Quantifying the Influence of Thermostatic Mixing Valves on Showering Behaviour, Water Consumption and Domestic Hot-Water Energy Demand

Introduction

Research Context

Materials and Methods

Data Analysis

A shower event was defined as the complete sequence of activities occurring between the first opening and the final closure of the faucet during a shower. Within a shower event, one or several water-flow sequences could be identified.

A water-flow sequence was defined as a continuous period during which either the hot-water flow rate or the cold-water flow rate was non-zero. The beginning of a sequence corresponded to the moment when either the hot-water or cold-water flow rate became non-zero, while its end corresponded to the moment when both flow rates returned to zero.

An example of two experimental shower signatures obtained during the shower stalls number 1 and 2 of a same session is given in Figure 2. The first signature corresponds to a thermostatic mixing valve whereas the second corresponds to a pressure balance faucet. Both shower events comprise two distinct water-flow sequences separated by a soaping interruption.

The shower signature from the shower stall N° 1 shows that the thermostatic faucet was initially used to draw hot water exclusively during the first 20 seconds (①), then the mixer was turned off for soaping (②), and finally the mixer was turned back on for rinsing (③). The signature from the shower stall N°2 shows that the use of the pressure balance faucet first allowed for simultaneous cold and hot water to be drawn (❶), then the measurement shows the faucet being turned off for soaping (❷) and finally turned back on for rinsing (❸).

The shower duration $T_{shower}$ was calculated as the sum of the durations of all water-flow sequences composing a given shower event. Consequently, when participants interrupted the water flow during soaping activities, several water-flow sequences could be observed within the same shower event, and the inactive periods corresponding to soaping were excluded from the shower duration.

For each water-flow sequence, steady-state values of mixed-water temperature and flow rate were calculated from the mean values measured between 15 s and 5 s before the end of the considered water-flow sequence. This period was selected to ensure that the system had reached steady-state operating conditions while avoiding the influence of flow termination. When a shower event contained several water-flow sequences, the characteristic values associated with the event were calculated as the arithmetic mean of the characteristic values obtained for each sequence.

The initial temperature adjustment duration $T_{reg}$ was defined as the time elapsed between the beginning of a water-flow sequence, identified by the first non-zero hot-water or cold-water flow rate, and the moment at which the mixed-water temperature reached a stable value. Temperature stability was considered achieved when the mixed-water temperature remained within ±0.2 °C of its steady-state value for at least 5 s. This threshold was selected because it is larger than the measurement uncertainty of the temperature sensors and remains below the magnitude of temperature fluctuations reported to affect users’ thermal perception during showering, which is on the order of 0.5 °C [18,32]. It therefore provides a conservative criterion for identifying steady-state thermal conditions.

Flow interruptions associated with soaping activities were identified as periods during which both hot-water and cold-water flow rates were equal to zero between two consecutive water-flow sequences belonging to the same shower event. The duration and number of these interruptions were recorded for each shower event. When several soaping events occurred during the same shower, the characteristic soaping duration was defined as the mean duration of all recorded interruptions.

Whenever a soaping event was identified, the readjustment duration after flow interruption ($T_{rereg}$) was calculated using the same methodology as for the initial temperature adjustment duration ($T_{reg}$). More specifically, $T_{rereg}$ was defined as the time elapsed between the reopening of the faucet, identified by the reappearance of a non-zero hot-water or cold-water flow rate, and the moment at which the mixed-water temperature reached steady-state conditions. Temperature stability was considered achieved when the mixed-water temperature remained within ±0.2 °C of its steady-state value for at least 5 s. When several soaping events occurred during the same shower, the characteristic readjustment duration was calculated as the mean value of all measured $T_{rereg}$ durations.

When a hydraulic disturbance was applied during the second step of the experimental campaign, the readjustment duration after hydraulic disturbance ($T_{regper}$) was calculated as the time elapsed between the initiation of the disturbance and the return of the mixed-water temperature to steady-state conditions. Temperature stability was assessed using the same criterion as that adopted for $T_{reg}$ or $T_{rereg}$.

The proportion of users turning off the water during soaping activities ($C_{stop}$) was calculated as the ratio between the number of shower events containing more than one water-flow sequence and the total number of shower events. The underlying assumption is that the occurrence of several water-flow sequences within a same shower event reflects a voluntary interruption of water flow for soaping purposes. This approach was considered representative of participants’ usual behaviour, as showering is generally regarded as a highly routinized and ritualized daily activity. Furthermore, participants were explicitly instructed to shower as they would under normal home conditions, and no incentives or recommendations regarding water-saving behaviours were provided during the experiments. Consequently, the observed frequency of flow interruptions was assumed to reflect participants’ habitual showering practices.

