Utilization of Multiple Short Heat Consumption Measurement Method for Diagnostics of Heat Source of Existing Building: Part 2: Practical use of the Method

This section presents the practical calculation of the number of ventilation air exchanges using the short measurement method for an existing multi-family building. The analyzes were carried out using archival materials and the analysis covered the days for which complete measurement data was required.

Nomenclature in the formulas is presented in the first part.

The object for the analysis is a thirty-year multi-family building. Building located in 3 climatic zone, with basement. The total number of dwellings in this building is 30, and the number of residents – 82 people. Exact details of the building being analyzed are provided in [1].

The building is supplied with heat from the district heating network through a double-function, exchanging, compact heat distribution node located in the cellar of the building. The heat node is a two-stage switch adapted for central heating and hot water supply. In heated rooms there are no heating cost allocators or other devices that allow you to determine the amount of heat consumed for heating the rooms.

In order to verify the method there were determined heat loss coefficients for the building H TV rz , H T rz , H V rz , and the number of the ventilation air changes n_V according to the equations from part 1. The average daily flow of internal heat gains ϕ_Z was also determined. Appropriate balance equations were obtained on the basis of the measurement data for 10 days moderately varying in daily temperature, selected from the group of 20 measurement days, mostly in February 2012. The selection of 20 days was the result of available and complete measurement data for these days. Therefore optimum days (days with a significant difference in midday temperature) are not selected for the analysis of the short-term in-situ measurement method, but the ones that may frequently occur in the practical application of the method (precise weather conditions cannot be predicted on measurement days for the method). The external climate data (air temperature, relative humidity of the air, wind velocity and direction, total and dispersed solar radiation intensity on the horizontal plane, temperature of the horizon) were received from the measurements of the meteorological station that lies 10 km away from the building. The consumption of the heat supplied to the installation, the flow and return temperatures of the mains and the installation part resulted from the registration of these quantities made by means of the heat meter mounted in the node. The building’s heat gain from solar radiation through the windows was determined using the SOLAR program [2]. After a preliminary analysis of the results of the check, it was assumed that the average daily heat gains flux from solar radiation contains 3/4 of the gains resulting from the radiation transmitted through the windows in the examined day and 1/4 of gains from radiation from the previous day. The estimation of an internal profit to determine the efficiency of use of the gains was conducted on the basis of the unit profits referred to 1m² of the usable area of the building, accepted as 4.5W/m² The average internal gains flux adopted to estimate the efficiency of gains use was 7kW, and the average daily exchange of air was 0.3h⁻¹ for the same purpose. The efficiency of the node and installation (node, transmission, emission and regulation of heat supply) was determined on the basis of the heat losses of the node components and the installation, and the heat flux taken from the heat network as well as the efficiency of regulation and the adopted emission. Based on dependencies (23, 26), estimated U-values for partitions and windows and known building dimensions, the temperature t ¯ e * * was determined. The efficiency of using internal gains was estimated on the basis of the total heat gains of the building: ϕ_u + ϕ_Z + ϕ_Z,tr (from people, appliances and solar radiation) and heat demand for compensating the heat loss of the building (penetration through partition walls and ventilation) ϕ_dem , using dependency: (36) η u = 1 − e − ϕ d e m ϕ u + ϕ Z + ϕ Z , t r where:

ϕ_u – measured, average utility heat flux for considered day, W,

ϕ_Z – average internal heat gains flux for considered day, W,

ϕ_Z,tr – average for considered day, differential heat flux from solar radiation through transparent components,

The method check was performed by calculating the average monthly required power of the node on the basis of H T rz determined by the multiple measurement method and comparing the determined volume with the average monthly heat flux delivered to the building, measured by the heat meter at the thermal node.

The average daily values of the used measurements for the group of 20 days accepted for analysis were presented in Table 1.

