1、4773 (RP-1037) Incorporate Radiant Heaters over 300F into Thermal Comfort Calculations Using BCAP Wen Wang Kirby S. Chapman Ali Keshavarz ABSTRACT heaters because of the high temperature at the burning surface, High-temperature radiant heaters-those with a surface temperature greater than 300F-typic
2、ally are applied in large occupied spaces, such as warehouses and aircraft hang- ers. These heaters eficiently deliver thermal comfort to specijc workstations without having to condition the entire occupied space as do other heating systems. The objective of this study was to enhance the Building Co
3、mfort Analysis Program (BCAP) methodoloa, which was developed under ASHRAE project RP-657, to reliably calcu- late the thermal comfort efect of high-temperature radiant heaters. This paper contains (1) a study ofthe types of high- temperature radiant heaters, (2) a review of thermal comfort and radi
4、ant heat transfer calculation methods, (3) an expla- nation of the new features of high-temperature heater model- ing, and (4) model applicationhalidation in a large space where a specijed workstation region should be maintained thermally comfortable using a high-temperature tubular heater: The deve
5、loped method can be used as a design tool for sizing andplacing high-temperature radiant systems or can be used in combination with other heating systems. INTRODUCTION Types of High-Temperature Radiant Heaters: Direct and Indirect For residential use, a direct radiant heater typically consists of a
6、porous ceramic or metal screen as a flat combus- tion surface, which is classified by the American Society of Heating Refrigerating and Air-conditioning Engineers (ASHRAE) as a surface combustion heater. Manufacturers standards often refer to these heaters as high-intensity radiant which can reach a
7、pproximately900“C (1 650F) under normal operating conditions (Solaronics 1994a, 1994b). In these types of heaters, the gas and air are pre-mixed, and the combustion takes place on the burner face. Figure 1 illustrates a typical gas-fired surface combustion heater with reflector. Sufficient room vent
8、ilation is necessary in order to use these heaters since the heater usually does not include a ventilating system. Generally, an indirect radiant heater has a tubular combustion cell. Since the combustion occurs in the tube and the heater has exhaust ventilation piping, no interaction takes place be
9、tween the room air and the combustion products. The tube is made of either a heat resistant steel or ceramic, while the shape of the tube depends on the design. Various shapes include: straight through, U-type, W-type, and blinded-end Figure 1 Gas-$red direct radiant heater (Solaronics, Inc. 1994a).
10、 Wen Wang is in the Mechanical Engineering Department, Iowa State University, Ames, Iowa. Kirby S. Chapman is a professor and Ali Keshavarz is a research professor at Kansas State University, Mahattan, Kansas. 346 02005 ASHRAE. Figure 2 Straight-through radiant tube heater (Solaronics, Inc. 1994b).
11、(Harder et al. 1987). A straight-through radiant tube, shown in Figure 2, is the simplest; however, it suffers from relatively large longitudinal thermal expansion that reduces its service life. Considerations for Radiant Heater Applications Radiant heaters are popular for heating a specific area or
12、 spot as opposed to an entire space. Spot and area heating actu- ally refer to different areas for which the radiant intensity field is desired. Spot heating is directed toward a specific area where occupants are most often present. Area heating refers to a section or zone of an occupied building an
13、d typically repre- sents more square feet of space than that of spot heating. Regardless of whether a high-temperature radiant heater is used for an area or spot, the body heat loss must be taken into account. Body heat loss depends upon (1) the temperature, (2) the flow conditions of the surroundin
14、g air, and (3) the clothing and activity of the individual(s). An energy balance analysis can be used to estimate the body surface heat loss and deter- mine heater size in order to provide a desirable amount of heat to the occupant. The optimal location of the heater depends on the geometry of the r
15、eflector. Use of direct high-temperature radiant heaters requires a higher rate of ventilation than indirect high-temperature radi- ant heaters. This is because the combusting gases of a direct radiant heater are directly exposed to the room air, whereas the combustion gases from an indirect radiant
16、 heater are exhausted to the atmosphere. The increased ventilation can lead to a lower room temperature, which influences the esti- mation of heat loss of the occupants or heat loss of the building and causes greater energy consumption. Therefore, this paper will focus on discussion of modeling indi
17、rect heaters since they have the above advantages over direct heaters. In addi- tion, for a large space such as warehouses, heaters with reflec- tors are often applied in order to improve the energy efficiency. While for small indoor spaces, such as resident houses, in which the whole room needs to
