fluctuation of N-S streets are higher. • Outlet in street aspect ratio results in reduced radiation and sunshine time. • Increase • Influence of shading on horizontal GHEs up to buried depth of 2.5 m.

A R T I C LE I N FO

A B S T R A C T

Keywords: Ground surface boundary condition Horizontal ground heat exchanger Heat pump Diurnal shading

In this paper, the effects of ground surface boundary conditions, especially diurnal shading, on performance of horizontal ground source heat pump (GSHP) systems were studied. Firstly, a GSHP system model, which consists of the heat transfer of horizontal ground heat exchangers (GHEs) and the integration of the heat pump, and the ground surface boundary model are introduced. The diurnal shading model for canyon streets is also introduced. Then, effects of ground surface boundary conditions and shading on horizontal GSHP systems are studied. Results show that different assumptions on ground surface boundary conditions have significant impact on outcomes and should carefully be considered during analysing. The outlet fluid temperature and fluctuation in North-South (N-S) streets are higher than those of East-West (E-W) streets. The increase in street aspect ratios and latitudes could decrease sunshine exposure time of the streets. Daily variations of solar radiation and shading influence the outlet temperatures of horizontal GHEs up to buried depth of 2.5 m. Therefore, the effects of solar radiation and shading should be considered when studying shallow horizontal GHEs.

1. Introduction Ground source heat pump (GSHP) systems have widely been used in space cooling/heating due to their high energy efficiency and ecofriendly features [1]. A typical GSHP system consists of geothermal heat pump and numerous ground heat exchangers (GHEs). GSHP systems can further be classified into horizontal and vertical systems according to configurations of GHEs. Compared to horizontal systems, vertical systems are more widely utilized. This is because vertical systems have higher efficiency while occupying less ground area, which is important especially in crowded urban areas. However, initial investments of vertical systems are also higher. Studies show that the installation cost of vertical GHEs is one of the main causes that prevents the widespread use of them with an average drilling cost of £20 to £30 per meter [2].

⁎

Thus, horizontal systems are often preferred over vertical systems when adequate space is available. The use of horizontal GSHP systems could provide viable alternative solutions with good compromise between efficiency and cost. Besides, horizontal GHEs can also be utilized as supplemental heat rejecters/absorbers for vertical GHEs for unbalanced building loads to reduce the required length of vertical GHEs and initial investment [3,4]. Heat transfer of horizontal GHEs can greatly be influenced by ground surface temperature since buried depth is relatively shallow [5,6] (usually less than 2 m [7]). Hence, the accurate modelling of ground surface boundary conditions would have much significance in designing and predicting the performances of horizontal GHEs [8,9]. In reality, boundary conditions at ground surface combine four main heat fluxes: solar radiation, infrared radiation, convection and evaporation.

Corresponding author. E-mail address: [email protected] (J. Mao).

https://doi.org/10.1016/j.applthermaleng.2019.02.080 Received 20 September 2018; Received in revised form 13 February 2019; Accepted 16 February 2019 Available online 18 February 2019 1359-4311/ © 2019 Published by Elsevier Ltd.

