Optimal ventilation of an apartment: where should you place your fan?

The problem

During a heatwave, the temperature in many apartments becomes difficult to bear, especially in homes with few openings. As soon as the outside air becomes cooler than the indoor air, a favorable period opens up: the goal is to evacuate the heat stored in the air and, more slowly, in the walls.

Methods and opinions differ for the next steps. Is it better to open wide and let natural convection take effect? Place a fan in front of the window to expel the hot air? Turn it around to let in fresh air? Or move it away so that its suction draws in a larger volume of air?

These actions seem intuitive, but their effects are less obvious than they appear. A high speed in front of the window does not mean that the entire dwelling is better renewed. To differentiate these strategies, SIL3X has constructed a progressive case study, from a simple thermal model to a three-dimensional CFD simulation.

What phenomenon is responsible for the flow?

Temperature alters the density of air

At pressures close to atmospheric pressure, warm air is slightly less dense than cold air. Under the influence of gravity, it tends to rise while the cooler, denser air tends to sink. When the apartment is warmer than the outside, this difference creates a pressure imbalance at the height of the window and naturally sets the air in motion, even in the absence of wind. This mechanism is the origin of natural convection.

The opening serves as both an entry and an exit

Although the case study has only one opening, when the inside is warmer than the outside, the pressure profiles cross at a neutral height from the window. Below, the cool air enters; above, the warm air exits. Saying that "the lower half draws in and the upper half expels" is a good mental image, but the neutral height depends on the temperature difference, stratification, and pressure losses.

By noting 𝐧 as the outward-oriented normal, the incoming and outgoing flows can be significant while almost compensating each other in a steady state.

What the fan brings

A desk fan draws in the surrounding air beyond the disc of its blades. Its position and orientation therefore influence the overall circulation. If placed too close to the opening and poorly aligned, it can create a short circuit : the cool air enters, is immediately taken by the fan and expelled outside without having passed through the room.

An effective placement must promote circulation on a volume scale: the warm air from the distant areas is brought towards the window, while the incoming cool air reaches the occupied areas before exiting. Therefore, the local speed in front of the window is not sufficient to judge the effectiveness of the sweep.

A two-level approach

Modelica: order of magnitude

Before embarking on a CFD simulation, using a 0D/1D model allows for checking the orders of magnitude. The air in the apartment is represented by a perfectly mixed volume. The TAeZoSysPro library [1], co-developed by SIL3X and EDF R&D, is used. The exchange with the outside is modelled by an opening [2]. The walls are modelled by thermal capacities and resistances. In this model, no ventilation is present and there is no wind.

Figure 1 : View of the 0D model with the thermal capacity of air, walls and opening for exchange with the outside.

The energy balance of the air is written as:

Figure 2 shows the evolution of temperatures over time, in blue the air temperature inside the room, in orange the temperature on the surface of the walls and in dashed lines, the imposed outside temperature. In the case of the 0D model, only an average temperature is evaluated on the room side, and not a local temperature. This amounts to considering the volume of the room perfectly mixed at all times, that is to say considering internal mixing in the room. Even with a significant flow rate, the walls, ceiling and floor continue to release the heat stored during the day. The characteristic time for air renewal is τ_air ≈ V/Q, but the actual inertia is greater as soon as the envelope is taken into account. The temperature on the surface of the walls decreases much less rapidly than the indoor air temperature. In reality, a human would perceive a felt temperature with a value between the average air temperature and the temperature of the walls that would exchange with the human body by radiation.

In order to best approach local phenomena, it is necessary to move to 3D. 

Code_Saturne : three-dimensional flows

The second level is based on Code_Saturne 9.2 [3]. Unlike the 0D model, the CFD solves in each cell the conservation of mass, momentum and energy, simultaneously tracking temperature, velocity and flow through the window. This tool allows for taking into account changes in topology within the air volume as well as the heterogeneity of temperatures, velocities, pressure...

The apartment measures 8 × 3.5 × 3 m, which is 84 m³. It has a single window of 1.40 × 1.40 m on x = 0, as well as three interior walls, the detailed configuration is represented in Figure 3.

Figure 3: 3D geometry of the apartment and aerodynamic domain.

An external mesh domain allows air to enter or exit freely; in the case of air return, the outside temperature is set to 22 °C. The potential temperature is initialized to 30 °C in the apartment and solids, compared to 22 °C outside. Three cases are monitored for 3,600 s; the case "high close extraction" stops at 2,700 s.

Table 1: Numerical parameters of the CFD study.

Representation of the fan

The modelled fan is a Rowenta VU2730F0, with a diameter of 0.30 m and a manufacturer's free flow rate of 0.75 m³/s, which is 2,700 m³/h. Code_Saturne represents it as a cylindrical volume zone with a radius of 0.16 m, featuring blades with a radius of 0.145 m and a hub with a radius of 0.035 m.

