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Determination of the economical optimum insulation thickness for VRF (variable refrigerant flow) systems
Energy 89 (2015) 835e844
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Determination of the economical optimum insulation thickness for VRF (variable refrigerant flow) systems €z b Abdullah Yildiz a, *, Mustafa Ali Erso a b
Department of Mechanical Engineering, Faculty of Engineering, Us¸ak University, 64200 Usak, Turkey Department of Electricity and Energy, Vocational College of Us¸ak, Us¸ak University, 64200 Usak, Turkey
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 February 2015 Received in revised form 18 May 2015 Accepted 8 June 2015 Available online 2 July 2015
This study deals with the investigation into optimum insulation thickness of installed inside building pipe network of VRF (variable refrigerant flow) systems. Optimum insulation thickness, energy savings over a lifetime of 10 years and payback periods are determined for high pressure gas pipelines, low pressure gas pipelines and low pressure liquid pipelines under the heating-only and cooling-only modes of the three-pipe VRF system using R-410A as refrigerant. By using the P1eP2 method, the value of the amount of the net energy savings is calculated. Under heating mode of VRF system, while the optimum insulation thickness varies between 16 and 20 mm depending on the pipe sections of high pressure gas pipeline, it varies from 11 to 13 mm for the pipe sections of low pressure liquid pipeline. Under cooling mode of VRF system, the optimum insulation thickness varies between 7 and 8 mm for pipe sections of low pressure gas pipeline and low pressure liquid pipeline. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Optimum insulation thickness Life-cycle analysis Variable refrigerant flow
1. Introduction VRF (variable refrigerant flow) systems use one external unit that is connected to several indoor units. VRF systems are popular because they require less outdoor plant space than conventional central air conditioning systems, are less disruptive in fitting to existing buildings (particularly when occupied), and are able to cool and heat through common pipework. These systems all use refrigerant as the cooling/heating medium rather than chilled water/hot water, which is used in conventional hydraulic systems circulated by pumps [1]. It is estimated that air conditioning systems consume about 50% of the total electricity use in the office buildings. Therefore, reducing energy use for space cooling and heating in buildings is a key measure for the energy-savings [2]. There are many strategies to reduce energy consumption, especially in heating and cooling devices. Using proper insulation in pipe network is perhaps the most effective way of energy conservation for the heating and cooling applications of VRF systems. To minimize the energy and insulation costs in addition to reducing the heat loss to the surroundings, the thickness of the insulation material needs to be
* Corresponding author. Tel.: þ90 276 2212136; fax: þ90 276 2212137. E-mail address: [email protected] (A. Yildiz). http://dx.doi.org/10.1016/j.energy.2015.06.020 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
optimized. The economic insulation thickness for a pipe is a function of a large number of parameters, such as pipe size, cost, conductivities of the pipe and the insulation material, operating and ambient temperatures, heat transfer coefficients at the inside and outside of the pipe, economic parameters and annual operation The concept of economic thermal insulation thickness considers the initial cost of the insulation system plus the ongoing value of energy savings over the expected service lifetime of the insulation [3]. Determining both the type of thermal insulation material and the economic thickness of the material used in the hot water or air service pipelines are the main subjects of many engineering investigations. Most studies estimated the heating energy requirement by the degree-time concept (degree-day, DD, or degree-hour, DH), which is one of the simplest methods applied under static conditions. Zaki and Al-Turki studied economic analysis of thermal insulation for a system of pipelines, from the oil industry, insulated by different materials composite layers. The analysis was based on an explicit nonlinear cost function that includes the annual energy losses and the insulation initial costs. In the analysis, rockwool and calcium silicate as insulation materials and a system of pipelines (0.1e0.273 m nominal size) with flow of superheated steam, furfural, crude oil, and 300-distillate was employed and ho was assumed constant, 10 W m2K1 [4]. Li and Chow analyzed methods for protecting water pipes, in cold regions against freezing, by thermal insulation material and heating cable. They
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Nomenclature
V x
a A b c C COP d D E_
h r Dt
ES h HDD Hu i k LCCA L m N Pr PP Q_ R Re t T U
high pressure gas pipeline area (m2) high pressure gas pipeline low pressure liquid pipeline price ($ kg1, $ m3) coefficient of performance inflation rate (%) diameter (mm) energy rate (J m1 year1) energy saving ($ m1) convection transfer coefficient (W m2 K1) heating degree-days ( C-days) lower heating value of the fuel (J kg1, J m3) interest rate (%) the heat transfer coefficient (Wm1 K1) life cycle cost analysis length (m) fuel consumption (kg m1 year1), (m3 m1 year1) lifetime (years) Prandtl number () payback period (years) heat transfer rate (kW, J m1 year1) thermal resistance (KW1) Reynolds number () wall thickness (mm) temperature (K) overall heat transfer coefficient (W m1 K1)
applied a thermoeconomic optimization analysis with a simple algebraic formula derived for estimating the optimum insulation thickness for tubes of different diameters varying from 0.02 m to 0.2 m. They investigated the effects of outdoor air conditions and design parameters on the optimum thickness. For the same outside-air temperature, the optimum insulation-thickness would become larger for lower design insulation envelope outsidetemperature. It was also found that the optimum insulation thickness was inversely proportional to the thermal conductivity and cost of the insulating material [5]. Ozturk et al. presented four different thermo-economic techniques for optimum design of hot water piping systems. They were as follows: the first one was a sequential optimization of pipe diameter based on minimization of total cost without considering heat losses and then of insulation thickness based on minimization of cost of insulation and heat losses. The second was simultaneous optimization of pipe diameter and insulation thickness based on the first law of thermodynamics and cost. The third was simultaneous determination of pipe diameter and insulation thickness based on maximization of exergy efficiency without considering cost. Finally, the fourth was simultaneous determination of pipe diameter and insulation thickness based on maximization of exergy efficiency and cost minimization. A case study was carried out for a hot water pipe segment, and the differences and merits of each method were discussed. Important parameters such as annual operation time, depreciation period, interest rate, fuel and electricity prices, and the thermoephysical parameters were assumed to be the same and constant for all methods [6]. Soponpongpipat et al. conducted the optimum thickness analysis of air conditioning duct's insulation, which composes of the layer of rubber and fiber glass insulator, by means of thermo-economics method. The effects of heat transfer
velocity (m s1), volume (m3) optimum insulation thickness (cm) efficiency density (kg m3) annual operation time
Subscripts a ambient an annual cl cooling load cond condenser evap evaporator f total fuel fg fiberglass F fuel hl heating load i inside in inlet ins insulation m mean o outside opt optimum out outlet R refrigerant s surface of pipe t total un-ins un-insulation 1, 2, …5, branch pipe 6, 7, 8, 9 main pipe
coefficient at inside and outside of duct on the optimum thickness of these insulators were studied. The galvanized steel duct diameter of 0.5 m with rubber insulator (k ¼ 0.035 W m1K1) and fiberglass insulator (k ¼ 0.045 W m1K1) was selected to show the study results. In order to study the change in optimum thickness when convective heat transfer coefficients were varied, the inside and outside duct convective heat transfer coefficient of 6, 10, 14, 18 and 22 W m2K1 were selected for calculation of optimum thickness. They demonstrated that the variation of inside and outside duct convective heat transfer coefficient does not affect optimum thickness but net saving increases when inside and outside duct convective heat transfer coefficient increases [7]. Keçebas¸ et al. calculated the optimum insulation thickness of pipes used in district heating pipeline networks, energy savings over a lifetime of 10 years, and payback periods for the five different pipe sizes and four different fuel types in the city of Afyonkarahisar/ Turkey. Rockwool as insulation material and a system of pipelines (50e200 mm nominal sizes) with flow of hot water were considered. The results showed that optimum insulation thicknesses varied between 0.085 and 0.228 m, energy savings varied between 10.041 $/m and 175.171 $ m1, and payback periods varied between 0.442 and 0.808 years depending on the nominal pipe sizes and the fuel types. The highest value of energy savings was reached in 250 mm nominal pipe size for fuel-oil fuel type, while the lowest value is obtained in 50 mm for geothermal energy. Considering the economic and environmental advantages, the geothermal energy ul and Keçebas¸ was a better choice and then natural gas [8]. Bas¸og investigated the energy, economic and environmental evaluations of thermal insulation in district heating pipeline. The optimum insulation thickness, energy saving over a lifetime of 10 years, payback period and emissions of CO, CO2 and SO2 are calculated for
€z / Energy 89 (2015) 835e844 A. Yildiz, M. Ali Erso
