Science and Technology for the Built Environment
ISSN: 2374-4731 (Print) 2374-474X (Online) Journal homepage: http://www.tandfonline.com/loi/uhvc21
An experiment-oriented simulation method for cooling capacity determination of cooling ceiling radiant panel system Yongli Yuan, Xu Zhang, Xiang Zhou & Jun Gao To cite this article: Yongli Yuan, Xu Zhang, Xiang Zhou & Jun Gao (2016) An experimentoriented simulation method for cooling capacity determination of cooling ceiling radiant panel system, Science and Technology for the Built Environment, 22:6, 831-844, DOI: 10.1080/23744731.2016.1192877 To link to this article: http://dx.doi.org/10.1080/23744731.2016.1192877
Accepted author version posted online: 15 Jun 2016. Published online: 15 Jun 2016. Submit your article to this journal
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Date: 12 May 2017, At: 19:58
Science and Technology for the Built Environment (2016) 22, 831–844 C 2016 ASHRAE. Copyright ISSN: 2374-4731 print / 2374-474X online DOI: 10.1080/23744731.2016.1192877
An experiment-oriented simulation method for cooling capacity determination of cooling ceiling radiant panel system YONGLI YUAN, XU ZHANG∗, XIANG ZHOU, and JUN GAO School of Mechanical Engineering, Tongji University, 204 Jiyang Building, 1239 Siping Road, Shanghai 200092, China
The correct evaluation of the heat transfer process is important to the radiant cooling/heating system’s design and operation. For different types of radiant systems, the cooled/heated surface and indoor environments are actually subject to the same heat transfer process. Thus some basic rules can be revealed to simplify the research or the design for the radiant systems. The purpose of this research is to establish a basic characteristic curve for cooling ceiling radiant panel system and provide a simple approach to determine its cooling capacity. Considering the limitations to conduct exhaustive experiments, this research applies an experimentoriented simulation method to determine the cooling capacity of cooling ceiling radiant panel systems. A model for capillary tube mats is first developed and then validated by available experimental data. Based on the validated model, more conditions are simulated and more data are generated to investigate the relationship between the specific cooling capacity and temperature difference. The model treats the cooling capacity as a function of cooled ceiling surface’s temperature and the air temperature at the third-boundary condition. Results show that the key variables, for example, the total heat flux density and the cooled ceiling surface’s temperature, agree well with the experimental data, thus it is feasible for the model to be used in the simulation. The coefficients for the simplified cooling capacity model are obtained by fitting the data generated from the model. In addition, it is found that the total heat transfer coefficient can also be expressed similarly to the correlation reported in a literature for the natural convective coefficient, but with different coefficients so as to include the effects of radiation indirectly. The experimental and simulation results reported in this study can provide guidance for engineering applications.
Introduction The cooling ceiling radiant panel (CCRP) system has been developed and applied in commercial and residential buildings all over the world throughout the past decades, and recently, has raised more attention (Hu and Niu 2012). The correct evaluation of the heat transfer process is important to the CCRP system’s design and operation. The general design considerations of CCRP systems are also introduced in ASHRAE Handbook (2012). The heat transfer coefficient as a fundamental parameter plays an essential role in calculating heating/cooling capacity and dimensioning of radiant systems. Some researchers tried to obtain accurate heat transfer coefficients by developing elabrate models for radiant panels, from simply treating the panel as plate fin (Kilkis et al. 1994), improved composite fin model (Liu et al. 2012), to semi-analytical model (Chuangchid
Received August 12, 2015; accepted April 27, 2016 Yongli Yuan is a PhD Student. Xu Zhang, PhD, is a Professor. Xiang Zhou, PhD, is an Associate Professor. Jun Gao, PhD, is a Professor. ∗ Corresponding author e-mail:
[email protected] Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/uhvc.
and Krarti 2001), thermal network model (Diaz, 2011; Weber and Johannesson, 2005), or even computation intensive numerical model (Corgnati 2009; Kim al. 2005; Niu and Kooi 1994). However, these models are usually case dependent, thus the results are not applicable to other conditions. To better help to determine the size of the radiant systems, a combined coefficient considering the factors of convection and radiation is needed (Causone et al. 2009; Cholewa et al. 2013; Koca et al. 2014). In addition, models or correlations for the heat transfer coefficients in a simple form are preferred. In the last few decades, many researchers focused on heat transfer coefficients. The work of Min et al. (1956) was an early effort that researched heat transfer coefficients. The authors obtained a series of equations for calculating heat flux density from radiant systems by convective heat transfer coefficients. One of the equations is applicable for cooled ceilings and heated floors as expressed in Equation 1 that the natural convective coefficient (h c ) is determined using three differently sized testing chambers: h c = 2.13 (Ta − Ts )0.31
(1)
Moreover, Trogisch et al. (1991) conducted an experiment under a temperature difference (Ta − Ts ) of 10 K, in order to estimate the cooling capacity. They established a general
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Table 1. Heat transfer coefficients in reference literatures. Researchers Trogisch (1991) Causone (2009) Chicote (2012) Awbi and Hatton (1999, 2000) Karadag (2009)
h c ,W/m2.K (Btu/hft2◦ )
h r ,W/m2.K (Btu/hft2◦ )
h total ,W/m2.K (Btu/hft2◦ )
3.5 (0.62) – 6.5 (1.14) 4.4 (0.77) 4.2 (0.74) h c = 2.175/L0.076 · (Ta − Ts )0.308 h c = 3.1 (Ta − Ts )0.22
5.5 (0.97) 5.6 (0.99) 5.4 (0.95) — —
9 (1.59) – 12 (2.11) 13.2 (2.32) 7.8 (1.37) – 9.3 (1.64) — h total = 11.5ε (Ta − Ts )0.09
characteristic curve from the experiment and the expression was also included in EN 15377-1 (2008). On the other hand, as suggested by Causone et al. (2009), the total heat transfer coefficient should not be calculated as the sum of the radiant and convective heat transfer coefficients directly, because the two coefficients inherently followed different physical laws. A series of experimental data in a climate chamber were used to evaluate the heat transfer coefficients between a radiant ceiling and room in typical conditions of occupancy of an office or residential building. However, the calculated total heat transfer coefficients may differ due to the selected air temperature locations. The total heat transfer coefficients, the convective coefficients, and the radiant coefficients were also obtained, respectively, in different reference temperatures. Andr´es-Chicote et al. (2012) experimentally evaluated heat transfer coefficients and cooling capacity for a cooled radiant ceiling. They also used average unheated (uncooled) surface temperature (AUST), Ta , and Top as different reference temperatures for determining the radiant heat transfer coefficient, the convective heat transfer coefficient, and the total heat transfer coefficient, respectively. A few published studies do not agree with the variables involved in these general correlations or its formal expression (EN 15377-1, 2008) like Awbi and Hatton (1999, 2000) and Glueck (1990). Awbi et al. (1999, 2000) experimentally researched values and equations of heat transfer coefficients, and investigated the effect of room surface sizes on h c in two test chambers, then gave the related correlation in Table 1 at the cooled ceiling and heated floor for an office room dimensioned 2.78 × 2.78 × 2.3 m (9.12 × 9.12 × 7.54 ft). The total heat transfer coefficients would be influenced by different internal surface colors. Thus, Karada˘g (2009) put forward a new approach to establish h c and h total correlations considering the air temperature as the indoor reference temperature by numerical simulations. He considered emissivity on ceiling radiant panel surfaces, obtained expressions as h total = f (ε, (Ta − Ts )) and gave the correlations of h c and h total separately in different room dimensions. The most valuable work has been done to establish practical heating/cooling capacity models for particular types of radiant ceiling systems, for example, Jeong and Mumma (2003, 2007). They also devoted themselves to building a simplified regression model for CCRP system directly from the fluid supply temperature. The model was used to estimate the cooling capacity of suspended metal ceiling radiant cooling panel in natural convection, and investigated the enhanced capacity under mixed convection condition.