Table 2. Extracted parameters from the experimental shower signatures.

Table 2. Extracted parameters from the experimental shower signatures.

Parameter	Symbol	Definition
Shower duration (s)	$T_{shower}$	Sum of water-flow sequence durations.
Number of soaping events	$N_{soap}$	Number of flow interruptions associated with soaping activities during the shower.
Soaping duration (s)	$T_{soap}$	Duration of the water flow stoppage during the shower.
Percentage of people who turn off the water while soaping (%)	$C_{stop}$	Ratio between showers associated with non-zero Nsoap and total number showers.
Mean mixed-water temperature (°C)	θshower	Arithmetic average of steady-state values of mixed-water temperature.
Initial temperature adjustment duration (s)	$T_{reg}$	Time elapsed between the first non-zero hot- or cold-water flow rate and the moment when the mixed-water temperature reaches steady-state conditions.
Readjustment duration after flow interruption (s)	$T_{rereg}$	Time elapsed between the reopening of the faucet following a soaping event, identified by the reappearance of a non-zero hot-water or cold-water flow rate, and the moment at which the mixed-water temperature reaches steady-state conditions. When several soaping events occur during the same shower, $T_{rereg}$ is calculated as the mean value of all measured readjustment durations.
Readjustment duration after hydraulic disturbance (s)	$T_{regper}$	Time elapsed between the onset of a hydraulic disturbance and the moment at which the mixed-water temperature returns to steady-state conditions.

All statistical analyses were performed in Python (version 3.14.5) using the SciPy, scikit-posthocs and statannotations packages. As the assumptions of normality and homoscedasticity were not systematically met, non-parametric methods were employed. Differences among multiple groups were first evaluated using the Kruskal-Wallis rank-sum test. When a significant overall effect was detected, pairwise post hoc comparisons were performed using Dunn’s test with Holm adjustment for multiple comparisons. For analyses involving showerhead type within each faucet technology, adjusted p-values were calculated separately and only significant pairwise differences were reported on the figures. Boxplots display the median, interquartile range, and extreme values, while diamonds indicate arithmetic means. Statistical significance was defined as p < 0.05 and is represented on all the figures by one, two, three or four stars corresponding to respectively to p<0.05, p<0.01, p<0.001 and p<0.0001.

For the online survey, descriptive statistics were calculated using weighting factors provided by the survey company to ensure representativeness of the French population. Shower and soaping durations ($T_{shower}$ and $T_{soap}$) were estimated based on two questions offering several response options (n) in the form of time intervals (i) (respectively five modalities from less than 2 minutes to more than 6 minutes and seven modalities from less than 15 seconds to more than 2 minutes). For each interval, a representative duration corresponding to the midpoint of the interval (m_i) was assigned (with the exception of the upper intervals for which the values were chosen using a conservative approach, respectively 7 minutes and 2.5 minutes). The average durations were then calculated as weighted averages of these representative durations, with the weight assigned to each interval being the number of respondents (N_i) who selected the corresponding option. Since respondents could select a modality corresponding to “I don’t know” the estimation of $T_{shower}$ and $T_{soap}$) was based respectively on 918 and 956 responses.

The percentage of people who turn off the water while soaping ($C_{stop}$) was calculated from the response to the question “During the shower, do you turn off the water while soaping up?” (Yes/No). As responses to this question were not mandatory the calculation was made with 985 responses.

These results were compared with measurements obtained during the experimental campaign to assess the consistency of reported and observed showering behaviours.

In addition, the percentage of people who feel hydraulic disturbance at home ($C_{per}$) could only be determined by the online survey from the response to the question “When you’re taking a shower and someone else in your household is using water at another fixture (kitchen sink, toilet), do you notice any disruption to your water pressure?” (Yes/No). The calculation was made with 1000 responses.

Table 3. Extracted parameters from the online survey.

Table 3. Extracted parameters from the online survey.

