A room fire creates temperature gradients and inhomogeneous time varying temperature, density, and flow fields. Experimental measurements of the room acoustic impulse/frequency response are presented and compared with a ray traced model. The results show that the fire causes wave-fronts to arrive earlier (due to the higher sound speed) and with more variation in the delay times (due to the sound speed perturbations). The frequency response shows that the modes are shifted up in frequency and high frequency (>2500 Hz) modes are significantly attenuated. Model results are compared with data and show good agreement in observed trends.

## 1. Introduction

The personal alert safety system (PASS) is a device carried by firefighters, mounted on their self-contained breathing apparatus. The device detects motion and emits an alarm sound if the firefighter has been stationary for too long (NFPA, 2007). Firefighters rely on the PASS alarm to alert others if they need to be rescued. Rescuers can follow the alarm sound to the source and extricate the downed firefighter.

The acoustic environment in a room fire is not well understood. Previous work on flames and acoustics has been focused on combustion efficiency (Cho, 2006; Narra, 2008), due to the impact of standing wave modes on turbine combustion. Other work has focused on acoustic scattering from flames and the impact of a fire on active sonar (Abbasi, 2013). This work aims to lay the groundwork for understanding the acoustic environment in a room with a fire present, in a manner similar to how the underwater acoustic environment is studied.

## 2. Environment in a room fire

At its simplest, a fire is an exothermic combustion reaction between fuel and oxygen, releasing heat and chemical byproducts. We will assume that the combustion byproducts have similar properties as air. This is consistent with analysis done in the fire modeling community (Peacock *et al.*, 2015). Hence, in this work both the air and the combustion products will be modeled as air with spatially dependent temperature and sound speed.

The fire creates hot air that rises due to buoyancy, thus creating a temperature gradient. Equation (1) shows the relationship between temperature, sound speed, and acoustic impedance,

where *T* is the temperature in K, *c* is the sound speed in ms^{−1}, *γ* is the adiabatic index of the medium, *ρ* is the density in kg m^{−3}, $Rspecific$ is the universal gas constant divided by the molecular weight of the gas, and *Z* is the specific acoustic impedance. For air $Rspecific=$ 287.08 J/kg K and $\gamma \u2248$ 1.4 for air.

The fire also entrains air and creates regions of turbulent flow and varying temperature distributions. The rising plume consists of two main turbulent scales, large and small (Quintiere, 2006). The small scale (high frequency) turbulent eddies are responsible for fuel-oxygen mixing and local combustion reactions. Large scale (low frequency) turbulent eddies are responsible for the entrainment of air in the fire mass. Both of these create chaotic, randomly arranged surfaces of acoustic impedance mismatch that can cause sound to scatter.

In Sec. 3, we compute the linear time invariant system (LTI) frequency/impulse response of a room fire. An evolving room fire is not a time invariant system. However, at a sufficiently small time scale we can assume time invariance, allowing us to use signal processing and analysis tools meant for linear time invariant systems, such as the discrete Fourier transform, on our measured data. One such time scale is the vortex shedding period for a fire. This is the period with which the fire pulsates and releases large annular vorticies from its base, and is representative of the large scale entrainment period for the fire. For pool fires, the vortex shedding period can be predicted by the empirical relationships in Eq. (2) adapted from Bejan (1991). Here *U* is the vortex shedding period in seconds

where *D* is the diameter of a circular pool fire in meters, and the constant *B *=* *2.3 m/s^{2}. Since a room fire is inherently not an LTI system, we can only use the impulse response measured to understand the changing system over time and the average behavior of the system.

The acoustic environment around the fire will change on the time scale of the vortex shedding period, therefore measurements assuming a linear time invariant system need to be taken over a time scale smaller than the vortex shedding period. The signal duration for the measurement shown in Sec. 3 was constrained by the need for a longer transmit signal (to prevent speaker artifacts and maximize the time-bandwidth product), and a shorter signal (to minimize variations in the temperature field in the room). The experiments discussed in Sec. 3 used a 30 × 30 cm square profile sand burner. Using Eq. (2), we can bound the vortex shedding period between $U=$ 0.36–0.43 s by using the side and diagonal of the burner as the diameter. In Sec. 3, 0.2 s long chirps were used to measure the transfer function. This ensured we did not violate the time invariant assumption during the measurement, and was found to provide sufficient SNR (signal-to-noise). This time scale is different from the room reverberation time. The transmit signal was followed by 0.5 s of acoustic recording to ensure the reverberation was captured.

## 3. Description of measurements

Room fire testing was conducted in the University of Texas burn facility. The total floor area is 5.6 m (*X*)* *×* *4.6 m (*Y*) and the height of the ceiling is 2.1 m (*Z*). Two receivers were placed in different locations in the room. A preliminary version of this experiment was published in (Abbasi *et al.*, 2013), and the experiment schematic and facility layout can be found in there. A log-frequency swept-sine signal was played through a speaker and recorded on the microphones in order to measure the system frequency response.

