Changes between Version 4 and Version 5 of doc/app/indoorequ
- Timestamp:
- Jul 30, 2019 1:54:38 PM (5 years ago)
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doc/app/indoorequ
v4 v5 7 7 PALM offers an embedded indoor model. It takes account of the heat transfer through exterior walls, the shortwave solar gains and the heat transport by ventilation. It also considers internal heat gains, the energy demand for heating and cooling of the building. According to the building energy concept, the energy demand results in an (anthropogenic) waste heat, that is directly transferred to the urban environment.\\ 8 8 9 The ICM has to work in tandem with the Urban surface model (USM) and the indoor model is only available if the USM activated. The used parameters for ICM can be find in the building database in the USM.\\ 9 The ICM has to work in tandem with the [wiki:doc/tec/usm Urban surface model (USM)] and the indoor model is only available if the USM activated. The used parameters for ICM can be find in the building database in the USM.\\ 10 11 All symbols and parameter are in [#point1 table 1]. 10 12 11 13 = Geometrical calculations = … … 51 53 52 54 [[Image(virtual_volume.png,300px, border=0)]] 53 55 '''Figure 1.''' ''Scheme of virtual facade area soecific indoor volume''\\ 56 \\ 54 57 {{{ 55 58 #!Latex … … 91 94 The ICM is based on an analytical solution of Fourier’s law considering a resistance model with five resistances ''R'' [K/W] and one heat capacity ''C'' [J/K] as seen in figure 2. 92 95 93 [[Image(5R1C_scheme.png,400px, border=0)]] 94 96 [[Image(5R1C_scheme.png,400px, border=0)]]\\ 97 '''Figure 2.''' ''Scheme of the 5R1C indoor model''\\ 98 \\ 95 99 The solution is based on a Crank-Nicolson scheme for a one-hour time step. Since the calculations are based on heat transfer coefficients, ''H'' [W/K] all figures and equations are based on heat transfer coefficients. This is the reciprocal value of ''R'' and takes short wave, long wave, convective and conductive heat transfer and heat transport (by air) into account. 96 100 97 98 '''Resistance and capacity calculations'''\\ 101 == Resistance and capacity calculations\\ 99 102 100 103 From a numerical perspective, this network consists of five reciprocal resistances ''H'' and one heat storage capacity ''C'':\\ … … 173 176 }}} 174 177 175 176 '''Thermal load and temperature calculations'''\\ 178 == Thermal load and temperature calculations\\ 177 179 178 180 The internal air load is calculated with the internal heat gains with respect of occupancy of the building. The schedule is a parameter of the USM. … … 254 256 }}} 255 257 256 257 '''Heating and Cooling Demand'''\\ 258 == Heating and Cooling Demand\\ 258 259 259 260 The heating and cooling demand ''Φ'',,HC,nd,, is disposed in 5 different stages as shown in figure 3. \\ 260 261 261 [[Image(Phi_HCnd_scheme.png,400px, border=0)]] 262 263 Stage 1: No heating or cooling necessary, because room temperature ''ϑ'',,air,, is between the set comfort temperatures when heating ''ϑ'',,heat,set,, or cooling ''ϑ'',,cool,set,, is needed. 262 [[Image(Phi_HCnd_scheme.png,400px, border=0)]]\\ 263 '''Figure 3.''' ''Scheme for heating and coolimg demand. Stage 2 is preparation for stage 3''\\ 264 265 '''Stage 1:''' No heating or cooling necessary, because room temperature ''ϑ'',,air,, is between the set comfort temperatures when heating ''ϑ'',,heat,set,, or cooling ''ϑ'',,cool,set,, is needed. 264 266 In this case the demand is: 265 267 {{{ … … 270 272 }}} 271 273 The calculated indoor air temperature is described as ''ϑ'',,air,0,, .\\ 272 Stage 2: If the room temperature is outside the comfort threshold, heating or cooling are needed. Then the heating/cooling power is calculated with 10 W m^-2^ as ''Φ'',,HC,10,, . 274 \\ 275 '''Stage 2:''' If the room temperature is outside the comfort threshold, heating or cooling are needed. Then the heating/cooling power is calculated with 10 W m^-2^ as ''Φ'',,HC,10,, . 273 276 {{{ 274 277 #!Latex … … 294 297 \end{align*} 295 298 }}} 296 Stage 3: Checking if the unlimited heating/cooling demand ''Φ'',,HC,nd,un,, lower as the maximal heating ''Φ'',,heat,max,, or cooling ''Φ'',,cool,max,, power, than is the heat/cooling demand ''Φ'',,HC,nd,, equal the unlimited heating/cooling demand ''Φ'',,HC,nd,un,, . 299 \\ 300 '''Stage 3:''' Checking if the unlimited heating/cooling demand ''Φ'',,HC,nd,un,, lower as the maximal heating ''Φ'',,heat,max,, or cooling ''Φ'',,cool,max,, power, than is the heat/cooling demand ''Φ'',,HC,nd,, equal the unlimited heating/cooling demand ''Φ'',,HC,nd,un,, . 297 301 {{{ 298 302 #!Latex … … 301 305 \end{align*} 302 306 }}} 303 Stage 4: If the unlimited heating or cooling demand is higher than the maximal heating ''Φ'',,heat,max,, or cooling ''Φ'',,cool,max,, power the heating demand is assumed as the maximum heating flux. 307 \\ 308 '''Stage 4:''' If the unlimited heating or cooling demand is higher than the maximal heating ''Φ'',,heat,max,, or cooling ''Φ'',,cool,max,, power the heating demand is assumed as the maximum heating flux. 304 309 {{{ 305 310 #!Latex … … 325 330 In this case, the set indoor temperature is not reachable. It will get higher than the requested indoor temperature in summer (cooling) cases and colder in winter (heating) cases. \\ 326 331 327 328 '''Heat fluxes and waste heat'''\\ 332 == Heat fluxes and waste heat\\ 329 333 330 334 ''q'',,wall,win,, is the heat flux through the walls and windows. … … 343 347 }}} 344 348 The anthropogenic heat parameter for heating c_(waste,heat) and cooling c_(waste,cool) are parameters of USM.\\ 345 346 [[Image(table1.png,500px, border=1)]] 349 \\ 350 351 '''Table 1.''' [=#point1] ''List of symbols and parameters of indoor model'' 352 [[Image(table1.png,800px, border=0)]]
