In Situ Measurement of Wall Thermal Properties: Parametric Investigation of the Heat Flow Methods Through Virtual Experiments Data

Energy retrofit of existing buildings is based on the assessment of the starting performance of the envelope. The procedure to evaluate thermal conductance through in situ measurements is described in the technical standard ISO 9869-1:2014, which provides two alternative techniques to process collected data: the Average Method (AM) and the Dynamic Method (DM). This work studies their effectiveness using virtual data from numerical simulations of three kinds of walls, performed using a Finite Difference model. The AM always provides acceptable estimates in winter, with better outcomes when indoor heat flux is considered in every case except the highly insulated wall. Summer conditions do not lead to acceptable measurements, despite the fulfillment of the check required by the standard. The DM results show acceptable estimations of the thermal conductance in both climates, for most of the virtual samples considered, although critically depending on some parameters of the DM that are left to the user’s discretion, without strict indications by the standard. This work highlights a possible approach for overcoming this issue, which requires deeper future investigation.


Introduction
To reduce the energy needs related to the existing building stock, great effort is oriented towards envelope renovation. As a first step in this direction, the thermal properties (thermal transmittance and conductance) of the existing building components are usually assessed through in situ measurements.
To this purpose, the international technical standard ISO 9869-1:2014 describes the so-called Heat Flow Meter method and two data processing techniques: the Average and the Dynamic Method.
Within the dedicated literature there is a wide variety of results (Atsonios et al., 2017;Gaspar et al., 2018;Lucchi et al., 2017). This is possibly due to the diversity of wall typologies investigated and boundary conditions occurring. Moreover, even when different walls are studied in the same work (Atsonios et al., 2017), experimental measurements are not performed at the same time.
To overcome the limitations inherent with experimental approaches, this work analyzes the efficacy of the Average and the Dynamic Method in finding the wall conductance by using virtual wall samples with different known properties, simulated through a Finite Difference model with controlled and repeatable boundary conditions. Moreover, these analyses are also aimed at looking for supplementary criteria concerning some key parameters of each methodology.

Methods and Materials
In this paper the Average and the Dynamic methods of analysis suggested by ISO 9869-1:2014 are applied to virtual data obtained through virtual Heat Flow Meter experiments i.e., heat transfer numerical simulations on wall components. The purpose of the data analysis is to derive the "experimental" thermal conductance, that in this case can be compared with the exactly known true value. In this section the experimental and data processing approaches by the standard are briefly illustrated. Secondly, the

The Dynamic Method
This second processing technique is suggested as a way of estimating the steady-state properties of a building element starting from highly variable tem-

The Numerical Model
In this work virtual experiments are performed using a one-dimensional Finite Difference model based on the one presented and validated in (Alongi et al., 2021). For a given k-th layer of the wall (k = 1÷K), the discretized version of the Fourier equation is: where k is the thermal diffusivity, T j i is the temperature at the i-th node (i = 1÷NFD) and at the j-th where ext and int are the heat flux densities at the outer and the inner edges of the domain, respectively, both positive when directed inward.

The Virtual Samples
The effectiveness of the two methods is evaluated on three walls with different thermophysical properties, used as virtual samples: a light and well insulated dry wall (W1); a heavy wall (W2); an externally insulated wall (W3). Layer sequences and material thermal properties are reported in Table 1 (density , thermal conductivity , specific heat c and thickness s), along with the following reference quantities, calculated as follows: where Ci [J•m -2 K -2 ] and Rcd,i [m 2 K•W -1 ] are the heat capacity per unit surface and the conductive resistance, respectively, of the i-th solid layer, Rcav,j is the convective-radiative resistance of the j-th gap. It can be noticed that for all the walls Cref is larger than 20 kJ m -2 K -1 . year is simulated, only the two most relevant 14-day periods are considered: from the 14 th to the 28 th of January for winter and from the 1 st to the 15 th of July for summer (Fig. 2).

Results And Discussion
The simulations provide the trends of the surface temperatures and the heat fluxes for each wall. For the sake of brevity, Fig. 3 shows only the results for W1 as an example, while

The Average Method Results
This method has been applied for each wall to the two complete 14-day periods, starting the average process at the beginning of each time window and considering the indoor and outdoor heat flux densities alternatively. Fig. 4 shows the conductance curves obtained in both periods for each wall investigated. The time needed to achieve a reliable estimation is actually the minimum time period

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In Situ Measurement of Wall Thermal Properties  never stabilizes around an asymptotic value (Fig. 3).
This oscillatory trend is also present in W2 and W3, wherever the heat flux is measured. These analyses show that the indications provided by the standard are only partially effective: first of all, a stable heat flux is not enough to achieve a reliable estimate of the thermal conductance, but it needs to be above a threshold (even the -6 to -4 W m -2 observed for W3 seem to suffice); more reliable outcomes are achieved with highly insulated walls when ext is used. Moreover, the constraints in the standard only deal with the apparent stability of the thermal conductance estimate and can be misleading in some cases, like what happens for W1 either considering i in the winter period or both heat flux densities in the summer period. Thus, the calculations required by the standard must be supported by a critical evaluation of the outcome and a visual inspection of the thermal conductance trend during the whole period.

The Dynamic Method Results
The DM has been tested on each wall considering several time windows within the two simulated periods to evaluate the shorter time needed to achieve a Outcomes for W1 are similar to those achieved with the AM: despite the better stability, int does not provide acceptable results, while better agreement between estimated and reference  is obtained using ext. Moreover, winter conditions lead to more stable results, while summer ones show a great dependence on M. In both seasons two days are enough to achieve acceptable results (Table 3).
As far as W2 is concerned, better outcomes are achieved using the heat flux density at the indoor surface both in January and in July, with a greater stability observable in the winter period (Table 3), when two days of data are enough. Indeed, the summer period needs a three-day data set and leads to a trend with a great dependence on the M parameter and, therefore, is more difficult to interpret. Finally, W3 seems to be more difficult to investigate:   Table 3 (grouped under best case) differs significantly from the respective lumped capacity reference ref (Eq. 10), suggesting that it is not possible to assign this physical meaning to 1.  Table 3 as S 2 loc min).
This behaviour has been observed in several other cases, when different time frames have been considered. Therefore, it suggests that a technician should perform a sensitivity analysis on M and evaluate the outcomes using the S 2 trend as described above. Yet, this observation only suggests a possible line of investigation: this approach will need further analyses to provide a mathematical explanation and verify its repeatability.

Conclusions
This work investigates the accuracy of the post processing techniques provided by the ISO 9869-1:2014 by means of numerical simulations on three virtual wall samples, and focuses on two 14-day periods in January and July.
The analyses on the AM show that the best period to implement this technique is winter, in agreement with the standard. However, even though the latter suggests considering the heat flux density at the surface where it is more stable, it has been proven that a proper amplitude of the signal is more important than stability when dealing with highly insulated walls. Moreover, the criteria included in the standard can be misleading at times, as observed for W1, either in summer or, if int is considered, in winter.
Thus, a careful analysis of the conductance trend with time is needed to verify convergence to a stable and reasonable value.
As far as the DM is concerned, it generally leads to acceptable outcomes with acquisition periods shorter than the AM in winter, and summer measurements can be used too. W1 shows the same be- However, there is a correspondence between an acceptable thermal conductance value and the local minimum of the S 2 for M near to N. This finding will need further investigations in order for it to be confirmed and formally systematized.