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When ground surface is covered by grass or shaded by surrounding trees or buildings, boundary conditions would become more complex. Existing analytical models for vertical GHEs usually assume that ground surface temperature is constant (equal to the initial ground temperature) [10,11]. Some studies indicate that the error is relatively small when evaluating the thermal behaviour of vertical GHEs at depths greater than 50 m [12]. Most numerical models for vertical GHEs assume known ground surface temperature which is a function of time [13,14]. This assumption could yield better results. Therefore, several numerical models in the literature use this kind of boundary condition for horizontal GHEs [15-17]. However, the exact ground surface temperature is hard to determine, especially in short-time scales, due to many influencing factors like natural swift variability of daily weather [18]. Besides, due to relatively shallow depth of horizontal GHEs, the released heat/cold could impact the ground surface temperature. Therefore, simplified boundary conditions have limitations, especially in modelling of horizontal GHEs. In recent years, more detailed boundary conditions have been employed to describe the influencing factors on ground surface [19-21]. Typically, these boundary conditions (Robin boundary) establish an energy balance equation describing an interdependent heat transfer process between ground surface and surrounding environment [22]. Using this approach, heat transfer in ground surface could accurately be calculated. This can not only be used in modelling of horizontal GHEs but also vertical GHEs [23]. For practical applications, it is not uncommon to place GHEs in vicinity of trees [24] or buildings or even beneath underground parking lots [25] and tunnels [26,27] for domestic cooling/heating supply. Hence, the influence of shade on performance of GHEs should be considered under these circumstances [28], especially in dense urban areas where current or future planned infrastructure could influence system performance at different degrees due to daily and seasonal changes of sun position. However, the overall impact of these factors on feasibility and operation of horizontal GHEs has so far not sufficiently been considered or quantified in the literature. Another key element to consider is the heat pump coefficient of performance (COP). GHEs are commonly used as part of GSHP systems [29], and their thermal loads are determined by building load and heat pump COP when used for cooling/heating supply. COP depends on both the building heat/cold demand and performance characteristics of specific heat pump. Thus, the influence of heat pump COP should be taken into account when establishing GSHP system dynamic model. In this paper, a GSHP model consisting of horizontal GHEs coupled with heat pump is proposed. The influences of ground surface boundary conditions on performance of horizontal GSHP systems are assessed by analysing outlet fluid temperatures and heat pump COP. Similarly, the influence of diurnal shading on horizontal GSHP systems is studied mainly from the following aspects: outlet temperatures with (E-W and N-S streets as examples) and without shading, the effect of street aspect ratios, latitudes and buried depths. The conclusion of this paper can give some reference on analysing the effect of ground surface boundary conditions and shading on horizontal GSHP system.

Fig. 1. Diagram of a typical horizontal ground source heat pump system (a) and the computational soil domain (b), dimensions in (m).

horizontal GSHP system under consideration is shown in Fig. 1. 2.1. Heat transfer of horizontal GHEs The energy equation for circulating fluid flow in the horizontal GHE can be written as [30]:

ρf Ap cp, f

∂Tf ∂t

+ ρf Ap cp, f u·∇Tf = Ap kf ∇ ·(∇Tf ) +

1 ρf Ap f |u|3 + Q wall 2 D dh (1)

−3

where ρf (kg m ) is the fluid density, Ap (m ) is the cross section area of pipe, cp,f (J kg °C−1) is the fluid heat capacity, Tf (°C) is the temperature of circulating fluid, t (s) is the time, u (m s−1) is the circulating fluid velocity, kf (W m−1 °C−1) is the fluid thermal conductivity, fD (–) is the Darcy friction factor that can be obtained from the Moody chart, dh (m) is the hydraulic pipe diameter. Furthermore, Qwall (W m−1) indicates the heat transfer between the pipe and surrounding ground, which can be expressed as:

2. Method

Q wall = heff (Text − Tf ) Horizontal GSHP systems mainly consist of two parts: horizontal GHEs and heat pump. When GSHP systems operate for cooling/heating, the circulating fluid would firstly receive the excessive heat/cold from the building through heat pump, and then rejects it to the ground when circulating in the pipe. The horizontal GSHP system model consists of heat transfer model of horizontal GHE and heat pump model. Heat transfer associated with horizontal GHE is composed of heat convection between the circulating fluid and pipe, heat conduction in pipe wall and heat transfer in adjacent ground. The coupling between heat pump and GHE is achieved by considering of inlet and outlet fluid temperatures. Ground surface boundary conditions including effect of diurnal shading are described in Section 2.2. A schematic diagram of a typical

2

(2)

where heff (W m−1 °C−1) is the equivalent convective heat transfer coefficient of pipe wall and Text (°C) is the temperature outside the pipe. For a circular pipe, heff can be described as:

