1 Introduction

Residential homes in Europe use 28% of Europe’s total energy use [1]. The heating of the ventilation air is a substantial part of this, varying depending on the performance of the building [2]. An efficient solution to lower energy costs is to install a mechanical supply and extract ventilation systems with heat or energy recovery. Installation of such systems are therefore becoming more and more common in residential buildings. Typical performance of heat recovery in residential ventilation systems shows temperature efficiencies of approximately 80% and above, which means that there is an extensive benefit from having heat recovery in ventilation systems. Both catalogue data [3,4,5] and scientific literature confirms this [6,7,8]. The efficiency is a matter of an optimization between fan electricity and heat recovery where a larger heat recovery unit gives higher efficiency and higher pressure drop, and apparently in the magnitude of 80% has been found to be a reasonable compromise.

Heat or energy recovery in ventilation systems have been used extensively and successfully in office buildings for decades but in residential buildings, as mentioned above, this is a rather new phenomenon. Non-residential buildings normally have a higher air change rate and moisture is seldom a problem, as is often the case in dwellings where specific processes like showering and cooking generate a lot of moisture [9]. This means that non-residential buildings do not have the same problems with frost and there is little experience of the problems that can occur due to freezing. Furthermore, the new experiences from implementation in residential buildings shows that the expected energy saving is not totally fulfilled compared to theoretical figures, probably to a large extent depending on inappropriate defrosting measures [10]. Here there is a balance between having too frequent defrosting with poor energy efficiency and avoiding frost formation that may mean that the operating staff need to manually defrost the heat exchanger with downtime sometimes up to several days. The efficiency of a heat recovery ventilation in frosting conditions have been shown to be remarkably lower and can decrease below 50% with working frost prevention and even lower without [11,12,13,14].

Heat exchangers have the greatest potential of saving energy in cold climates, where incoming and exhaust air temperature difference is the greatest. However, the lower the outdoor temperature, the greater the risk of frost formation. When the outdoor temperature is low enough to bring the temperature of the exhaust air bellow its saturation point, latent energy of the exhaust air stream is released, heat is transferred to the supply air stream and condensation forms on the walls of the heat exchanger. Condensation is a welcome side effect as it increases the total amount of energy that can be transferred [15]. If the temperature of the heat exchanger drops below zero, condensation can turn into frost which can cause various problems to the heat exchanger. Accumulated frost shuts off heat exchanger pathways and reduces exhaust air flow. In extreme scenarios, the heat exchanger must be turned off for long periods of time for ice to be melted. Because water expands while freezing, ice deforms the heat exchanger, lowering the efficiency and introducing leakages and an increased pressure drop over the whole system [16].

The perfect system should be able to take advantage of condensation while preventing condensate turning into frost. However, practically energy simulation software on the market, do not have a good way to model energy use, moisture flows, and different defrosting strategies for different types of heat exchangers. Furthermore, since moisture supplied indoors are directly related to occupant behavior better knowledge is needed of the moisture generation within residential buildings.

In order to attain the desired energy savings and avoid problems with frost, a greater understanding of how the whole ventilation system works together with the building and its occupants is required. Even if programs exist to simulate buildings and installation systems, methods must be developed to properly include frost formation and defrosting in relation to moisture generation by user behavior.

1.1 Aim

The main aim of this paper is to propose a simulation model that can handle condensation and frost formation in heat exchangers dependent on moisture concentration and outdoor climate conditions.

Objectives of this paper are firstly, to get representative data on moisture generation in residential buildings and to analyze selected indoor and outdoor climate conditions, secondly, to propose a reasonable simulation model, thirdly, to analyze risk of frost formation and discuss different frost protection strategies.

1.2 Limitations

This study is limited to Nordic weather conditions alone and measurements of moisture production are taken from measurements in a building which is assumed to represent the general moisture production in apartment buildings.

The study focuses on cross flow heat plate exchangers and enthalpy wheel heat exchanger. The study analyzed different heat exchangers, disregarding their prices.

It also focuses on risk factors of frost and a few frost strategies, leaving out transmission losses and energy use of fans, motors, and buildings’ heating systems. In reality, the heat exchanger would stop working after frost formation. In the paper the frost is considered continuously removed so that the heat exchanger could theoretically continue working.

1.3 Paper outline

The paper starts with an introduction including the rather sparse literature in the field of frosting in heat recovery ventilation of buildings. The research gap is given before the aim, followed by limitations. Methods describe the used theory, the outdoor climate, the measurements and the approach for the heat recovery units. The aim of the paper is accomplished both in the Method section, where the proposed method of a simulation model, and in the Result and Discussion section, where the quantification of the measured moisture generation and the frosting problem is made as well as how frost protection influences energy use. Finally short conclusions are made based on the aim.

2 Method

The process for developing the simulation model for the examined heat exchangers is first to make a description of the outdoor climate for the investigated cities. To get a good representation of different Nordic climates the following cities are examined: Kiruna, Östersund, Karlstad, Stockholm, Gothenburg, and Copenhagen. Secondly the moisture generation within residential buildings and indoor climate condition needs to be described, which is done by measurements in 36 apartments. Thereafter a simplified simulation model that can handle condensation and frost formation in heat exchangers dependent on moisture concentration and outdoor climate conditions is proposed. To be able to consider condensation and freezing in different areas of the heat exchanger a more detailed simulation model is proposed. Finally, measurements are performed for a small air handling unit so that simulation results could be verified.

2.1 Outdoor climate

Outdoor conditions are extracted from Energy Plus weather format files [17]. Files contain atmospheric pressure, dry bulb temperature and relative humidity (RH) for every hour of a year. Examined cities are Kiruna, Östersund, Karlstad, Stockholm, Gothenburg and Copenhagen, see Fig. 1 with mean temperature of January. These cities have outdoor climate data and provide a good distribution over all Swedish outdoor conditions, but also other Scandinavian, North European and North American climates, from a climate with low to high amount of freezing problems.