Parameter	Symbol	Definition
Shower duration (s)	$T_{shower}$	${\displaystyle \frac{{\sum }_{i=1}^n{m}_i\times N_i}{{\sum }_{i=1}^n{N}_i}}$
Soaping duration (s)	$T_{soap}$	${\displaystyle \frac{{\sum }_{i=1}^n{m}_i\times N_i}{{\sum }_{i=1}^n{N}_i}}$
Percentage of people who turn off the water while soaping	$C_{stop}$	Ratio of the number of responses from people who declare interrupting flow during shower to the number of responses from the total sample
Percentage of people who feel hydraulic disturbance at home	$C_{per}$	Ratio of the number of responses from people who declare feeling hydraulic disturbance to the number of responses from the total sample

Results

Quantification of Model Parameters

Initial Temperature Adjustment Duration

Figure 7 presents the distribution of the initial temperature adjustment durations according to faucet technology. A significant effect of faucet technology was observed on initial temperature adjustment duration. Thermostatic mixing valves exhibited the shortest adjustment durations, with a median value close to 26 s and a mean value of the same order of magnitude. In comparison, adjustment times were substantially longer for pressure-balance valves, mechanical mixers and two-handle mixers, whose mean values ranged from approximately 48 to 69 s.

Statistical analyses confirmed that the adjustment duration associated with thermostatic mixing valves was significantly lower than that observed for all other faucet technologies. On average, the adjustment time was reduced by approximately 45 to 60% compared with conventional systems, depending on the technology considered. These results are consistent with the operating principle of thermostatic mixing valves, which automatically regulate the proportion of hot and cold water required to reach the target temperature, thereby limiting the user interventions required during the start-up phase.

Soaping Activities and Consequences

The soap application durations and the number of soap applications were calculated only for shower signatures showing at least one interruption in the water flow during the shower. This data was extracted from 105 showers out of the 200 experiments conducted. In addition, the same parameter was evaluated from the online survey without discriminating against the type of faucet. The results are presented in Table 4 for these two parameters.

The results show that the type of faucet has no significant influence on behaviour (soap use time, turning off the water, etc.). The ritual behaviour of soaping up while showering does not seem to be affected by the type of faucet or shower head.

Regarding the proportion of individuals who temporarily stopped the water flow while showering to apply soap, the discrepancy between the experimentally observed value (62%) and the survey-based estimate (72%) highlights the limitations of relying solely on either direct measurements or self-reported data to characterize behavioural parameters. While the experimental campaign captures actual practices, self-reported data likely better reflect long-term habits but may be affected by social desirability bias. Consequently, a conservative compromise value of 66% was adopted for $C_{stop}$, balancing observed and declared behaviours and reducing the uncertainty associated with each method individually.

Following a soaping event, users may need to readjust the water temperature when reopening the faucet. The experimental results showed that the readjustment duration after flow interruption ($T_{rereg}$) was significantly lower for thermostatic mixing valve than for two-handle mixer (Figure 8).

Nevertheless, the readjustment duration differences between the thermostatic mixing valves and the two others faucets are close to being statistically significant (p=0.07), especially since the sample size used for the analysis is smaller than the one used for initial adjustment temperature duration due to the 62% of people who turned off the water during the shower. This result can be explained by the ability of thermostatic valves to maintain the selected temperature setting during flow interruptions, allowing the desired temperature to be restored rapidly when the water flow resumes. Consequently, thermostatic mixing valves reduce the effort and time required to return to comfortable showering conditions after soaping activities.

Hydraulic Disturbance During the Shower

According to the online survey, 41% of respondents reported experiencing hydraulic disturbances in their dwelling that could lead to sudden temperature fluctuations while showering. This proportion was retained as the value of the parameter $C_{per}$ in the proposed model. The result suggests that hydraulic disturbances constitute a frequent situation in residential buildings and may therefore contribute significantly to overall shower adjustment durations. However, this phenomenon does not appear systematically during showering and we propose setting the frequency of occurrence at 1 shower out of every 3.

The second step of the experimental campaign was specifically designed to evaluate the readjustment duration following a hydraulic disturbance ($T_{regper}$). This parameter was assessed only for mechanical mixers and two-handle mixer. Thermostatic mixing valves and pressure-balance valves were not considered in this analysis, as their operating principles are specifically intended to compensate automatically for supply pressure fluctuations and maintain a stable outlet temperature without requiring user intervention.

The results presented in Table 4 show that the mean readjustment duration following a hydraulic disturbance was approximately from 30 to 35 s for both mechanical mixers and two-handle mixers. This indicates that, when exposed to a sudden temperature variation resulting from a pressure disturbance elsewhere in the plumbing system, users generally required about half a minute to recover comfortable showering conditions and restore their preferred water temperature.

Table 4. Readjustment durations after a hydraulic disturbance (in seconds) for the two-handle mixing tap and the mechanical mixer tap.

Table 4. Readjustment durations after a hydraulic disturbance (in seconds) for the two-handle mixing tap and the mechanical mixer tap.

	Two-handle mixing tap	Mechanical mixer tap
$T_{regper}$ (s)	35,2	31,4

Discussion

Conclusions

References

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