# Experimental characterization of the aeraulic behaviour of centrifugal fans in specific functioning modes and numerical comparisons with the SYLVIA code

Nicolas Le Roux

► To cite this version:

Nicolas Le Roux. Experimental characterization of the aeraulic behaviour of centrifugal fans in specific functioning modes and numerical comparisons with the SYLVIA code. The 17th ROOMVENT Conference (ROOMVENT 2024), Apr 2024, Stockholm, Sweden. pp.04003, 10.1051/e3sconf/202567204003. hal-05444744

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# Experimental characterization of the aeraulic behaviour of centrifugal fans in specific functioning modes and numerical comparisons with the SYLVIA code

Nicolas Le Roux¹*

¹Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PSN-RES/SCA/LEMAC, F-91400, Saclay, France

**Abstract.** The purpose of this paper is to present results obtained in the frame of the VentilSTAR program. This program has been carried out to perfect the modelling of fans in the SYLVIA code, developed by the French Institute for Radiological Protection and Nuclear Safety (IRSN) notably to simulate airflows in ventilation systems. The aeraulic behaviour of fans in normal functioning is well-known, but specific functioning modes could occur when fans are submitted to severe aeraulic conditions due to incidental or accidental cases. These modes correspond to turbine and reverse modes when negative values are reached for total head and airflow rate, respectively. For some ventilation modes, the fans can be stopped. To model these modes, transient behaviour during starting and stopping operations, as well as the behaviour of a stopped fan, must also be known. Thus, the objectives of the VentilSTAR program are to experimentally characterize the aeraulic behaviour of fans in these modes, to compare results with the numerical results of the SYLVIA code, and to propose improvements of the modelling of fans if needed.

## 1 Context and objectives

The experimental program VentilSTAR comes from a need of the French Institute for Radiological Protection and Nuclear Safety (IRSN) to perfect the modelling of fans in the SYLVIA code in some specific functioning modes. The SYLVIA code is a zonal code developed by IRSN and dedicated to the study of ventilation, fire and airborne contamination [1, 2, 3]. It notably enables to simulate ventilation system behaviour in case of thermal or mechanical situations, in terms of airflow rates, pressures, temperatures and concentrations (gas and aerosol). The ventilation modelling is based on representing the network with nodes and branches, for which the mass and energy conservation equations and the generalized Bernoulli equation are applied, respectively.

Fan functioning in normal conditions is well-known and is modelled in the SYLVIA code considering the fan curve, usually provided in the manufacturer's data sheets for several power supply frequencies, as illustrated on Fig. 1.

The aeraulic behaviour of a fan, in steady state, is given by the fan curve corresponding to the evolution of the total head (total difference pressure between the upstream node and the downstream node of the fan) as a function of the airflow rate through the fan.

As shown on Fig. 1, two specific functioning modes could occur when fans are submitted to severe aeraulic conditions due to incidental or accidental cases (rupture of a high pressure equipment or fire for example). These modes correspond to turbine and reverse modes when

negative values are reached for fan head and airflow rate, respectively. However, due to the lack of model, these modes are modelled considering extrapolation of the normal mode.

<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Fan curve for several power supply frequencies.</figcaption></figure>

In addition, in some ventilation regimes, fans can be stopped and must therefore be modelled as a resistant element to considerer their head losses. Until now, a quadratic law between pressure difference and airflow rate is proposed in the SYLVIA code to estimate the aeraulic resistance of the fan stopped. Note that the aeraulic resistance is the parameter defined in the SYLVIA code to characterize the head losses of resistant elements. A transient model also exists to simulate startup and shutdown operations. The law for stopped fan and the transient model are based on specific experiments on one fan and thus require more experimental validations.

The objectives of the VentilSTAR program are to experimentally characterize the aeraulic behaviour of

<footnote>* Corresponding author: nicolas.le-roux@irsn.fr</footnote>
fans in these modes, to compare results with the numerical results of the SYLVIA code, and to propose improvements of the modelling of fans if needed.