Some researchers mainly concentrate on how to deepen the understanding of the heat transfer process in a radiant system by obtaining results from the experiment in a climate chamber. However, considering the limitation of experimental conditions, the experimental data from literatures cannot completely quantify the heat flux density and total heat transfer coefficients. In this study, a simple approach to obtain the heat transfer performance of the radiant panel is presented. In this approach, a model of radiant panel is developed first and then validated with limited experimental data, and based on the validated model, more conditions are simulated and more data are generated and then the heat transfer performance of the radiant panel is investigated. To the best of the author’s knowledge, this article presents a flexible approach, which is alternative to the costly and time-consuming experiment for establishing a basic characteristic curve of the CCRP system. Remainder of this article is organized as follows. Section 2 introduces the development of a simplified model for capillary tube mats-based CCRP system. Section 3 discusses the validation of the model based on the experiment. Case studies and evaluation of cooling capacity and total heat transfer coefficients for CCRP system are carried out in Section 4. And Section 5 concludes this study. Capillary tube mats-based CCRP model development Determination of key variables For total heat flux density (qtotal ) in the CCRP system, natural convection and thermal radiation are always the predominant heat transfer processes when ignoring solar radiation and ventilation. Thus, qtotal can be treated as the sum of the natural convection heat flux density (qc ) and the radiation flux (qr ): qtotal = qc + qr
(2)
The qc is determined by the convective heat transfer coefficient and temperature difference as Equation 3, and qr can be calculated based on the method proposed by Davies (2004) with simplified room radiation exchange as in Equation 4: (3) qc = h c (Ta − Ts ) qr = σ (AUST + 273)4 − (Ts + 273)4 = h r (Ti − Ts ) (4)
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The temperature difference (Ta − Ts ) actually includes the effects of the floor and internal wall surface temperatures indirectly (Karada˘g 2009). In addition, as is shown in Table 1 and illustrated in literatures (Feustel and Stetiu 1995; Olesen 2002), the radiant heat transfer coefficient is very stable, that is to say, trying to neglect the impact caused by the difference between AUST and Ta will not greatly affect the calcultation result. But it should be noted here that the assupmtion may not work well beyond certain conditions (surface temperature of climate chamber within 18∼33◦ C (65∼92◦ F; Causone et al. 2009). The calculation for qtotal can be treated as: qtotal = h total (Ta − Ts )
(5)
The heat flux density between the ceiling surface and the chamber is calculated by subtracting transmitted heat losses from the enthalpic flux, ineffective heat flux is hardly transferred from panels backward toward the upper slab, so qtotal =
c p,w ·mw · Tw,r tn − Tw,sup − qhl A
(6)
The total heat transfer coefficient has always been one crucial factor to investigate the cooling capacity of a radiant system. Based on the heat balance theory, the total heat transfer coefficient would be quantified by solving two simultaneous equations (Equations 5 and 6), and the h total could be calculated as: h total =
c p,w ·mw ·(Tw,r tn −Tw,sup ) A
Ta − Ts
− qhl
(7)
where qhl has been tested previously by the extra checking experiment, and the value of 4.5 W/m2 (1.4 Btu/h-ft2) is used in this research. Model implementation Fluent is one of the most widely used commercial software for the numerical solutions. Due to its accuracy, robustness, and convenience, it is used for simulating engineering fluid flow and heat transfer problems (Dubovsky 2001). Fluent has two different solution methods, “segregated” and “coupled.” As suggested by Karadag˘a and Teke (2007), the semi-implicit method for pressure-linked equations (SIMPLE) algorithm is highly recommended to be used in “segregated” solution method. On the other hand, considering the Reynolds number is below a critical value of approximately 2040 in the case of water flowing through a straight pipe with a circular cross-section, chilled water flowing in capillary tubes could be treated as laminar and steady state at low water velocities for heat transfer models (Avila et al. 2011). In this study, the water flow in the capillary tubes was constant with a low water velocitiy of 0.11 m/s (0.36 ft/s). The Reynolds number was smaller than 2040. Thus, SIMPLE algorithm and Laminar model were thus selected for this study. Second order upwind schemes were used to solve the basic governing equations of the discrete such as momentum, energy
Fig. 1. Detailed view of the capillary tube mats.
while standard equation was chosen for the pressure term. The residual values are taken 10−6 for energy, 10−3 for momentum and turbulence. Capillary tube mats are made up of several “U” pipes as shown in Figure 1. For saving the computer resources, some assumptions are made to simplify the model as shown in Figure 2,and are detailed as below: (1) Take one single “U” that is embedded into the plaster module into consideration. (2) The upper side of the radiant panel is assumed to be adiabatic because of the thermal insulation material covered on the upper side will pass few heat flux density. (3) Front and behind sides of the computational domain are assumed to be adiabatic because of a small temperature gradient. (4) Left and right sides of the computational domain are viewed as a periodic boundary condition. (5) The bottom of the computational domain is set as q = h total (Ta − Ts ), determine parameters are total heat transfer coefficient and indoor air temperature. The range of
Fig. 2. Boundary conditions for single “U.”