nominal pipe sizes and fuel types based on heating loads in Afyonkarahisar/Turkey. The results show that the highest value of optimum insulation thickness, energy savings, emissions and the lowest payback period are reached for a nominal pipe size of 200 mm [9]. Keçebas¸ optimized insulation thickness by using exergy method and life-cycle cost concept for the case of using various fuels such as coal, natural gas and fueleoil. The optimum insulation thickness decreased with the increasing of inlet temperature of fuel, and with the decreasing of excess air coefficient, temperatures of stack gases and combustion chamber. The optimum insulation thicknesses were determined as 0.065, 0.071, 0.099 m with a rate of 68.27%, 71.54% and 77.85% in the exergetic saving for natural gas, coal and fueleoil fuels, respectively. The optimum insulation thickness for the exergoeconomic optimization was higher than that of energoeconomic optimization [10]. Kayfeci estimated the optimum insulation thickness, energy savings, annual costs and payback period for various pipe diameters and insulation materials of the heating systems in Isparta/Turkey and in the regions with different degree-day values by using LCCA (life cycle cost analysis) method. As a fuel, natural gas was used in the study. EPS (expanded polystyrene) insulation material with a DN (nominal diameter) of 250 mm provides the highest energy savings, while the lowest value was found to be in fiberglass insulation material with DN 50 mm [11]. Kayfeci et al. reported on the use of ANNs (artificial neural networks) to predict insulation thickness and LCC (life cycle costs) for pipe insulation applications. Using the collected data set and LCC analysis results for training, a three-layer feed forward ANN model based on a back propagation algorithm was developed. The developed ANN model has a very practical use of determining the optimum thickness of insulation for any location in the world when just the input parameters of the ANN model are known [12]. Kaynaklı carried out a literature review of papers that addressed the optimum economic thickness of the thermal insulation on a pipe or duct with different geometries used in various industries. The heat transfer equations, the basic results, the optimization procedures and the economic analysis methods used in the studies were presented comparatively. Additionally, a practical application example based on optimizing the insulation thickness on a pipe was performed, and the effective parameters of the optimum thickness were investigated [13]. On the other hand, only a limited number of analytical techniques were applied to analyze the optimization of the pipes. Sahin studied optimized numerically the variation in the thermal insulation thickness of a pipe for space applications to minimize the radiative heat loss to the ambient. The thickness of the insulation was assumed to be linearly varying along the pipe because this scenario is easy to implement in practice. It was found that a linearly decreasing insulation thickness with a minimum slope along the pipe provides the best insulation under the radiation heat transfer condition [14]. Sahin and Kalyon obtained an explicit analytical solution for the insulation thickness variation over a pipe to maintain a uniform outer surface temperature. They considered heat transfer on the outer surface of the insulation considered a combination of convection and radiation. It was shown that the insulation thickness variation that provides uniform surface temperature was independent of the convection and radiation heat transfer coefficients [15]. Bahadori and Vuthaluru presented optimum economic thickness of thermal insulations predicted rapidly as a function of steel pipe and equipment diameter and thermal conductivity of insulation by proposing simple correlation. The correlation was as a function of steel pipe diameter and thermal conductivity of insulation for surface temperatures at 100, 300, 500 and 700 C. A simple interpolation formula generalized this correlation for wide range of surface temperatures. The proposed correlation covered pipeline diameter and surface temperature up
837
to 0.5 m and 700 C, respectively. The derived polynomials were applied to calculate new coefficients to predict optimum economic thickness of thermal insulations [16]. Bahadori and Vuthaluru formulated simple correlations for the estimation of heat flow through insulation, thermal resistance and thermal insulation thickness for flat surfaces, ducts and pipes. The proposed correlation covered the temperature difference between ambient temperature and outside temperature up to 250 C and the temperature drop through insulation up to 1000 C. The proposed simple correlation calculates the thermal thickness for flat surfaces up to 200 mm and predicts the thermal thickness for ducts and pipes with outside diameters up to 2400 mm. The accuracy of the proposed method tested and it was found to be in excellent agreement with the reported data for the wide range of conditions, where the average absolute deviation between reported data and the proposed correlation was around 3.25% [17]. As witnessed in literature, researches focused on economic thermal insulation thicknesses of hot water or air service pipelines by means of heating degree days and analytical optimization techniques. In those studies, the effect of different parameters such as pipe diameter, working fluid, interest rate inflation rate, energy source, fuel type, insulation materials on economic optimum pipe insulation is investigated. This study is different from the previously conducted ones as follows: (i) economic optimum insulation thickness analysis is applied to installed inside the building pipeline of the VRF systems, (ii) R-410 as working fluid and seamless copper pipe as pipe material are used, (iii) analyses carried out for both heating and cooling modes of VRF system. 2. Description of system Basically, a VRF system is a refrigerant system that varies the refrigerant flow rate with the help of the variable speed compressor and the EEVs (electronic expansion valves) located in each indoor unit to match the space cooling or heating load in order to maintain the zone air temperature at the indoor set temperature. The indoor units (located in each zone) are connected to the outdoor unit in parallel with the refrigerant pipes [18]. Generally, the VRF systems have either two-pipe or three-pipe configurations and they are operated with or without ice thermal storage tanks. The two-pipe (a HPGP (high pressure gas pipe), a LPLP (low pressure liquid pipe)) VRF systems are the general ones that can be used for cooling or heating depending on the season. On the other hand, the three-pipe (a HPGP (high pressure gas pipe), a LPGP (low pressure gas pipe), and a LPLP (low pressure liquid pipe)) VRF systems work best, when there is a need for some of the spaces to be cooled and some of them to be heated during the same season. This generally occurs in the winter season in medium-sized to large sized commercial buildings with a substantial core such as computer rooms [18]. The three-pipe VRF systems use branch selector boxes (located before each indoor unit) and they can be operated in five different modes: a. Cooling-only mode: All indoor units are in cooling operation. b. Heating-only mode: All indoor units are in heating operation. c. Cooling-principal mode: Cooling is the principal mode in the concurrent heating and cooling operation. d. Heating-principal mode: Heating in the principal mode in the concurrent heating and cooling operation. e. Heat recovery mode: Heat is balanced between indoor units while the outdoor unit heat exchanger is closed [18]. In this study, economical optimum insulation thickness is analyzed for heating-only and cooling-only modes of three-pipe
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€z / Energy 89 (2015) 835e844 A. Yildiz, M. Ali Erso
VRF systems, shown in Fig. 1 and Fig. 2 respectively, in which the pipes are networked inside a building. The system uses R-410 refrigerant as working fluid. In Figs. 1 and 2, a1-a9 numbered pipe sections are high pressure gas pipeline, b1-b9 numbered pipe sections are low pressure gas pipeline and c1-c9 numbered pipe sections are low pressure liquid pipeline. Low pressure gas pipeline is closed for heating-only mode of VRF system, whereas, high pressure gas pipeline is closed for cooling-only mode of VRF system.
3. Analyses 3.1. Analysis of VRF (variable refrigerant flow) system The following assumptions are made in thermodynamically analysis of the VRF system: 1. Steady-state and ideal conditions are evaluated. 2. R-410 refrigerant is used as working fluid. 3. The evaporation and condensation temperatures for both heating and cooling modes are taken as 283 K and 323 K, respectively. 4. Kinetic and potential energy changes are negligible. 5. The temperature and pressure drops through the duct are neglected. 6. Ambient temperature of the pipelines network is assumed as indoor temperature of building because the pipelines of the VRF system are installed inside the building. Ambient temperatures (Ta) are assumed as 293 K for heating mode in winter season and 303 K for cooling mode in summer season. The thermodynamic properties of the R-410 refrigerant are calculated by means of REFPROP 9.0. The system operation parameters and thermodynamic properties correspond to the parameters are given in Table 1. In the VRF system, 1, 2, 3, 4 and 5 numbered pipe sections of high pressure gas pipeline, low pressure gas pipeline and low pressure liquid pipelines are branch pipes, whereas, 6, 7, 8 and 9 numbered pipe sections of high pressure gas pipeline, low pressure gas pipeline and low pressure liquid pipelines are main pipes. Indoor units capacities based on heating and cooling loads for each of the zone are chosen from manufacturer catalogs. For example, while heating load value equals to 16 kW and cooling load value equals to 14 kW for indoor unit in Zone 5. Indoor units of the VRF system operate as condenser in heatingonly mode. Since indoor units capacities based on heating load
values are known in each of the zones, mass flow rates in each branch pipes of high pressure gas pipelines are calculated from Eq. (1).
_R¼ m
Q_ hl hcond;in hcond;out
(1)
When it comes to cooling mode, indoor unit of the VRF system operates as evaporator and since indoor units capacities based on cooling load values are known in each of zones, mass flow rates in each branch pipes of low pressure gas pipelines are calculated from Eq. (2).
_R¼ m
Q_ cl hevap;out hevap;in
(2)
Then, heat loads of main pipe sections in both heating-only mode and cooling-only mode are calculated as:
Q_ 6 ¼ Q_ 5 þ Q_ 4
(3)
Q_ 7 ¼ Q_ 5 þ Q_ 4 þ Q_ 3
(4)
Q_ 8 ¼ Q_ 5 þ Q_ 4 þ Q_ 3 þ Q_ 2
(5)
Q_ 9 ¼ Q_ 5 þ Q_ 4 þ Q_ 3 þ Q_ 2 þ Q_ 1
(6)
Mass flow rates of 6, 7, 8 and 9 numbered main pipe sections in both high pressure gas pipeline and low pressure gas pipeline are determined as:
_ R;5 þ m _ R;4 _ R;6 ¼ m m
(7)
_ R;5 þ m _ R;4 þ m _ R;3 _ R;7 ¼ m m
(8)
_ R;5 þ m _ R;4 þ m _ R;3 þ m _ R;2 _ R;8 ¼ m m
(9)
_ R;9 ¼ m _ R;5 þ m _ R;4 þ m _ R;3 þ m _ R;2 þ m _ R;1 m
(10)
After the mass flow rate values of high and low pressure gas pipelines are calculated, the pipe diameters for each of branch pipes of the VRF system are selected from manufacturer catalogs. As to the main pipe diameters of the VRF system, they are determined from manufacturer catalogs based on heat loads of indoor units attached to main pipe sections. The velocities of R-410 refrigerant in each of pipe sections are calculated by,
Fig. 1. Schematic view of heating-only mode for three-pipe VRF system.
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Fig. 2. Schematic view of cooling-only mode for three-pipe VRF system.