18、be maintained thermally comfortable, heaters without reflectors are generally used and the bounding walls act as the reflecting surfaces. In this paper, to visualize the radiant asymmetry distribution more clearly, the heater without reflector case is analyzed. However, the BCAP modeling procedure c
19、an be applied to the heaters with reflectors in a similar way. RADIATIVE TRANSFER EQUATION AND MATHEMATICAL MODELS The radiative transfer equation (RTE) is the most general technique for modeling and determining radiative heat trans- fer in an enclosed space. To solve this equation in its most funda
20、mental forms, knowledge of view factors is not required. In fact, view factors can be calculated by solving for the radi- ative heat transfer. A drawback, however, is that a computer simulation is virtually required due to the difficultly of the equation. Several such computer solution techniques ha
21、ve been developed over the last several decades. The radiative transfer equation directly provides the radi- ant intensity at each point, wavelength, and direction in the enclosed space. Once the intensity field is known, the local radiant heat fluxes can be calculated by integrating the inten- sity
22、 over the solid angle. The general form of the radiative transfer equation (Viskanta and Mengiic 1987; Siegel and Howell 1981; zisik 1977) is given by ar, ai, ar, p-+-+q- = ax av az The intensities and properties in Equation 1 have the subscript h to designate that each quantity is a function of wav
23、elength. The variables p, 6, and q are the directional cosines that describe the direction of the radiant intensity. The variables K and CF represent the medium absorption coefficient and the medium scattering coefficient. The absorption coefficient must be greater than zero. As the absorption coeff
24、icient increases, the more the medium participates in radiant absorption and emission and thus impacts the radiative exchange process between surfaces. The participating medium can either increase or decrease the inten- sity magnitude, which depends upon the absorption coeffi- cient, the medium temp
25、erature, and the temperature of the surrounding surfaces. The scattering coefficient describes how the intensity in a specific direction is scattered into differ- ent directions. The intensity from a different direction also can be scattered into the direction of concern. While the scattering coeffi
26、cient is important in industrial processes such as glass making, it has little relevance in the building environment and can be assumed to be zero. For the special case of a typical occupied room where the absorption and scattering coeffi- cients can be assumed zero, the RTE equation reduces to at,
27、ar, ar, ax ay az p-+s-+q- = o. ASHRAE Transactions: Research 347 A number of solution techniques to the RTE equation have been developed. Each method consists of a different modeling scheme and utilizes different assumptions. The most general methods to solve the RTE are (1) the mean beam length met
28、hod, (2) Hottels zone method, (3) the Monte Carlo method, and (4) the discrete ordinates method. Hotte1 and Sarofim (1 967) first evolved the notion of mean beam length to determine radiative transfer from the products of combus- tion to its enclosure (Modest 1993). This method, while considered cla
29、ssic, has become more obsolete with the advancement of computers. Hottels zone method (1967) has the disadvantage of excessive computational time required to obtain such accuracy and the lack of applicability for a system with complex geometry (Viskanta and Ramadhyani 1988). The Monte Carlo method i
30、s a numerical method that depends on statistical probabilities. Drawbacks of this method include the heavy reliance upon computer resources, the complicated modeling process even for a simple system, and inherent statistical errors (Howell 1968; Modest 1993). By contrast, the discrete ordinates meth
31、od has been reported to give more accurate and faster solutions than other solution techniques (Fiveland 1984) and it was used by the BCAP methodology. Discrete Ordinates Method The discrete ordinates method was first applied to neutron transport theory and is described by Carlson and Lathrop (1963)
32、. This method considers discrete directions and nodes on the surface and calculates the radiant intensity at each point and direction. The enclosure space is divided into control volumes. Equation 2 is integrated over each three-dimensional control volume. The resulting equation for a gray surface i
33、n a discrete direction, j, is P = ar+Ax+(l-a)$ = aEy+Ay+(i-a)Ey (5) = a(+Az+(l-a)zi, The interpolation factor, a, is set equal to 1 to avoidnega- tive intensities, which are physically impossible and yield unstable solutions. Fiveland (1984, 1988) reports that a = 1 will always provide positive inte