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Fig. 3. The climate chamber (4.2 × 3.6 × 3.6 m).
h total and Ta would be measured through the following experiment. (6) Pipe inlet is set as a velocity boundary condition and the outlet is set to outflow. (7) All the materials are assumed to be isotropic mediums. The three-dimensional physical model of capillary tubes was meshed appropriately by ICEM CFD, and the unstructured grids were generated. There were 2,818,000 cells and 571,000 nodes in the grid. In addition, in order to check the solution sensitivity of the grid, a grid dependency study was performed. Increasing the number of cells from 2,818,000 to 4,227,000 (by about 150%), only enhanced the solution by less than 1% for the surface temperature and return water temperature of the radiant system. Experimental validation of the simplified model The climate chamber The experiments were conducted in a climate chamber that located in a lager laboratory room as shown in Figure 3. The climate chamber is composed of inner surfaces, floor and ceiling, all the surfaces are made of stainless steel plates. The chamber has a floor area of 15.12 m2 (23436 ft2) with an internal height 2.60 m (9 ft). At the center of the south wall, there is a 2.76 m2 (4278 ft2) double-glazed observation window. All the internal wall surfaces are covered with white paper for ensuring an emissivity of 0.9 (EN-14240, 2004). Moreover, except the south wall, all the external surfaces are covered by 18 metal panels, each with a copper pipe area of 0.51 m2 (791 ft2), and every six panels are viewed as a group. The south wall is insulated with 100 mm (4 in.)-thick XPS (extruded polystyrene) insulation board. For getting a uniform internal surface temperature distribution, each group is connected in parallel. In addition, to eliminate the impact of forced convection caused by ventilation for circulating or dehumifying, there is no ventilation and humidity source in the test chamber and by this way the (natural) free convection is assured. Temperature controlled circulating water in copper pipes permits internal wall surface temperatures to be regulated in a range from 10◦ C to 40◦ C (50◦ F to 104◦ F). To fix an approximately steady air temperature in each experimental condition, the dummies are placed in two rows, symmetrically along the longest center line of the chamber as shown in Figure 4. The internal combined with an
Fig. 4. Distributed dummies in the chamber.
external heat source method in this experiment also regulates air temperature deviation less than 0.5◦ C (33◦ F). Radiant ceiling panels and the experimental principle Schematic of the hydraulic circuit is presented in Figure 5. Supply water temperatures to the panel are varied according to test conditions. The water supply system for testing radiant panels is composed of an air source heat pump, water tank, water pump, flow controlling valve, flow meter, and other accessories. Water is transported to the panel by a water pump and returned to the water tank through flexible 20 mm (0.8 in.)-diameter plastic pipes. Moreover, the mounted flow controlling valve is set-up to allow a constant water mass flow value in every test. In order to regulate the internal wall surface temperature of the chamber, different water temperatures in copper pipes of the external wall surfaces are supplied by another water supply system. This water supply system is also constituted by air-cooled heat pumps, open water tank, water pumps, manifolds, etc. The hydraulic radiant ceiling is composed of six capillary tube mats with a water circuit in each mat. Capillary tube mats are connected in parallel and are embedded into the gypsum plaster. The detailed material parameters of the capillary tube mats are shown in Table 2 and Figure 6. The radiant ceiling panels are supported and placed at a height of 2.4 m (8 ft) above the floor. The plaster panel area of
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Fig. 5. Overview of hydraulic circuits and climate chamber. Table 2. Detailed panel specification. Panel Single capillary tube mat length: 3000 mm (118.1 in.), wide: 660 mm (26.0 in.); Gypsum plaster height: 9 mm (0.35 in.), plaster height: 10 mm (0.39 in.); Insulation height: 35 mm (1.38 in.)
Pipe Pipe external diameter: 4.3 mm (0.17 in.); Internal diameter: 2.6 mm (0.10 in.); Pipe distance: 20 mm (0.79 in.)
capillary tube mats is 12 m2 (18600 ft2), almost accounts for 79% area of climate chamber. Thermal insulation is laid over the gypsum plaster in order to ensure that the heat transfer from the water to the upper air zone is minimized. According
Fig. 6. Capillary tube embedded into the plaster.
to a careful calculation, 35 mm (1.4 in.) thickness adopted in this study could ensure the heat loss to the upper air zone less than 0.5%. Therefore, thermal balance of the radiant system considers the convective heat transfer on the water side, conduction through the tube to the tube wall and the tube wall to the ceiling surface, the natural convection between ceiling surface and the indoor air, and the thermal radiation from the ceiling surface. The emissivity of the plaster panel surface has been evaluated using a thermo-graphic camera and surface temperature sensors, the value of 0.9 is obtained. Data acquisition system In the climate chamber, totally 21 K-type thermocouple sensors with the accuracy of ±0.5◦ C (32.9◦ F) are used to measure the temperatures of wall, floor and window as shown Figure 7. These test points are arranged based on area-weighted method. Other four sensors are hanged vertically in the center of the chamber at 0.75 (2.5), 1.5 (5.0), 1.9 (6.2), and 2.38 m (7.8 ft), to measure the air temperature. Several platinum resistance temperature sensors with the accuracy of ±0.2◦ C (32.4◦ F)
Fig. 7. Temperature thermocouples location on the internal surface.
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Science and Technology for the Built Environment from experimental measurements in this study and those from literatures (Andr´es-Chicote et al. 2012; Causone et al. 2009) are presented. Although each set of data has a different trend line, the total heat flux density has a clear function of temperature difference (Ta − Ts ). It is obvious that the total heat flux density for each (Ta − Ts ) is lower than that reported in Causone et al. (2009), but is similar to that reported in Andr´es-Chicote et al. (2012). Thus the results are credible and the differences can be explained by different experimental conditions.
Fig. 8. Temperature thermocouples arrangement on the ceiling surface.