The actual flow rate results from the operating point between this curve and the system pressure drop: the manufacturer's free flow rate is therefore not imposed in the room.

All tested cases direct the flow towards the window, thus towards the outside. The blowing, fan turned towards the inside, was not simulated: the study does not allow for classifying extraction and blowing.

The four compared cases

All cases share the same mesh, the same numerical settings and the same treatment of the external floor. Only the presence of the fan, its height and its distance from the window vary. The different configurations are detailed in Table 2.

Table 2: details of the different configurations retained as well as the averaged results.

How to interpret the results?

The average air temperature is the first indicator, but it is not enough. The analysis retains four quantities :

1. Average temperature in the indoor volume.
2. Incoming debit converted to ACH renewal rate.
3. Temperatures at the probes — bottom and top of the window, centre and top of the room — to assess stratification.
4. to the probes near the window — positive sign: entry; negative sign: exit.

Five point probes are placed at (0.5 ; 2.5 ; 1.5) m and (0.5 ; 2.5 ; 2.5) m near the window, (4.0 ; 1.75 ; 1.5) m at the centre, (4.0 ; 1.75 ; 2.7) m at the upper part and (−0.5 ; 2.5 ; 2.0) m outside. These point velocities complement the surface flow balance; they do not replace it.

The renewal rate is the average incoming flow over the last moments of the simulation, converted to volumetric flow and then related to a volume of 84 m³. It describes the amount of air exchanged, but not on its own the quality of the sweep.

Results

Overall comparison

All cases show two phases: a rapid drop in temperature in the first 10 minutes, followed by a slowdown. The fans close to the window stand out after 15 minutes, with about 25.5 °C compared to 27.4 °C for the reference. The curve "high close extraction" stops at 45 minutes and is not extrapolated to 60 minutes.

Reference case: window only

In the reference case, in the absence of a fan, it is possible to compare the average temperature in the volume to that obtained using the 0D approach. Figure 6 shows the evolution of the average temperature for the CFD model (dashed blue line) and the air temperature for the 0D model (solid blue line). 

Figure 6 : Comparison of the temperature evolution between the 0D case and the CFD case in the absence of a fan.

The dynamics and the temperature difference between the two models are close despite a complex internal geometry that is difficult to capture in 0D. The air temperature is underestimated by the 0D model, which was expected as the 0D model assumes that the air is mixed at all times, whereas the CFD case shows a temperature heterogeneity, as reported in Table 3.

Table 3 : average temperature in the room and at the edges of the window at different times. 

Figure 7 : temperature field in the absence of ventilation.

The opening alone creates a bidirectional exchange: fresh air at the bottom and warm air at the top. The room remains stratified, with a 1.4 °C difference between the top of the room and the bottom of the window after 30 minutes. After 60 minutes, the average air is still 5 °C above the outside: the nocturnal balance has not been reached.

With fan: placement takes precedence over flow rate

Table 4 : comparisons of the final state of the different CFD cases.

The two fans near the window multiply the flow by about six, nearly 2,400 m³/h, and lower the temperature by an additional 1.7 to 1.8 °C compared to the reference at the same moment. The difference of 0.1 °C between the high and low positions is too small to classify them solidly. The fan at the back of the room, despite an ACH close to 20 vol/h, only gains 0.4 °C: a high flow at the window does not guarantee better overall cooling.

The following visualisation compares the three-dimensional evolution of temperature in the four configurations. The views use the same orientation and scale, ranging from 22 to 31 °C, in order to compare the progression of the fresh air, the persistence of the warm layer at the ceiling, and the level of homogenisation within the dwelling.

Without a fan, marked stratification persists: the cooler air gradually occupies the lower part while a warm layer remains under the ceiling. Fans placed near the window accelerate the cooling of a large part of the volume and further reduce this warm layer. In contrast, the fan placed at the back of the room produces significant mixing, but maintains a generally higher temperature. The comparison confirms that the flow at the window is not sufficient to characterise the effectiveness of the cooling: circulation must also promote a useful sweep of the entire dwelling.

It is interesting to compare again the average temperature evaluated in 0D to the overall average temperature for the 4 CFD cases. Figure 8 shows the evolution of the air temperature for the 0D model (solid blue line) in relation to the average temperatures of the different CFD cases. The CFD case with the fan at the back of the room (dashed purple line with x markers) is very close to the 0D curve. In this 3D case, the air inside the room is mixed by the fan, without increasing the flow at the opening. This results in a homogeneous temperature inside the room, which brings this case closer to the assumptions of the 0D case.

Figure 8: Comparison of the evolution of temperatures between the 0D case and the different CFD cases.

Jet, suction and local recirculation around the fan

The previous results show that a high flow rate at the window does not guarantee effective cooling on its own. To understand the influence of placement, we now observe the circulation directly created around the fan in the three configurations. We seek to determine where the drawn air comes from, how the jet reaches the window, and whether part of the air set in motion quickly returns to the device instead of contributing to a useful sweep of the room. Figure 9 compiles the field lines in steady state for the different cases. It is thus possible to identify any potential local recirculation and relate it to the measured thermal performances.

