ANTOUARD Florence ILLON Arnaud RAQUIN Thomas Apéndice 2: capítulo 12.2 de la norma ISO 13790 Project de Fin de arrera 45
Table 8 alculation procedure for dynamic parameters for the different types of methods Type of method Dynamic parameters Input data and boundary conditions Seasonal or monthly method 12.2 12.3 Simple hourly method 12.2 12.3 Detailed simulation method Not applicable 12.3 12.2 Dynamic parameters 12.2.1 Monthly and seasonal method 12.2.1.1 Gain utilization factor for heating The dimensionless gain utilization factor for heating, η,gn, is a function of the heat balance ratio, and a numerical parameter, a that depends on the building inertia, as given by Equations (53) to (56): if 1: if 1: if < 0: a 1 η, gn (53) a + 1 1, gn a a + 1 η (54) η 1/, gn (55) with Q,gn (56) Q,ls (for each month or per season and for each building zone) is the dimensionless heat balance ratio for the heating mode: Q,ht is the total heat transfer for the heating mode, determined in accordance with 7.2.1.3, expressed in megajoules; Q,gn are the total heat gains for the heating mode, determined in accordance with 7.2.1.3, expressed in megajoules; a is a dimensionless numerical parameter depending on the time constant,, defined by Equation (57): a a,0 + (57),0 a,0 is a dimensionless reference numerical parameter, determined in accordance with Table 9; 66 ISO 2007 All rights reserved
is the time constant of the building zone, determined in accordance with 12.2.1.3, expressed in hours;,0 is a reference time constant, determined in accordance with Table 9, expressed in h. The parameter values are empirical values and may also be determined at national level, depending on the purpose of the calculation; in absence of national values the given tabulated values may be used. NOTE 1 See also annex I for explanation and derivation and annex for justification and future conversion. Table 9 Values of the numerical parameter a 0, and reference time constant,0 Type of method a,0,0 (h) Monthly calculation method 1,0 15 Seasonal calculation method 0,8 30 Values of a,0 and,0 may also be provided at national level. Figure 5 illustrates gain utilization factors for monthly the calculation method and for various time constants. NOTE 2 The gain utilization factor is defined independently of the heating system characteristics, assuming perfect temperature control and infinite flexibility. A slowly responding heating system and a less-than-perfect control system can significantly affect the use of the heat gains. Key 1 timeconstant 8 hours (low inertia) 2 timeconstant 1 day 3 timeconstant 2 days 4 timeconstant 7 days 5 timeconstant infinite (high inertia) Figure 5 Illustration of gain utilization factor for heating mode, for 8 hours, 1 day, 2 days, 1 week and infinite time constants, valid for monthly calculation method ISO 2007 All rights reserved 67
12.2.1.2 Loss utilization factor for cooling The dimensionless loss utilization factor for cooling, η,ls, needed for the monthly or seasonal cooling method, is a function of the heat balance ratio for cooling, and a numerical parameter, a that depends on the building thermal inertia, as given by Equations (58) to (61): if > 0 and 1: if 1: a 1 ( a + 1) c η,ls (58) 1 a η,ls (59) a +1 if < 0: η 1 (60),ls with Q,gn (61) Q,ls (for each month or per season and each building zone) is the dimensionless heat balance ratio for the cooling mode; Q,ht is the total heat transfer by transmission and ventilation for the cooling mode, determined in accordance with 7.2.1.3, expressed in megajoules; Q,gn are the total heat gains for the cooling mode, determined in accordance with 7.2.1.3, expressed in megajoules; a is a dimensionless numerical parameter depending on the time constant,, definedby Equation (62): a a,0 + (62),0 a,0 is a dimensionless reference numerical parameter, determined in accordance with Table 10; is the time constant of the building zone, determined in accordance with 12.2.1.3, expressed in hours;,0 is a reference time constant, determined in accordance with Table 10, expressed in h. Values of a,0 and,0 are given in Table 10. The parameter values are empirical values and may also be determined at national level, depending on the purpose of the calculation; in absence of national values the given tabulated values may be used. NOTE 1 See also annex I for explanation and procedures for the derivation of the parameter values. Bibliography [2] and section 2.1 of [12] provide background information on the development of the method. 68 ISO 2007 All rights reserved
Table 10 Values of the numerical parameter a 0, and reference time constant,0 Type of method a,0,0 (h) Monthly calculation method 1,0 15 Seasonal calculation method 0,8 30 Values of a,0 and,0 may also be provided at national level. NOTE 2 The loss utilization factor is defined independently of the cooling system characteristics, assuming perfect temperature control and infinite flexibility. A slowly responding cooling system and a less-than-perfect control system can significantly affect the utilization of the losses. Figure 6 illustrates loss utilization factors for the monthly calculation method and for various time constants. Key 1 timeconstant 8 hours (low inertia) 2 timeconstant 1 day 3 timeconstant 2 days 4 timeconstant 7 days 5 timeconstant infinite (high inertia) Figure 6 Illustration of loss utilization factor for 8 hours, 1 day, 2 days, 1 week and infinite time constants, valid for monthly calculation method 12.2.1.3 Building time constant The time constant of the building zone,, expressed in hours, characterises the internal thermal inertia of the conditioned zone both for the heating and/or cooling period. It is calculated as given by Equation (63): m (63) tr,adj /3600 + ve,adj m is the internal heat capacity of the building or building zone, calculated in accordance with 12.3.1, expressed in joules per kelvin; ISO 2007 All rights reserved 69