Table 1 The system operation parameters and thermodynamic properties correspond to the parameters. Parameters
TR,m (K)
P (kPa)
h (kJkg1)
Evaporation condition Condensation condition Evaporator inlet Evaporator outlet Condenser inlet Condenser outlet
283 323 283 283 343.19 323
1088.4 3070.6 1088.4 1088.4 3070.6 3070.6
e e 285.850 428.700 456.710 285.850
VR ¼
_R m r R Ac
Q_ ¼ UAs TR;m Ta
(12)
where U is the overall heat transfer coefficient of pipe layers and is calculated by Eq. (13), As is the total surface area of pipe, TR,m is the average working fluid temperature of inside pipe and Ta is the ambient temperature of the pipelines networked inside building and the value for the heating and cooling modes is assumed as 293 K and 303 K respectively. TR,m is 323 K for the low pressure liquid pipeline and 343.19 K for high pressure gas pipeline under heating mode and this value is 283 K for both the low pressure gas pipeline and low pressure liquid pipeline under cooling modes.
(11)
The mass flow rates and velocity values calculated by using the selected pipe dimensions by Eqs (1)e(11) for branch pipelines and for main pipelines of heating and cooling modes of the VRF system are summarized in Table 2 and Table 3, respectively.
U¼
1 Rt
(13)
where Rt are the total thermal resistances, which are calculated by Eqs. (14) and (15) for uninsulated and insulated pipe systems.
ln
Rt;unins
3.2. Heat loss through pipelines of the VRF system Optimum pipe insulation thickness analyses of the VRF system is calculated for unit length of pipeline considering heat losses from throughout pipe surface. Flexible insulation foam is chosen for the insulation of the piping network of VRF system with thermal conductivity of 0.039 Wm1K1 and cost insulation of 600 $m3. The pipe materials for piping system of VRF system are taken as seamless copper pipe with thermal conductivity of 400 Wm1K1. The annual heat losses are calculated by;
Rt;ins ¼
ro
ri 1 1 ¼ þ þ hi As;i 2pLpipe kpipe ho As;o
ln rio
ln
(14)
rins ro
1 1 þ þ þ hi As;i 2pLpipe kpipe 2pLpipe kins ho A0o
(15)
where, kins is the heat transfer coefficient of insulation material and it must be kept in mind that the outside surface area of the last layer of duct system is A0o ¼ 2pLrins .
Table 2 The pipe dimensions, mass flow rates and velocity values for heating-only of the VRF system. Operation mode
Heating mode
Pipeline
HPGP
LPLP
Parameter
Q_ (kw) D (mm) t (mm) _ (kgs1) m V (ms1) Q_ (kw) D (mm) t (mm) _ (kgs1) m V (ms1)
Branch pipe sections
Main pipe sections
1
2
3
4
5
6
7
8
9
4 9.52 0.8 0.023 4.36 4 6.35 0.8 0.023 9.50
5 12.70 0.8 0.029 2.77 5 6.35 0.8 0.029 11.87
8 15.88 1.0 0.047 2.84 8 9.52 0.8 0.047 6.83
10 15.88 1.0 0.059 3.55 10 9.52 0.8 0.059 8.54
16 15.88 1.0 0.094 5.676 16 9.52 0.8 0.094 13.66
26 22.22 1.0 0.153 4.35 26 12.70 0.8 0.153 11.30
34 28.58 1.0 0.2 3.29 34 12.70 0.8 0.2 14.78
39 28.58 1.0 0.229 3.77 39 12.70 0.8 0.229 16.96
43 28.58 1.0 0.252 4.16 43 15.88 1.0 0.252 11.96
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Table 3 The pipe dimensions, mass flow rates and velocity values for cooling-only of the VRF system. Operation mode
Pipeline
Cooling mode
LPGP
LPLP
Parameter
Q_ (kw) D (mm) t (mm) _ (kgs1) m V (ms1) Q_ (kw) D (mm) t (mm) _ (kgs1) m V (ms1)
Branch pipe sections
Main pipe sections
1
2
3
4
5
6
7
8
9
3.6 6.35 0.8 0.025 34.56 3.6 6.35 0.8 0.025 1.26
4.5 6.35 0.8 0.032 43.19 4.5 6.35 0.8 0.032 1.58
7.1 9.52 0.8 0.050 24.51 7.1 9.52 0.8 0.050 0.90
9 9.52 0.8 0.063 31.07 9 9.52 0.8 0.063 1.13
14 9.52 0.8 0.098 48.34 14 9.52 0.8 0.098 1.76
23 22.22 1.0 0.161 12.18 23 12.70 0.8 0.161 1.48
30.1 28.58 1.0 0.211 9.23 30.1 12.70 0.8 0.211 1.93
34.6 28.58 1.0 0.243 10.61 34.6 12.70 0.8 0.243 2.22
38.2 28.58 1.0 0.268 11.71 38.2 15.88 1.0 0.268 1.57
The convection heat transfer coefficients for the inside and outside surface of piping system hi and ho are calculated as [19];
hi ¼
Parameters
0:023Re0:8 Pr0:4 kR Dpipe
(16)
ho ¼ Nuo
kair Dpipe
Nuo ¼ 0:3 þ h
(17) pffiffiffiffiffiffi kair RePr1=3
1 þ ð0:4=PrÞ2=3
i1=4
h i4=5 1 þ ðRe=282000Þ5=8 (18)
In Eqs. (16) and (17), Reynolds number (Re) is calculated by;
rair Vair Dpipe mair
Ct;ins ¼ Cins Vins
3.3. Life cycle analysis and optimization of insulation thickness Life-cycle cost analysis is often applied to energy systems. A lifecycle cost analysis can show that spending more initially on additional building insulation can produce a net savings (due to reduced heating and cooling costs) over the lifetime of a building. In this study, determination of the amount energy cost calculated using LCCA method. This method is a practical and can be used for optimization the insulation thickness of pipelines. The design parameters used in economic analyses are given in Table 4. The annual total energy cost, Cf, is given
Q_ Dt Hu helectricity COP
CF
(20)
where, Dt is annual operation time of the VRF system under heating-only mode or cooling-only mode, Hu is lower heating value of energy source and CF is fuel cost. The annual fuel consumption is,
mf;an
Operation time (hours) Heating-only mode Cooling-only mode System performance (COP) In the heating-only mode In the cooling-only mode Insulation material (flexible insulation foam) kins Cins Interest rate (%) Inflation rate (%) Life time (years)
Values 3.599 106 JkW1h1 0.1059 $ kWh1 0.99 2100 900 4.02 3.48 0.039 Wm1K1 600 $m3 4.5 9.4 10
(19)
where, r is the density of working fluid or ambient air, D is the pipe diameter, m is the dynamic viscosity and V is the speed of working fluid or speed of ambient air. The velocity of ambient air is assumed of 0.2 ms1 in these analyses.
Cf ¼
Energy source (Electricity) Hu CF
helectricity
and
Re ¼
Table 4 The design parameters used in economic analyses [19,20].
UA TR;m Ta Dt ¼ Hu helectricity COP
(21)
The total investment cost of insulation is given by the following equation
(22)
where, Cins is the cost of insulation material and Vins is the volume of material used in insulation. The first cost of insulation may be treated as capital investment. It is possible to calculate the present worth of the net amount of energy savings via insulation using a well-known method known as the P1eP2 method. P1 has relation with inflation rate d, interest rate i, and lifetime N. P2 is the ratio of the life cycle expenditures incurred because of the additional capital investment to the initial investment. The equation for P1 is defined as [11].
P1 ¼
" # 1 1þi N 1 if isd di 1þd
P2 ¼ 1 þ P1 Ms Rv ð1 þ dÞN
(23)
(24)
where Ms is the ratio of the annual maintenance and operation cost to the original first cost, Rv is the ratio of the resale value to the first cost. P2 can be taken as 1.0 if the maintenance and operation cost is zero. If the increase rate is equal to discount rate, P1 is calculated from
P1 ¼
N if i ¼ d 1þi
(25)
The total cost of heating with the insulated piping system can be calculated by the following equations
Ct ¼ P1 Cf þ P2 Ct;ins
(26)
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Fig. 3. Effects of insulation thickness on the total cost for HPGP main pipe sections (left side) and LPGP main pipe sections (right side) under heating mode and cooling mode of the VRF system.
Energy savings ($ m1) obtained during the lifetime of insulation material can be calculated as follows [21]:
ES ¼ Ct;unins Ct;ins
(27)
where, Ct,un-ins and Ct,ins are the total heating costs of the building when insulation is not and is applied, respectively.
Energy savings can be expressed as % by the following equation:
ES 100 Ct;unins
(28)
Then, pay-back period, PP is calculated by solving the following equation for PP:
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€z / Energy 89 (2015) 835e844 A. Yildiz, M. Ali Erso
Fig. 4. Comparison of energy savings for both HPGP and LPLP under heating mode of the VRF system.
" # Ct;ins 1 1 þ i PP ¼ 1 di 1þd ES
Fig. 5. Comparison of energy savings for both LPGP and LPLP under cooling mode of the VRF system.
(29)
where, Cins/ES is the simple pay-back period and this value does not take interest rate into account. ES is the annual energy savings obtained by insulation.