2π

heff = 1 ri hi

+

r ln ⎛ o ⎞ ⎝ ri ⎠ kp

(3)

where ri (m) and ro (m) are internal and external radiuses of the pipe, respectively. kp (W m−1 °C−1) is the pipe thermal conductivity, and hi (W m−2 °C−1) is convection coefficient inside the pipe that can be obtained from: 161

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C. Li, et al.

hi = Nu

kf

evaporation (Ew) from free-water surface can be evaluated as follows: (4)

dh

Ew = F (u)(PsS − Pa)

where Nu (–) represents the Nusselt number with a value of 3.66 in laminar and transitional conditions (Re < 3000). Under turbulent conditions (Re > =3000), it can be calculated by the Gnielinski correlation [30]:

Nuturb =

(fD /8)(Re−1000) Pr 1 + 12.7(fD /8)1/2 (Pr 2/3 − 1)

(Pa) is the saturated where F(u) is a function of the wind velocity u, vapor pressure at the surface, and Pa (Pa) is the vapor pressure in the atmosphere above the surface. Dunkle [37] estimated F(u) from convective heat transfer coefficient (hc) according to Eq. (13):

(5)

F (u) = 0.0168hc

where Re (–) is the Reynolds number, and Pr (–) is the Prandtl number. The heat transfer in the ground can be expressed as Eq. (6), and it couples with the circulating fluid via the heat exchange term Qwall:

ρs cp, s

∂Ts = ks ∇ ·(∇Ts ) − Q wall ∂t

(12) PsS

(13)

In the temperature range −10 °C ≤ T ≤ 30 °C, the saturated vapour pressure PS can be estimated from temperature T (°C) by means of the linear equation: (14)

P S = aT + b

(6)

where ρs (kg m−3) is the ground density, cp,s (J kg °C−1) is the ground heat capacity, Ts (°C) is the ground temperature.

with a = 103 Pa/°C and b = 609 Pa. Therefore, the latent heat flux from ground surface caused by evaporation can be calculated from the following expression [38]:

2.2. Ground surface boundary conditions

Ew = 0.0168fhc [(aTss + b) − ra (aTa + b)]

where ra (–) is the relative humidity of the air above the ground surface, f (–) is the fraction depending mostly on the ground cover and its humidity. For bare soil, this would increase with soil humidity: f = 1 for saturated soils, f = 0.6–0.8 for moist soils, f = 0.4–0.5 for dry soils and f = 0.1–0.2 for arid soils.

2.2.1. General boundary conditions A general energy balance equation can be used to define the boundary conditions in ground surface. The energy balance can be expressed by Eq. (7) when taking into consideration the solar radiation, infrared radiation, convective and evaporative heat fluxes [20,31]:

− ks

∂Tss 4 4 = (1 − αs ) R + εss σ (Tsk y, K − Tss, K ) + hc (Ta − Tss ) − E w ∂z

2.2.2. Diurnal shading Munoz-Criollo et al. [39] proposed constant factor to modify incoming solar radiation, effecting shading due to nearby surface features like trees or buildings on ground surface temperature. In this work, this parameter is further modified to express dependency with time:

(7)

where Tss (°C) and Tss,K (K) are the temperature and absolute temperature of the ground surface, z (m) is the depth, αs (–) is the solar albedo, R (W m−2) is the magnitude of solar radiation, εss (–) is the infrared emissivity of the ground surface, σ (W m−2 K−4) is the Stefan–Boltzmann constant, Tsky,K (K) is the absolute temperature of the sky, hc (W m−2 °C−1) is the convective heat transfer coefficient, Ta (°C) is the air temperature, Ew (W m−2) is the latent heat flux due to evaporation. The solar radiation (R) and air temperature (Ta) can be obtained from local weather stations. The Analytical expressions can be used to represent more general situations [32]. Here, the analytical expressions for annual solar radiation and air temperature proposed by Mihalakakou et al. [33] are employed:

(8)

2πt Ta (t ) = Tm + Tv sin ⎛ − φa⎞ ⎝ t0 ⎠

(9)