Fig. 1
figure 1

Location of cities used in the analysis, with average temperatures during January

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Since freezing in exhaust air stream can only happen when temperature drops below 0 °C, the number of hours when it can happen are of interest. Using the Eq. (1) and having prescribed efficiency, one can estimate how many hours the heat exchanger is at risk of frost formation.

$$t_{outdoor} = \frac{{t_{eal} - t_{eae} }}{{\varepsilon_{s} \frac{{C_{min} }}{{C_{e} }}}} + t_{eae} .^{\circ} {\text{C}}$$
(1)

where \(\varepsilon_{s}\) sensible effectiveness %; \(t_{sae} =\) supply air entering dry-bulb temperature. °C; \(t_{sal} =\) supply air leaving dry-bulb temperature. °C; \(t_{eae} =\) exhaust air entering dry-bulb temperature. °C; \(t_{eal} =\) exhaust air leaving dry-bulb temperature. °C; \(C_{min} = smaller\, of\, c _{ps } \cdot m _{s }\, and\, c _{pe } \cdot m _{e } \cdot {\text{kJ/s}} \cdot {\text{K}}\); \(c_{pe} =\) exhaust moist air specific heat at constant pressure. \({\text{kJ/kg}} \cdot {\text{K}}\); \(c_{ps} =\) supply moist air specific heat at constant pressure. \({\text{kJ/kg}} \cdot {\text{K}}\); \(m_{e} = {\text{exhaust dry air mass flow rate}}.{\text{ kg}}/{\text{s}}\).

2.2 Indoor climate conditions and psychrometric calculations

Indoor temperature and relative humidity are measured in 36 apartments in the Swedish city Karlstad together with the outdoor temperature and relative humidity to give input data to the simulations of how often frosting occurs. The apartments ranging in size from 60 to 92 m2, averaging on 74.75 m2. Each apartment has an exhaust ventilation system.

Total exhaust air flow is 0.35 l/s/m2 and is available in ducts in the attic, where measuring equipment is placed. The temperature and relative humidity are measured in the exhaust duct from each apartment. Outdoor temperature and relative humidity are measured. The relative humidity sensors have a specified accuracy of ± 1.5% relative humidity (RH) for RH between 0 and 80%, and ± 2% RH for RH between 80 and 100%. The temperature has a specified accuracy of ± 0.25 °C for temperatures lower than 0 °C, and ± 0.1 °C for temperatures above 0 °C. The interval between the measurements is 6 min and they we are collected during a year.

Moisture supply is calculated using psychrometric calculations, based on measured temperatures and relative humidity. The difference between the vapor content, measured in each apartment’s exhaust air and in the outdoor air, defines the apartment's moisture supply. In this way a specific moisture supply from an individual apartment for each hour during the year could be set. It can be assumed that the moisture supply is rather representative also for other cities in similar outdoor climate.

To perform heat exchanger analysis, number of moist air properties are required.

Water vapor saturation pressure values are obtained using following formulas derived from the Hyland–Wexler equation [18] and coefficients are taken from ASHRAE fundaments [19].

The saturation pressure over ice from temperatures ranging of − 100 to 0 °C is given by

$$ln p_{ws} = \frac{{C_{1} }}{T} + C_{2} + C_{3} T + C_{4} T^{2} + C_{5} T^{3} + C_{6} T^{4} + C_{7} \;lnT, {\text{Pa}}$$
(2)

where C1 = − 5674.5359, C2 = 6.3925247, C3 = − 0.009677843, C4 = 0.00000062215701, C5 = 0.0000000020747825, C6 = − 0.0000000000009484024, C7 = 4.1635019.

The saturation pressure over ice from temperatures ranging of 0 to 200 °C is given by

$$ln p_{ws} = \frac{{C_{8} }}{T} + C_{9} + C_{10} T + C_{11} T^{2} + C_{11} T^{2} + C_{12} T^{3} + C_{12} \;lnT, {\text{Pa}}$$
(3)

where C8 = − 5800.2206, C9 = 1.3914993, C10 = − 0.048640239, C11 = 0.000041764768, C12 = − 0.000000014452093, C13 = 6.5459673.

\(p_{ws} = {\text{saturation pressure}},{\text{ Pa}}\); \(T = {\text{absolute temperature }},{\text{ K}} =\,^{\circ} {\text{C}} + 273.15{ },{\text{ K}}\).

Moist air is considered a mixture of independent perfect gases (dry air and water vapor). Humidity ratio W is expressed as:

$$W = 0.621{ }945{ }\frac{{p_{w} }}{{p - p_{w} }}, {\text{kg}}_{{\text{w}}} {\text{/kg}}_{{{\text{da}}}}$$
(4)

From relative humidity:

$$W = \frac{{0.621945 \phi p_{s} }}{{p_{tot} - \phi p_{s} }}, {\text{kg}}_{{\text{w}}} {\text{/kg}}_{{{\text{da}}}}$$
(5)

where \(p = {\text{total preasurre}},{\text{ Pa}}\); \(p_{w} = {\text{partial preasure of water vapor}},{\text{Pa}};{ }\) ϕ-relative humidity, %

Specific volume v of moist air mixture is expressed in terms of a unit mass of dry air:

$$v = 0.287\frac{{042\left( {t + 273.15} \right)\left( {1 + 1.607{ }858W} \right)}}{p}{ },{\text{m}}^{{3}} {\text{/kg}}_{{{\text{da}}}}$$
(6)

To find out humidity ratio indoors, the formula is derived to include moisture supply from the occupants:

$$W = { }\left( {\frac{{w_{se} }}{sv}} \right) + \left( {\frac{msp}{{3600}}/Q_{e} } \right) \cdot 0.833,{\text{kg}}_{{\text{w}}} {\text{/kg}}_{{{\text{da}}}}$$
(7)

2.3 Heat exchangers for heat and energy recovery

Heat exchangers can be categorized as heat recovery ventilation, Fig. 2 left, and energy recovery ventilation, Fig. 2 right. In a heat recovery ventilation heat exchanger, heat flows over the surface where the heat exchange occurs. In an energy recovery ventilation heat exchanger, the exchange happens through a heat transferring mass that is cooled by the incoming air and heated by the exhaust air.