When omitted in generalized balance equation the arrangement (12 – part 1) 102 H T V r z ⋅ ( t ¯ i − t ¯ e * * ) + H b ⋅ t ¯ e 1 ⋅ ( t ¯ i − t ¯ e ) = ϕ u ( t ¯ e ) ⋅ η t r t ( t ¯ e ) + ϕ Z ⋅ η e h g ( t ¯ e ) + ϕ Z , t r ( t ¯ e ) ⋅ η e h g ( t ¯ e ) the component containing H_b (H_b = 0) and accepting: ϕ_Z = 7kW, ϕ Z = ϕ Z ⋅ η e h g ( t ¯ e ) , and also H TV = H TV rz and transformation of the equation H_TVj can be determined: (37) H T V j = ϕ u ( t ¯ e 1 ) ⋅ η t r t ( t ¯ e j ) + ϕ Z ⋅ η e h g ( t ¯ e j ) + ϕ Z , t r ( t ¯ e j ) ⋅ η e h g ( t ¯ e j ) ( t ¯ i − t ¯ e j * * ) H_TVj specified for each day of the 20-day group is given in Table 2.

The order of days accepted in Tables 1, 2, 3 is related to the increasing value of the coefficient H_TVj and the creation of pairs of days which differ significantly in day temperature t ¯ e . The average value of the coefficient H_TV for a group of 20 days is: 103 H ¯ T V = 2.66 W / K .

Days for which high values H_TV have been obtained are also characterized by high daily gains of heat from solar radiation at relatively high average daily outside air temperatures t ¯ e . It can be assumed that such states were accompanied by simultaneous intense uncontrolled opening of windows to avoid overheating of rooms. The result of excessive ventilation of the spaces could have been the operation of the c.o. with increased efficiency due to the opening of thermostatic radiator valves.

Inserting H T V = H ¯ T V = 2.66 W / K into the equation: (38) ϕ Z j = H T V r z ⋅ ( t ¯ i − t ¯ e j * * ) − [ ϕ u ( t ¯ e j ) ⋅ η t r t ( t ¯ e j ) + ϕ Z , t r ( t ¯ e j ) ⋅ η e h g ( t ¯ e j ) ] the values of the average daily gains of heat from internal sources ϕ_Zj can be determined for particular days from 20-day group – Table 3.

On the basis of the determined values ϕ_Zj compared to the expected value (ϕ_Z ~ 7kW), the 10-day group presented in Table 4 was selected for further analysis.

The expected value of internal gains ϕ_Z is ϕ_Z ~ 7 kW, which corresponds to a unit flow of 4.5 W/m² of the heated building’s surface. This value is relevant to –

given in [3] 3.2–6.0 W/m² for multi-family buildings and 2.5–3.5 W/m² for single-family houses.

Daily average heat gains significantly different from expected are due to the conditions of use of the building deviating from the average. One of the conditions of success of the method is to meet the appropriate measurement conditions. These conditions have already been mentioned. It should be emphasized that it is important to include days without rain and snow and with moderate winds. If during the minimum number of days there is rain, snow or intense wind, the measuring line should be extended by the appropriate number of days. As measurement days it should also be avoided very cloudy days and days with moderate outside temperature (not higher than 5(7)°C, as an average daily temperature) and at the same time very sunny days which would be accompanied by significant overheating of rooms and / or opening of windows by residents. Generally, however, the more intense solar radiation occurs in the days preceding the measurement day, and yet on this day – but without causing significant overheating of rooms with closed windows – the greater the difference between ( t i − t ¯ e ** ) and ( t i − t ¯ e ) , which increases the accuracy of determination of loss factors H T rz and H V rz .

On the days of measurement and at least one day before, the internal air temperature in the heated rooms should be constant. The deviation from the stabilized temperature should not exceed 0.5°C. When measuring the windows in the building and the entrance door should be closed. All automatic air diffusers should be open. If the windows are equipped with fittings with micro ventilation, the window handles should be set to this function. In the absence of automatic diffusers it is acceptable to periodically aerate the space with a duration of up to 10 minutes and a frequency not exceeding 8 hours. Compliance with these conditions affects the accuracy of the method presented.