are placed inside the water tank. The water tank temperature set-points are fixed differently in each test condition for obtaining various wall surface temperatures of the climate chamber. Some major parameters of water supply system for radiant panel are also measured, such as the supply water flow, supply and return water temperatures. Two temperature sensors are placed at the inlet and outlet of the panel piping separately to measure the water temperature, while the flow valve is used to regulate the water flow. Other 6 Ktype thermocouple sensors are uniformly distributed on the plaster panel surface, as shown in Figure 8, data are transmitted to and recorded in Fluke 2635A every 60 s during the entire test. According to the ASHRAE Standard (1382013), all the experiments are conducted under steady state conditions. Experimental condition and results The experiment includes 12 tests, the designed indoor air temperature changes from 24◦ C to 30◦ C (75◦ F∼86◦ F), while the supply water temperature is allowed to change in a range from 14◦ C to 20◦ C (57◦ F ∼68◦ F). Indoor air temperatures are set equal to AUST in the entire experiment. The different combinations of indoor air temperature and water supply temperature set-points are tested twice. For the purpose of proving that different mass flow values would not obviously affect the cooling capacity, some extra tests were conducted previously. In order to achieve the turbulent flow distribution, a water mass flow value of 0.24 m3/h (0.06 L/s) is supplied in every test. The detailed experimental conditions and results are presented in Table 3 (24/20 stands for 20◦ C (68◦ F) water temperature and 24◦ C (75◦ F) air temperature. Cooling output Total cooling capacity as shown in Figure 9 is calculated on the basis of experimental parameters. Both the data derived
Heat transfer coefficients Figure 10 shows the variation of the total heat transfer coefficient as a function of temperature difference (Ta − Ts ). We can see that the total heat transfer coefficient varies in a wide range of 7.6 to 9.8 W/m2·K (1.3∼1.7 Btu/hft2◦ F), with an average value of 8.5 W/m2·K (1.5 Btu/hft2◦ F). As a comparison, the total heat transfer coefficient obtained under a free convective experiment by Andr´es-Chicote et al. (2012) fluctuates in a range from 7.8 to 9.3 W/m2·K (1.4∼1.6 Btu/hft2◦ F). The previously mentioned experiment including 12 tests has provided a wide enough operation conditions. However, for getting a detailed basic characteristic curve of ceiling radiant cooling system, a simplified numerical model is established following. The experimental data are used as input parameters or constraints to form the boundary conditions of the numerical model. Comparison of experimental and numerical results Twelve of the experimental data in Table 3 (for instance, air temperature, supply water temperature, and total heat transfer coefficient) are used as input boundaries for numerical cases. Comparing the experimental results with the simulated data to verify the credibility of the simulation method, results are shown in Figure 11. Then, numerical cases are completed to correlate the total heat transfer coefficient as a function of temperature difference (Ta − Ts ) and establish a characteristic curve of the cooling radiant system, which is independent of the system types. As shown in Figure 11, results of the simulation agree well with the experimental data. Figure 11a shows that the numerical cooling capacity agrees with that from experiment, with a difference less than 10%. Simulated surface temperatures are 0.5◦ C (33◦ F) higher than experimental data shown in Figure 11b. The little difference can be explained by the surface temperature fluctuation during the experiment, while the temperature is assumed to stability in numerical model. In conclusion, the built numerical model can effectively predict the specific cooling capacity in different test conditions. Simplified correlation development for CCRP system Determination of boundary conditions The specified maximum or minimum surface temperature is limited by the system characteristics (EN 15377-2, 2008). Sixty-four groups of simulations are completed for
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23.9 (75.0) 20.2 (68.4) 8.8 (1.5) 21.4 (70.5) 21 (69.8) 25.4 (8.1)
Case
Ta Tw,sup h total Tw,r tn Ts qtotal
28 (82.4) 20.1 (68.2) 8.1 (1.4) 22.1 (71.8) 22.4 (72.3) 45.4 (14.4)
2 28/20 (82.4/68) 28 (82.4) 18.1 (64.6) 8.2 (1.4) 20.6 (69.1) 21.1 (70.0) 56.6 (17.9)
3 28/18 (82.4/64.4) 28.1 (82.6) 16.2 (61.2) 8.4 (1.5) 19.3 (66.7) 19.9 (67.8) 68.7 (21.8)
4 28/16 (82.4/60.8) 27.9 (82.2) 14.1 (57.4) 9.3 (1.6) 17.9 (64.2) 18.7 (65.7) 85.2 (27.0)
5 28/14 (82.4/57.2) 30.1 (86.2) 14.1 (57.4) 9 (1.6) 18.5 (65.3) 19.3 (66.7) 97.5 (30.9)
6 30/14 (86/57.2) 24.1 (75.4) 20.2 (68.4) 7.7 (1.4) 21.2 (70.2) 21.1 (70.0) 23.2 (7.4)
7 24/20 (75.2/68) 27.9 (82.2) 20.1 (68.2) 7.6 (1.3) 22.1 (71.8) 22.4 (72.3) 41.8 (13.3)
8 28/20 (82.4/68)
Unit for temperature T is◦ C (◦ F), for heat flux density q is W/m2 (Btu/[ft2h]), for heat transfer coefficient h is W/m2·K (Btu/hft2◦ F).
1 24/20 (75.2/68)
Table 3. Measured and calculated parameters for radiant cooling tests.
28 (82.4) 18.1 (64.6) 8.1 (1.4) 20.6 (69.1) 21.4 (70.5) 53.4 (16.9)
9 28/18 (82.4/64.4)
27.9 (82.2) 16.2 (61.2) 8.6 (1.5) 19.3 (66.7) 20.1 (68.2) 67.3 (21.3)
10 28/16 (82.4/60.8)
28.1 (82.6) 14.1 (57.4) 9.4 (1.7) 17.9 (64.2) 19.1 (66.4) 85 (26.9)
11 28/14 (82.4/57.2)
29.8 (85.6) 14.1 (57.4) 9.8 (1.7) 18.5 (65.3) 19.9 (67.8) 97.3 (30.8)
12 30/14 (86/57.2)
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Fig. 9. Comparison experimental total cooling capacity with literatures.
Science and Technology for the Built Environment obtaining more sufficient data. Total heat transfer coefficients ranging from 7.6 to 9.8 W/m2·K (1.3∼1.7 Btu/hft2◦ F) are derived from 12 groups of experimental data. Therefore, for each simulation (different supply water temperature), the total heat transfer is set to change from 7.0 to 10.0 W/m2·K (1.2∼1.8 Btu/hft2◦ F) with an increment of 0.5 W/m2·K (0.1 Btu/hft2◦ F) in the simulation, except when the total heat transfer coefficient is 8.5 or 8.7 W/m2·K (1.49◦ F∼1.53 Btu/hft2◦ F). The indoor air temperature is set at 24.0◦ C or 26.0◦ C (75.2◦ F∼78.8◦ F), while the supply water temperature is 14.0 (57.2), 16.0 (60.8), 18.0 (64.4), and 12.0◦ C (53.6◦ F) for 24.0◦ C (75.2◦ F) indoor air temperature condition (13.0◦ C [55.4◦ F] for 26.0◦ C [78.8◦ F] indoor air temperature condition). Simulation results for the 64 combinations of the indoor air temperature, the supply water temperature, and the total heat transfer coefficient are tabulated in Table 4 (for instance, 24.0/12.0-7.0 stands for 12.0◦ C [53.6◦ F] water temperature, 24.0◦ C [75.2◦ F], air temperature and 7.0 [1.2 Btu/hft2◦ F] total heat transfer coefficient). Correlation for the cooling capacity
Fig. 10. Experimental results of total heat transfer coefficients.
As stated in Section 3, the proposed simulation method should, first, be tested and verified through 12 sets of experimental data as shown in Figure 11. It is obvious that the simulation results agree well with experimental data as shown in Figure 12. In addition, the simulation results show that total heat flux density can be obtained as a function of temperature difference (Ta − Ts ), i.e., qtotal = 7.21 (Ta − Ts )1.09 . As expected, total cooling capacity increases with growing temperature difference. The empirical correlations could be used to reasonably predict the specific cooling capacity of capillary tube mats based on CCRP system. The average air temperature can be reliably used in calculations to replace the operative temperature, because of (Ta − Ts ) includes the effects of the internal wall surface and floor temperatures indirectly. It is notable in Figure 12 that the total heat flux density seems scatter in certain (Ta − Ts ) range. This is because in the simulation, the boundary condition includes air temperature,
Fig. 11. The comparison of numerical data with the experimental results. a. The specific cooling capacity. b. Cooled radiant ceiling surface temperature.