Fig. 2
figure 2

Heat recovery ventilation (HRV) and Energy recovery ventilation (ERV)

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The HRV and ERV systems facilitate energy transfer from exhaust room temperature air to incoming supply outdoor temperature air during winter and opposite during the summer, via metal plate surface. Temperature efficiency facilitates only sensible heat transfer. The energy efficiency facilitates total, sensible and latent energy transfer.

The heat exchangers efficiency depends on its geometry, arrangement of air streams and material. According to ASHRAE [20], counter flow exchangers, which is a subset of HRV, have theoretical maximum temperature efficiency approaching 100%, but the actual temperature efficiency is typically lower. Typical cross flow unit’s effectiveness is 75 to 85%. A typical enthalpy wheel, which is a subset of ERV, has a theoretical temperature efficiency of 80%. However, energy efficiency consists of moisture and sensible heat efficiency that are not necessarily the same.

In practice, due to construction and size limitations, designs that use crossflow are typically favored. That is why crossflow exchangers are chosen to be the main subject of this project.

2.4 Transient state simplified heat exchanger simulation

In real life conditions efficiency is not constant, it changes over time depending on the temperature difference, the amount of condensation and heat capacity rate. The thermal capacity is a product of mas flow rate and specific heat. In the simplified simulation, latent and sensible efficiency is a constant. In most cases it is more than enough for an engineer to use an average efficiency to select the HRV/ERV. Manufacturers provide measurements of average efficiency for balanced flow conditions.

By using measurements (relative humidity outdoors and indoors, temperature indoors and outdoors) for each individual apartment for every hour of the year (chapter 2.2), and statistical weather conditions in different parts of Sweden (chapter 2.1), calculations are coded in a python model [20], using formulas for steady state heat recovery ventilation (chapter 2.4.1) and steady state total energy recovery ventilation (chapter 2.4.2), and iterated over every hour of the year, a transient state model for sensible heat and totally energy recovery can be set up.

2.4.1 Steady state sensible heat recovery ventilation

Steady state analysis is performed based on theoretical worst-case scenarios—highest moisture supply under negative temperatures, ASHRAE Standard 8413 defines efficiency of a heat recovery system:

$$\varepsilon_{s} = \frac{{Actual\,transfer\,of\,energy}}{{Maximum\,posible\,transfer\,between\,airstreams}},{\text{ \% }}$$
(8)
$${\text{Actual energy trasfer}} = q_{s} = Q_{s} \rho_{s} c_{ps} \left( {t_{sae} - t_{sal} } \right) = { }Q_{e} \rho_{e} c_{pe} \left( {t_{eae} - t_{eal} } \right),{ }$$
(9)
$$Maximum\,posible\,transfer\,between\,airstreams = C_{min} \left( {t_{ee} - t_{se} } \right)$$
(10)
$$C_{min} = smaller\,of{ }Q_{s} \rho_{s} c_{ps}\,and\,Q_{e} \rho_{e} c_{pe} { }$$
(11)

Assuming no water vapor condensation in the HRV, leaving supply air temperature is:

$$t_{sal} = { }t_{sae} - \varepsilon_{s} \frac{{C_{min} }}{{Q_{s} \rho_{s} c_{ps} }}\left( {t_{sae} - { }t_{eae} } \right),\;^{\circ} {\text{C}}$$
(12)

Leaving exhaust air temperature is:

$$t_{eal} = { }t_{eae} - \varepsilon_{s} \frac{{C_{min} }}{{Q_{e} \rho_{e} c_{pe} }}\left( {t_{sae} - { }t_{eae} } \right),\;^{\circ} {\text{C}}$$
(13)

where \(\varepsilon_{s} =\) sensible effectiveness, %; \(t_{sae} =\) supply air entering dry-bulb temperature, °C; \(t_{sal} =\) supply air leaving dry-bulb temperature, °C; \(t_{eae} =\) exhaust air entering dry-bulb temperature, °C; \(t_{eal} =\) exhaust air leaving dry-bulb temperature, °C; \(\rho_{s} =\) density of dry supply air, \({\text{kg}}_{{{\text{da}}}} {\text{/m}}^{{3}}\); \(\rho_{e} =\) density of dry exhaust air, \({\text{kg}}_{{{\text{da}}}} {\text{/m}}^{{3}}\); \(Q_{s} =\) volume flow rate of supply air, \(m^{3} { }/s\); \(Q_{e} =\) volume flow rate of exhaust air, \({\text{m}}^{{3}} {\text{/s}}\); \(c_{ps} =\) supply moist air specific heat at constant pressure, \({\text{kJ/kg}} \cdot {\text{K}}\); \(c_{pe} =\) exhaust moist air specific heat at constant pressure, \({\text{kJ/kg}} \cdot {\text{K}}\).

2.4.2 Steady state total energy recovery ventilation

Steady state analysis is performed based on theoretical worst-case scenarios – highest moisture supply under negative temperatures. ASHRAE Standard 84 defines efficiency of a heat recovery system:

$$\varepsilon_{L} = \frac{Actual\, transfer\, of\, moisture}{{Maximum\, posible\, transfer\, between\, airstreams}}$$
(14)
$$Total\, transfer\, of\, energy = q_{s} = Q_{e} \rho_{e} c_{pe} \left( {t_{eae} - t_{eal} } \right) + m_{e} h_{fg} \left( {w_{eae} - w_{eal} } \right)$$
(15)
$$Maximum\, posible\, transfer\, between\, airstreams = C_{min} \left( {t_{ee} - t_{se} } \right), {\text{kJ/kg}}$$
(16)
$$C_{min} = smaller\, of\, Q_{s} \rho_{s} c_{ps}\, and\, Q_{e} \rho_{e} c_{pe} ,{\text{kJ/kg}} \cdot {\text{K}}$$
(17)

Assuming there was no water vapor condensation in the HRV, leaving supply air water content is:

$$w_{sal} = w_{sae} - \varepsilon_{L} \frac{{m_{w,min} }}{{m_{s} }}\left( {w_{sae} - w_{eae} } \right), {\text{ kg}}_{{\text{w}}} /{\text{kg}}_{{{\text{da}}}}$$
(18)

Leaving exhaust air water content is:

$$w_{eal} = w_{sae} + \varepsilon_{L} \frac{{m_{w,min} }}{{m_{s} }}\left( {w_{sae} - w_{eae} } \right), {\text{ kg}}_{{\text{w}}} /{\text{kg}}_{{{\text{da}}}}$$
(19)

where \(\varepsilon_{L} =\) latent efficiency, %; \(\rho_{s} =\) density of dry supply air, \({\text{kg/m}}^{{3}}\); \(\rho_{e} =\) density of dry exhaust air, \({\text{kg/m}}^{{3}}\); \(Q_{s} =\) volume flow rate of supply air, \({\text{m}}^{{3}} {\text{/s}}\); \(Q_{e} =\) volume flow rate of exhaust air, \({\text{m}}^{{3}} {\text{/s}}\); \(m_{s} =\) supply dry air mass flow rate, \({\text{kg/s}}\).