The program has been carried out according to the five following phases: normal (phase 1), turbine mode (phase 2), inverse mode (phase 3), stopped fan (phase 4), transient mode during startup and shutdown operations (phase 5).

First, the fans tested, the experimental bench set-up on STARMANIA facility and the metrology used are presented. Then, experimental results are detailed for each phase of the program and each fan tested. Results are compared with the current numerical models of the SYLVIA code and improvements are proposed if needed.

# 2 Methodology

## 2.1 Fans studied

Tests were conducted for three centrifugal fans. Centrifugal fans are generally considered in ventilation systems due to their ability to overcome head losses. A view of the three fans is given on Fig. 2, presented in descending order from left to right, in terms of size and nominal functioning points. These points are presented on paragraph 3.1 concerning the normal functioning mode.

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** View of the three centrifugal fans studied.</figcaption></figure>

The manufacturers are SOLYVENT for fan n°1 (left view), ASEA for fan n°2 (middle view) and DELTA NEU for fan n°3 (right view). In the following of this paper, fans are called by their number defined above.

## 2.2 Experimental bench

Experiments were carried out on the STARMANIA facility of IRSN, represented on Fig. 3, which is a specific bench for studying the behaviour of containment equipments outside of their normal use in case of accidental situation.

<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Schematic diagram of the STARMANIA facility.</figcaption></figure>

This bench is equipped with an aeraulic blower that can reach a wide range of airflow rates until 20 000 m³/h.

A view of the VentilSTAR bench is presented on Fig. 4 for the fan n°1. This one is made up of the fan studied connected to the STARMANIA facility with a straight upstream duct and a straight downstream duct followed by a flexible duct. The bench, and notably the straight ducts, have been designed according to the EN ISO 5801 standard relating to the performance testing of industrial fans using standardized airways [4].

<figure><img src="image_5.png" /><figcaption>**Fig. 4.** View of the VentilSTAR bench set on the STARMANIA facility for fan n°1.</figcaption></figure>

## 2.3 Metrology

The measured values are the fan power supply frequency *f* (Hz), the rotation speed of the fan blades *ω* (rpm), the static pressure drop of the fan *ΔP* (Pa) (pressure difference between upstream and downstream of the fan) and the airflow rates *Q* (m³/h) passing through the fan.

The fan power supply frequency *f* is measured on the frequency converter, the value of which is also controlled. Thus, this measure is only a check of the controlled value. Concerning the blades rotation speed *ω*, this one is measured by an optical tachymeter set up on the fan studied.

The pressure difference $\Delta P$ is measured using differential pressure sensors chosen according to the range needed, the uncertainty of which is equal to 1 %. Upstream and downstream measurement sections are defined according to the EN ISO 5801 standard [4] to avoid improper values due to airflow heterogeneity. In addition, spatial mean values of pressure are measured, using a system of four sampling tubes, for each section, connected to one of the sensor terminals.

The airflow rates *Q* are mainly measured using the ultrasonic flowmeter or the Annubar pitot tube flowmeter located on the STARMANIA facility (Fig. 3). In addition, for low values of airflow rates notably for fan n°2 and n°3, a specific Annubar Pitot tube flowmeter was installed directly on the VentilSTAR bench. The uncertainty on those values depends on the sensor (about 10 % max.) and are represented by error bars on graphs given in the following chapter.

A LabVIEW program was developed to acquire all the measured signals and to control the power supply frequency. The signal acquisition frequency is set at 2 Hz. For the phases studied in steady states (phase 1 to 4), values are averaged over a duration of 30 seconds
and standard deviations are integrated into the uncertainty calculation.

## 3 Results

Results obtained are given in the paragraphs 3.1 to 3.5 for the five phases of the VentilSTAR program: normal, reversal and inverse modes, stopped fan, transient mode during startup and shutdown operations. Due to the pages limitation and to discuss all the main conclusions of the VentilSTAR program, results are not presented for each fan in case of similar results between fans.