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14.8 (58.6) 15.4 (59.7) 60.3 (19.1) 24/14–7.0 (75.2/57.2–1.2) 16.5 (61.7) 17.0 (62.6) 50.3 (15.9) 24/16–7.0 (75.2/60.8–1.2) 18.0 (64.4) 18.5 (65.3) 40.2 (12.7) 24/18–7.0 (75.2/64.4–1.2) 19.4 (66.9) 19.7 (67.5) 30.2 (9.6) 26/13–7.0 (78.8/55.4–1.2) 16.2 (61.2) 16.9 (62.4) 65.4 (20.7) 26/14–7.0 (78.8/57.2–1.2) 16.9 (62.4) 17.6 (63.7) 60.3 (19.1) 26/16–7.0 (78.8/60.8–1.2) 18.5 (65.3) 19.0 (66.2) 50.3 (15.9) 26/18–7.0 (78.8/64.4–1.2) 20.0 (68.0) 20.4 (68.7) 40.2 (12.7)
Tw,r tn Ts qtotal Case
15.1 (59.2) 15.7 (60.3) 63.3 (20.1) 24/14–7.5 (75.2/57.2–1.3) 16.6 (61.9) 17.2 (63.0) 52.8 (16.7) 24/16–7.5 (75.2/60.8–1.3) 18.1 (64.6) 18.6 (65.5) 42.2 (13.4) 24/18–7.5 (75.2/64.4–1.3) 19.6 (67.3) 20.0 (68.0) 31.7 (10.0) 26/13–7.5 (78.8/55.4–1.3) 16.3 (61.3) 17.1 (62.8) 68.6 (21.7) 26/14–7.5 (78.8/57.2–1.3) 17.1 (62.8) 17.8 (64.0) 63.3 (20.1) 26/16–7.5 (78.8/60.8–1.3) 18.6 (65.5) 19.2 (66.6) 52.8 (16.7) 26/18–7.5 (78.8/64.4–1.3) 20.1 (68.2) 20.6 (69.1) 42.2 (13.4)
24/12–7.5 15.1 (59.2) 15.8 (60.4) 66.2 (21.0) 24/14–8.0 (75.2/57.2–1.4) 16.7 (62.1) 17.3 (63.1) 55.2 (17.5) 24/16–8.0 (75.2/60.8–1.4) 18.2 (64.8) 18.7 (65.7) 44.2 (14.0) 24/18–8.0 (75.2/64.4–1.4) 19.5 (67.1) 19.9 (67.8) 33.1 (10.5) 26/13–8.0 (78.8/55.4–1.4) 16.5 (61.7) 17.2 (63.0) 71.8 (22.8) 26/14–8.0 (78.8/57.2–1.4) 17.2 (63.0) 17.9 (64.2) 66.2 (21.0) 26/16–8.0 (78.8/60.8–1.4) 18.7 (65.7) 19.3 (66.7) 55.2 (17.5) 26/18–8.0 (78.8/64.4–1.4) 20.2 (68.4) 20.7 (69.3) 44.2 (14.0)
24/12–8.0 15.2 (59.4) 15.9 (60.6) 69.0 (21.9) 24/14–8.5 (75.2/57.2–1.5) 16.8 (62.2) 17.4 (63.3) 57.5 (18.2) 24/16–8.5 (75.2/60.8–1.5) 18.3 (64.9) 18.8 (65.8) 46.0 (14.6) 24/18–8.5 (75.2/64.4–1.5) 19.6 (67.3) 20.0 (68.0) 34.5 (10.9) 26/13–8.5 (78.8/55.4–1.5) 16.6 (61.9) 17.4 (63.3) 74.8 (23.7) 26/14–8.5 (78.8/57.2–1.5) 17.3 (63.1) 18.1 (64.6) 69.0 (21.9) 26/16–8.5 (78.8/60.8–1.5) 18.8 (65.8) 19.4 (66.9) 57.5 (18.2) 26/18–8.5 (78.8/64.4–1.5) 20.3 (68.5) 20.8 (69.4) 46.0 (14.6)
24/12–8.5 15.2 (59.4) 16.0 (60.8) 70.1 (22.2) 24/14–8.7 (75.2/57.2–1.5) 16.8 (62.2) 17.5 (63.5) 58.4 (18.5) 24/16–8.7 (75.2/60.8–1.5) 18.3 (64.9) 18.8 (65.8) 46.7 (14.8) 24/18–8.7 (75.2/64.4–1.5) 19.6 (67.3) 20.0 (68.0) 35.1 (11.1) 26/13–8.7 (78.8/55.4–1.5) 16.5 (61.7) 17.3 (63.1) 76.0 (24.1) 26/14–8.7 (78.8/57.2–1.5) 17.4 (63.3) 18.2 (64.8) 70.1 (22.2) 26/16–8.7 (78.8/60.8–1.5) 18.8 (65.8) 19.5 (67.1) 58.4 (18.5) 26/18–8.7 (78.8/64.4–1.5) 20.3 (68.5) 20.8 (69.4) 46.7 (14.8)
24/12–8.7
24/12–9.0 15.3 (59.5) 16.1 (61.0) 71.7 (22.7) 24/14–9.0 (75.2/57.2–1.6) 16.9 (62.4) 17.6 (63.7) 59.7 (18.9) 24/16–9.0 (75.2/60.8–1.6) 18.4 (65.1) 18.9 (66.0) 47.8 (15.2) 24/18–9.0 (75.2/64.4–1.6) 19.7 (67.5) 20.1 (68.2) 35.8 (11.3) 26/13–9.0 (78.8/55.4–1.6) 16.6 (61.9) 17.4 (63.3) 77.7 (24.6) 26/14–9.0 (78.8/57.2–1.6) 17.5 (63.5) 18.2 (64.8) 71.7 (22.7) 26/16–9.0 (78.8/60.8–1.6) 18.9 (66.0) 19.6 (67.3) 59.7 (18.9) 26/18–9.0 (78.8/64.4–1.6) 20.4 (68.7) 20.9 (69.6) 47.8 (15.2)
Unit for temperature T is◦ C (◦ F), for heat flux density q is W/m2 (Btu/[ft2h]), for heat transfer coefficient h is W/m2·K (Btu/hft2◦ F).
Tw,r tn Ts qtotal
Tw,r tn Ts qtotal Case
Tw,r tn Ts qtotal Case
Tw,r tn Ts qtotal Case
Tw,r tn Ts qtotal Case
Tw,r tn Ts qtotal Case
Tw,r tn Ts qtotal Case
24/12–7.0
Case
Table 4. Simulated parameters for radiant cooling panel.