⎜

−2

Rs = Rd (1 − Ds (t ))

where Rs (W m ) is the effective solar radiation when considering shading, Rd (W m−2) is the solar radiation during day, and Ds(t) (–) is a diurnal shading factor defined as a function of time t (s). The solar radiation during day could be simplified by regular sinusoidal curve [40]:

Rd (t ) =

1 2π 1 2π R 0 sin ⎡ (t − tr ) ⎤ + R 0 sin ⎡ (t − tr ) ⎤ ⎢ td ⎥ ⎢ ⎥ 2 2 ⎣ ⎦ ⎣ td ⎦

(17)

where R0 (W m ) is the highest magnitude of solar radiation during day, td (s) is the period of one day, tr (s) is the time of sunrise. For a canyon street (Fig. 2), Ds is defined as the ratio of shaded strip width Xt (m) to street width W (m) expressed as [41]:

⎟

⎟

Ds (t ) =

−2

where Rm (W m ), Rv (W m ) and Tm (°C), Tv (°C) are the mean and amplitude of annual solar radiation and air temperature during the period of year t0 (s), respectively. φr (rad) and φa (rad) are corresponding phase angles. Numerous formulations could be used to calculate the sky temperature. Here, it is calculated with the use of the following formula [34]:

Tsky = 0.0552·Ta1.5

(16)

−2

−2

2πt − φr ⎞ R (t ) = Rm + Rv sin ⎛ ⎝ t0 ⎠ ⎜

(15)

Xt cos(e − et ) H = W tan βt W

(18)

(10)

The convective heat transfer coefficient at ground surface is expressed as [35]:

hc = 5.7 + 3.8v

(11)

−1

where v (m s ) is the wind velocity above the ground surface. The exact estimation of heat flow during evaporation from natural surfaces is complex. Several models have been developed to calculate the evaporation rate from soil and free-water surfaces as a function of meteorological conditions. Penman [36] showed that energy due to

Fig. 2. Scheme of horizontal ground heat exchangers beneath a canyon street. 162

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16

where βt (rad) is the sun altitude angle, e (rad) and et (rad) are respectively the streets and solar azimuth angles measured from the south at time t (s), and H (m) is the height of the building. For an East-West (E–W) oriented street (e = 0), the shading factor at daytime t reduces to:

cos et H tan βt W

12

Temperature (oC)

Ds (t ) =

14

(19)

while for a North-South (N–S) oriented street (e = −π/2), the shading factor will follow:

Ds (t ) =

sin et H tan βt W

10 8 6 4

(20)

2

The value of Ds(t) should be below one. A value of one would mean fully shaded street, otherwise partially shaded. In this paper, heat flux of diffuse radiation is neglected.

0

Ds (t ) = min(Ds (t ) , 1)

-2 -22

-14

-12

-10

-8

-6

-4

-2

0

Table 1 The parameters used in the numerical study.

The coupling between heat pump and GHE is achieved by considering inlet and outlet fluid temperatures. The inlet fluid temperature of GHE can be computed using the outlet fluid temperature from preceding time step by: (22)

where Tf,i (°C) and Tf,o (°C) are inlet and outlet fluid temperatures, QGHE (W) is the thermal load of the GHE, and Vf (m3 s−1) is the volumetric flow rate. In heating mode, the thermal load of GHE (QGHE) is lower than that of the building and it can be expressed as:

1 heating ⎞ QGHE = QBuilding ⎛⎜1 − ⎟ COP heating ⎠ ⎝

-16

Fig. 3. Initial ground temperature profile.

2.3. Coupling with heat pumps

QGHE ρf cp, f Vf

-18

Depth (m)

The infrared radiation of ground surface in canyon street can also be affected by nearby buildings. Here, the effective infrared radiation influenced by nearby buildings is calculated by modifying the value of infrared emissivity of the ground surface (εss) [42].