2.4.3 Simulating different heat exchangers arrangements

The moisture supply is different in every apartment, due to different amount and behaviors of residents. Redirecting exhaust air from more than one apartment into one heat exchanger could reduce moisture load on the heat exchanger.

To analyze the risk of frost, different heat exchanger set-ups are simulated; one for the whole building, one for 18 apartments, one for nine apartments, one for four apartments and one for each apartment. The set up with groups of 18, 9, and 4 apartments are randomly grouped using a Python script. The fewer heat exchangers are used, the bigger they needed to be, which was accounted for in the Python script. Bigger units get more moisture, but the air flow is higher. To access the risk of frost formation, hours of condensation under negative exhaust air leaving temperatures are counted for every apartment.

2.5 Transient state detailed heat exchanger simulation

Because the simplified model does not take into account condensation and freezing in different areas of the heat exchanger, due to non-uniform temperatures across the heat exchanger, the detailed model is developed. The detailed model took into account the temperature stratification across the heat exchanger and condensation affect. The input used for the detailed model is the same as used for the simplified model, measurements (relative humidity outdoors and indoors, temperature indoors and outdoors) for each individual apartment for every hour of the year (chapter 2.2), and statistical weather conditions in different parts of Sweden (chapter 2.1).

2.5.1 Steady state detailed model

To perform a detailed analysis the heat exchanger 2d cross section is subdivided into small squares and the calculation is performed on each individual square level, see Fig. 3. Consequently, the more in detail the cross area is subdivided, the more accurate the results will be.

Fig. 3
figure 3

Schematic representation of a cross flow heat exchanger with 72.7% sensible effectiveness. The heat exchanger is subdivided into 7 × 7 granularity

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The rate of energy transfer depends on operating conditions, geometry of the heat exchanger, heat transfer surface area and thermal conductivity of the walls separating the streams. During the analysis two modes of energy transfer are considered. The first mode is the energy transfer driven by the dry bulb temperature difference between cross-streams, as described in chapter 2.5.2. Second mode is latent heat transfer, when water vapor condenses on the walls in the heat exchanger and releases latent heat to another air stream as sensible heat, as described in chapter 2.5.3.

2.5.2 Energy transfer due to dry bulb temperature difference

In practice, efficiency is not constant, it changes over time depending on heat capacity rate. The thermal capacity is a product of mass flow rate and specific heat. The simplified model used efficiency only, which means that the model is dimensionless. To perform calculations on individual 2d square level, the dimensions of the heat exchanger are introduced. To define the dimensions, UA-value of the heat exchanger is used.

Size and thermal conductivity of the heat exchanger (UA-value) are taken into account, using the effective NTU (ε-NTU) method. Knowing prescribed effectiveness of the heat exchanger and the heat capacity ratio according to Eq. (20), one could use Fig. 4 [15] to see the NTU value for the prescribed efficiency. Once the NTU value is established, a heat exchanger can be chosen to match the required surface area and the U value (UA-value) according to Eq. (21).

$$C_{r} = \frac{{\left( {mc_{p} } \right)_{min} }}{{\left( {mc_{p} } \right)_{max} }}$$
(20)
$$UA = { }NTU\left( {mc_{p} } \right)_{min}$$
(21)
Fig. 4
figure 4

Effectiveness of cross flow heat exchanger with both fluids unmixed according to Eq. (22)

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Temperatures of the incoming air streams and the NTU value affects minimum heat capacity and heat capacity ratio. Having prescribed overall heat transfer coefficient (UA) one can estimate how NTU according to Eq. (23) and efficiency according to Eq. (22) variate under different inlet conditions.

$$\varepsilon = 1 - {\text{exp}}\left\{ {\left( {\frac{1}{{C_{r} }}} \right)NTU^{ - 0.22} \left[ {{\text{exp}}\left( { - C_{r} \cdot NTU^{0.78} } \right) - 1} \right]} \right\},\%$$
(22)
$$NTU = { }\frac{UA}{{\left( {mc_{p} } \right)_{min} }}$$
(23)

where \(c_{p} =\) moist air specific heat at constant pressure, \({\text{kJ/kg}} \cdot {\text{K}}\); \(m = {\text{dry air mass flow rate}},{\text{ kg}}/{\text{s}}\); \(\varepsilon_{s} =\) sensible effectiveness %

Substituting the NTU value with Eq. (23), the final equation for the model is created:

$$\varepsilon = 1 - {\text{exp}}\left\{ {\left( {\frac{1}{{C_{r} }}} \right)\left( {\frac{UA}{{C_{min} }}} \right)^{ - 0.22} \left[ {{\text{exp}}\left( { - C_{r} \cdot \left( {\frac{UA}{{C_{min} }}} \right)^{0.78} } \right) - 1} \right]} \right\}, \%$$
(24)

Finally, efficiency calculated by Eq. (24), is used in ASHARE equations, Eqs. (12) and (13), described in the simplified model.

