ALF 3.2 (Annual Loss Factor) – A design tool for energy efficient houses
The new calculation method was developed using heating energy simulation results from SUNCODE simulations. SUNCODE is a thermal simulation program used widely for heating energy use calculations by the New Zealand government and designers.
The development was conducted in three stages:
All three steps were performed for all four heating schedules, three heating set-points, as well as for ten New Zealand climate regions. The simulated climates are:
The calculated ALF-values and AGF-values were then extrapolated to approximately 80 other New Zealand locations.
1. In order to determine the ALF-values due to conductance and infiltration, simulation runs were conducted using buildings with no thermal mass and no solar or internal gains. The building heat conductance was calculated according to the simulation model description (Areas, R-values, Volume, Infiltration rate). The ratio of simulated heating energy and total building conductance (equivalent to the Total Specific Heat Loss) gave the ALF-values for each heating schedule, heating level and location.
2. The same buildings were then simulated again, this time including a range of different thermal mass levels (again without internal or solar gains). The resulting heating energy was compared to the buildings with no mass and the functional relation between the additional energy requirement and increased mass level was determined. This relationship was defined by an additional term (the Effective Thermal Mass) which – multiplied by the ALF-value – corrected the difference between mass-less and mass-including buildings. The relationship between the Effective Thermal Mass and the Total Thermal Mass was determined. The numeric expressions are:
Schedule 1: ETM = 3.612 x (1 - Exp(-TM x 0.0367))
Schedule 2: ETM = 3.034 x (1 - Exp(-TM x 0.0843))
Schedule 3: ETM = 1.536 x (1 - Exp(-TM x 0.0652))
Schedule 4: ETM = 0.06585 x (1 - Exp(-TM x 0.0753))
where ETM is the Effective Thermal Mass Density and TM is the Thermal Mass Density.
The following two graphs illustrate the effect of including the mass warm up energy in calculating annual heating energy requirements.
Caption: ALF calculated heating energy versus SUNCODE simulated energy. The left compares the calculated heating energy without taking into account the energy required to heat up thermal mass. The graph to the right compares the results when considering thermal mass.
3. The buildings were simulated again, this time including a range of mass and solar gain levels. The results were compared with the same buildings without solar gains. The heating energy reduction due to the gains was then compared to the total solar gains, which were derived from weather data input files. The ratio of the heating energy reduction and the total solar gains gave the Useful Fraction of the gains. These Useful Fractions were analysed and functional relations between them, the Gain/Load Ratio, the Effective Thermal Mass Density and the Specific Heat Loss Density were established.
The following equations were determined:
Schedule 1:
A = 0.904, B = -0.379, C = -0.244
a = A + B / ETM ^ 2 + C x GLR ^ 0.5
b = 0.125 x SHLD + 0.587
Schedule 2:
A = 1.075, B = -2.45, C = -0.158
a = A + B / ETM ^ 2 + C x GLR ^ 1.5
b = 0.15 x SHLD + 0.518
Schedule 3:
A = 0.98, B = 0.099, C = -0.645
a = A + B x ETM ^ 2 + C x GLR ^ 0.5
b = 0.05 x SHLD + 0.839
Schedule 4:
A = 0.779, B = 81.62, C = -0.556
a = A + B x ETM ^ 2 + C x GLR ^ 0.5
b = 0.0353 x SHLD + 0.9
ETM is the Effective Thermal Mass Density, GLR the Gain/Load Ratio and SHLD Specific Heat Loss Density.
The Useful Fraction for each schedule is then given by a/b.
4. The ALF-values and the AGF-values were extrapolated to approximately 80 other New Zealand locations. The ALF-value extrapolation was based on average monthly temperatures using the following formula:
ALF-value = a x DegMonths + b. The following values were used for a and b:
Schedule | 1 |
2 |
3 |
4 |
---|---|---|---|---|
16%deg;C |
a = 143: b = -736 |
a = 208: b = -829 |
a = 364: b = -2142 |
a = 616: b = -2699 |
18%deg;C |
a = 174: b = -315 |
a = 250: b = -268 |
a = 445: b = -1146 |
a = 739: b = -1141 |
20%deg;C |
a = 205: b = 110 |
a = 292: b = 297 |
a = 528: b = -28 |
a = 864: b = 538 |
DegMonths are the degree months during the heating season with base 18%deg;C, i.e. the sum of the differences between 18%deg;C and the average monthly temperature for all the months with average temperatures < 11.5%deg;C (heating season).
Example:
The following are the monthly average temperatures at a particular New Zealand location: 18.5, 18.9, 17.3, 14.2, 10.4, 9.3, 10.3, 13.4, 13.5, 15.4, 17.0, 17.2. The winter months are the months with temperatures lower than 11.5%deg;C, i.e. 10.4, 9.3 and 10.3. The winter degree months are (18-10.4) + (18-9.3) + (18-10.3) = 7.6+8.7+7.7 = 24.
The AGF-values were interpolated using monthly sunshine hours from NIWA and the geographic latitude of the locations. Some of the AGF-values were interpolated using sunshine data maps as no sunshine hour records were available. The numeric function for calculating the AGF-values is AGF-value = (-a x SunHours x (Lat + 40%deg;) + b) x 0.84. SunHours are the number of sunshine hours during the heating season, Lat is the geographic latitude of the location. The values for a and b were:
Sched. | 1 |
2 |
3 |
4 |
---|---|---|---|---|
N |
a = 0.0221 b = 165.5 |
a = 0.0228 b = 179.7 |
a = 0.0335 b = 291.2 |
a = 0.0336 b = 291.2 |
NE |
a = 0.0138 b = 81.1 |
a = 0.0162 b = 105.3 |
a = 0.0275 b = 218.1 |
a = 0.0282 b = 218.2 |
E |
a = 0.0111 b = 53.2 |
a = 0.0142 b = 74.4 |
a = 0.0214 b = 134.3 |
a = 0.0225 b = 134.4 |
SE |
a = 0.0111 b = 53.2 |
a = 0.0134 b = 60.0 |
a = 0.0180 b = 90.7 |
a = 0.0188 b = 90.8 |
S |
a = 0.0111 b = 53.2 |
a = 0.0122 b = 60.0 |
a = 0.0167 b = 87.7 |
a = 0.0169 b = 87.6 |
SW |
a = 0.0164 b = 61.0 |
a = 0.0173 b = 64.9 |
a = 0.0217 b = 95.6 |
a = 0.0219 b = 95.6 |
W |
a = 0.0252 b = 130.2 |
a = 0.0263 b = 132.5 |
a = 0.0308 b = 163.2 |
a = 0.0309 b = 163.2 |
NW |
a = 0.0296 b = 192.5 |
a = 0.0305 b = 196.4 |
a = 0.0370 b = 253.7 |
a = 0.0371 b = 253.7 |
Horiz. |
a = 0.0252 b = 130.2 |
a = 0.0279 b = 140.0 |
a = 0.0394 b = 225.7 |
a = 0.0398 b = 225.6 |
These interpolation functions allow the ALF and AGF-values to be calculated for any New Zealand location if monthly average temperatures and the monthly number of sunshine hours are known.
The developed model was compared with the SUNCODE simulation results for a different, larger house design. The result of the comparison is shown in the following graph and shows a good correlation between the SUNCODE and ALF results.
Caption: Comparison of SUNCODE and ALF energy calculations
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