4. Results and discussion The optimum insulation thickness based on energy-cost analysis is studied widely for hot water and hot air heating piping systems in the literature. In this study, economical optimum insulation thickness of piping system for both heating-only and cooling-only modes of the VRF system using R-410 refrigerant as working fluid are studied. The variations of the insulation thickness, fuel and total costs with respect to main pipe sections of HPGP (high pressure gas pipeline) under heating mode of the VRF system are demonstrated on the left side of Fig. 3 one after another, whereas, variations of these costs with respect to main pipe sections of LPGP (low pressure gas pipeline) under cooling mode of the VRF system are shown on the right side of this figure. As shown in Fig. 3, the cost of the fuel decreases as insulation thickness increases under both heating and cooling modes. However, the insulation cost increases linearly with insulation thickness. The total cost is the sum of the cost of fuel and
Fig. 6. The optimum insulation thicknesses for pipe sections of the VRF system.
insulation material. The insulation thickness at the minimum total cost is determined as the optimum insulation thickness. When it comes to energy savings, the variations emerging for all pipe sections of HPGP and LPLP under heating mode of the VRF system are presented successively on Fig 4, whereas, variations of energy savings with respect to all pipe sections of LPGP and LPLP under cooling mode of the VRF system are demonstrated on Fig. 5. The optimum insulation thickness is achieved when the energy savings start to drop thanks to the increased thickness of insulation
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optimum insulation thickness xopt ¼ rinsro is obtained. MATLAB optimization toolbox is used to determine the optimum insulation thickness. The variations of the optimum insulation thicknesses with respect to each of the pipe sections for all the pipelines under both heating-only mode and cooling-only mode of the VRF system are represented in Fig. 6. As seen in Fig. 6, under heating-only mode of VRF system, while the optimum insulation thickness varies between 15.73 and 19.64 mm depending on the pipe sections of HPGP, whereas, it varies from 11.17 mm to 13.23 mm for the pipe sections of LPLP. Besides, as seen in Fig. 6, under cooling-only mode of VRF system, while the optimum insulation thickness varies between 6.65 and 8.13 mm depending on the pipe sections of LPGP, whereas, it varies from 6.72 mm to 7.89 mm for the pipe sections of LPLP. While the highest values of optimum insulation thicknesses are obtained on main pipe sections of both HPGP and LPLP under heating-only mode, the lowest values of optimum insulation thicknesses are obtained on branch pipe sections of both LPGP and LPLP under cooling-only mode. The highest optimum insulation thicknesses calculated for each of pipe section of LPLP must be selected because LPLP of the VRF system is used under both heating-only and cooling-only modes. Optimum insulation thicknesses for HPGP, LPGP and LPLP change respect to with pipe diameter and mass flow rate. The pipe diameter and mass flow rate depend on heat loads on the pipe sections. In order to satisfy the increasing heat loads on pipe sections, the larger pipe diameter and the higher mass flow rate are required. Therefore, as heat load values on the pipe sections increases, the pipe diameter and mass flow rate increase. Also, as the heat load on the pipe sections increases, optimum insulation thicknesses increase. Therefore, the highest optimum insulation thicknesses for these pipelines are selected. As a result, optimum insulation thicknesses for HPGP, LPGP and LPLP of the investigated VRF system are determined as 20, 8 and 13 mm, respectively. The variations of the payback period for each of pipelines are shown in Fig. 7 for both heating mode and cooling mode of the VRF system. Under heating mode of VRF system, while the payback periods vary between 0.13 and 0.19 years depending on the pipe sections of HPGP, whereas, they vary from 0.15 to 0.18 years for the pipe sections of LPLP. Under cooling mode of VRF system, the payback periods vary between 0.22 and 0.44 years depending on the pipe sections of LPGP, whereas, they varies from 0.23 to 0.33
Fig. 7. Payback periods versus pipe sections.
material. The energy savings is at maximum level under optimum insulation thickness. The energy savings depend upon the insulation thickness and heat load values on the pipe sections. Insulating the pipe sections up to optimum insulation thickness increases energy savings; however, over insulation more than optimum insulation thickness decreases energy saving. Besides, energy saving increases as heat load increases for both operation modes of VRF the system and for each of the pipelines. As witnessed in Fig. 4, in the heating-only mode of the VRF system, while the energy saving values vary from 19.07% to 58.50% for the pipe sections of HPGP, these values vary from 40.00% to 56.41% for the pipe sections of LPLP. Here, negative values for energy saving shows that energy saving is not obtained. Furthermore, the more insulation than insulation of 0.035 m on branch pipe sections of LPLP is loss money for the heating mode because it does not provide energy savings. As seen in Fig. 5, in the cooling mode of the VRF system, while the energy saving values vary from 255.90% to 47.66% for the pipe sections of LPGP, these values vary from 255.66% to 46.03% for the pipe sections of LPLP. Under the cooling-only mode, the more insulation than insulation of 0.02 m for all pipe sections of LPGP and LPLP is loss money. The outside radius of insulated piping system can be determined by minimizing Eq. (26) or maximizing Eq. (27). So, the differential of S or Ct with respect to r2 is taken and set equal to zero, then the
Table 5 The optimum insulation thickness, energy savings and payback periods for heating mode of the VRF system. Operation mode
Heating mode
Pipeline
HPGP
LPLP
Parameter
Xopt (mm) ES (%) PP (years) Xopt (mm) ES (%) PP (years)
Branch pipe sections
Main pipe sections
1
2
3
4
5
6
7
8
9
16 58.11 0.13 11 55.10 0.15
17 58.30 0.15 11 55.49 0.150
18 58.33 0.16 12 55.65 0.16
18 58.43 0.16 12 56.01 0.16
18 58.76 0.16 12 56.58 0.16
19 58.09 0.18 13 56.44 0.17
20 57.30 0.19 13 56.68 0.17
20 57.35 0.19 13 56.79 0.17
20 57.55 0.19 13 56.16 0.18
Table 6 The optimum insulation thickness, energy savings and payback periods for cooling mode of the VRF system. Operation mode
Cooling mode
Pipeline
LPGP
LPLP
Parameter
Xopt (mm) ES (%) PP (years) Xopt (mm) ES (%) PP (years)
Branch pipe sections
Main pipe sections
1
2
3
4
5
6
7
8
9
7 48.69 0.22 7 47.15 0.23
7 48.77 0.22 7 47.21 0.23
7 47.85 0.26 7 46.38 0.27
7 47.93 0.26 7 46.44 0.27
7 48.04 0.25 7 46.52 0.27
8 42.57 0.38 8 45.34 0.30
8 39.97 0.44 8 45.38 0.30
8 40.04 0.44 8 45.40 0.30
8 40.08 0.44 8 44.07 0.33
844
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years for the pipe sections of LPLP. While the shortest payback periods are determined at main pipe sections of LPGP under cooling mode, the longest payback periods are carried out at branch pipe sections of HPGP under heating mode. The optimum insulation thickness, energy savings and payback periods based on analyzed pipe sections of HPGP, LPGP and LPLP for given VRF system are summarized in Table 5 for heating mode and in Table 6 for cooling mode.
5. Conclusions There are many studies on the optimum insulation thickness computations in the heating pipe performed based mainly on the heating load and other parameters such as the costs of the insulation material and energy, efficiencies of the heating system, the lifetime, and the current inflation and discount rates. In this study, the optimum insulation thickness is studied for the pipe network of the three-pipe VRF system working both heating and cooling mode. Considering the results of the analyses, the following main conclusions can be drawn from the present study: a. The optimum insulation thickness increases as the heat loads on the pipes increase. b. While the energy saving values vary from 19.07% to 58.50% for the pipe sections of HPGP, these values vary from 40.00% to 56.41% for the pipe sections of LPLP in the heating mode of the VRF system. c. While the energy saving values vary from 255.90% to 47.66% for the pipe sections of LPGP, these values vary from 255.66% to 46.03% for the pipe sections of LPLP in the cooling mode of the VRF system. d. While the optimum insulation thickness varies between 16 and 20 mm depending on the pipe sections of HPGP, whereas, it varies from 11 to 13 mm for the pipe sections of LPLP under heating mode of VRF system, e. The optimum insulation thickness varies between 7 and 8 mm depending on the pipe sections of LPGP and LPLP under cooling mode of VRF system. f. Low pressure liquid pipeline (c1-c9) is active under both heating and cooling modes. Therefore, while optimum insulation thickness is determined for these pipes, the highest optimum insulation thickness value must be selected.
As a result, optimum insulation thicknesses for HPGP, LPGP and LPLP of the VRF system are determined as 20, 8 and 13 mm, respectively.