2.5.3 Energy transfer due to latent heat

In cold climate conditions, as the sensible energy is transferred from the exhaust air stream to supply air stream, the dry bulb temperature of exhaust air drops below dew point temperature, causing formation of water droplets on the walls of the heat exchanger. Condensation increases the sensible effectiveness by increasing the heat transfer rate. According to ASHRAE Handbook [20], one kilogram of condensed moisture transfers about 2440 kJ to incoming air at room temperature. To account for condensation effect on the heat exchanger supply air leaving temperature, Eq. (12) is adjusted:

$$t_{sal} = t_{sae} - \varepsilon_{s} \frac{{C_{min} }}{{Q_{s} \rho_{s} c_{ps} }}\left( {t_{sae} - t_{eae} } \right) + \frac{2440 \cdot cond }{{Q_{s} \rho_{s} c_{ps} }}, \;^{\circ} {\text{C}}$$
(25)

2.5.4 Steady state parametric study

The parametric study is performed to find out the optimal conditions of the transient simulation, and to find out how changing different parameters affects exhaust air behavior in the heat exchanger. The more detailed the simulation is the longer it takes. At some point the level of detail becomes redundant because the change to results becomes insignificant compared to the time required to run the simulation. The outdoor and indoor conditions for the base model of the parametric study remains the same as in previous chapters. The focus of the parametric study is to evaluate what effect changing different parameters (grid detail level, UA-value, air flow, indoor temperature) will have on the heat exchanger’s efficiency and frost formation mass.

2.6 Tests of frost protection strategies

The estimation of risk of frost is a three-step process. The first step is to find out the water content of exhaust air entering, using Eq. (5). The second step is to estimate the water content at saturation of exhaust air leaving, using Eq. (4). The final step is to convert the water content from kg-w/kg-da to kg-w/m3 by using Eq. (6) for specific volume, of both exhaust air entering and exhaust air leaving at saturation, and finally to subtract them. If the humidity content of the exhaust air entering is higher than humidity content of the exhaust air leaving, and the temperature of the exhaust air leaving is lower than zero, a subtraction of the humidity content results in a volume of water that is considered frozen on the heat exchanger’s walls.

By repeating these steps for every hour of the year, the number of hours when condensation occurred during the year, and the total volume of condensation are estimated. To avoid frost formation three different strategies are tested by comparing their total energy use. The total energy use is the energy required to heat the supply air leaving the heat exchanger to a predefined supply air temperature (21 °C) and/or to preheat supply air entering the heat exchanger while maintaining the heat exchanger frost free.

  • Supply air entering with 100% bypass is a frost control strategy that prevented frost while maintaining 100% ventilation. It eliminates the amount of cold supply air entering the heat exchanger. Face and bypass frost control starts when the supply air temperature drops below frost threshold value. As supply air temperature reaches a frost threshold temperature, bypass dampers will close to bypass the supply air, until the temperature rises above the threshold value again.

  • Preheat frost control is a strategy that prevented frost while maintaining 100% ventilation. The incoming outdoor air is preheated to zero degrees Celsius before entering the heat exchanger. The preheater must be sized for the coldest outdoor air temperature.

  • Combination of bypass and preheating is a strategy that prevented frost while maintaining 100% ventilation, 25%, 50% or 75% of the incoming outdoor air is bypassed, while preheating the remaining part of the supply air.

2.7 Measurements of an air handling unit

To verify the simulation model, measurements are performed in a freezing storage facility on a normal small apartment or house air handling unit. The unit is purchased on the market, and has a heat exchanger between supply and exhaust air with a mix between counter and cross flow setup. The maximum airflow is 55 l/s. The unit is supplied with air with variable temperature from − 31 to 20 °C to sort out when frosting starts. The indoor environment is held at approximately 20 °C and the indoor side is humidified to an RH of approximately 40%. The frost is detected by weighing the heat recovery unit after letting condensation drain out and compare it to a dry and clean heat recovery unit. The frost protection supplied by the manufacturer is switched of during the measurements. The loggers were from Onset Hobo with errors of ׅ ± 0.2° for temperature C and ± 2.5% for RH and the flow was measured by the air handling unit with unknown accuracy. Weight was measured with an industrial scale with an accuracy of 1 g.

3 Results and discussion

3.1 Outdoor climate conditions and indoor climate conditions

In Fig. 5 number of hours is shown for reaching outdoor temperature below − 5 °C, between − 5 and 0 °C and above 0 °C in different cities, calculated with Eq. (1). If the outdoor temperature drops below − 5 °C, the exhaust air will drop below 0 °C if the heat exchanger’s sensible efficiency is 80%, and indoor temperature is 21 °C. Kiruna has the greatest number of hours with risk of frost about 2900 h in a year when temperature was below − 5 °C. Copenhagen has the lowest number of hours with a risk of frost about 100 h in a year.

Fig. 5
figure 5

Hours reaching different outdoor temperatures in different cities

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In Fig. 6 total moisture supply is presented for the measurements of the 36 apartments. The moisture supply is significantly higher in apartments Lg19 and Lg26, 33 and 28 kg/m2/year respectively.

Fig. 6
figure 6

Total moisture supply in kg per m2 of apartment area

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In Fig. 7 a violin chart presents hourly total moisture supply in grams per m2 of apartment area per year for the 10 apartments with highest median value. The width of each ’’violin’’ represented the frequency of data points in each apartment. The maximum moisture supply condition was 17 g/m2/h·75 m2 = 1.3 kg/h in apartment Lg17.

Fig. 7
figure 7

Total moisture supply in gram per m2 of apartment area per every hour of the year for the top 10 most risky apartments

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The amount of moisture supply per year is unevenly varying from 33 to 5 kg/m2/year, which suggested that having one heat exchanger for several apartments could reduce the risk of moisture load per heat exchanger, consequently reducing the risk of frost accumulation. Even though most of the data points are within the range of 0 to 5 g/m2, the frost protection system has to be designed to perform well under the peak conditions, which is 17 g/m2.

3.2 Steady state simplified simulation

As a basis for simplified dynamic model, steady state calculations are performed on the worst-case scenarios for two kinds of theoretical heat recovery systems—sensible recovery ventilation unit and total energy recovery unit. Since Kiruna has the greatest risk of frost, the steady state calculations were chosen to represent the worst-case scenario that could happen in this city. Outdoor supply air enters the sensible heat recovery ventilation unit at – 27 ℃ and at relative humidity of 90%, the supply air flow is approximated 0.35 l/(s m2). The indoor temperature was 21 ℃ and moisture supply was 1.2 kg-water/h per apartment. The energy recovery unit’s sensible heat efficiency \(\varepsilon_{s} = { }\) 80%. The building is assumed to be at sea level and at the atmospheric pressure. The amount of frost in the heat exchangers unit under steady state conditions is determined with the equations described in Chapter 2.