For proper determining of coefficient H_b it is good to include measurement of the midday temperature range: − 10 ° C ≤ t ¯ e ≤ 5 ( 7 ) ° C . Among the days of measurement should also be several days from − 3 ° C ≤ t ¯ e ≤ 3 ° C .

Estimated values of average daily heat yields diverging from expectations suggest that these conditions are exceeded. Days of exceeding can not be included in the analysis of determining the building’s heat loss coefficients and the number of air exchanges.

Accepting once more ϕ_Z = ϕ_Z ⋅η_ehg ( t ¯ e ) and inserting values included in Table 4 into (8 – part 1), the following sequence of equations is obtained:

H T V r z ⋅ ( t ¯ i + 6.28 ) = 60.50 + ϕ Z

By subtracting one another from the next pair of equations (pairing equations of similar values and differing by several degrees), to obtain a positive value of the difference, we obtain:

1., 2. H T V r z ⋅ ( 5.59 ) = 14.13 kW / K

The solution of this redundant arrangement in regard to H TV rz by means of determinants leads to: H TV rz = 2.63 kW/K.

After inserting the resulting value into (13 – part 1) using a 10-day group and taking into account ϕ_Z = ϕ_Z ⋅η _ehg t ¯ e it results in: (39) H b ⋅ t ¯ e 1 ⋅ ( t ¯ i − t ¯ e 1 ) − ϕ Z

H_b ⋅ (−336.81) − ϕ_Z = −7.83 kW/K²

The solution of this redundant system in regard to H_b and ϕ_Z by means of determinants leads to: H b = − 0.00152 kW / K 2 i ϕ Z = 6.97 kW .

Substituting these values into the arrangement (20 – part 1 ), taking into account ϕ_Z = ϕ_Z ⋅η_ehg ( t ¯ e ) for the following days of the considered group gives:

H T r z ⋅ ( 26.28 ) + H V r z ⋅ ( 30.90 ) = 67.51 kW / K

The solution of this arrangement are the following values of heat loss coefficients: H T r z = 2.29 kW / K and H V r z = 0.31 kW / K .

The value of H V r z = 0.31 kW / K corresponds to the number of air exchanges for t ¯ e = 0 ° C : n V = 0.23 h − 1

For the corrected efficiencies η_trt , to the condition shown in Table 5, and using the given procedure, it is obtained: H T V r z = 2 , 62 kW / K , H b = − 0.00152 kW / K 2 and ϕ Z = 6.52 kW , H T r z = 2.26 kW / K and H V r z = 0.32 kW / K, n V = 0 , 24 h − 1 . Table 5.

The average daily value of the 10-day group with corrected η_trt

The value of ϕ_Z , after considering the average efficiency η_ehg = 0.95, is: ϕ_Z = 6.86 kW ≈ 7kW.

Designated H_b have negative value.

A positive value would mean an increasing average number of air exchanges with an increase in the average temperature t ¯ e . The explanation for such a result can only be a change in the airflow resistance of the ventilation system caused by increasing unsealing, tilting, opening of the windows, with the increase of the average temperature t ¯ e . In case of constant tightness of this system and close to the constant influence of wind on the building, the change in a function of the temperature t ¯ e the number of ventilation air changes n_V ( t ¯ e ) should be close to the dependence: (40) n V ( t ¯ e 1 ) n V ( t ¯ e 2 ) ∼ t 1 − t ¯ e 1 t 1 − t ¯ e 2 so it should grow with decreasing temperature t ¯ e .