References [1] Shin Y, Karng SW, Kim SY. Indoor unit fault detector for a multi-split VRF system in heating mode. Int J Refrig 2014;40:152e60. [2] Aynur TN, Hwang Y, Radermacher R. Simulation comparison of VAV and VRF air conditioning systems in an existing building for the cooling season. Energy Build 2009;41:1143e50. [3] Kaynakli O. A review of the economical and optimum thermal insulation thickness for building applications. Renew Sustain Energy Rev 2012;16: 415e25. [4] Zaki GM, Al-Turki AM. Optimization of multilayer thermal insulation for pipelines. Heat Transf Eng 2000;21:63e70. [5] Li YF, Chow WK. Optimum insulation-thickness for thermal and freezing protection. Appl Energy 2005;80:23e33. _ Karabay H, Bilgen E. Thermo-economic optimization of hot water [6] Ozturk IT piping systems: a comparison study. Energy 2006;31:2094e107. [7] Soponpongpipat N, Jaruyanon P, Nanetoe S. The thermo-economic analysis of the optimum thickness of double-layer insulation for air conditioning duct. Energy Res J 2010;1:146e51. [8] Keçebas A, Alkan MA, Bayhan M. Thermo-economic analysis of pipe insulation for district heating piping systems. Appl Therm Eng 2011;31:3929e37. ul YA, Keçebas¸ A. Economic and environmental impacts of insulation in [9] Bas¸og district heating pipelines. Energy 2011;36:6156e64. [10] Keçebas¸ A. Determination of insulation thickness by means of exergy analysis in pipe insulation. Energy Convers Manage 2012;58:76e83. [11] Kayfeci M. Determination of energy saving and optimum insulation thicknesses of the heating piping systems for different insulation materials. Energy Build 2014;69:278e84. [12] Kayfeci M, Yabanova I, Keçebas¸ A. The use of artificial neural network to evaluate insulation thickness and life cycle costs: pipe insulation application. Appl Therm Eng 2014;63:370e8. [13] Kaynakli O. Economic thermal insulation thickness for pipes and ducts: a review study. Renew Sustain Energy Rev 2014;30:184e94. [14] Sahin AZ. Optimal insulation of ducts in extraterrestrial applications. Int J Energy Res 2004;28:195e203. [15] Sahin AZ, Kalyon M. Maintaining uniform surface temperature along pipes by insulation. Energy 2005;30:637e47. [16] Bahadori A, Vuthaluru HB. A simple method for the estimation of thermal insulation thickness. Appl Energy 2010;87:613e9. [17] Bahadori A, Vuthaluru HB. A simple correlation for estimation of economic thickness of thermal insulation for process piping and equipment. Appl Therm Eng 2010;30:254e9. [18] Aynur TN. Variable refrigerant flow systems: a review. Energy Build 2010;42: 1106e12. [19] Incropera FP, Dewitt DP. Introduction to heat transfer. 3rd ed. New York: John Wiley Sons; 1996. [20] The Central Bank of the Republic of Turkey. www.tcmb.gov.tr [11.10.14]. € [21] Yıldız A, Gürlek G, Erkek M, Ozbalta N. Economical and environmental analyses of thermal insulation thickness in buildings. J Therm Sci Technol 2008;28:25e34.
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Determination of the economical optimum insulation thickness for VRF (variable refrigerant flow) systems €z b Abdullah Yildiz a, *, Mustafa Ali Erso a b
Department of Mechanical Engineering, Faculty of Engineering, Us¸ak University, 64200 Usak, Turkey Department of Electricity and Energy, Vocational College of Us¸ak, Us¸ak University, 64200 Usak, Turkey
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 February 2015 Received in revised form 18 May 2015 Accepted 8 June 2015 Available online 2 July 2015
This study deals with the investigation into optimum insulation thickness of installed inside building pipe network of VRF (variable refrigerant flow) systems. Optimum insulation thickness, energy savings over a lifetime of 10 years and payback periods are determined for high pressure gas pipelines, low pressure gas pipelines and low pressure liquid pipelines under the heating-only and cooling-only modes of the three-pipe VRF system using R-410A as refrigerant. By using the P1eP2 method, the value of the amount of the net energy savings is calculated. Under heating mode of VRF system, while the optimum insulation thickness varies between 16 and 20 mm depending on the pipe sections of high pressure gas pipeline, it varies from 11 to 13 mm for the pipe sections of low pressure liquid pipeline. Under cooling mode of VRF system, the optimum insulation thickness varies between 7 and 8 mm for pipe sections of low pressure gas pipeline and low pressure liquid pipeline. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Optimum insulation thickness Life-cycle analysis Variable refrigerant flow
1. Introduction VRF (variable refrigerant flow) systems use one external unit that is connected to several indoor units. VRF systems are popular because they require less outdoor plant space than conventional central air conditioning systems, are less disruptive in fitting to existing buildings (particularly when occupied), and are able to cool and heat through common pipework. These systems all use refrigerant as the cooling/heating medium rather than chilled water/hot water, which is used in conventional hydraulic systems circulated by pumps [1]. It is estimated that air conditioning systems consume about 50% of the total electricity use in the office buildings. Therefore, reducing energy use for space cooling and heating in buildings is a key measure for the energy-savings [2]. There are many strategies to reduce energy consumption, especially in heating and cooling devices. Using proper insulation in pipe network is perhaps the most effective way of energy conservation for the heating and cooling applications of VRF systems. To minimize the energy and insulation costs in addition to reducing the heat loss to the surroundings, the thickness of the insulation material needs to be
* Corresponding author. Tel.: þ90 276 2212136; fax: þ90 276 2212137. E-mail address: [email protected] (A. Yildiz). http://dx.doi.org/10.1016/j.energy.2015.06.020 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
optimized. The economic insulation thickness for a pipe is a function of a large number of parameters, such as pipe size, cost, conductivities of the pipe and the insulation material, operating and ambient temperatures, heat transfer coefficients at the inside and outside of the pipe, economic parameters and annual operation The concept of economic thermal insulation thickness considers the initial cost of the insulation system plus the ongoing value of energy savings over the expected service lifetime of the insulation [3]. Determining both the type of thermal insulation material and the economic thickness of the material used in the hot water or air service pipelines are the main subjects of many engineering investigations. Most studies estimated the heating energy requirement by the degree-time concept (degree-day, DD, or degree-hour, DH), which is one of the simplest methods applied under static conditions. Zaki and Al-Turki studied economic analysis of thermal insulation for a system of pipelines, from the oil industry, insulated by different materials composite layers. The analysis was based on an explicit nonlinear cost function that includes the annual energy losses and the insulation initial costs. In the analysis, rockwool and calcium silicate as insulation materials and a system of pipelines (0.1e0.273 m nominal size) with flow of superheated steam, furfural, crude oil, and 300-distillate was employed and ho was assumed constant, 10 W m2K1 [4]. Li and Chow analyzed methods for protecting water pipes, in cold regions against freezing, by thermal insulation material and heating cable. They
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Nomenclature
V x
a A b c C COP d D E_
h r Dt
ES h HDD Hu i k LCCA L m N Pr PP Q_ R Re t T U
high pressure gas pipeline area (m2) high pressure gas pipeline low pressure liquid pipeline price ($ kg1, $ m3) coefficient of performance inflation rate (%) diameter (mm) energy rate (J m1 year1) energy saving ($ m1) convection transfer coefficient (W m2 K1) heating degree-days ( C-days) lower heating value of the fuel (J kg1, J m3) interest rate (%) the heat transfer coefficient (Wm1 K1) life cycle cost analysis length (m) fuel consumption (kg m1 year1), (m3 m1 year1) lifetime (years) Prandtl number () payback period (years) heat transfer rate (kW, J m1 year1) thermal resistance (KW1) Reynolds number () wall thickness (mm) temperature (K) overall heat transfer coefficient (W m1 K1)
applied a thermoeconomic optimization analysis with a simple algebraic formula derived for estimating the optimum insulation thickness for tubes of different diameters varying from 0.02 m to 0.2 m. They investigated the effects of outdoor air conditions and design parameters on the optimum thickness. For the same outside-air temperature, the optimum insulation-thickness would become larger for lower design insulation envelope outsidetemperature. It was also found that the optimum insulation thickness was inversely proportional to the thermal conductivity and cost of the insulating material [5]. Ozturk et al. presented four different thermo-economic techniques for optimum design of hot water piping systems. They were as follows: the first one was a sequential optimization of pipe diameter based on minimization of total cost without considering heat losses and then of insulation thickness based on minimization of cost of insulation and heat losses. The second was simultaneous optimization of pipe diameter and insulation thickness based on the first law of thermodynamics and cost. The third was simultaneous determination of pipe diameter and insulation thickness based on maximization of exergy efficiency without considering cost. Finally, the fourth was simultaneous determination of pipe diameter and insulation thickness based on maximization of exergy efficiency and cost minimization. A case study was carried out for a hot water pipe segment, and the differences and merits of each method were discussed. Important parameters such as annual operation time, depreciation period, interest rate, fuel and electricity prices, and the thermoephysical parameters were assumed to be the same and constant for all methods [6]. Soponpongpipat et al. conducted the optimum thickness analysis of air conditioning duct's insulation, which composes of the layer of rubber and fiber glass insulator, by means of thermo-economics method. The effects of heat transfer
velocity (m s1), volume (m3) optimum insulation thickness (cm) efficiency density (kg m3) annual operation time
Subscripts a ambient an annual cl cooling load cond condenser evap evaporator f total fuel fg fiberglass F fuel hl heating load i inside in inlet ins insulation m mean o outside opt optimum out outlet R refrigerant s surface of pipe t total un-ins un-insulation 1, 2, …5, branch pipe 6, 7, 8, 9 main pipe