### 3.1 Phase 1: normal functioning mode

The first phase consists in determining the fan curves in the normal functioning mode, corresponding to the quadrant for positive values of pressure drop and airflow rates (Fig. 1). These curves are generally known and provided in the manufacturer's data sheets.

Knowing that similar results have been obtained for the three fans, an example of results is only given for fan n°1 on Fig. 5. The top graph presents the measured values of (Q; ΔP) couples for five supply frequencies from 10 to 50 Hz. As it is commonly done for centrifugal fans, a second order polynomial regression is considered for each frequency to describe the behaviour law between the difference pressure ΔP and the airflow rate Q; regression coefficients higher than 0.98 are obtained. The bottom graph shows that the rotation speed can be considered as constant for each frequency. Small decreases of the rotation speed with the increasement of airflow rates are identified, but deviations are less than 6 % and thus are negligible on view of the EN ISO 5801 standard [4].

<figure><img src="image_6.png" /><figcaption>Fig. 5. Fan curves in normal mode for fan n°1 ((Q; ΔP) on the top graph and (Q; ω) on the bottom graph).</figcaption></figure>

Considering that rotation speed is constant, mean values can be calculated for each frequency and the theoretical similarity laws given by Equations (1) to (3) can be applied from one operating frequency to another one [4].

$$ \frac{\omega}{\omega_0} = \frac{f}{f_0} \qquad (1) $$

$$ \frac{Q}{Q_0} = \frac{\omega}{\omega_0} \qquad (2) $$

$$ \frac{\Delta P}{\Delta P_0} = \left(\frac{\omega}{\omega_0}\right)^2 \qquad (3) $$

For each fan, similarity laws have been applied to transpose measured values obtained for each frequency at the rotation speed obtained for 50 Hz. Fig. 6 presents the corresponding curves for fan n°1.

<figure><img src="image_7.png" /><figcaption>Fig. 6. Curves of fan n°1 in normal mode transposed to the rotation speed of 2929 rpm (f = 50 Hz).</figcaption></figure>

A polynomial regression given by Equation (4) can be defined to model the aeraulic behaviour of fans in normal mode (the regression coefficient r² is higher than 0.98 for each fan).

$$ \Delta P = a \cdot Q^2 + b \cdot \omega \cdot Q + c \cdot \omega^2 \qquad (4) $$

The polynomial coefficients and the mean speed rotations for a frequency of 50 Hz are given on Table 1 for the three fans.

<table><caption>Table 1. Mean speed rotations at 50 Hz and polynomial coefficients for the three fans.</caption><thead><tr><th>Fan</th><th>ω<sub>50Hz</sub> (rpm)</th><th>a (-)</th><th>b (-)</th><th>c (-)</th></tr></thead><tbody><tr><td>n°1</td><td>2929</td><td>-4.5 10<sup>-5</sup></td><td>6.6 10<sup>-5</sup></td><td>5.5 10<sup>-4</sup></td></tr><tr><td>n°2</td><td>2958</td><td>-7.3 10<sup>-4</sup></td><td>5.2 10<sup>-4</sup></td><td>6.6 10<sup>-4</sup></td></tr><tr><td>n°3</td><td>2907</td><td>-1.6 10<sup>-3</sup></td><td>2.4 10<sup>-4</sup></td><td>1.4 10<sup>-4</sup></td></tr></tbody></table>

### 3.2 Phase 2: turbine mode

For turbine mode, the aeraulic blower of STARMANIA was used to generate overflows through the fan studied. The aeraulic blower and control dampers were adjusted to measure several (Q; ΔP) couples from the normal mode until the turbine mode corresponding to the quadrant for Q > 0 and ΔP < 0 (Fig.1).

