The causes of air movement in hidden indoor micro-environments: measurements in historic bookshelves

Monitoring locations

Charlecote Park

Charlecote Park house is a Tudor mansion built in 1558. The library and the dining room were added as a new extension to the Tudor mansion in the 1830s. The bookshelves in the library were built between 1835 and 1839 [8]. The monitored bookshelf sits next to a window in the north external wall. A second window is located on the west wall. The library is part of the visitor route. Visitors enter the room from the hallway (east entrance) and walk parallel to the wall where the monitored bookshelf is located (north-facing). However, the bookshelf is set apart from the route as visitors circulate through the centre of the room, as can be seen in Fig. 1a. Visitors are directed to the west wall and exit the room through the south wall towards the adjacent room.

Figure 1

Floor plans of Charlecote Park library (a), Ham House library (b) and Blickling Hall long gallery (c) with location of the bookshelves monitored and visitor routes (approximate scale).

Monitoring methods

For each case study, air movement, RH and T were monitored to characterise the bookshelf and the general room environments. These indoor environmental parameters were monitored simultaneously behind the books in each bookshelf and the room, in the space right next to each bookshelf. Monitors, including the anemometers used to monitor air movement, were placed at 1–2 m high to increase the chances of detecting air movement caused by visitors in the space. However, this was not possible in the case of Blickling Hall because the area is accessible by the public and the anemometer was hung on the bookshelf.

Air movement (m/s) was monitored every second with two WindSonic Ultrasonic anemometers (Gill Instruments Ltd, Hampshire, UK) (accuracy: ±2% at 12 m/s; resolution: 0.01 m/s; threshold: 0.01 m/s; response time: 0.25 s; range: 0–60 m/s), each with a SpaceLogger.W8.Wireless logger (Richard Paul Russell Ltd, Hampshire, UK) to record the collected data. On shelves, the anemometer was placed against the back of the bookshelves, as seen in Fig. 2. The space taken by the anemometer, from where books were removed, was covered with a piece of foam (height 28 cm, width 17 cm), placed flush with the spine of the books to close this space and mimic the presence of books.

Figure 2

Cross section of bookshelf with gaps behind the shelves (1) anemometer installed in shelf, (2) next to books (3) and with a piece of foam covering the space taken by the anemometer, (4) temperature and RH of the shelf (T₁/RH₁) measured next to the anemometer; anemometer installed in the room (5) where temperature and RH was also measured (T₀/T₀).

A second anemometer was placed in front of each bookshelf monitored to measure the air movement in the room. At Ham House, the anemometer was placed at 50 cm from the shelf, at 100 cm height (measured at the centre of the anemometer), using a tripod. The anemometer was used horizontally to measure the air movement on a vertical plane, perpendicular to the bookshelf. In Blickling Hall, the anemometer was hung from the bookshelf, at a height of 220 cm, as it was not possible to place it in the space next to the bookshelf given the visitors’ circulation. In Charlecote Park, the anemometer was placed at 106 cm from the bookshelf, at a height of 126 cm. In the three properties, T and RH were monitored within the bookshelf, next to the head of the anemometer. Equally, in each room T and RH were monitored next to the anemometer except in Blickling Hall where the monitor was placed next to the spine of the books, as seen in Table 1.

Table 1.

Bookshelves monitored and its context in the respective historic properties, with type of gaps in shelves and monitored periods

	Charlecote Park	Ham House	Blickling Hall
Location of studied room (red dot) (north points up)
View of the shelf with anemometers in the shelf (dashed line) and in the room (circled), and T and RH monitor in the room (arrow)
Position and dimensions of the shelf studied	149 cm wide and 27 cm high. The shelf is at 118 cm from the floor	96 cm wide, 45 cm high and 27 cm deep. The shelf is at 114 cm from the floor	40 cm high and 77 cm from the floor
Gap on the shelf	No gap	Continuous gap. 1.5 cm wide.	Continuous gap. Approximately 3 cm wide
Monitoring times	Summer: 20–24/07/19 (open to the public daily 11:30 to 16:00) Winter: 05–08/02/20 (closed to the public) and 16-20/02/20 (open to the public)	Summer: 04–08/07/19 (open to the public daily 12:00 to 16:00) Winter: 24–28/01/20 (closed to the public)	Summer: 14–18/08/19 (open to the public daily 12:00 to 17:00)
Heating in the room	Yes (conservation heating: low level wet system heating plus electric radiators on local humidistats)	Yes (conservation heating controlled by building management system)	Yes (conservation heating: wet system heating plus electric radiators on local humidistats)
Bookshelf wall	External (facing north)	Internal (facing southeast)	Internal
Visitor movement	Visitors enter the room but do not walk past the bookcase.	Visitors enter the room but do not walk past the bookcase.	Visitors enter the room and may walk in front of the bookcase.