Tf , i = Tf , o +

-20

(21)

Item

Value

Fluid thermal conductivity, kf Fluid thermal capacity, ρfcp,f Circulating fluid velocity, u Thermal conductivity of pipe wall, kp Ground thermal conductivity, ks Ground thermal capacity, ρscp,s Solar albedo, αs Infrared emissivity of ground surface, εss Wind velocity, v Annual solar radiation parameters Rm, Rv, φr Annual air temperature parameters Tm, Tv, φa Daily solar radiation parameters R0, tr COP function coefficients a′, b′, c′

0.51 W m−1 °C−1 3.9 MJ m−3 °C−1 0.4 m s−1 0.6 W m−1 °C−1 2 W m−1 °C−1 2.5 MJ m−3 °C−1 0.15 0.9 1.5 m s−1 228 W m−2, 117 W m−2, π/2 rad 14.2 °C, 15.8 °C, π/2 rad 250 W m−2, 6 h −0.003, 0.056, 5.784 for cooling −0.001, 0.133, 3.257 for heating

as adiabatic. The circulating pipe fluid is water and parameters used in numerical analysis are shown in Table 1.

(23)

and in cooling mode it is calculated according to:

1 cooling ⎞ QGHE = QBuilding ⎜⎛1 + ⎟ COP cooling ⎠ ⎝

3.1. Grid independent test and model validation (24)

where a′(–), b′(–) and c′(–) are coefficients of the COP function.

The numerical model is developed based on finite element method for spatial discretization and backward difference time stepping scheme. As the pipeline exhibited steep temperature gradient, relatively fine mesh was used near the pipe. To verify the independence of grid, outlet fluid temperatures are compared for four cases of total 4-noded tetrahedral elements: 3133, 5291, 7471 and 9406. The buried depth of horizontal GHE is 2 m and annual building load for horizontal GHE is expressed as:

3. Effects of ground surface boundary conditions

Q=

In this section, numerical simulations are carried out to investigate the effects of ground surface boundary conditions on the performance of horizontal GSHP system. Assuming that horizontal GHEs are placed in parallel of pipe spacing 2 m (Fig. 1), lengths, internal pipe diameters and external pipe diameters of GHEs are 50 m, 0.025 m, 0.032 m, respectively. The computational soil domain is 2 m, 90 m, and 22 m along the x, y, and z (depth) directions, respectively. Initial ground temperature profile (Fig. 3) by means of 10-years preliminary simulation using below parameters and by ignoring the influence of daily solar radiation and diurnal shading. The ground surface boundary condition is provided in Section 2.2 and the remaining boundaries are considered

where A0 (W) is the highest magnitude of the load in each year (taken as 1000 W) and Ф (rad) is phase angle (taken as π/2 rad). Fig. 4 presents the highest outlet fluid temperatures of four different mesh sizes. The highest outlet temperatures were compared because outlet temperatures and their differences were the biggest at elevated building loads. The test results revealed that the highest outlet temperature tends to converge toward a constant value when the number of elements exceeds 7471. The outlet temperature difference between the last two cases is around 0.01 °C. Therefore, 9406 was selected as the element number. The validation of the heat transfer model of the horizontal GHE can

Normally, the COP of a specific heat pump is not constant and can be expressed as either the ratio of heat removed from or supplied to the heat reservoir over the electrical power consumed by heat pump, or as linear [43] or quadratic [44] function of GHE outlet temperature:

COP = a′Tf2, o + b′Tf , o + c′

(25)

163

3 2π 1 2π A0 sin ⎛ t - ϕ⎞ + A0 sin ⎛ t - ϕ⎞ 4 4 ⎝ t0 ⎠ ⎝ t0 ⎠ ⎜

⎟

⎜

⎟

(26)

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C. Li, et al.

32.8

32.6 32.5

Temperature ( oC)

Highest outlet temperatures

32.7

32.4 32.3 32.2 32.1 32.0 3000

4000

5000

6000

7000

8000

9000

10000

34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2

Tf,o Energy balance equation Tf,o Equal to air temperature 0

1

2

3

4

Number of elements

5

6

7

8

9

10

11

12

Time (month)

(a)

Fig. 4. Results of the grid independent test. 6.2

be seen in Ref. [45] and the accuracy the of ground surface boundary condition model can be seen in Refs. [31,33] etc.