As for the phase 1, measures have been done for several frequencies and similar results have been obtained for the three fans. Fig. 7 presents the measured values of (Q; ΔP) couples on the top graph and (Q; ω) couples on the bottom graph, obtained for four supply frequencies from 10 to 40 Hz on fan n°1. The polynomial model defined in paragraph 3.1 is also presented in dashed line on the top graph and the (Q; ω) couples measured in normal mode are displayed with grey marks on the bottom graph.

Note that experiments with a supply frequency of 50 Hz could not be done for fan n°1, due to an electrical
overload of the frequency converter for high values of ($Q$; $ΔP$) couples (for this same reason, fan curve in normal mode has not completely been determined at 50 Hz as shown on Fig. 5).

<figure><img src="image_8.png" /><figcaption>**Fig. 7.** Measurements in turbine mode for fan n°1 ($Q$; $ΔP$) on the top graph and ($Q$; $ω$) on the bottom graph).</figcaption></figure>

Fig. 7 shows that, for small overflows generated by STARMANIA, measured values are not in the turbine quadrant but are similar to those obtained in normal mode. Then, ($Q$; $ΔP$) couples seem to follow the polynomial regression defined in normal mode, even if a slight increase of ($Q$; $ΔP$) values are identified for 30 and 40 Hz. Note that this phenomenon has not been identified for fan n°2 and n°3.

Concerning the rotation speeds, even if values slightly decrease for $ΔP > 0$ and increase for $ΔP < 0$, deviations are less than 8 % and can be considered as constant.

Thus, as for normal mode, similarity laws given by Equations (1) to (3) have been applied to transpose values obtained for each rotation speed to the rotation speed corresponding to a frequency of 50 Hz. Results are given on Fig. 8 to Fig. 10 for the three fans. The polynomial model, determined in normal mode, is extrapolated to cover the range of measurements in turbine mode (solid line). A linear extrapolation is also presented in dashed line and corresponds to the law considered in the SYLVIA code to model the turbine mode, before the VentilSTAR program (this linear extrapolation is determined from the two last points of the nominal fan curve).

<figure><img src="image_9.png" /><figcaption>**Fig. 8.** Curves of fan n°1 in turbine mode transposed to the rotation speed of 2929 rpm ($f = 50$ Hz).</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 9.** Curves of fan n°2 in turbine mode transposed to the rotation speed of 2958 rpm ($f = 50$ Hz).</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 10.** Curves of fan n°3 in turbine mode transposed to the rotation speed of 2907 rpm ($f = 50$ Hz).</figcaption></figure>

Thus, results presented on Fig. 8 to Fig. 10 lead to the conclusion that extrapolation of the polynomial model obtained in normal mode should be considered to accurately model the turbine mode, instead of the linear extrapolation considered until now (regression coefficients higher than 0.98 have been obtained with the polynomial models). Modifications are currently in progress in the SYLVIA code to considerer the extrapolation proposed.

## 3.3 Phase 3: reverse mode

For reverse mode, the aeraulic blower of STARMANIA was used to generate reversal flows through the fan studied. To do this, specific isolation valves on STARMANIA were opened or closed to inverse the direction of airflow entering the test bench (Fig. 3). Then, the aeraulic blower and control dampers were adjusted to measure several couples ($Q$; $ΔP$) in the reverse mode corresponding to the quadrant for $Q < 0$ and $ΔP > 0$ (Fig. 1).

Experimental results obtained for the three fans are discussed for this mode, because different behaviours have been identified, notably for the rotation speeds. ($Q$; $ω$) couples obtained for the reverse mode are presented on Fig. 11 for the three fans. Values measured for the normal mode are also presented on these graphs (gray symbols).

For fan n°1, the first graph of Fig. 11 shows that the rotation speed decreases with the increase of the reversal airflow rate, notably for tests at 10 Hz for which deviations are about 34 %. However, fan blades are still rotating in the normal direction. For tests performed from 20 to 50 Hz, deviations are less than 5 % meaning that rotation speed can be considered as constant. In addition, mean speed rotations for each frequency are
quite similar in normal and reverse modes. For fan n°2, results are almost like those obtained for fan n°1. A slight decrease of the rotation speed is observed with the increase of the reversal airflow rate.