The calculations show that the ERV unit has a significantly lower amount of theoretical frost (0.783 kg-w), which is almost a half of the same figure for the HRV unit (1.583 kg-w). This would suggest that having an ERV would be more beneficial compared to HRV in colder climates due to moisture transfer to the supply air stream.

3.3 Simulating different heat exchangers arrangements

Table 1 presents number of hours with risk of frost formation in a building situated in different cities and with different number of HRV units. When the building has multiple heat exchangers, each unit tends to have different number of hours with risk of frost formation. The table represents the average number of hours in each specific scenario.

Table 1 Number of hours with risk of frost formation per city and by number of HRV units in the apartment building
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In Table 2 the amount of frost formation in kilograms that could theoretically occur in HRV units is presented, without any strategy of protection from frost applied.

Table 2 Amount of frost formation per city and by number of HRV units in the apartment building
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Table 3 presents number of hours with risk of frost formation in a building situated in different cities and with different number of ERV units. When the building has multiple heat exchangers, each unit tends to have different number of hours with risk of frost formation. The table represents the average number of hours in each specific scenario.

Table 3 Number of hours with risk of frost formation per city and by number of ERV units in the apartment building
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In Table 4 the amount of frost formation in kilograms that could theoretically occur in ERV units is presented, without any strategy of protection from frost applied.

Table 4 Amount of frost formation per city and by number of ERV units in the apartment building
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The simulation with the simplified model shows that the number and the arrangements of the plate heat exchangers in the building did not make a significant difference regarding hours when the risk of freezing occurs. The biggest difference is found between having one unit for the whole building and having one unit for each apartment, 36 units in total. However, the difference in theoretical amounts of frost-formation is significant. The fewer units are used, the lower the theoretical frost-load. Even though the number of hours of risk does not change significantly, reducing the number of heat exchangers could lead to lower load of frost formation and less energy-requiring frost protection strategies.

On the other hand, in the building with ERV unit, both the risk of frost formation and the theoretical frost-load decrease significantly due to reduction of the number of enthalpy wheel units in the building, making reducing the number of enthalpy wheel units a valid strategy to reduce the risk of frost.

3.4 Detailed heat exchanger simulation

The main difference between the simplified model and the detailed model is that instead of dimensionless efficiency used in the simplified model, the detailed model uses a UA-value of 0.15 and a grid detail level of 100 × 100. Other input parameters for the simulations are the same as for the simplified steady state calculations in chapter 3.2. Based on the steady state conditions and the UA-value, the efficiency was calculated to be 80%, which is comparable to the simplified steady state calculations in chapter 3.2.

First a simulation is made considering only the energy transfer due to dry bulb temperature difference. The detailed simulation results are presented in a heat map of exhaust air, revealing the temperature distribution and the cold corner of the heat exchanger, see Fig. 8. Frost appears in more than 50% of the heat exchanger’s cross section, and condensation appears in approximately 20%, see Fig. 9.

Fig. 8–9
figure 8

Heat map of exhaust air temperature distribution (left), and heat map representing the distribution of frost and condensation within heat exchanger exhaust air channels (right)

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A comparison of the results from the simplified and the detailed models are given in Table 5. The detailed model shows that frost and condensation appear at the same time in different areas of the cross section of the heat exchanger. The main difference between the simplified model and the detailed model was that the simplified model, as opposed to the detailed model, did not separate areas of frost and condensation, assuming that they appear across the whole heat exchanger, making the simplified model insufficient for these types of analyses. Other results does not differ significantly.

Table 5 Results of the simplified and the detailed simulation model and by considering condensation effects
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Secondly a simulation is made also considering energy transfer due to latent heat. The detailed simulation results are presented in a heat map of exhaust air, see Fig. 10. Frost and condensation areas in the cross section of the heat exchanger was about 30% and 30% respectively, see Fig. 11. The results of considering condensation effects are also given in Table 5.

Fig. 10–11
figure 9

Heat map of exhaust air temperature distribution. (left), and Heat map representing the distribution of frost and condensation within heat exchanger exhaust air channels (right)

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Frost and condensation areas in the cross section of the heat exchanger shifted from about 50% to 30% and from about 20% to 30% respectively. With condensation taken into account, energy recovery increases due to latent energy transfer. Condensation and frost decreases by 9% and 32% respectively, due to the increase of supply air leaving temperature. The final model, which includes condensation effect, is more accurate compared to the simplified and the detailed models. The results differs significantly, making the analysis of such a type more valid.

3.4.1 Measurements of frosting limit

The measurements of the air handling unit showed sensible temperature efficiencies according to Fig. 12, where also the figures are given when the frost protection is on at an outdoor temperature of − 29 °C. This corresponds to the catalogue data, particularly below maximum flow. At 35 l/s, it is found that frost is forming below − 4 °C outdoor temperature, which corresponds to an exhaust temperature of around 0 °C with the measured temperature efficiency of 83%.

Fig. 12
figure 10

Sensible temperature efficiency of measured heat recovery unit with and without frosting protection on

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3.4.2 Steady state parametric study

The results from the parametric study of the grid detail level are plotted in Fig. 13. The line chart and the bar chart, which shares the x axes, represented exhaust air leaving temperature and frost in kilograms, respectively.

Fig. 13
figure 11

Relationship between grid detail level and change of exhaust air temperature and frost volume in kg

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The results from the parametric study of UA-value of the heat exchanged is plotted in Fig. 14. The line chart and the bar chart, which shares the x axes, gives exhaust air leaving temperature and frost in kilograms, respectively.

Fig. 14
figure 12

Relationship between UA-value and the change of the exhaust air temperature and frost volume in kg

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The results from the parametric study of exhaust air entering are plotted in Fig. 15. The line chart and the bar chart, which shares the x axes, presented exhaust air leaving temperature and frost in kilograms, respectively.