6.0 5.8 5.6

3.2. Influence of the selection of ground surface boundary conditions on calculation results

5.4 5.2

COP

There are two main ways to calculate heat flux on ground surface when analysing heat transfer of horizontal GHEs. One is based on establishing the energy balance equation on ground surface and the other by assuming known ground surface temperature as a function of time (usually equal to air temperature). To evaluate the impact of the selection of boundary conditions on calculation results, outlet fluid temperatures and heat pump COP of one-year period are calculated under the two mentioned conditions with initial ground temperature depicted in Fig. 3, buried depth and building load described in Section 3.1.

5.0 4.8 4.6 4.4 4.2 4.0

Energy balance equation Equal to air temperature

3.8 3.6

0

1

2

3

4

• Case 1: Establishing energy balance equation on ground surface •

5

6

7

8

9

10

11

12

Time (month)

(b)

(Eqs. (7)–(15)). The daily variations of solar radiation (Eq. (8)) and air temperature (Eq. (9)) are ignored. Case 2: Assuming ground surface temperature equal to air temperature (Eq. (9)).

Fig. 5. Outlet fluid temperatures (a) and heat pump COP (b) of two different boundary conditions. 0.8

The analysis data are illustrated in Fig. 5. It can be seen that results of two different boundary conditions show similar trends. However, significant differences can be observed especially when building load is high. These accounted for approximately to 0.4 °C of outlet fluid temperature and 0.06 of heat pump COP for around month 7. This demonstrates that the performance of shallow horizontal GHEs could greatly be influenced by assumptions regarding boundary conditions at the ground surface, leading to relatively large variations in results. Fig. 6 shows the outlet fluid temperature differences between the two mentioned boundary conditions for three buried depths: 1 m, 1.5 m and 2 m. As buried depth decreased, the outlet temperature difference between the two boundary conditions increases, with the highest difference as 0.7 °C corresponding to around month 7 at depth 1 m. Therefore, accurate modelling the ground surface boundary condition has much effect on the exact calculation/prediction of the operation of horizontal GHEs, especially for shallow buried depths.

Temperature difference ( oC)

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1

Buried depth 2.0m Buried depth 1.5m Buried depth 1.0m

-0.2 -0.3 0

1

2

3

4

5

6

7

8

9

10

11

12

Time (month)

3.3. Influence of diurnal shading on horizontal GSHP systems

Fig. 6. Temperature differences between two boundary conditions of three buried depths.

For practical applications, horizontal GHEs could be placed beneath streets, hence their performance could be affect by nearby buildings. Fig. 7(a) shows the shading factors of E-W and N-S streets located at 58oN as an example under four different street aspect ratios (H/W) of 0.4, 0.6, 0.8 and 1.0. The shading factor of E-W streets is recorded as

zero at both sunrise and sunset times, and reaches maximum at noon. However, reverse trends are noticed for N-S streets. It can also be seen that the shading factor increases quickly to 1 (fully shaded) with the

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1.1 1.0 0.9 0.8

Temperature (oC)

Shading factor

0.7 0.6 0.5 0.4 0.3

H/W=0.4 H/W=0.6 H/W=0.8 H/W=1.0

H/W=0.4 H/W=0.6 H/W=0.8 H/W=1.0

0.2 0.1

E-W streets N-S streets

0.0 -0.1

6

7

8

9

10

11

12

13

14

15

16

17

18

8.0 7.5 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 25.0

25.5

27.0

27.5

28.0

28.5

29.0

29.5

30.0

Tf,o E-W streets Tf,o N-S streets 0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30

Time (day)

(a)

(a) 4.4

260

Without shading E-W streets N-S streets

240 220 200

3.39

140 120 100 60 40

3.38 3.37

160

H/W=0.4 H/W=0.6 H/W=0.8 H/W=1.0

3.40

4.2

180

80

3.41

4.3

COP

Solar radiation(W m -2)

26.5

Tf,o Without shading

Time (hour)