coefficient at inside and outside of duct on the optimum thickness of these insulators were studied. The galvanized steel duct diameter of 0.5 m with rubber insulator (k ¼ 0.035 W m1K1) and fiberglass insulator (k ¼ 0.045 W m1K1) was selected to show the study results. In order to study the change in optimum thickness when convective heat transfer coefficients were varied, the inside and outside duct convective heat transfer coefficient of 6, 10, 14, 18 and 22 W m2K1 were selected for calculation of optimum thickness. They demonstrated that the variation of inside and outside duct convective heat transfer coefficient does not affect optimum thickness but net saving increases when inside and outside duct convective heat transfer coefficient increases [7]. Keçebas¸ et al. calculated the optimum insulation thickness of pipes used in district heating pipeline networks, energy savings over a lifetime of 10 years, and payback periods for the five different pipe sizes and four different fuel types in the city of Afyonkarahisar/ Turkey. Rockwool as insulation material and a system of pipelines (50e200 mm nominal sizes) with flow of hot water were considered. The results showed that optimum insulation thicknesses varied between 0.085 and 0.228 m, energy savings varied between 10.041 $/m and 175.171 $ m1, and payback periods varied between 0.442 and 0.808 years depending on the nominal pipe sizes and the fuel types. The highest value of energy savings was reached in 250 mm nominal pipe size for fuel-oil fuel type, while the lowest value is obtained in 50 mm for geothermal energy. Considering the economic and environmental advantages, the geothermal energy ul and Keçebas¸ was a better choice and then natural gas [8]. Bas¸og investigated the energy, economic and environmental evaluations of thermal insulation in district heating pipeline. The optimum insulation thickness, energy saving over a lifetime of 10 years, payback period and emissions of CO, CO2 and SO2 are calculated for
€z / Energy 89 (2015) 835e844 A. Yildiz, M. Ali Erso
nominal pipe sizes and fuel types based on heating loads in Afyonkarahisar/Turkey. The results show that the highest value of optimum insulation thickness, energy savings, emissions and the lowest payback period are reached for a nominal pipe size of 200 mm [9]. Keçebas¸ optimized insulation thickness by using exergy method and life-cycle cost concept for the case of using various fuels such as coal, natural gas and fueleoil. The optimum insulation thickness decreased with the increasing of inlet temperature of fuel, and with the decreasing of excess air coefficient, temperatures of stack gases and combustion chamber. The optimum insulation thicknesses were determined as 0.065, 0.071, 0.099 m with a rate of 68.27%, 71.54% and 77.85% in the exergetic saving for natural gas, coal and fueleoil fuels, respectively. The optimum insulation thickness for the exergoeconomic optimization was higher than that of energoeconomic optimization [10]. Kayfeci estimated the optimum insulation thickness, energy savings, annual costs and payback period for various pipe diameters and insulation materials of the heating systems in Isparta/Turkey and in the regions with different degree-day values by using LCCA (life cycle cost analysis) method. As a fuel, natural gas was used in the study. EPS (expanded polystyrene) insulation material with a DN (nominal diameter) of 250 mm provides the highest energy savings, while the lowest value was found to be in fiberglass insulation material with DN 50 mm [11]. Kayfeci et al. reported on the use of ANNs (artificial neural networks) to predict insulation thickness and LCC (life cycle costs) for pipe insulation applications. Using the collected data set and LCC analysis results for training, a three-layer feed forward ANN model based on a back propagation algorithm was developed. The developed ANN model has a very practical use of determining the optimum thickness of insulation for any location in the world when just the input parameters of the ANN model are known [12]. Kaynaklı carried out a literature review of papers that addressed the optimum economic thickness of the thermal insulation on a pipe or duct with different geometries used in various industries. The heat transfer equations, the basic results, the optimization procedures and the economic analysis methods used in the studies were presented comparatively. Additionally, a practical application example based on optimizing the insulation thickness on a pipe was performed, and the effective parameters of the optimum thickness were investigated [13]. On the other hand, only a limited number of analytical techniques were applied to analyze the optimization of the pipes. Sahin studied optimized numerically the variation in the thermal insulation thickness of a pipe for space applications to minimize the radiative heat loss to the ambient. The thickness of the insulation was assumed to be linearly varying along the pipe because this scenario is easy to implement in practice. It was found that a linearly decreasing insulation thickness with a minimum slope along the pipe provides the best insulation under the radiation heat transfer condition [14]. Sahin and Kalyon obtained an explicit analytical solution for the insulation thickness variation over a pipe to maintain a uniform outer surface temperature. They considered heat transfer on the outer surface of the insulation considered a combination of convection and radiation. It was shown that the insulation thickness variation that provides uniform surface temperature was independent of the convection and radiation heat transfer coefficients [15]. Bahadori and Vuthaluru presented optimum economic thickness of thermal insulations predicted rapidly as a function of steel pipe and equipment diameter and thermal conductivity of insulation by proposing simple correlation. The correlation was as a function of steel pipe diameter and thermal conductivity of insulation for surface temperatures at 100, 300, 500 and 700 C. A simple interpolation formula generalized this correlation for wide range of surface temperatures. The proposed correlation covered pipeline diameter and surface temperature up
837
to 0.5 m and 700 C, respectively. The derived polynomials were applied to calculate new coefficients to predict optimum economic thickness of thermal insulations [16]. Bahadori and Vuthaluru formulated simple correlations for the estimation of heat flow through insulation, thermal resistance and thermal insulation thickness for flat surfaces, ducts and pipes. The proposed correlation covered the temperature difference between ambient temperature and outside temperature up to 250 C and the temperature drop through insulation up to 1000 C. The proposed simple correlation calculates the thermal thickness for flat surfaces up to 200 mm and predicts the thermal thickness for ducts and pipes with outside diameters up to 2400 mm. The accuracy of the proposed method tested and it was found to be in excellent agreement with the reported data for the wide range of conditions, where the average absolute deviation between reported data and the proposed correlation was around 3.25% [17]. As witnessed in literature, researches focused on economic thermal insulation thicknesses of hot water or air service pipelines by means of heating degree days and analytical optimization techniques. In those studies, the effect of different parameters such as pipe diameter, working fluid, interest rate inflation rate, energy source, fuel type, insulation materials on economic optimum pipe insulation is investigated. This study is different from the previously conducted ones as follows: (i) economic optimum insulation thickness analysis is applied to installed inside the building pipeline of the VRF systems, (ii) R-410 as working fluid and seamless copper pipe as pipe material are used, (iii) analyses carried out for both heating and cooling modes of VRF system. 2. Description of system Basically, a VRF system is a refrigerant system that varies the refrigerant flow rate with the help of the variable speed compressor and the EEVs (electronic expansion valves) located in each indoor unit to match the space cooling or heating load in order to maintain the zone air temperature at the indoor set temperature. The indoor units (located in each zone) are connected to the outdoor unit in parallel with the refrigerant pipes [18]. Generally, the VRF systems have either two-pipe or three-pipe configurations and they are operated with or without ice thermal storage tanks. The two-pipe (a HPGP (high pressure gas pipe), a LPLP (low pressure liquid pipe)) VRF systems are the general ones that can be used for cooling or heating depending on the season. On the other hand, the three-pipe (a HPGP (high pressure gas pipe), a LPGP (low pressure gas pipe), and a LPLP (low pressure liquid pipe)) VRF systems work best, when there is a need for some of the spaces to be cooled and some of them to be heated during the same season. This generally occurs in the winter season in medium-sized to large sized commercial buildings with a substantial core such as computer rooms [18]. The three-pipe VRF systems use branch selector boxes (located before each indoor unit) and they can be operated in five different modes: a. Cooling-only mode: All indoor units are in cooling operation. b. Heating-only mode: All indoor units are in heating operation. c. Cooling-principal mode: Cooling is the principal mode in the concurrent heating and cooling operation. d. Heating-principal mode: Heating in the principal mode in the concurrent heating and cooling operation. e. Heat recovery mode: Heat is balanced between indoor units while the outdoor unit heat exchanger is closed [18]. In this study, economical optimum insulation thickness is analyzed for heating-only and cooling-only modes of three-pipe
838
€z / Energy 89 (2015) 835e844 A. Yildiz, M. Ali Erso
VRF systems, shown in Fig. 1 and Fig. 2 respectively, in which the pipes are networked inside a building. The system uses R-410 refrigerant as working fluid. In Figs. 1 and 2, a1-a9 numbered pipe sections are high pressure gas pipeline, b1-b9 numbered pipe sections are low pressure gas pipeline and c1-c9 numbered pipe sections are low pressure liquid pipeline. Low pressure gas pipeline is closed for heating-only mode of VRF system, whereas, high pressure gas pipeline is closed for cooling-only mode of VRF system.
3. Analyses 3.1. Analysis of VRF (variable refrigerant flow) system The following assumptions are made in thermodynamically analysis of the VRF system: 1. Steady-state and ideal conditions are evaluated. 2. R-410 refrigerant is used as working fluid. 3. The evaporation and condensation temperatures for both heating and cooling modes are taken as 283 K and 323 K, respectively. 4. Kinetic and potential energy changes are negligible. 5. The temperature and pressure drops through the duct are neglected. 6. Ambient temperature of the pipelines network is assumed as indoor temperature of building because the pipelines of the VRF system are installed inside the building. Ambient temperatures (Ta) are assumed as 293 K for heating mode in winter season and 303 K for cooling mode in summer season. The thermodynamic properties of the R-410 refrigerant are calculated by means of REFPROP 9.0. The system operation parameters and thermodynamic properties correspond to the parameters are given in Table 1. In the VRF system, 1, 2, 3, 4 and 5 numbered pipe sections of high pressure gas pipeline, low pressure gas pipeline and low pressure liquid pipelines are branch pipes, whereas, 6, 7, 8 and 9 numbered pipe sections of high pressure gas pipeline, low pressure gas pipeline and low pressure liquid pipelines are main pipes. Indoor units capacities based on heating and cooling loads for each of the zone are chosen from manufacturer catalogs. For example, while heating load value equals to 16 kW and cooling load value equals to 14 kW for indoor unit in Zone 5. Indoor units of the VRF system operate as condenser in heatingonly mode. Since indoor units capacities based on heating load
values are known in each of the zones, mass flow rates in each branch pipes of high pressure gas pipelines are calculated from Eq. (1).
_R¼ m
Q_ hl hcond;in hcond;out
(1)
When it comes to cooling mode, indoor unit of the VRF system operates as evaporator and since indoor units capacities based on cooling load values are known in each of zones, mass flow rates in each branch pipes of low pressure gas pipelines are calculated from Eq. (2).