The coefficient H_b is the result of the dependence: (41) H b ⋅ t ¯ e 1 ⋅ ( t ¯ i − t ¯ e 1 ) = [ n V ( t ¯ e = 0 ) − n V ( t ¯ e 1 ) ] ⋅ c p ⋅ ρ p ⋅ ( t ¯ i − t ¯ e 1 ) (42) H b ⋅ t ¯ e 1 = [ n V ( t ¯ e = 0 ) ] ⋅ n V ( t ¯ e = 0 ) − n V ( t ¯ e 1 ) n V ( t ¯ e = 0 ) ⋅ c p ⋅ ρ p (43) H b ⋅ t ¯ e 1 = [ n V ( t ¯ e = 0 ) ] ⋅ [ 1 − t i − t ¯ e 1 t i ] ⋅ c p ⋅ ρ p

The coefficient H_b is equal to : (44) t ¯ e 1 ≠ t i ; H b = H V r z V B ⋅ t ¯ e 1 ⋅ [ 1 − t i − t ¯ e 1 t i ] and

t ¯ e = 0 ; H_b = 0.

These dependencies refer to the turbulent air flow in the ventilation system components.

In the case of transitional air flow, the result is: (45) t ¯ e 1 ≠ t i ; H b = H V r z V B ⋅ t ¯ e 1 ⋅ [ 1 − t i − t ¯ e 1 t i 3 / 2 ] and

t ¯ e ; H_b = 0.

For example, for t_i = 20°C and t ¯ e 1 = − 10 ° C coefficient H_b is: H b = H V r z V B ⋅ t ¯ e 1 ⋅ [ 1 − t i − t ¯ e 1 t i ] = 0 , 08 − 10 ⋅ [ 1 − 30 20 ] = − 0 , 00178 kW / K 2 , H b = H V r z V B ⋅ t ¯ e 1 ⋅ [ 1 − t i − t ¯ e 1 t i ] = = 0 , 08 − 10 ⋅ [ 1 − 3 20 3 / 2 ] = − 0 , 00248 kW / K 2 .

For the considered conditions t ¯ e 1 = − 10 ° C in case of poor external windiness, the value |H_b | > 0.00178 (0.00248) kW/K² is a sign of increased ventilation capacity due to increased opening of the air distribution slots (air flow control elements) or window opening. On the other hand, the value of |H_b | ≈ 0.00178 (0.00248) kW/K² is the sign of absence of change in airflow resistance through the ventilation system (ventilation slots or leakiness in windows, air gaps between rooms, exhaust grates and ventilation ducts and air flow from ducts) for the considered external conditions.

In the case of value H_b > 0, the area of its validity does not for sure cover the whole range of the outside temperature of the heating period, but only a certain part thereof, for example determined by temperature t ¯ e > − 10 ° C ( − 5 ° C ) . Usually at low temperatures, the tightness of the windows remains constant – the windows are closed, possibly with microventilation at constant setting. For H_b < 0 it is possible to assume the range of change of ventilation intensity according to H_b for the entire temperature range t ¯ e of the heating season. H_b < 0 means that the change in intensity of the ventilation coincides in some way with the change in the density of the outside air, mainly caused by the change in temperature t ¯ e , with the tendency to decrease in intensity with decreasing the difference.

In order to initially verify the method the average monthly heat consumption streams for the three months (February 2012, January 2013 and February 2013) in the considered building on the basis of the results obtained for determination of heat loss coefficients. Designated monthly streams of heat consumption were compared with the results of the heat consumption measurements for central heating in the considered building. In the verification the inclusion of these months was related to the availability of measured data. Monthly average heat consumption stream for installation c.o. can be generally expressed as: (46) ϕ u m = H T • r z ( t ¯ e m ) ⋅ ( t i − t ¯ e m ) + H V r z ⋅ ( t i − t ¯ e m ) + H b ⋅ t ¯ e m ⋅ ( t i − t ¯ e m ) − ( ϕ Z m + ϕ Z , t r t m ( t ¯ e m ) ) ⋅ η e h g ( t ¯ e m ) η t r t ( t ¯ e m ) , kW ,

The values H T • r z ( t ¯ e m ) for each month are derived from the dependency: (47) H T • r z ( t ¯ e m ) = H T r z − A n ⋅ U n + A n ⋅ U n ⋅ t i − t ¯ n m t i − t ¯ e m where

t ¯ n m – the average monthly temperature in the basement.

The data for the months included in the verification are given in Tables 6 and 7.