15.6 (60.1) 16.4 (61.5) 74.3 (23.6) 24/14–9.5 (75.2/57.2–1.7) 17.0 (62.6) 17.7 (63.9) 61.9 (19.6) 24/16–9.5 (75.2/60.8–1.7) 18.4 (65.1) 19.0 (66.2) 49.5 (15.7) 24/18–9.5 (75.2/64.4–1.7) 19.9 (67.8) 20.3 (68.5) 37.1 (11.8) 26/13–9.5 (78.8/55.4–1.7) 16.9 (62.4) 17.7 (63.9) 80.5 (25.5) 26/14–9.5 (78.8/57.2–1.7) 17.6 (63.7) 18.4 (65.1) 74.3 (23.6) 26/16–9.5 (78.8/60.8–1.7) 19.0 (66.2) 19.7 (67.5) 61.9 (19.6) 26/18–9.5 (78.8/64.4–1.7) 20.4 (68.7) 21.0 (69.8) 49.5 (15.7)
24/12–9.5
15.7 (60.3) 16.5 (61.7) 76.8 (24.3) 24/14–10.0 (75.2/57.2–1.8) 17.1 (62.8) 17.8 (64.0) 64.0 (20.3) 24/16–10.0 (75.2/60.8–1.8) 18.5 (65.3) 19.1 (66.4) 51.2 (16.2) 24/18–10.0 (75.2/64.4–1.8) 19.9 (67.8) 20.3 (68.5) 38.4 (12.2) 26/13–10.0 (78.8/55.4–1.8) 17.0 (62.6) 17.9 (64.2) 83.2 (26.4) 26/14–10.0 (78.8/57.2–1.8) 17.7 (63.9) 18.5 (65.3) 76.8 (24.3) 26/16–10.0 (78.8/60.8–1.8) 19.1 (66.4) 19.8 (67.6) 64.0 (20.3) 26/18–10.0 (78.8/64.4–1.8) 20.5 (68.9) 21.1 (70.0) 51.2 (16.2)
24/12–10.0
840
Science and Technology for the Built Environment
Fig. 12. Simplified correlation for the total cooling capacity.
supply water temperature, and heat transfer coefficient (restricted within the range identified in experiment). Therefore, besides the variable (Ta − Ts ), the heat transfer coefficient is also varied. That is to say, even if the (Ta − Ts ) is the same, but if the heat transfer condition is different (caused by varying air temperature, or supply water temperature), the total heat flux density will be different as well. Therefore, in order to more accurately capature the characterstics of the total heat flux density, a correction term with respect to heat transfer condition (air temperature and supply water temperature) is added to the original correlation, namely, qtotal = 7.21 (Ta − Ts )1.09 +24 Ts − Tw,sup − Ta − Tw,sup /3
(8)
After the correction, the correlation can capature the variation of the total heat flux density well. The difference between the simulated and the calculated by the corrected correlation is smaller than 6.8%, with an average value of 1.1%, as shown in Table 5. And the coefficient of determination (R2) is 0.9867.
(Causone et al. 2009) that when choosing the air temperature at specific height of the test chamber, the heat transfer coefficient would be very close to the ones reported in the literatures, which shows that the reference temperature selection has some impact on the heat transfer coefficient calculation. However, the reference temperature used for these literatures are not anyway clearly specified thus the difference between the results in this study and the literatures are reasonable. Actually, air temperature is often used as reference by designers (Causone et al. 2009). Results obtained in this study also support it that it is more convenient to use air temperature to calculate the total coefficient as an alternative for engineering design in some circumstances. Similarly as the total heat flux density, the heat transfer coefficient seems scatter in certain (Ta − Ts ) range. Again, this is because the heat transfer condition varies (caused by varying air temperature, or supply water temperature) even if the (Ta − Ts ) is the same. A correction term with respect to supply water temperature is added to the original correlation. In addition, the correction term also makes use of the relationship between the heat flux density and heat transfer coefficient, namely, h total = 7.1 (Ta − Ts )0.09 Ta − Tw,sup +24 Ts − Tw,sup − / (Ta − Ts ) 3 (9) After the correction, the correlation can capature the variation of the total heat coefficient well. The difference between the simulated and the calculated by the corrected correlation is smaller than 9%, with an average value of 0.3%, as shown in Table 6. And the coefficient of determination R2 is 0.9775.
Correlation for the heat transfer coefficient The total heat transfer coefficient for a CCRP system is also discussed in this research. The values of h total is indirectly calculated according to Equation 7. The numerical results are graphically presented in Figure 13. In this study, the numerical total coefficients fluctuate in a range from 7.0 to 10.2 W/m2·K (1.2∼1.8 Btu/hft2◦ F) with (Ta − Ts ) moving from 2.3◦ C to 10.4◦ C (36.1◦ F∼50.7◦ F). Furthermore, based on the simulation data, a new correlation for the total heat transfer coefficient is deduced as h total = 7.1 (Ta − Ts )0.09 . The total heat transfer coefficients in this study are lower than those reported in some literatures (Causone et al. 2009; EN 15377-1 2008; Karada˘g 2009). The difference is probably caused by the selection of the reference temperature. It is found
Fig. 13. Simplified correlation for the total heat transfer coefficient.