<figure><img src="image_12.png" /><figcaption>**Fig. 11.** ($Q$; $\omega$) couples in reverse and normal modes (fan n°1 on the top graph, fan n°2 on the middle graph, fan n°3 on the bottom graph).</figcaption></figure>

For fan n°3, rotation direction reversals of the fan blades have been highlighted when the airflow rates generated by the aeraulic blower of STARMANIA in the opposite direction exceed a threshold value. This one increases with increasing power supply frequency, which explains why this phenomenon has not been identified at 50 Hz. For the same reason, these reversals are obtained only for fan n°3 because this one is the least powerful in terms of functioning fan curve. Similar phenomena would probably occur with higher reversal flows generated by STARMANIA through the two other fans. These tests could not be carried out for reasons of resistance of the frequency converter (overheating, safety shutdown). Thus, for fan n°3, rotation speeds could not be considered as constant and similarity laws are no more valid when rotation direction reversal occurs.

Because of this discontinuity behaviour, ($Q$; $\Delta P$) couples measured for fan n°3 can no longer be modelled by a single polynomial law, contrary to ($Q$; $\Delta P$) couples measured for fan n°1 and n°2. These results are presented on Fig. 12. For fan n°3, values corresponding to rotation direction reversals of the fan blades are represented by symbols with no filled colour.

<figure><img src="image_13.png" /><figcaption>**Fig. 12.** ($\Delta P$; $Q$) couples measured in reverse mode and polynomial model defined in normal mode (fan n°1 on the top graph, fan n°2 on the middle graph, fan n°3 on the bottom graph).</figcaption></figure>

Fig. 12 shows that the behaviour obtained in reverse mode for fan n°3 is discontinuous and disparate from a power supply frequency to another one. For fan n°1 and n°2, behaviour is continuous for each supply frequency and seems to be similar from one power supply frequency to another one, which is logical considering that rotation speed is constant and thus similarity laws can be applied. To check this, results have been transposed to the rotation speed given on Table 1 corresponding to 50 Hz as for normal and turbine modes. The corresponding graphs are presented on Fig. 13 to Fig. 15.

<figure><img src="image_14.png" /><figcaption>**Fig. 13.** Curves of fan n°1 in reverse mode transposed to the rotation speed of 2929 rpm ($f = 50$ Hz).</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Fig. 14. Curves of fan n°2 in reverse mode transposed to the rotation speed of 2958 rpm (f = 50 Hz).</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 15. Curves of fan n°3 in reverse mode transposed to the rotation speed of 2907 rpm (f = 50 Hz).</figcaption></figure>

On each graph, the polynomial model defined in normal mode and a polynomial extrapolation, considered on the SYLVIA code until now and defined from the normal curve to model the reverse mode, are presented in dashed line. These graphs show that the polynomial extrapolations do not fit with experimental values. To accurately model the reverse mode, a polynomial interpolation from experimental values have been defined for each fan. Note that, for fan n°3, the interpolation law has been calculated without considering values obtained in the cases of rotation direction reversals of the fan blades (symbols with no filled colour).

As for the normal mode, the polynomial model can be written by Equation (4) considering the coefficients given on Table 2 for the three fans (the regression coefficient r² is higher than 0.99 for each fan).