NOTE See discussion in G.7 whether or not the corrected internal heat capacity should be used, including the surface resistance, in accordance with A.3 in ISO 13786:2007. tr,adj is a representative value of the overall heat transfer coefficient by transmission, adjusted for the indoor-outdoor temperature difference, calculated in accordance with 8.3, expressed in watts per kelvin; ve,adj is a representative value of the overall heat transfer coefficient by ventilation, adjusted for the indoor-outdoor temperature difference, calculated in accordance with 9.3, expressed in watts per kelvin. Representative values of tr,adj and ve,adj are values that are representative for the dominating (heating or cooling) season, to be determined in accordance with a procedure which may be specified at national level. NOTE E.g. the monthly value for a mid-winter month in case of a heating dominated climate, or the monthly value for a mid-summer month in case of a cooling dominated climate Alternatively, it may be nationally decided, for specific applications and building types, to use default values as function of the type of construction. In absence of national values, the values from 12.3.1.2 may be used. The values can be approximate, and a relative uncertainty ten times higher than that of the heat transfer is acceptable. 12.2.2 Simple hourly method; coupling to thermal mass The split of the transmission heat transfer coefficient for opaque elements op into em and ms (see 7.2.2) is calculated as given by Equations (64) and (65): and: em 1/(1/ op 1/ ms ) (64) ms h ms A m (65) ms is the coupling conductance between nodes m and s, expressed in watts per kelvin; h ms is the heat transfer coefficient between nodes m and s, with fixed value h ms 9,1, expressed in watts per square metres kelvin; A m is the effective mass area, expressed in square metres. The effective mass area A m, is calculated as given by Equation (66): Where A m m 2 / (Σ A j κ j 2 ) (66) A m is the effective mass area, expressed in square metres; m is the internal heat capacity, determined in accordance with 12.3.1, expressed in joules per kelvin; A j is the area of the element j, expressed in square metres; κ j is the internal heat capacity per area of the building element j, determined in accordance with 12.3.1, expressed in joules per square metres kelvin. 70 ISO 2007 All rights reserved
Alternatively, it may be nationally decided, for specific applications and building types, to use default values as function of the type of construction. In absence of national values, the values from 12.3.1.2 may be used. The values can be approximate, and a relative uncertainty ten times higher than that of the heat transfer is acceptable. 12.3 Boundary conditions and input data 12.3.1 Monthly, seasonal and simple hourly method 12.3.1.1 Internal heat capacity of the building For the monthly and seasonal method, the internal heat capacity of the building zone, m, expressed in joules per kelvin, is calculated by summing the heat capacities of all the building elements in direct thermal contact with the internal air of the zone under consideration, as given by Equation (67): m Σ κ j A j (67) NOTE See discussion in G.7 whether or not a correction is needed for the internal heat capacity for the monthly and seasonal method, to take into account the surface resistance. For the simple hourly method, the internal heat capacity of the building zone, m, expressed in joules per kelvin, is calculated by summing the heat capacities of all the building elements in direct thermal contact with the internal air of the zone under consideration, as given by Equation (68): m Σ κ j A j (68) κ j A j is the internal heat capacity per area of the building element j, determined in accordance with lause 7 of ISO 13786:2007 (detailed method) or, as more simple alternative, in accordance with ISO 13786:2007, Annex A, with maximum effective thickness as given in Table 11, expressed in joules per square metres kelvin; is the area of the element j, expressed in square metres. Table 11 Maximum thickness to be considered for internal heat capacity Application Determination of the gain or loss utilization factor (period of variations 1 day) Maximum thickness (m) 0,10 Alternatively, it may be nationally decided, for specific applications and building types, to use default values as function of the type of construction. In absence of national values, the values from 12.3.1.2 may be used. The values may be approximate, and a relative uncertainty ten times higher than that of the heat transfer is acceptable. ISO 2007 All rights reserved 71
12.3.1.2 Default values for dynamic parameters In absence of national values, the following values may be used: Table 12 Default values for dynamic parameters Monthly and seasonal method Simple hourly method lass a) m (J/K) b) A m (m 2 ) m (J/K) Very light 80 000 A f 2,5 A f 80 000 A f Light 110 000 A f 2,5 A f 110 000 A f Medium 165 000 A f 2,5 A f 165 000 A f eavy 260 000 A f 3,0 A f 260 000 A f Very heavy 370 000 A f 3,5 A f 370 000 A f a): May be specified at national level. b) See discussion in G.7 whether or not a correction is needed for the internal heat capacity for the monthly and seasonal method, to take into account the surface resistance. 12.3.2 Detailed simulation methods For detailed dynamic simulations methods, the input data on heat transmission elements are in general more detailed than for the seasonal, monthly or simple hourly methods. The heat capacities and thermal resistances of all layers of all building elements shall be based upon the same layers as used in 8.4(thermal transmission properties). 13 Indoor conditions 13.1 Different modes There are different modes for heating and cooling to consider, such as: ontinuous or quasi-continuous heating and/or cooling at constant set-point. Night time and/or weekend reduced set-point or switch off. Unoccupied periods (e.g. holidays). omplicated situations, such as periods with boost modes, with (optionally) a maximum heating or cooling power during the boost period The procedures are partly general and partly applicable to specific types of methods only. A summary is given in Table 13. 72 ISO 2007 All rights reserved