34、nsities. Substituting Equation 5 into Equation 4 yields AZAY + CAAX i AXAY( tp = (6) AZA + AA + AXAY Equation 6 is written for all the discrete directions for each control volume. An S4 approximation has 24 discrete directions at each control volume. The values for $, CJ, and 11 must satisfy the int
35、egral of the solid angle over all the direc- tions, the half-range flux, and the diffusion theory. A complete table of values that satisSl these conditions is tabulated and available from Fiveland (1988) and Chapman et al. (1992). The Ax, Ay, and Az values are determined by the size of the control v
36、olume. The r, ,4, and I, values are known from the previous iteration. Initially, the intensities are set to beginning values. The solution is iterative around a loop fi-omp = 1 top equals the total number of control volumes until the solution converges. With the known intensity, the incident radiat
37、ion on the surface can be written as (Siegel and Howell 1981) x + Axy i- Ayz + Az For a radiant heat flux in the x-direction, Equation 7 is approximated using a quadrature (Fiveland 1988) and (3) becomes The discrete ordinates method designates the directions grad = xd!J. (8) j for j. The higher ord
38、ers of approximation have more prescribed directions and can increase the accuracy of the results; however, the larger order approximations require more computational time. The control volume intensity along one side is assumed to be independent of the other two directions. For example, the The calc
39、ulated radiant heat flux values are substituted into the total energy balance equations to solve temperatures and other parameters. The S4 approximation has been found to be a reasonable compromise between accurate results and a low computational time (Fiveland 1988). THERMAL COMFORT STUDY AND inten
40、sity along the x interface is not affected by the y and z directions (Patankar 1980). The equation then becomes MODE LING FEATU RE FOR HI G H-TEM P E RATU RE RADIANT HEATING SYSTEM pjAzAY(r,+Ax-() + cAzAx(+-) (4) ASHRAE Standard 55 (ASHRAE 1992) defines thermal , +qjxy(4+Az-d) = o. comfort as “the c
41、ondition of mind that expresses satisfaction with the thermal environment.“ The thermal comfort variables are (1) activity level, (2) clothing insulation value, (3) air velocity, (4) humidity, (5) air temperature, and (6) mean radi- ant temperature. For most design situations, the activity level and
42、 clothing value are determined by room usage, while air This equation contains six interface intensities. By assuming that the intensity profile across the control volume is linear, the intensity at the center of the control volume, point p, is (Truelove 1988; Fiveland 1988) 348 ASHRAE Transactions:
43、 Research velocity and humidity depend on the thermal distribution system for the entire building. In an individual room, the air temperature and mean radiant temperature are the general variables controlled by the design engineers. The mean radiant temperature (MRT) indicates the radiant energy exc
44、hange in a with the radiative transfer equation and relevant boundary conditions. In the BCAP methodology, TMR, Tai, and Top at user-defined locations are calculated and stored in a file. In addition, the average TMRT for the entire room is calculated and printed into room summary information. room
45、and is defined as ?the uniform surface temperature of an imaginary black enclosure in which the radiation from the occupant equals the radiant heat transfer in the actual non- uniform enclosure? (Fanger 1967). To combine the influence of air temperature and MRT, Fanger (1967) suggests using the oper
46、ative temperature (Top) to measure local thermal comfort. The operative temperature is approximately the average of the air temperature and the mean radiant temperature and is more indicative of the temperature the occupant feels. In the BCAP methodology the mean radiant temperature is calculated us
47、ing the radiant intensity values (DeGreef and Chapman and DeGreef 1998): The BCAP model demonstrates its predominant advan- tage over the classical ASHRAE method to calculate the radi- ant parameters for the high-temperature heater case. Since the heaters are usually at an elevated temperature, they
48、 offer a unique challenge to the view factor method if the heaters are positioned on one of the wall surfaces. In such cases the surface needs to be subdivided into smaller surfaces until the assumption that the surface is at a uniform temperature is valid. This necessitates calculating a large numb
49、er of view factors between the point under analysis and the surfaces as the number of surfaces increase. On the other hand, if the heaters are positioned inside the air space of the room, the view factor calculation becomes complicated since some areas are shaded by others. Furthermore, the presence of furniture or any other equipment of complex shapes makes the accurate calculation of necessary view factors extremely tedious, while in the (9) This equation provides an alternate approach to calculat- ing the TMRT as specified in the ASHRAE Handbook-Funda- m