<table><caption>**Table 2.** Polynomial coefficients defined to model the reverse mode.</caption><thead><tr><th>Fan</th><th>a<sub>reverse</sub> (-)</th><th>b<sub>reverse</sub> (-)</th><th>c<sub>reverse</sub> (-)</th></tr></thead><tbody><tr><td>n°1</td><td>1.6 10<sup>-4</sup></td><td>-2.3 10<sup>-4</sup></td><td>6.3 10<sup>-4</sup></td></tr><tr><td>n°2</td><td>1.9 10<sup>-3</sup></td><td>-5.0 10<sup>-4</sup></td><td>1.4 10<sup>-4</sup></td></tr><tr><td>n°3</td><td>1.2 10<sup>-3</sup></td><td>-9.5 10<sup>-5</sup></td><td>6.6 10<sup>-4</sup></td></tr></tbody></table>

Although it has been shown that fan behaviour can be modelled by a the well-known polynomial model given by Equation (4), the definition of the polynomial coefficients remains the main difficulty given that (Q; ΔP) values in this mode are generally not known. In addition, from experiments done in the VentilSTAR program, it has not been possible to define laws to link the polynomial coefficients in reverse mode with the ones in normal mode, due to the disparity of values between each fan. However, in the next version of the SYLVIA code, it will be possible to model the turbine

mode considering a polynomial model given by Equation (4) with coefficients defined by user.

### 3.4 Phase 4: stop mode

This phase concerns the characterization of the aeraulic behaviour of stopped fans. For these tests, the aeraulic blower of STARMANIA was used to generate airflows through the fan studied in stop mode. To do this, the aeraulic blower and control dampers were adjusted to measure several (ΔP; Q) couples, in the two airflow directions through the fan.

Given that almost similar experimental behaviour has been identified for the three fans, experimental results are only presented for fan n°1 on Fig. 16. First, these results show that aeraulic behaviour is not similar in the two airflow directions, which is logical due to the asymmetrical geometry of centrifugal fans.

The top graph of Fig. 16 shows that, beyond a value of airflow rate (about ± 500 m³/h depending on the airflow directions), the fan blades start rotating and the rotation speed ω is proportional to the airflow rate Q. The same discontinuity phenomenon has been also identified for fan n°2, even more significantly, around ± 500 m³/h depending on the airflow directions. This is not the case for fan n°3, the blades of which start immediately rotating. Thus, the rotation speed ω is proportional to the airflow rate Q in all the measurement range for fan n°3.

<figure><img src="image_17.png" /><figcaption>Fig. 16. Experimental characterization of fan n°1 in stop mode ((Q; ω) on the top graph and (Q; ΔP) on the bottom graph).</figcaption></figure>

On the bottom graph of Fig. 16, quadratic interpolations given by Equation (5) are considered, the definition of which corresponds to the RES_QUAD model used on the SYLVIA code for resistant elements with ρ the air density (kg.m⁻³) and R the aeraulic resistance (m⁻⁴).

$$ \Delta P = \rho \cdot R \cdot Q^2 \quad (5) $$

The values of aeraulic resistances calculated from Equation (5) for the three fans and the associated regression coefficients r² are given on Table 3. Ratio
between aeraulic resistances obtained in normal and reverse flow directions are also given.

In addition, values calculated from an empirical law, given by Equation (6) and recommended in the documentation of SYLVIA to have an estimation of the aeraulic resistance, are also presented.

$$R_{\text{law}} = \frac{9 \Delta P_{\text{normal}}}{10 \rho \cdot Q_{\text{normal}}^2} \quad (6)$$

This law depends on the normal functioning point of the fan. As an example and to compare experimental values with values calculated from Equation (6), ($Q_{normal}$; $\Delta P_{normal}$) couples have been chosen in the middle of the normal curve obtained at 50 Hz for each fan, by considering an airflow rate $Q_{normal}$ equal to half of the maximum airflow rate (this one is obtained for $\Delta P = 0$).