Figure 9: Streamlines for the different fan placements.

When the fan is close to the window, the rapid heart of the jet travels a short distance before exiting. Upstream, the blue lines show that the device draws in a larger volume of air from the room. The high position promotes the extraction of the layer of warm air located under the ceiling, while the low position forces an exit at the lower part of the opening and locally opposes the natural organisation of the exchange.

When the fan is placed at the back of the room, a narrow jet connects the device directly to the window, but many slow trajectories remain strongly curved and concentrated around its suction area. This arrangement suggests a local re-aspiration of part of the air set in motion and a less effective sweep of the space. It is consistent with the thermal result: despite a significant flow at the window, this configuration cools the apartment less effectively than the two positions close to the opening.

Structure of the exchange at the window

The pointwise normal component U_x, positive at the inlet and negative at the outlet, suggests different organisations:

Table 5: comparison of normal velocities at the opening, at the top and bottom of the opening.

High fan, close to window. The organisation is consistent with the natural movement: warm air is expelled at the top at 5.3 m/s and cool air enters at the bottom. The temperature reaches 25.4 °C at 45 minutes. However, the shorter duration prevents concluding that this placement is better than the low position.

Low fan, close to window. The thermal performance is almost identical, despite an inverted local pattern: the jet exits at the bottom of the window at 2.1 m/s. The two window probes are almost at the same temperature, but there remains a 1.5 °C difference between the bottom of the window and the top of the room.

High fan, at the back. The air becomes quite homogeneous, between 26.7 and 27.0 °C at the probes, but remains about 1.3 °C warmer than in configurations close to the window: homogeneity and cooling are not synonymous.

Probe temperatures at the end of calculation

Table 6: comparison of probe temperatures in steady state.

The fans near the window keep the four indoor probes between 24.6 and 26.1 °C. The 'room corner' case is the most uniform, but not the coolest: the spatial extent is an indicator of mixing, not a measure of thermal performance.

Discussion

Air temperature is only part of comfort

A fan also enhances the feeling of coolness through convection on the skin, regardless of the average air temperature. This study focuses on housing cooling and air renewal, not on a complete model of thermal comfort.

The walls hinder night-time cooling

Over the simulated 45 to 60 minutes, the interior walls remain close to 30–31 °C, while the air reaches 25–27 °C. Air has a low thermal capacity in front of the envelope: a night-time ventilation must last several hours to also cool, at least partially, the walls.

The reference is not a case of perfectly calm air

The Code_Saturne weather module generates about 0.9 m/s along the facade. The case without a fan therefore combines buoyancy and external flow; it does not represent pure natural convection. Absolute flows and neutral height could differ in truly calm weather.

The fan model remains simplified

The volumetric area and the curve Δp(Q) represent the average action of the fan, without detailed geometry of the blades. Only the extraction mode has been tested. The number of meshes, mesh independence and comparable cuts of temperature and streamlines are not documented here. The values should therefore be read as a comparison between four variants of the same model, and not as guaranteed universal performances.

Conclusion

In this simulated case, opening a single window already creates a significant air exchange: about 5 renewals per hour and −3.7 °C in 60 minutes. This exchange combines buoyancy and external flow; it remains bidirectional, with a low entry and a high exit, while the walls continue to release their heat.

The addition of a fan directed outward and placed about 1 m from the window significantly improves cooling: −5.1 °C in 45 minutes for the high position and −5.2 °C in 60 minutes for the low position, which is 1.7 to 1.8 °C gain compared to the reference at the same moment. The renewal is multiplied by about six. The available data do not allow for a distinction between the two heights; the high position simply follows the natural direction of the hot air exit.

Conversely, a fan at the back of the room only provides a 0.4 °C gain despite a flow rate four times higher than the reference. The decisive criterion is not "does it blow hard?", but "does the outside air actually traverse the entire volume before exiting?".

To go further

• Compare supply to extraction, not tested here.
• Study other distances, for example 0.5 m and 2 m, and other window geometries.
• Document mesh independence and compare CFD cuts at identical scales.
• Confront flow rates and temperatures with measurements in a real apartment.

References

[1] P. Borel, R. ulouel, F. Marsollier et A. Chupin, TAeZoSysPro: A Modelica Library for Thermal Aeraulic and Buildings Thermodynamics Calculations,  DOI 10.3384/ecp218293.

[1] M. W. Liddament, Air Infiltration Calculation Techniques – An Application Guide , AIVC, Coventry, EMPA Dübendorf, Haustechnik (1989)

EDF R&D, Code_Saturne 9.2 — Documentation utilisateur, code-saturne.org.

Rowenta, Turbo Silence Extreme+ VU2730F0, Ø 30 cm, débit libre constructeur 45 m³/min.