841
60.9 (19.3) 0.9% 24/14–7.0 (75.2/57.2–1.2) 52.1 (16.5) 3.6% 24/16–7.0 (75.2/60.8–1.2) 42.2 (13.4) 5.1% 24/18–7.0 (75.2/64.4–1.2) 28.2 (8.9) −6.8% 26/13–7.0 (78.8/55.4–1.2) 69.6 (22.1) 6.5% 26/14–7.0 (78.8/57.2–1.2) 63.7 (20.2) 5.7% 26/16–7.0 (78.8/60.8–1.2) 52.1 (16.5) 3.6% 26/18–7.0 (78.8/64.4–1.2) 40.7 (12.9) 1.4%
24/12-7.0 (75.2/53.6-1.2)
65.2 (20.7) 3.0% 24/14–7.5 (75.2/57.2–1.3) 55.1 (17.5) 4.3% 24/16–7.5 (75.2/60.8–1.3) 43.7 (13.9) 3.6% 24/18–7.5 (75.2/64.4–1.3) 32.7 (10.4) 3.1% 26/13–7.5 (78.8/55.4–1.3) 72.5 (23.0) 5.7% 26/14–7.5 (78.8/57.2–1.3) 66.6 (21.1) 5.3% 26/16–7.5 (78.8/60.8–1.3) 55.1 (17.5) 4.3% 26/18–7.5 (78.8/64.4–1.3) 43.7 (13.9) 3.6%
24/12-7.5 (75.2/53.6-1.3) 66.6 (21.1) 0.7% 24/14–8.0 (75.2/57.2–1.4) 56.5 (17.9) 2.4% 24/16–8.0 (75.2/60.8–1.4) 45.2 (14.3) 2.3% 24/18–8.0 (75.2/64.4–1.4) 31.2 (9.9) −5.8% 26/13–8.0 (78.8/55.4–1.4) 74 (23.5) 3.0% 26/14–8.0 (78.8/57.2–1.4) 68.1 (21.6) 2.9% 26/16–8.0 (78.8/60.8–1.4) 56.5 (17.9) 2.4% 26/18–8.0 (78.8/64.4–1.4) 45.2 (14.3) 2.3%
24/12-8.0 (75.2/53.6-1.4) 68.1 (21.6) −1.3% 24/14–8.5 (75.2/57.2–1.5) 58 (18.4) 0.9% 24/16–8.5 (75.2/60.8–1.5) 46.7 (14.8) 1.5% 24/18–8.5 (75.2/64.4–1.5) 32.7 (10.4) −5.3% 26/13–8.5 (78.8/55.4–1.5) 76.9 (24.4) 2.7% 26/14–8.5 (78.8/57.2–1.5) 71 (22.5) 2.9% 26/16–8.5 (78.8/60.8–1.5) 58 (18.4) 0.9% 26/18–8.5 (78.8/64.4–1.5) 46.7 (14.8) 1.5%
24/12-8.5 (75.2/53.6-1.5) 69.6 (22.1) −0.8% 24/14–8.7 (75.2/57.2–1.5) 59.5 (18.9) 1.8% 24/16–8.7 (75.2/60.8–1.5) 46.7 (14.8) 0.0% 24/18–8.7 (75.2/64.4–1.5) 32.7 (10.4) −6.9% 26/13–8.7 (78.8/55.4–1.5) 75.4 (23.9) −0.8% 26/14–8.7 (78.8/57.2–1.5) 72.5 (23.0) 3.4% 26/16–8.7 (78.8/60.8–1.5) 59.5 (18.9) 1.8% 26/18–8.7 (78.8/64.4–1.5) 46.7 (14.8) 0.0%
24/12-8.7 (75.2/53.6-1.5) 71 (22.5) −1.0% 24/14–9.0 (75.2/57.2–1.6) 60.9 (19.3) 2.1% 24/16–9.0 (75.2/60.8–1.6) 48.2 (15.3) 0.8% 24/18–9.0 (75.2/64.4–1.6) 34.2 (10.8) −4.5% 26/13–9.0 (78.8/55.4–1.6) 76.9 (24.4) −1.1% 26/14–9.0 (78.8/57.2–1.6) 72.5 (23.0) 1.1% 26/16–9.0 (78.8/60.8–1.6) 60.9 (19.3) 2.1% 26/18–9.0 (78.8/64.4–1.6) 48.2 (15.3) 0.8%
24/12-9.0 (75.2/53.6-1.6)
Unit for temperature T is◦ C (◦ F), for heat flux density q is W/m2 (Btu/[ft2h]), for heat transfer coefficient h is W/m2·K (Btu/hft2◦ F).
qcorr t Diff%
qcorr t Diff% Case
qcorr t Diff% Case
qcorr t Diff% Case
qcorr t Diff% Case
qcorr t Diff% Case
qcorr t Diff% Case
qcorr t Diff% Case
Case
Table 5. Calculated total heat flux density using corrected correlation.
75.4 (23.9) 1.4% 24/14–9.5 (75.2/57.2–1.7) 62.4 (19.8) 0.8% 24/16–9.5 (75.2/60.8–1.7) 49.7 (15.8) 0.3% 24/18–9.5 (75.2/64.4–1.7) 37.2 (11.8) 0.3% 26/13–9.5 (78.8/55.4–1.7) 81.2 (25.7) 0.9% 26/14–9.5 (78.8/57.2–1.7) 75.4 (23.9) 1.4% 26/16–9.5 (78.8/60.8–1.7) 62.4 (19.8) 0.8% 26/18–9.5 (78.8/64.4–1.7) 49.7 (15.8) 0.3%
24/12-9.5 (75.2/53.6-1.7)
76.8 (24.3) 0.0% 24/14–10.0 (75.2/57.2–1.8) 63.9 (20.3) –0.2% 24/16–10.0 (75.2/60.8–1.8) 51.2 (16.2) –0.1% 24/18–10.0 (75.2/64.4–1.8) 37.2 (11.8) −3.1% 26/13–10.0 (78.8/55.4–1.8) 84.1 (26.7) 1.1% 26/14–10.0 (78.8/57.2–1.8) 76.8 (24.3) 0.0% 26/16–10.0 (78.8/60.8–1.8) 63.9 (20.3) −0.2% 26/18–10.0 (78.8/64.4–1.8) 51.2 (16.2) −0.1%
24/12-10.0 (75.2/53.6-1.8)
842
6.9 (1.22) −1.0% 24/14–7.0 (75.2/57.2–1.2) 7.3 (1.29) 1.6% 24/16–7.0 (75.2/60.8–1.2) 7.55 (1.33) 4.4% 24/18–7.0 (75.2/64.4–1.2) 6.42 (1.13) −7.3% 26/13–7.0 (78.8/55.4–1.2) 7.52 (1.32) 5.0% 26/14–7.0 (78.8/57.2–1.2) 7.46 (1.31) 4.0% 26/16–7.0 (78.8/60.8–1.2) 7.32 (1.29) 1.6% 26/18–7.0 (78.8/64.4–1.2) 7.15 (1.26) −1.2%
24/12-7.0 (75.2/53.6-1.2)
7.7 (1.36) −1.2% 24/14–7.5 (75.2/57.2–1.3) 8 (1.41) 2.7% 24/16–7.5 (75.2/60.8–1.3) 7.97 (1.40) 1.9% 24/18–7.5 (75.2/64.4–1.3) 8.04 (1.42) 1.6% 26/13–7.5 (78.8/55.4–1.3) 8.01 (1.41) 4.0% 26/14–7.5 (78.8/57.2–1.3) 7.99 (1.41) 3.5% 26/16–7.5 (78.8/60.8–1.3) 7.97 (1.40) 2.6% 26/18–7.5 (78.8/64.4–1.3) 7.97 (1.40) 1.9%
24/12-7.5 (75.2/53.6-1.3) 8 (1.41) −1.0% 24/14–8.0 (75.2/57.2–1.4) 8.3 (1.46) 0.8% 24/16–8.0 (75.2/60.8–1.4) 8.4 (1.48) 1.4% 24/18–8.0 (75.2/64.4–1.4) 7.48 (1.32) −7.1% 26/13–8.0 (78.8/55.4–1.4) 8.27 (1.46) 1.0% 26/14–8.0 (78.8/57.2–1.4) 8.27 (1.46) 0.8% 26/16–8.0 (78.8/60.8–1.4) 8.31 (1.46) 0.8% 26/18–8.0 (78.8/64.4–1.4) 8.4 (1.48) 1.4%
24/12-8.0 (75.2/53.6-1.4) 8.3 (1.46) −2.9% 24/14–8.5 (75.2/57.2–1.5) 8.7 (1.53) −1.1% 24/16–8.5 (75.2/60.8–1.5) 8.85 (1.56) 0.6% 24/18–8.5 (75.2/64.4–1.5) 8.04 (1.42) −6.4% 26/13–8.5 (78.8/55.4–1.5) 8.8 (1.55) 1.1% 26/14–8.5 (78.8/57.2–1.5) 8.86 (1.56) 1.6% 26/16–8.5 (78.8/60.8–1.5) 8.66 (1.53) −1.1% 26/18–8.5 (78.8/64.4–1.5) 8.85 (1.56) 0.6%