4.1

3.36

4.0

3.34

3.9

3.32

3.8

3.30

3.7

3.28

3.35 3.33 3.31 3.29 3.27 25.0

3.6

H/W=0.4 H/W=0.6 H/W=0.8 H/W=1.0

3.3 3.2 2

4

6

8

10

12

14

16

18

20

26.0

26.5

27.0

27.5

28.0

28.5

29.0

29.5

30.0

Without shading E-W streets N-S streets

3.4

0 0

25.5

3.5

20 -20

26.0

22

24

0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30

Time (day)

Time (hour)

(b)

(b)

Fig. 8. Outlet fluid temperatures (a) and heat pump COP (b) of E-W and N-S streets with and without shading.

Fig. 7. Shading factors (a) and solar radiations (b) of E-W and N-S streets under four street aspect ratios (H/W).

outlet temperatures of E-W and N-S streets in the 30th day are 0.20, 0.11 and 0.43, 0.28 °C, respectively. The latter is attributed to total amount and fluctuation of solar radiation of N-S streets are higher than those of E-W streets (shown in Fig. 7(b)). Therefore, the direction of streets can also impact the performance of horizontal GHEs.

increase of street aspect ratio for E-W streets. The corresponding solar radiation for four street aspect ratios are shown in Fig. 7(b) and solar radiation without shading is also shown for reference.

3.3.1. Influence of shading The effects of shading on performance of horizontal GHEs are studied by assuming the street aspect ratio of 0.6, solar radiations of Fig. 7(b), building load constant of −1000 W, and other parameters such as initial ground temperature, buried depth etc. are same with those in Section 3.1. Fig. 8 shows the outlet fluid temperatures and corresponding heat pump COP for E-W and N-S streets without shading. Compared to outlet temperature without shading, these with shading are lower. At the end of the 30th day, outlet fluid temperatures are 0.11 and 0.28 °C for E-W and N-S streets, while 0.58 °C is recorded without shading. The corresponding heat pump COP values without shading are 0.0618 and 0.0396 higher than those for E-W and N-S streets, respectively. The reason for this hs to do with shading, which causes ground surface to receive less solar radiation and leads to lower ground temperature. Therefore, shading shows negative effect on GHEs in heating mode while it is expected to be beneficial in cooling mode. Comparison of outlet temperatures of E-W and N-S streets (red and blue lines in Fig. 8(a)) indicates that both values and fluctuations of N-S streets are higher than those of E-W streets. The highest and lowest

3.3.2. Influence of street aspect ratios (H/W) The street aspect ratios might influence the amount and intensity of the solar radiation reaching the ground. For a certain street, a bigger street aspect ratio would mean a higher building. Due to the relative position of the street and the adjacent building, the solar radiation intensity reaching the ground can be quite different per day for E-W and N-S streets with variable street aspect ratios. As street aspect ratio rise (Fig. 7(b)), the total amount of solar radiation and the solar radiation intensity reduces at noon for E-W streets. Above 0.8, the solar radiation for E-W streets at noon drops down to zero, indicating fully shaded streets. The increase in street aspect ratio for N-S streets reduces the total amount of solar radiation and sunshine exposure time The outlet fluid temperatures of E-W and N-S streets in four street aspect ratios (H/W) are shown in Fig. 9. The other calculation parameters are same as those in Section 3.3.1. Because increasing street aspect ratio reduces the amount of solar radiation, outlet fluid temperatures decrease as street aspect ratio rise for both E-W and N-S streets. For example, outlet temperature for E-W streets decreases from 0.27 to 0.00 °C at the end of the 30th day as street aspect ratio rises 165

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8.0 7.5 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5

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Fig. 9. Outlet fluid temperatures of E-W (a) and N-S (b) streets at different street aspect ratios (H/W).