Fig. 15
figure 13

Relationship between exhaust air entering and the change of the exhaust air temperature and frost volume in kg

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The results from the parametric study of air flow is plotted in Fig. 16. The line chart and the stacked bar chart, which shares the x axes, reveals heat exchanger efficiency and frost and condensation in kilograms, respectively.

Fig. 16
figure 14

Effect of different air flows on volume of condensation and frost and heat exchanger efficiency

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When the grid detail level is at its minimum, 10 × 10, the amount of frost is at its highest. Increasing the grid detail level results in a drop of the amount of frost without lowering exhaust air leaving temperature significantly. When the grid detail level reaches 40 × 40, the drop of the amount of frost stabilizes until the grid detail level is increased to 100 × 100. After that an insignificantly small effect to frost formation is noticed.

Changing UA-value affects the efficiency of the heat exchanger. Increasing it results in a higher risk of frost formation and lower exhaust air temperature. At the UA-value of 0.19 the efficiency is around 80%. This UA-value is selected as the size of the heat exchanger of this study.

The amount of frost formation is not significantly affected by the changes in temperature of exhaust air entering.

When increasing the air flow up to 1.1, the amount of frost also increases while the amount of condensation decreases. When the air flow becomes 1.1 and higher, the amount of frost starts to decrease, and condensation disappears. Efficiency is at its highest when the air flow is 0.35 l/(s·m2). Increasing the airflow decreases efficiency.

3.4.3 Comparison of different heat recovery ventilation-models

In Fig. 17 hours at risk of frost formation, grouped by the city, are presented for the estimation using the transient simplified sensible heat recovery ventilation model, transient simplified total heat recovery ventilation model and transient detailed sensible heat recovery ventilation model respectively.

Fig. 17
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Hours at risk of frost formation, grouped by the city, estimated using transient simplified sensible heat recovery ventilation model (A), transient simplified total heat recovery ventilation model (B) and transient detailed sensible heat recovery ventilation model (C)

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Every cities’ boxplot in Fig. 17 represents 36 data points, one data point represents one apartment, and one point represent total amount of hours when there is risk for frost to be formed. Box plots show the five-number summary of a set of data including the minimum score, first (lower) quartile, median, third (upper) quartile, outliers (circle) and maximum score [21].

For the transient simplified sensible heat recovery ventilation model, the heat recovery system has the lowest risk of frost formation when it is placed in Copenhagen, having the maximum of 490 h of frost per year. The highest risk of frost formation is in Kiruna with the maximum of 3650 h of frost per year. Majority of data points from Copenhagen, Gothenburg and Karlstad are below 500 h of frost per year, putting them in the same category. There are a few outliers in every city with a higher risk of frost formation. Even though Copenhagen and Gothenburg has relatively warm weather conditions, HRV still has a risk of frost formation. Even though the highest instances are solitary and much higher than the majority of data points, they must be covered by the frost protection systems.

For the transient simplified total heat recovery ventilation model, the energy recovery system has the lowest risk of frost formation when it is placed in Copenhagen, having the maximum of 260 h of frost per year, with many data points at zero hours of frost per year. The highest risk of frost formation is in Kiruna with the maximum of 2400 h of frost per year. Majority of data points from Copenhagen, Gothenburg, Östersund, Karlstad and Stockholm are between zero and 250 h of frost per year, putting them in the same category.

Risk of frost formation becomes significantly lower in every city when HRV is changed into ERV. Kiruna remains the city with the highest risk of frost formation. However, with ERV instead of HRV it reaches the same level of frost formation risk as Copenhagen and Gothenburg (the cities with the lowest risk with HRV) does with HRV instead of ERV.

For the transient detailed sensible heat recovery ventilation model, the heat recovery system has the lowest risk of frost formation when it is placed in Copenhagen, having the maximum of 600 h of frost per year. The highest risk of frost formation is again in Kiruna with the maximum of 4850 h of frost per year. Copenhagen is the only city with majority of data points below 500.

The detailed model uncovered many hours of risk of frost formation that are not included in the simplified model. As a result, there is a more distinct difference between the cities and much higher risk of frost formation in every city overall. The outliers become much closer to the majority of data points, compared to the simplified model.

3.5 Frost protection strategies

Different frost protection strategies with bypass or pre-heating of the ventilation supply air are examined using the calculation model and simulating Kiruna weather conditions. In Fig. 18 energy recovered and energy use for heating and pre-heating of the supply ventilation air are presented for different strategies.

Fig. 18
figure 16

Energy use and saving by different frost perfection strategy. 100% by-pass is not included in the picture as it would only increase the energy use needed to supply and buy heat to the ventilation system

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Bypass strategies, while effective at eliminating the risk of frost in heat recovery unit, are not performing as well from energy perspective. The red and blue parts in Fig. 17, representing the energy needed to buy and supply heat to the air, should be small from an energy perspective. The more air is by-passed, the fewer the opportunities are to recover energy from exhaust air, leading to lower supply air temperatures, thus higher energy need for heating a living space. The system without a bypass damper performed the best in regard to total energy use (energy for heating plus Energy to preheat incoming air).

3.6 Overall discussion

The first objective to get representative data on moisture generation in residential buildings and analyze selected indoor and outdoor conditions is reached. Measurements of relative humidities and temperatures were performed in 36 apartments and should be plausible representative for residential buildings. Expressed as indoor vapor content minus outdoor vapor content, the total average of the 36 apartments was 1.6 g/m3 at 0 °C outdoor temperature compared with 1.9 g/m3 for a material with 81 apartments with mechanical ventilation in three cities in Sweden (not yet published) or 2.1 g/m3 winter time in 325 apartments with mechanical ventilation [22, 23] measured difference between indoor and outdoor vapor content in 100 bedrooms and 79 living room in 101 single family detached houses during 2002 and 2004. During periods with outdoor temperatures at or below 5 °C, the average moisture supply was 1.8 g/m3. Moisture supply figures of up to 4 g/m3 are given for use in moisture design of dwellings in Sweden [9], but should include a margin also for naturally ventilated buildings. The measured apartments may have been slightly drier than the references’ results show, but still, the difference is small.