24/12-8.5 (75.2/53.6-1.5) 8.6 (1.51) −2.3% 24/14–8.7 (75.2/57.2–1.5) 9 (1.59) 0.6% 24/16–8.7 (75.2/60.8–1.5) 8.85 (1.56) −1.7% 24/18–8.7 (75.2/64.4–1.5) 8.04 (1.42) −9.0% 26/13–8.7 (78.8/55.4–1.5) 8.53 (1.50) −2.6% 26/14–8.7 (78.8/57.2–1.5) 9.16 (1.61) 2.5% 26/16–8.7 (78.8/60.8–1.5) 9.02 (1.59) 0.6% 26/18–8.7 (78.8/64.4–1.5) 8.85 (1.56) −1.7%
24/12-8.7 (75.2/53.6-1.5) 8.9 (1.57) −2.4% 24/14–9.0 (75.2/57.2–1.6) 9.4 (1.66) 1.2% 24/16–9.0 (75.2/60.8–1.6) 9.32 (1.64) −0.2% 24/18–9.0 (75.2/64.4–1.6) 8.64 (1.52) −5.2% 26/13–9.0 (78.8/55.4–1.6) 8.8 (1.55) −2.8% 26/14–9.0 (78.8/57.2–1.6) 9.16 (1.61) −0.9% 26/16–9.0 (78.8/60.8–1.6) 9.39 (1.65) 1.2% 26/18–9.0 (78.8/64.4–1.6) 9.32 (1.64) 0.0%
24/12-9.0 (75.2/53.6-1.6)
Unit for temperature T is◦ C (◦ F), for heat flux density q is W/m2 (Btu/[ft2h]), for heat transfer coefficient h is W/m2·K (Btu/hft2◦ F).
h corr t Diff%
h corr t Diff% Case
h corr t Diff% Case
h corr t Diff% Case
h corr t Diff% Case
h corr t Diff% Case
h corr t Diff% Case
h corr t Diff% Case
Case
Table 6. Calculated total heat transfer coefficient using corrected correlation.
9.8 (1.73) 0.1% 24/14–9.5 (75.2/57.2–1.7) 9.8 (1.73) −0.5% 24/16–9.5 (75.2/60.8–1.7) 9.81 (1.73) −1.0% 24/18–9.5 (75.2/64.4–1.7) 9.93 (1.75) −1.3% 26/13–9.5 (78.8/55.4–1.7) 9.65 (1.70) 9.1% 26/14–9.5 (78.8/57.2–1.7) 9.78 (1.72) 0.1% 26/16–9.5 (78.8/60.8–1.7) 9.78 (1.72) −0.5% 26/18–9.5 (78.8/64.4–1.7) 9.81 (1.73) −1.0%
24/12-9.5 (75.2/53.6-1.7)
10.1 (1.78) −1.2% 24/14–10.0 (75.2/57.2–1.8) 10.2 (1.80) −1.4% 24/16–10.0 (75.2/60.8–1.8) 10.31 (1.82) −1.2% 24/18–10.0 (75.2/64.4–1.8) 9.93 (1.75) −5.8% 26/13–10.0 (78.8/55.4–1.8) 10.25 (1.81) −0.2% 26/14–10.0 (78.8/57.2–1.8) 10.11 (1.78) −1.2% 26/16–10.0 (78.8/60.8–1.8) 10.17 (1.79) −1.4% 26/18–10.0 (78.8/64.4–1.8) 10.31 (1.82) −1.2%
24/12-10.0 (75.2/53.6-1.8)
Volume 22, Number 6, August 2016
843
Conclusions
Acknowledgment
In this study, an experiment-oriented simulation method for cooling capacity determination of CCRP system is proposed. A model for capillary tube mats is developed first and then validated by available experimental data, and based on the validated model, more conditions are simulated and more data are generated to investigate the key variables of the CCRP systems. The results of the simulation lead to a new correlation for the total cooling capacity and the total heat transfer coefficient. The correlations have clear physical meaning and are simple in expression. Very few sensors/measurements are needed to obtain the overall heat transfer performance of the radiant panels, thus the correlations can be applied in engineering applications for more conveniences. In this article, only the performance of the radiant panel under free convection and radiation is analyzed. Future work could be carried out in several aspects such as the integrated impact of ventilation (forced convenction), humidity issue, etc.
The authors would like to thank the Landsea Company for supporting the specialized radiant panel.
Nomenclature A = Surface area of the heating/cooling panel, m2 (ft2) AUST = Average unheated (uncooled) surface temperature, ◦ C (◦ F) cp = Specific heat capacity, J/kg·K (Btu/1bh◦ F) h boud = Input heat transfer coefficient for simulation, W/m2·K (Btu/h-ft2 ◦ F) hc = Convective heat transfer coefficient, W/m2·K (Btu/h-ft2 ◦ F) hr = Radiant heat transfer coefficient, W/m2·K (Btu/hft2 ◦ F) h total = Total heat transfer coefficient, W/m2·K (Btu/h-ft2 ◦ F) L = Hydraulic diameter, m (ft) mw = Water mass flow, kg/s (1b/s) qc = Natural convective heat flux, W/m2 (Btu/h-ft2) qhl = Heat losses due to transmission, W/m2 (Btu/h-ft2) qr = Radiation heat flux, W/m2 (Btu/h-ft2) qtotal = Heat flux density, W/m2 (Btu/h-ft2) Ta = Indoor air dry bulb temperature, ◦ C (◦ F) Ti = Internal surface temperature, ◦ C (◦ F) = Indoor operative temperature, ◦ C (◦ F) Top Tw,r tn = Return water temperature, ◦ C (◦ F) Tw,sup = Supply water temperature, ◦ C (◦ F) Ts = Cooled radiant ceiling surface temperature, ◦ C (◦ F) Greeks v = Water velocity, m/s (ft/s) ε = Emissivity σ = Stefan–Boltzmann constant Subscripts boun = boundary corrt = corrected variable
Funding This research has been supported by the National Natural Science Foundation of China under Grant No. 51308396.
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