Table 6 presents the values of coefficients H T • r z ( t ¯ e m ) determined on the basis of the ceiling area above the unheated basement A_n = 380 m² and coefficient U_n = 1.50 W/(m²K) and for H T m = 2.24 kW/K estimated on the basis of the regulations in force during the construction period.

The monthly (for February 2012, January 2013 and February 2013) average power of the heat distribution node working in the analyzed building determined on the basis of the values determined by the method of multiple measurements for the months analyzed is: The relative divergence of the monthly (for February 2012, January 2013 and February 2013) average power of the heat distribution node working in the analyzed building is: ( ϕ u m ) o = [ 1.94 ⋅ ( 20 + 5.0 ) + 7.5 + 0.0015 ⋅ 5.0 ⋅ ( 20 + 5.0 ) . − ( 7.0 + 7.71 ) ⋅ 0.99 ] / 0.94 = 44.12 kW ( ϕ u m ) o = [ 1.98 ⋅ ( 20 + 0.99 ) + 6.3 + 0.0015 ⋅ 0.99 ⋅ ( 20 + 0.99 ) − ( 7.0 + 3.21 ) ⋅ 0.99 ] / 0.93 = 40.63 kW ( ϕ u m ) o = [ 2.02 ⋅ ( 20 − 1.38 ) + 5.21 + 0.0015 ⋅ 1.38 ⋅ ( 20 − 1.38 ) − ( 7.0 + 4.43 ) ⋅ 0.98 ] / 0.93 = 34.04 kW

The relative divergence of the monthly (for February 2012, January 2013 and February 2013) average power of the heat distribution node working in the analyzed building is: | Δ ( ϕ u m ) o | = | ( 46.94 − 44.12 ) / 46.94 | = 0.060 | Δ ( ϕ u m ) o | = | ( 39.80 − 40.63 ) / 39.80 | = 0.021 | Δ ( ϕ u m ) o | = | ( 36.23 − 34.04 ) / 36.23 | = 0.060

Taking into account in the building’s heat balance the average monthly flow of heat gains from solar radiation through the non-transparent partitions it can be written:

The differences in calculated and measured values disclosed in the analysis are the result of the simultaneous influence of many factors. The most important are: (48) ϕ u m = H T • r z ( t ¯ e m ) ⋅ ( t i − t ¯ e m ) + H V r z ⋅ ( t i − t ¯ e m ) + H b ⋅ t ¯ e m ⋅ ( t i − t ¯ e m ) − ϕ Z s s m − ( ϕ Z m + ϕ Z , t r m ( t ¯ e m ) ) ⋅ η e h g ( t ¯ e m ) η t r t ( t ¯ e m ) , kW –

the inaccuracy of thermal efficiency prediction of node and central heating installation and the efficiency of using internal heat gains,

These mentioned and other deviations were related to the lack of control of the building’s exploitation during the measured days. The measured values of these days were archival values. The basic criterion for selecting these days was the completeness of the required measurement data. Therefore, it may be assumed that the days taken into account did not fully meet the required conditions. The major disadvantage of the data measured such way was the lack of information on the use of the building on the days of measurement. This concerns the actions of the occupants such as: time spent in building (long-term or short or full absence in the apartment during the measuring days) intensity of ventilation of the apartments (long-term windows opening or short-term half-opening), indoor temperature (constant, variable, normal or reduced), type and intensity of activities (typical or unusual). Any deviation from the average of these operating characteristics, covered by lack of knowledge, was failing to meet the required conditions for proper use of the method and was a significant impediment to proper use of this method.

The publication presents the original method of multiple daily measurements for determining the values allowing to designate the building’s thermal characteristics. The multiple daily measurement method allows to specify the following main values: total heat loss coefficient H TV rz , heat loss coefficient associated with heat transfer through the external partitions H T rz , heat loss coefficient for ventilation H V rz and associated with it the amount of ventilation air exchange n [1/h]. The complementary value is the coefficient H_b of variation in ventilation intensity with the change in outdoor temperature.