_R¼ m
Q_ cl hevap;out hevap;in
(2)
Then, heat loads of main pipe sections in both heating-only mode and cooling-only mode are calculated as:
Q_ 6 ¼ Q_ 5 þ Q_ 4
(3)
Q_ 7 ¼ Q_ 5 þ Q_ 4 þ Q_ 3
(4)
Q_ 8 ¼ Q_ 5 þ Q_ 4 þ Q_ 3 þ Q_ 2
(5)
Q_ 9 ¼ Q_ 5 þ Q_ 4 þ Q_ 3 þ Q_ 2 þ Q_ 1
(6)
Mass flow rates of 6, 7, 8 and 9 numbered main pipe sections in both high pressure gas pipeline and low pressure gas pipeline are determined as:
_ R;5 þ m _ R;4 _ R;6 ¼ m m
(7)
_ R;5 þ m _ R;4 þ m _ R;3 _ R;7 ¼ m m
(8)
_ R;5 þ m _ R;4 þ m _ R;3 þ m _ R;2 _ R;8 ¼ m m
(9)
_ R;9 ¼ m _ R;5 þ m _ R;4 þ m _ R;3 þ m _ R;2 þ m _ R;1 m
(10)
After the mass flow rate values of high and low pressure gas pipelines are calculated, the pipe diameters for each of branch pipes of the VRF system are selected from manufacturer catalogs. As to the main pipe diameters of the VRF system, they are determined from manufacturer catalogs based on heat loads of indoor units attached to main pipe sections. The velocities of R-410 refrigerant in each of pipe sections are calculated by,
Fig. 1. Schematic view of heating-only mode for three-pipe VRF system.
€z / Energy 89 (2015) 835e844 A. Yildiz, M. Ali Erso
839
Fig. 2. Schematic view of cooling-only mode for three-pipe VRF system.
Table 1 The system operation parameters and thermodynamic properties correspond to the parameters. Parameters
TR,m (K)
P (kPa)
h (kJkg1)
Evaporation condition Condensation condition Evaporator inlet Evaporator outlet Condenser inlet Condenser outlet
283 323 283 283 343.19 323
1088.4 3070.6 1088.4 1088.4 3070.6 3070.6
e e 285.850 428.700 456.710 285.850
VR ¼
_R m r R Ac
Q_ ¼ UAs TR;m Ta
(12)
where U is the overall heat transfer coefficient of pipe layers and is calculated by Eq. (13), As is the total surface area of pipe, TR,m is the average working fluid temperature of inside pipe and Ta is the ambient temperature of the pipelines networked inside building and the value for the heating and cooling modes is assumed as 293 K and 303 K respectively. TR,m is 323 K for the low pressure liquid pipeline and 343.19 K for high pressure gas pipeline under heating mode and this value is 283 K for both the low pressure gas pipeline and low pressure liquid pipeline under cooling modes.
(11)
The mass flow rates and velocity values calculated by using the selected pipe dimensions by Eqs (1)e(11) for branch pipelines and for main pipelines of heating and cooling modes of the VRF system are summarized in Table 2 and Table 3, respectively.
U¼
1 Rt
(13)
where Rt are the total thermal resistances, which are calculated by Eqs. (14) and (15) for uninsulated and insulated pipe systems.
ln
Rt;unins
3.2. Heat loss through pipelines of the VRF system Optimum pipe insulation thickness analyses of the VRF system is calculated for unit length of pipeline considering heat losses from throughout pipe surface. Flexible insulation foam is chosen for the insulation of the piping network of VRF system with thermal conductivity of 0.039 Wm1K1 and cost insulation of 600 $m3. The pipe materials for piping system of VRF system are taken as seamless copper pipe with thermal conductivity of 400 Wm1K1. The annual heat losses are calculated by;
Rt;ins ¼
ro
ri 1 1 ¼ þ þ hi As;i 2pLpipe kpipe ho As;o
ln rio
ln
(14)
rins ro
1 1 þ þ þ hi As;i 2pLpipe kpipe 2pLpipe kins ho A0o
(15)
where, kins is the heat transfer coefficient of insulation material and it must be kept in mind that the outside surface area of the last layer of duct system is A0o ¼ 2pLrins .
Table 2 The pipe dimensions, mass flow rates and velocity values for heating-only of the VRF system. Operation mode
Heating mode
Pipeline
HPGP
LPLP
Parameter
Q_ (kw) D (mm) t (mm) _ (kgs1) m V (ms1) Q_ (kw) D (mm) t (mm) _ (kgs1) m V (ms1)
Branch pipe sections
Main pipe sections
1
2
3
4
5
6
7
8
9
4 9.52 0.8 0.023 4.36 4 6.35 0.8 0.023 9.50
5 12.70 0.8 0.029 2.77 5 6.35 0.8 0.029 11.87
8 15.88 1.0 0.047 2.84 8 9.52 0.8 0.047 6.83
10 15.88 1.0 0.059 3.55 10 9.52 0.8 0.059 8.54
16 15.88 1.0 0.094 5.676 16 9.52 0.8 0.094 13.66
26 22.22 1.0 0.153 4.35 26 12.70 0.8 0.153 11.30
34 28.58 1.0 0.2 3.29 34 12.70 0.8 0.2 14.78
39 28.58 1.0 0.229 3.77 39 12.70 0.8 0.229 16.96
43 28.58 1.0 0.252 4.16 43 15.88 1.0 0.252 11.96
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Table 3 The pipe dimensions, mass flow rates and velocity values for cooling-only of the VRF system. Operation mode
Pipeline
Cooling mode
LPGP
LPLP
Parameter
Q_ (kw) D (mm) t (mm) _ (kgs1) m V (ms1) Q_ (kw) D (mm) t (mm) _ (kgs1) m V (ms1)
Branch pipe sections
Main pipe sections
1
2
3
4
5
6
7
8
9
3.6 6.35 0.8 0.025 34.56 3.6 6.35 0.8 0.025 1.26
4.5 6.35 0.8 0.032 43.19 4.5 6.35 0.8 0.032 1.58
7.1 9.52 0.8 0.050 24.51 7.1 9.52 0.8 0.050 0.90
9 9.52 0.8 0.063 31.07 9 9.52 0.8 0.063 1.13
14 9.52 0.8 0.098 48.34 14 9.52 0.8 0.098 1.76
23 22.22 1.0 0.161 12.18 23 12.70 0.8 0.161 1.48
30.1 28.58 1.0 0.211 9.23 30.1 12.70 0.8 0.211 1.93
34.6 28.58 1.0 0.243 10.61 34.6 12.70 0.8 0.243 2.22
38.2 28.58 1.0 0.268 11.71 38.2 15.88 1.0 0.268 1.57
The convection heat transfer coefficients for the inside and outside surface of piping system hi and ho are calculated as [19];
hi ¼
Parameters
0:023Re0:8 Pr0:4 kR Dpipe
(16)
ho ¼ Nuo
kair Dpipe
Nuo ¼ 0:3 þ h
(17) pffiffiffiffiffiffi kair RePr1=3
1 þ ð0:4=PrÞ2=3
i1=4
h i4=5 1 þ ðRe=282000Þ5=8 (18)
In Eqs. (16) and (17), Reynolds number (Re) is calculated by;
rair Vair Dpipe mair
Ct;ins ¼ Cins Vins
3.3. Life cycle analysis and optimization of insulation thickness Life-cycle cost analysis is often applied to energy systems. A lifecycle cost analysis can show that spending more initially on additional building insulation can produce a net savings (due to reduced heating and cooling costs) over the lifetime of a building. In this study, determination of the amount energy cost calculated using LCCA method. This method is a practical and can be used for optimization the insulation thickness of pipelines. The design parameters used in economic analyses are given in Table 4. The annual total energy cost, Cf, is given
Q_ Dt Hu helectricity COP
CF
(20)
where, Dt is annual operation time of the VRF system under heating-only mode or cooling-only mode, Hu is lower heating value of energy source and CF is fuel cost. The annual fuel consumption is,
mf;an
Operation time (hours) Heating-only mode Cooling-only mode System performance (COP) In the heating-only mode In the cooling-only mode Insulation material (flexible insulation foam) kins Cins Interest rate (%) Inflation rate (%) Life time (years)
Values 3.599 106 JkW1h1 0.1059 $ kWh1 0.99 2100 900 4.02 3.48 0.039 Wm1K1 600 $m3 4.5 9.4 10
(19)
where, r is the density of working fluid or ambient air, D is the pipe diameter, m is the dynamic viscosity and V is the speed of working fluid or speed of ambient air. The velocity of ambient air is assumed of 0.2 ms1 in these analyses.
Cf ¼
Energy source (Electricity) Hu CF
helectricity
and
Re ¼
Table 4 The design parameters used in economic analyses [19,20].
UA TR;m Ta Dt ¼ Hu helectricity COP
(21)
The total investment cost of insulation is given by the following equation
(22)
where, Cins is the cost of insulation material and Vins is the volume of material used in insulation. The first cost of insulation may be treated as capital investment. It is possible to calculate the present worth of the net amount of energy savings via insulation using a well-known method known as the P1eP2 method. P1 has relation with inflation rate d, interest rate i, and lifetime N. P2 is the ratio of the life cycle expenditures incurred because of the additional capital investment to the initial investment. The equation for P1 is defined as [11].
P1 ¼
" # 1 1þi N 1 if isd di 1þd
P2 ¼ 1 þ P1 Ms Rv ð1 þ dÞN
(23)
(24)
where Ms is the ratio of the annual maintenance and operation cost to the original first cost, Rv is the ratio of the resale value to the first cost. P2 can be taken as 1.0 if the maintenance and operation cost is zero. If the increase rate is equal to discount rate, P1 is calculated from
P1 ¼
N if i ¼ d 1þi
(25)
The total cost of heating with the insulated piping system can be calculated by the following equations
Ct ¼ P1 Cf þ P2 Ct;ins
(26)
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Fig. 3. Effects of insulation thickness on the total cost for HPGP main pipe sections (left side) and LPGP main pipe sections (right side) under heating mode and cooling mode of the VRF system.