Modelling the stack effect

To further explore the available data, air velocities (m/s) for the monitored period were predicted using a simple model (Eq. 1), which was adapted from an equation used to calculate the draft flow rate caused by thermal forces alone [11]. While this model does not provide an exact representation of the physics of this system, it has the advantage of requiring inputs that align with the available data. If measurements of surface temperatures at the back of the shelves and the walls were available, it is preferable to explore the use of correlations for flow between isothermal flat plates, using the Rayleigh number. The advantage of the stack effect equation is that it requires the temperature inside and outside the air column of interest:

$v=C\sqrt{2gh\frac{T_i-T_0}{T_i},}$ (1)

where C is the discharge coefficient (usually from 0.65 to 0.70), g is the gravitational acceleration (9.81 m/s²), h is the height or distance (m), T_i is the average inside (the bookshelf) temperature (K) and T₀ is the outside (in the room) air temperature (K) [11]. In buildings, h is taken as the height of the air column. In this case, we have used the height of the bookshelves. This is an arbitrary choice, and it could be argued that other dimensions, such as the height of an individual shelf, could also be appropriate. To estimate the discharge coefficient C for each of the case studies, Eq. 1 was rearranged in the shape of a linear equation of slope k:

$v=k\sqrt{\frac{T_i-T_0}{T_i}},$ (2)

where $\hspace{0.17em}k=C\sqrt{2gh}.$ This equation is normally used in air columns, where the internal temperature is measured at the base of the column and the external temperature is measured at the top. In our case, we use the internal temperature of the shelf as T_i and the external temperature as T₀. With the available data this equation provides a good approximation to the driving thermal flow in this geometry. The comparison with the measurements allows a discussion on potential improvements to this simple model.

Temperature and humidity

In general, the T and RH in the bookshelves follow the indoor conditions of the room, both during summer and winter. This is clearly seen in Fig. 3. The results show that shelves in general have a buffering effect [12], generating dampened fluctuation amplitudes of T and RH. This is especially clear in the T fluctuations in Charlecote Park, and the T and RH fluctuations in Ham House in the summer.

Figure 3

T and RH inside the bookshelves and within the rooms (vertical lines correspond to the night period, 00:00 am).

In Charlecote Park, the indoor RH recorded in the summer was mostly lower on the shelf than in the room. In the winter, we can see that the RH in the shelf is higher than in the room, possibly due to lower T influenced by the external wall. In Ham House, the room and shelf temperatures show a daily oscillation in the summer with a small delay in the T within the shelf. The RH in both are also similar, with minimal differences, which are close to the error of the equipment (±0.35 °C and ±2.5% RH). The absolute humidity inside and outside the shelf are also similar (7.27 g/m³ inside and 7.24 g/m³ outside in the winter, 11.7 g/m³ inside and 11.6 g/m³ outside in the summer). This similarity indicates that differences in RH are possibly due to differences of T, rather than the presence of sources or sinks of water. In Blickling Hall, the T and RH both in the room and the shelf are very stable, with values in the shelf slightly higher but with a smoother behaviour, which could be evidence of buffering likely due to the thermal insulation properties and hygroscopic nature of the books. In this case, there is also no significant difference between the absolute humidity inside (11.7 g/m³ on average) and outside (12.1 g/m³ on average), indicating again that temperature dictates the changes in RH.

Outdoor data of wind conditions obtained from the Met Office weather stations near the properties for the monitored periods showed no correlation with the indoor air movement measured. During the winter period, indoor conditions of RH in Charlecote Park and Ham House showed no correlation with the outdoor RH. During the summer, only the RH conditions in Charlecote Park followed the outdoor trend but with delays. Ham House and Blickling Hall showed no correlation with outdoor RH. In the winter, temperatures indoors showed no correlation with the outdoor T conditions in all three libraries. During the summer period, a correlation was observed in all three libraries, showing an influence of the outdoor T on the indoor T.

The monitored properties display a diversity of hygrothermal conditions, as seen in Fig. 3. The temperature differences between the inside and outside of the shelves are small. However, as we shall see in the following sections, it is possible to relate this data with the observed air movement.

Air velocity in the bookshelves and the rooms

Air movement in the rooms usually displays a daily pattern that coincides with the opening hours of the libraries. This relationship is consistent in the three properties in the summer (Fig. 4), when the buildings are open to visitors. In these cases, air velocities in the shelf follow the changes in air velocities in the room. In the winter, the air velocity in the rooms is lower and it loses the periodicity. The air movement within the shelves is always an order of magnitude smaller than in the room, often close to the measurement threshold of the instrument (0.01 m/s).