<table><caption>Table 3. Aeraulic resistances of stopped fans.</caption><thead><tr><th>Fan</th><th>R<sub>normal</sub><br>(m<sup>-4</sup>)</th><th>R<sub>reverse</sub><br>(m<sup>-4</sup>)</th><th>R<sub>reverse</sub>/<br>R<sub>normal</sub></th><th>R<sub>law</sub><br>(m<sup>-4</sup>)</th></tr></thead><tbody><tr><td>n°1</td><td>306<br>(r<sup>2</sup> = 0.998)</td><td>4 687<br>(r<sup>2</sup> = 0.987)</td><td>15.3</td><td>1023</td></tr><tr><td>n°2</td><td>4 378<br>(r<sup>2</sup> = 0.975)</td><td>11 766<br>(r<sup>2</sup> = 0.960)</td><td>2.7</td><td>13 900</td></tr><tr><td>n°3</td><td>13 988<br>(r<sup>2</sup> = 1.000)</td><td>244 831<br>(r<sup>2</sup> = 0.996)</td><td>17.5</td><td>34 796</td></tr></tbody></table>

Table 3 shows that aeraulic behaviour of fans in stop mode can be modelled by a quadratic law given by Equation (5) (note that the airflow rate $Q$ is expressed in $m^3/s$ in Equation (5)).

Although laws obtained for the three fans well fit the experimental values given the regression coefficient $r^2$, the quadratic interpolation is the most accurate for fan n°3 and less accurate for fan n°2. This can be explained by the discontinuity of the rotation speed behaviour with the airflow rate between the no rotation and the rotation of the fan blades beyond a threshold value of airflow rate. As it can be shown on the bottom graph of Fig. 16, ($Q$; $\Delta P$) values obtained for values around the start of the rotation do not perfectly match the fitting law.

In addition, the main difficulty remains the determination of an accurate value of aeraulic resistance without measured data or manufacturer data in stop mode. Values calculated from the recommended law given in SYLVIA, with hypothetic ($Q_{normal}$; $\Delta P_{normal}$) couples, do not correspond to experimental values. Moreover, the calculated value of aeraulic resistance can vary by several orders of magnitude depending on the ($Q_{normal}$; $\Delta P_{normal}$) couple chosen.

To have an estimation of the aeraulic resistance, it would be better to considerer the polynomial coefficients $a$ obtained in normal mode (Table 1) by calculating it as for the calculation of resistances (Equation (5)), i.e. with the airflow rate $Q$ in $m^3/s$, then divided it by the air density and finally take the absolute value. In other terms, this is equivalent to consider the classical polynomial Equation (7) with a rotation speed equal to zero and a change of the $\Delta P$ sign (due to the resistant behaviour instead of motor behaviour in

normal mode). In this way, values equal to $491 \text{ m}^{-4}$ for fan n°1, $7908 \text{ m}^{-4}$ for fan n°2, $17451 \text{ m}^{-4}$ for fan n°3 are obtained and allow us to find the orders of magnitude of the aeraulic resistance of stopped in the normal flow direction. Deviations can notably be explained by the rotation of the blades beyond a threshold value, although the values are calculated from the polynomial law considering $\omega = 0$.

Note that, due the resistances of all the other components of a ventilation network, an accurate determination of the aeraulic resistance of stopped fans is not necessary and an estimation as given above is satisfying.

Finally, Table 3 shows also that values of aeraulic resistances are largely higher in reverse mode than in normal mode. From these results, it can be defined that, to get an estimation of the order of magnitude of the aeraulic resistance in reverse mode, a value ten times greater than the value in normal mode can be considered.

## 3.5 Phase 5: startup and shutdown transient mode

This last phase consists in characterizing the transient behaviour of the fans during startup and shutdown sequences. To do this, ramp functions were considered for the power supply frequency, corresponding to linear variations from 0 to 50 Hz in 10, 15, 30 and 60 seconds for the startup phases (and inversely from 50 to 0 Hz for the shutdown phases).

Transient results obtained for the three fans are similar. Examples are given for the startup of fan n°3 on Fig. 17 and for the shutdown of fan n°2 on Fig. 18, both for a startup and shutdown duration of 30 seconds.

On each graph, results obtained with the ON_OFF model of the SYLVIA code are compared with experimental results. Note that, given results obtained on fan n°1, improvements have been already done on the SYLVIA code to properly simulate those transient phases, notably during the shutdown operations.