Fig. 10. Outlet fluid temperatures of E-W (a) and N-S (b) streets at different latitudes.

from 0.4 to 1.0, while it decreases from 0.38 to 0.15 °C for N-S streets during this period. Therefore, the increase in street aspect ratio for E-W streets is higher than that of N-S streets.

could cause fluctuations in circulating water per day. Fig. 11 shows the outlet fluid temperatures of horizontal GHEs under E-W and N-S streets of different buried depths. The other parameters used in this section are same as in Section 3.3.1. Comparison of outlet temperatures of E-W and N-S streets of same depths suggests higher fluctuations in N-S streets. This is because the solar radiation fluctuation of N-S streets is higher than that of E-W streets (shown in Fig. 7(b)). As buried depth increases, the outlet temperature fluctuation decreases. For buried depth of 2.0 m, the differences between the highest and lowest outlet temperatures of E-W and N-S streets in the 30th day are 0.09 and 0.15 °C, respectively. The difference in E-W streets is less than 0.1 °C, which can be neglected. As buried depth increases to 2.5 m for the horizontal GHE beneath N-S streets, the difference reduces to 0.11 °C in the 30th day. In practical applications, the buried depth of horizontal GHEs is often set to less than 2 m. Therefore, the effect of solar radiation and shading should be considered when studying the operation characteristics of horizontal GHEs, especially at short-term period.

3.3.3. Influence of latitudes Latitudes could also impact shading. As latitude raise, sun altitude angle would decrease, further resulting in the increase of shaded strip width (Xt). To evaluate the influence of shading of different latitudes on horizontal GSHP system, outlet fluid temperatures (Fig. 10) of E-W (a) and N-S (b) streets in four different latitudes of 30°, 45°, 60° and 75° are compared. The solar radiation without shading of the four latitudes and other parameters, such as the street aspect ratio, the buried depth, etc. are all assumed the same as in Section 3.3.1. Form the figures it can be seen that with the increase of latitudes outlet temperatures are decreasing both in E-W (a) and N-S (b) streets. For example, the outlet temperature of E-W streets at the 30th day reduces from 0.41 °C to −0.02 °C as latitude rises from 30° to 75°. The fluctuation in outlet temperature also declines with latitude. The reason for this has to do with the increase in latitude leads to reduction in solar radiation. The increase in latitude can also result in fully shaded E-W streets at noon, N-S streets would be fully shaded in early morning and late afternoon, which shows the same effect of the increase in street aspect ratio.

4. Conclusion In this paper, the influence of ground surface boundary conditions, especially diurnal shading, on performance of horizontal GSHP system is studied. The outlet fluid temperatures and heat pump COP of horizontal GSHP system under two different boundary conditions are first

3.3.4. Influence of buried depths The above analysis revealed that solar radiation and diurnal shading 166

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Fig. 11. Outlet fluid temperatures of E-W (a) and N-S (a) streets at different buried depths.

compared. The effects of diurnal shading are then studied. To be more specific, outlet temperatures with (E-W and N-S streets as examples) and without shading, effect of street aspect ratios, latitudes and buried depths on horizontal GHEs are studied. Main conclusions are as follows:

Acknowledgement

(1) Different assumptions regarding ground surface boundary conditions shows similar but significant impact on performance of horizontal GHEs, especially when building load is high and buried depth of GHEs is shallow. Hence, they should carefully be considered when analysing. (2) The outlet fluid temperature and fluctuation in N-S streets are higher than those of E-W streets due to shading. The increase in street aspect ratio results in reduced solar radiation and sunshine time both in E-W and N-S streets. The effect of increased street aspect ratio of E-W streets is higher than that of N-S streets. (3) At constant street aspect ratio, the increase in latitudes results in the increase of shaded strip width of streets, further leading to the decrease of the solar radiation. This can also result in declined sunshine exposure time in both E-W and N-S streets. (4) Daily variations in solar radiation and shading showed impact on outlet temperatures of horizontal GHEs up to buried depth of 2.5 m. Therefore, the effect of solar radiation and shading should be considered when studying the performance of shallow horizontal GHEs especially at short-time period. Overall, these findings could be helpful when analysing the effects of ground surface boundary conditions especially shading on horizontal GSHP systems.

References

This work was support by National Natural Science Foundation of China (NO. 51608524).

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