Figure 4

Air velocity measured inside the bookshelves and in front of them (vertical lines correspond to the night period, 00:00 am).

In some properties, there is a correlation between the air movement in the room and the air movement within the shelf. This is most obvious in Charlecote Park in the summer, where air movement in the shelf is more active whenever there is air movement in the room. It can be hypothesised that the air pressure differences caused in the room either by the movement of visitors or the room’s ventilation from doors being open and closed directly affect the air movement within the shelf.

It is possible that the increase in air movement during open hours, corresponding to the peaks monitored in the room, is the result of other activities within the building; the library in Charlecote Park is adjacent to the Great Hall, where people enter the building. Thus, the increased indoor air velocities observed during visiting hours (and in the bookshelf with a smaller amplitude) could be due to general movement in the building, such as opening and closing the external doors, rather than exclusively due to people moving (walking) in the library.

During the winter period, when Charlecote Park is closed to visitors (first 4 days of monitoring: 05–08/02/20), air movement was higher both in the room and the shelf, compared with open days. This could be explained by the work carried out by staff during this period preparing the room before reopening it to the public. The increase of air movement occurred mainly around midday, coinciding with working hours and the opening and closing of the external and interior doors, similarly to the summer period.

The air movement in the Ham House and Blickling Hall rooms does not seem to be correlated with the air movement recorded in the shelves. In fact, in the summer period, the air movement in the Ham House shelf decreases when in the room it increases. In this case, the air movement in the shelf does not seem to be caused by increased air movement in the room. During this period, the property was closed to the public, but the staff were involved in works in an adjacent room and the library was used as a passageway. Their circulation in the room may explain the variation of air movement measured during this period. Therefore, air motion in the rooms alone does not explain the air movement detected within the shelves in all cases. To explore other possible causes, it is necessary to examine the differences in T between the shelf and the room.

Air velocity and temperature differences

As seen in Fig. 3, it is difficult to generalise about the temperatures of the bookshelves in relation to the room. The T difference changes throughout the day (between room and shelves), with most shelves experiencing periods where they are warmer or colder than the rooms. We have used Eq. 1 to explore whether these T differences are sufficient to cause the observed air movements. Figure 5 shows the relationship between the measured air velocity and T differences in each monitoring location. Note that the T differences between the rooms and the shelves are expressed in terms of $\sqrt{(T_i-T_o)/T_i}.$ This allows the calculation of $C\sqrt{2gh}$ as the slope of the linear regression. It can be observed that in all the libraries during the summer, there is a relationship between air velocity and the T difference between the shelf and the room. While the Pearson correlation coefficients are considered moderate to strong (r² ranges from 0.51 to 0.68) [13] it is evident that there exists a connection between these two variables. However, in the winter (Charlecote Park and Ham House), this relationship is non-existent, so we have not conducted the regression analysis.

Figure 5

Scatterplots of velocity and the temperature difference between the interior and the exterior of the bookshelves. A linear regression line is present only in the scenarios that display a potential correlation.

Fitting a linear model to the data allows us to estimate the value of the discharge coefficient, C, which gives an idea of the resistance offered by the shelves to air movement resulting from stack effect. C is a unitless coefficient which ranges from 0 (no air flow) to 1 (no resistance to air flow).

Table 2 summarises these results. The estimated discharge coefficients are significantly lower than the value of 0.65 proposed for buildings in the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) handbook [11], indicating a high resistance to air flow. This is to be expected given the very narrow spaces available for airflow. We found, however, no statistical relationship between these coefficients and the space available for air flow behind the shelves.

The estimated coefficients can be used within Eq. 1 to predict air velocity. The calculated air velocity is shown below next to the measured air velocity (Fig. 6). There is a significant overlap in the data for Ham House in the summer and Blickling Hall. It is interesting to note that, in these two libraries, there is no apparent relationship between air movement in the room and within the shelves, as seen in Fig. 4. There is, however, a remarkable fit between the measured and predicted air movement in the shelves, which could indicate that air motion is caused by T differences only. This relationship is not present in Ham House and Charlecote Park in the winter, with the exception of the first 2 days in Charlecote Park in the summer, which could be explained by the activities within the house during those 2 days.

Figure 6

Modelled and measured air velocities behind the books (vertical lines correspond to the night period, 00:00 am).

This correlation is not observed for the winter period. However, note that this does not necessarily mean there is no stack effect. It is not possible to determine if the stack effect is not present or if it is present on a smaller scale at the same time as pressure differentials have a stronger influence. It is conceivable that a pressure differential is the main mechanism responsible for the air movement monitored during the winter period, masking any potential stack effect.

Research ethics statement

Not applicable to this article.

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