Energy savings ($ m1) obtained during the lifetime of insulation material can be calculated as follows [21]:
ES ¼ Ct;unins Ct;ins
(27)
where, Ct,un-ins and Ct,ins are the total heating costs of the building when insulation is not and is applied, respectively.
Energy savings can be expressed as % by the following equation:
ES 100 Ct;unins
(28)
Then, pay-back period, PP is calculated by solving the following equation for PP:
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€z / Energy 89 (2015) 835e844 A. Yildiz, M. Ali Erso
Fig. 4. Comparison of energy savings for both HPGP and LPLP under heating mode of the VRF system.
" # Ct;ins 1 1 þ i PP ¼ 1 di 1þd ES
Fig. 5. Comparison of energy savings for both LPGP and LPLP under cooling mode of the VRF system.
(29)
where, Cins/ES is the simple pay-back period and this value does not take interest rate into account. ES is the annual energy savings obtained by insulation.
4. Results and discussion The optimum insulation thickness based on energy-cost analysis is studied widely for hot water and hot air heating piping systems in the literature. In this study, economical optimum insulation thickness of piping system for both heating-only and cooling-only modes of the VRF system using R-410 refrigerant as working fluid are studied. The variations of the insulation thickness, fuel and total costs with respect to main pipe sections of HPGP (high pressure gas pipeline) under heating mode of the VRF system are demonstrated on the left side of Fig. 3 one after another, whereas, variations of these costs with respect to main pipe sections of LPGP (low pressure gas pipeline) under cooling mode of the VRF system are shown on the right side of this figure. As shown in Fig. 3, the cost of the fuel decreases as insulation thickness increases under both heating and cooling modes. However, the insulation cost increases linearly with insulation thickness. The total cost is the sum of the cost of fuel and
Fig. 6. The optimum insulation thicknesses for pipe sections of the VRF system.
insulation material. The insulation thickness at the minimum total cost is determined as the optimum insulation thickness. When it comes to energy savings, the variations emerging for all pipe sections of HPGP and LPLP under heating mode of the VRF system are presented successively on Fig 4, whereas, variations of energy savings with respect to all pipe sections of LPGP and LPLP under cooling mode of the VRF system are demonstrated on Fig. 5. The optimum insulation thickness is achieved when the energy savings start to drop thanks to the increased thickness of insulation
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optimum insulation thickness xopt ¼ rinsro is obtained. MATLAB optimization toolbox is used to determine the optimum insulation thickness. The variations of the optimum insulation thicknesses with respect to each of the pipe sections for all the pipelines under both heating-only mode and cooling-only mode of the VRF system are represented in Fig. 6. As seen in Fig. 6, under heating-only mode of VRF system, while the optimum insulation thickness varies between 15.73 and 19.64 mm depending on the pipe sections of HPGP, whereas, it varies from 11.17 mm to 13.23 mm for the pipe sections of LPLP. Besides, as seen in Fig. 6, under cooling-only mode of VRF system, while the optimum insulation thickness varies between 6.65 and 8.13 mm depending on the pipe sections of LPGP, whereas, it varies from 6.72 mm to 7.89 mm for the pipe sections of LPLP. While the highest values of optimum insulation thicknesses are obtained on main pipe sections of both HPGP and LPLP under heating-only mode, the lowest values of optimum insulation thicknesses are obtained on branch pipe sections of both LPGP and LPLP under cooling-only mode. The highest optimum insulation thicknesses calculated for each of pipe section of LPLP must be selected because LPLP of the VRF system is used under both heating-only and cooling-only modes. Optimum insulation thicknesses for HPGP, LPGP and LPLP change respect to with pipe diameter and mass flow rate. The pipe diameter and mass flow rate depend on heat loads on the pipe sections. In order to satisfy the increasing heat loads on pipe sections, the larger pipe diameter and the higher mass flow rate are required. Therefore, as heat load values on the pipe sections increases, the pipe diameter and mass flow rate increase. Also, as the heat load on the pipe sections increases, optimum insulation thicknesses increase. Therefore, the highest optimum insulation thicknesses for these pipelines are selected. As a result, optimum insulation thicknesses for HPGP, LPGP and LPLP of the investigated VRF system are determined as 20, 8 and 13 mm, respectively. The variations of the payback period for each of pipelines are shown in Fig. 7 for both heating mode and cooling mode of the VRF system. Under heating mode of VRF system, while the payback periods vary between 0.13 and 0.19 years depending on the pipe sections of HPGP, whereas, they vary from 0.15 to 0.18 years for the pipe sections of LPLP. Under cooling mode of VRF system, the payback periods vary between 0.22 and 0.44 years depending on the pipe sections of LPGP, whereas, they varies from 0.23 to 0.33
Fig. 7. Payback periods versus pipe sections.
material. The energy savings is at maximum level under optimum insulation thickness. The energy savings depend upon the insulation thickness and heat load values on the pipe sections. Insulating the pipe sections up to optimum insulation thickness increases energy savings; however, over insulation more than optimum insulation thickness decreases energy saving. Besides, energy saving increases as heat load increases for both operation modes of VRF the system and for each of the pipelines. As witnessed in Fig. 4, in the heating-only mode of the VRF system, while the energy saving values vary from 19.07% to 58.50% for the pipe sections of HPGP, these values vary from 40.00% to 56.41% for the pipe sections of LPLP. Here, negative values for energy saving shows that energy saving is not obtained. Furthermore, the more insulation than insulation of 0.035 m on branch pipe sections of LPLP is loss money for the heating mode because it does not provide energy savings. As seen in Fig. 5, in the cooling mode of the VRF system, while the energy saving values vary from 255.90% to 47.66% for the pipe sections of LPGP, these values vary from 255.66% to 46.03% for the pipe sections of LPLP. Under the cooling-only mode, the more insulation than insulation of 0.02 m for all pipe sections of LPGP and LPLP is loss money. The outside radius of insulated piping system can be determined by minimizing Eq. (26) or maximizing Eq. (27). So, the differential of S or Ct with respect to r2 is taken and set equal to zero, then the
Table 5 The optimum insulation thickness, energy savings and payback periods for heating mode of the VRF system. Operation mode
Heating mode
Pipeline
HPGP
LPLP
Parameter
Xopt (mm) ES (%) PP (years) Xopt (mm) ES (%) PP (years)
Branch pipe sections
Main pipe sections
1
2
3
4
5
6
7
8
9
16 58.11 0.13 11 55.10 0.15
17 58.30 0.15 11 55.49 0.150
18 58.33 0.16 12 55.65 0.16
18 58.43 0.16 12 56.01 0.16
18 58.76 0.16 12 56.58 0.16
19 58.09 0.18 13 56.44 0.17
20 57.30 0.19 13 56.68 0.17
20 57.35 0.19 13 56.79 0.17
20 57.55 0.19 13 56.16 0.18
Table 6 The optimum insulation thickness, energy savings and payback periods for cooling mode of the VRF system. Operation mode
Cooling mode
Pipeline
LPGP
LPLP
Parameter
Xopt (mm) ES (%) PP (years) Xopt (mm) ES (%) PP (years)
Branch pipe sections
Main pipe sections
1
2
3
4
5
6
7
8
9
7 48.69 0.22 7 47.15 0.23
7 48.77 0.22 7 47.21 0.23
7 47.85 0.26 7 46.38 0.27
7 47.93 0.26 7 46.44 0.27
7 48.04 0.25 7 46.52 0.27
8 42.57 0.38 8 45.34 0.30
8 39.97 0.44 8 45.38 0.30
8 40.04 0.44 8 45.40 0.30
8 40.08 0.44 8 44.07 0.33
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years for the pipe sections of LPLP. While the shortest payback periods are determined at main pipe sections of LPGP under cooling mode, the longest payback periods are carried out at branch pipe sections of HPGP under heating mode. The optimum insulation thickness, energy savings and payback periods based on analyzed pipe sections of HPGP, LPGP and LPLP for given VRF system are summarized in Table 5 for heating mode and in Table 6 for cooling mode.
5. Conclusions There are many studies on the optimum insulation thickness computations in the heating pipe performed based mainly on the heating load and other parameters such as the costs of the insulation material and energy, efficiencies of the heating system, the lifetime, and the current inflation and discount rates. In this study, the optimum insulation thickness is studied for the pipe network of the three-pipe VRF system working both heating and cooling mode. Considering the results of the analyses, the following main conclusions can be drawn from the present study: a. The optimum insulation thickness increases as the heat loads on the pipes increase. b. While the energy saving values vary from 19.07% to 58.50% for the pipe sections of HPGP, these values vary from 40.00% to 56.41% for the pipe sections of LPLP in the heating mode of the VRF system. c. While the energy saving values vary from 255.90% to 47.66% for the pipe sections of LPGP, these values vary from 255.66% to 46.03% for the pipe sections of LPLP in the cooling mode of the VRF system. d. While the optimum insulation thickness varies between 16 and 20 mm depending on the pipe sections of HPGP, whereas, it varies from 11 to 13 mm for the pipe sections of LPLP under heating mode of VRF system, e. The optimum insulation thickness varies between 7 and 8 mm depending on the pipe sections of LPGP and LPLP under cooling mode of VRF system. f. Low pressure liquid pipeline (c1-c9) is active under both heating and cooling modes. Therefore, while optimum insulation thickness is determined for these pipes, the highest optimum insulation thickness value must be selected.
As a result, optimum insulation thicknesses for HPGP, LPGP and LPLP of the VRF system are determined as 20, 8 and 13 mm, respectively.
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