On the top graph, the supply frequency f and the rotation speed are expressed in a dimensionless form to be comparable to the ratio $\gamma$ of SYLVIA corresponding to the ratio between the temporal rotation speed $\omega$ and the normal rotation speed ($\omega_{50Hz}$ in this example). Graphs show that temporal evolutions obtained with SYLVIA are very close to the experimental results. The very low temporal deviation comes from the inertia of the blades but is negligible for a startup duration of 30 seconds. Similar conclusions have been obtained for a startup duration of 10 seconds, although the phase shift is lightly more significant. In addition, deviations obtained for low values of airflow rates come from the uncertainties of the flowmeter chosen to measure values until the fan is completely started.

As for the startup phase, the example of shutdown phase for fan n°2, given on Fig. 18, shows that numerical and experimental results are very close.
<figure><img src="image_18.png" /><figcaption>**Fig. 17.** Experimental and numerical transient behaviour of fan n°3 for a starting duration of 30 seconds (dimensionless frequency $f/f_{50Hz}$ and rotation speed $\omega/\omega_{50Hz}$ on the top graph, difference pressure $\Delta P$ on the middle graph and airflow rate $Q$ on the bottom graph).</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Fig. 18.** Experimental and numerical transient behaviour of fan n°2 for a shutdown duration of 30 seconds (dimensionless frequency $f/f_{50Hz}$ and rotation speed $\omega/\omega_{50Hz}$ on the top graph, difference pressure $\Delta P$ on the middle graph and airflow rate $Q$ on the bottom graph).</figcaption></figure>

Thus, from these tests carried out for startup and shutdown of fans, the ON_OFF model currently

implemented in SYLVIA has been validated. Note that a low phase shift can be identified, notably for short starting or shutdown durations (about 10 seconds), due to the inertia of the blades.

## 4 Conclusion

Experimental results obtained on three centrifugal fans have been presented and compared to the numerical results of the SYLVIA code to perform the modelling of fans, notably for specific functioning modes.

First, it has been confirmed that the normal functioning mode can be modelled by a second order polynomial equation, relating the pressure difference, the airflow rate and the speed rotation.

Then, it has been concluded that this polynomial model can be extrapolated to simulate the turbine mode.

Concerning the reverse mode, this one must also be modelled with a second order polynomial equation, the main difficulty of which remains the determination of the polynomial coefficients knowing that no values in reverse mode are usually known. From experimental results obtained on the three fans, no similar behaviour has been highlighted to link the normal functioning with the reverse functioning. However, the possibility of set up the polynomial coefficients in reverse mode will be proposed in the SYLVIA code. In addition, for high reverse airflow rates, it has been identified for the lower fan (fan n°3) that the functioning can be strongly modified due to the inversion of the blades rotation.

For the stop mode, it has been shown that aeraulic behaviour is different according to the airflow direction. For this reason, two aeraulic resistances values must be defined. The first one in the normal direction can be estimated from the polynomial coefficient $a$ of the normal functioning model. The second one in the reverse direction can be estimated considering a value ten times greater than the value in normal mode.

Finally, the ON_OFF model currently implemented in SYLVIA has been validated from these tests carried out for starting and shutdown of fans.

Note that thermal effects have not been experimentally studied. Fan modelling in the SYLVIA code considers the thermal variations, considering density variations calculated from the ideal gas law for weakly compressible flows.

## References

1. J-P. Joret, W. Plumecocq, SYLVIA – a software to study ventilation network, fire, and airborne contamination, submitted to RoomVent 2024

2. https://gforge.irsn.fr/api/docman/10258/binary/SYLVIA_english.pdf?version=latest

3. N. Le Roux, X. Faure, C. Inard, S. Soares, L. Ricciardi, *Reduced-scale study of wind influence on mean airflows inside buildings equipped with ventilation systems*, Building and Environment, 58:231-244 (2012)

4. *Fans - Performance testing using standardized airways*, EN ISO 5801 (2017)