In this study, the moisture generation found in one building is used together with outdoor climate data from other cities. The studies above indicate that this method can be used since the moisture generation is rather. There is a relation to the outdoor temperature, which means that moisture generation in Kiruna may be higher than the measured one in this study. Contradictory to this, [23] found lowest moisture generation out of four cities in Kiruna, which is the most northern city.

The part of the analysis, that can be found in the Sect. 3.1 led to conclusion that the risk for the frost in the heat exchanger was highest in Kiruna and then Östersund due low outdoor air temperatures during the winter. This is expected since Kiruna is the coldest city and it is generally known (unpublished) from interviews with HVAC companies in Kiruna that freezing in heat recovery ventilation is a substantial problem that must be managed and takes time.

The other part of the analysis that can be found in the Sect. 3.3 led to the conclusion that the moisture supply was unevenly occurring within building’s apartments, suggesting that the moisture load in a heat exchanger could be reduced by having less, but bigger heat exchangers that gather exhaust air streams from several apartments at once. Another very important aspects of this is that different residential units will give very different efficiency of the heat recovery if actual frosting is taken into account depending on the very varying moisture load in different apartments as well as over time. Thus, there is a need for statistical approach, and, for example, an apartment air handling unit with heat recovery must handle the worst apartment, since it is not generally an option for the designer or constructor to choice what inhabitant will move into which apartment. This need for a statistical and not deterministic approach has been analyzed regarding energy use and power need [24, 25].

The second objective, to propose a reasonable simulation model, is reached. In the process, which is described in Sects. 3.2 to 3.3, several increasingly detailed and sophisticated frost simulation models are built: the simplified simulation models, the detailed model that enables to analyze frost accumulation across cross section area of square shaped plate heat exchangers, and, in the final version of the model, the additional calculations were added to include the condensation effect. Including the condensation effect in the detailed model made a big difference to the results. The final model was proven to be worthy to use in further investigations, due to results that more accurately represent real world conditions. What is also shown is that the condensation effect means that knowledge of the moisture conditions of the entering exhaust air is important information to take into account in software used in practice. Two very used software by consultants in Sweden to design for proper energy use are IDA ICE [26] and VIP Energy [27] and they don’t take this into account which means that there is a potential for developing knowledge and software.

The third objective, to discuss and investigate risk of frost formation and different frost protection strategies, is reached. The final detailed model, which is discussed in Sect. 3.3, resulted in decreasing the amount of condensation and frost, compared to the simplified model. This happened because the detailed model revealed that frost occurs not uniformly across the cross section but starting in the cold corner and where exhaust air and supply air cross each other. Running the transient simulation models, that are discussed in the Sects. 3.4, shows that even though Copenhagen and Gothenburg has relatively warm weather conditions, heat recovery systems still has a risk of frost formation. Risk of frost formation becomes significantly lower in every city when heat recovery ventilation is changed into energy recovery ventilation. Even though heat recovery ventilation is simulated only with the simplified model, it is safe to assume that it will still be effective in reality. Although bypass strategies, which are discussed in the Sect. 3.5, are effective at eliminating the risk of frost in heat recovery unit, they are not as efficient from an energy perspective. The more air by-passes the cross-flow plate heat exchanger, the fewer opportunities there are to recover energy from exhaust air, which leads to lower supply air temperatures and higher energy need for heating a living space. To pre-heat the ventilation supply air shows to be more effective. This implies, however, that both a pre and post heater may be required increasing costs and space of the equipment.

The figures given on efficiencies of heat recovery ventilation may well be valid in non-frosting conditions, but in frosting conditions they will not. Figure 17 indicates a simulated efficiency far lower than the more than 80% given in catalogues etc., which is also expected [3,4,5,6,7,8]. Particularly when the outdoor temperature is low, a high efficiency would be most useful, which means that the maximum power saving with heat recovery ventilation will not be as high as the energy saving. In practice it is also common to design the power and the energy supply components for a case without heat recovery, and with a proper frost protection system this should be able to be avoided.

Analyze different frost protection strategies further, both in simulations and practice, design a detailed model for enthalpy wheels with their influence on the indoor relative humidity and design different shapes of cross flow heat exchanger are topics that are suggested as possible further academic work and implementing better calculations of the heat recovery unit is needed in practice. A special case of frost protection is to pre heat the air by help of the ground, through liquid loops and a heat exchanger or directly with air ducts in the ground, but the last strategy must be designed with moisture and mold risks in mind. Worth to note is also that the Kiruna outdoor climate is rather warm compared to many other places in the North. Other future work may be to analyze in what types of buildings frost protection actually may be neglected.

4 Conclusions

The practical software used in business are shown to often be too simple to cover an analysis of the frosting problem in heat recovery ventilation and in turn give a plausible value of the energy use for heating the ventilation air, and in good low energy housing this will be substantial also for the total energy use. A more complicated approach taking into account condensation and the moisture generation in the residential buildings is needed to increase the precision of energy and power simulations. Also variations of moisture load over time as well as between different residential units must be considered.

To use a model that takes into account frost and condensation helps with the precision of predictive simulations. For example for ERV, the recovered heat increases by 33% by taking condensation into account. Connecting several apartments to one bigger air handling unit also lowers the risk of frost by excluding extreme situations. For example, in Kiruna in northern Sweden, the number of frost formation hours goes from 485 to 350 while the frost formation mass goes from 885 to 280 kg by combining 36 apartments. For the HRV there can be up to 4400 h of frost formation in northern Sweden while it can be down to 300 h in the south, pointing out that this problem has a quantitatively high influence on the recovered energy in the north. Also the measurements support that even with almost zero moisture added, there will be frost if it is cold outside.

The fact that frost occurs, as is shown in this study, but also shown in practice, means that a frost protection system is a must, at least in residential buildings, even in south Swedish outdoor climate. The energy calculations may not differ much in south Sweden compared to the actual outcome, but the maximum power need will differ more, and the practical air handling units must incorporate working frost protection systems to avoid freeze ups.

Having frost protection systems that can detect if there really is frost and not just low temperatures can save energy and at times power. There is a variation between different apartments’ moisture generation that means that a central air handling unit serving several apartments lower the draw back from frost protection.