The sweep was a 0.2 s long chirp, logarithmically modulated from 100 to 5000 Hz. The signal was generated by a matlab^{®} program, and converted to analog signal using an NI-9263 analog output module at a 100 kHz sample rate. The instantaneous frequency for a log frequency sweep (matlab, 2014) is

where *t* is time, *f*_{0} is the start frequency, *f*_{1} is the end frequency, and *t*_{1} is duration of the sweep. The chirp signal was directed to a QSC MX-700 Power Amplifier, and a Peavey PV 12 M stage monitor loudspeaker radiated sound into the room. The received signal was recorded by two PCB Peizotronics U130D20 microphones placed in the room. Both microphones were wrapped in 5-cm-thick Kaowool blanket S (Morgan Advanced Materials, 2019) (ceramic refractory fiber blanket) to prevent thermal damage. The microphones were pre-amplified by PCB Piezotronics model 480E09 ICP Sensor Signal Conditioners. Simultaneous digitization at 100 kHz was performed using an NI-9215 Analog Input Module (BNC). Both the NI-9215 and the NI-9178 were installed in a NI-cDAQ 9178 CompactDAQ chassis. A custom data-acquisition program was developed in matlab^{®} to interface with the data-acquisition hardware. Acoustic data acquisition began 0.1 s before the chirp played, and continued for 0.5 s after the end of the chirp, to observe the reverberation.

The fire was created using a 30 cm × 30 cm × 20 cm square profile propane sand burner. A Dwyer gas flowmeter was used to control the propane flow-rate into the burner, and thereby control the heat release rate (HRR). For this experiment, a 150 kW heat release rate was chosen. This is a low heat release rate compared to a typical real room fire, however, safety and equipment survivability requirements limited the HRR. More details about the design of the burn structure and the burners can be found in Weinschenk (2011).

The frequency response of the system was determined from the discrete Fourier transforms of the microphone signals and the input chirp as described in Müller and Massarani (2001) and Schafer and Oppenheim (1989). Equations (4) and (5) describe this method,

and

where $st(t)$ is the transmit signal and $sr(t)$ is the received signal. The discrete Fourier transform of *x*(*t*) is DFT[*x*(*t*)], the inverse discrete Fourier transform of *x*(*f*) is IDFT[*x*(*f*)], the real part of *x*(*t*) is Re[*x*(*t*)], *H*(*f*) is the complex frequency response of the system, and *h*(*t*) is the impulse response of the system.

## 4. Experimental results

Figure 1 shows the results from the experiment described in Sec. 3. Figure 1(a) shows the impulse response of the system over the course of the experiment. Each horizontal row of pixels in Fig. 1(a) is a single impulse response measurement. Time *t* on the horizontal axis is the delay time of the impulse response. Time *T* along the experiment increases down the vertical axis. Ignition (*T *=* *35.0 s) and extinction (*T *=* *207.9 s) times are marked by the solid-red and dashed-blue lines, respectively. Before ignition, there is no fire present, therefore the impulse responses have stable consistent amplitudes and delays. After ignition, the arrivals tend to advance to earlier delay times. The first and second arrivals shift very little over the course of the experiment. Based on the numerical modeling shown in Sec. 6, we assert those are the direct path and floor reflection paths. These stay in the relatively cool lower part of the room and are impacted the least by the fire. Paths that strike the ceiling first travel through the hot (higher sound speed) region and therefore are impacted more. Later arrivals spend more time in the high speed region and are impacted more than earlier arrivals.

Figure 1(b) shows the frequency response of the system over time. Each row of pixels shows the frequency response for a single measurement. Time *T* along the experiment increases down the vertical axis. Ignition (*T *=* *35.0 s) and extinction (*T *=* *207.9 s) times are marked by the solid-red and dashed-blue lines, respectively. At the start of the experiment, the frequency response is very stable. Clear peaks and nulls are observed and the levels are stable. Immediately after ignition the higher frequency (*f * >* *2500 Hz) modes disappear. The lower frequency modal structure is distorted initially, as the room fills with hot gas, but becomes stable again after some time has elapsed (near *T *=* *100 s). This indicates the system reached a more stable state, where large scale temperature distribution is steady and slowly varying. The diminished higher frequency content indicates that on the small length scale the system is still chaotic. The lower frequencies have longer wavelengths, and larger time period, that are more robust to changes in delay time due to the sound speed perturbation.

## 5. Numerical model

### 5.1 Fire modeling

In this section, an open source computational fluid dynamics model FDS (Fire Dynamics Simulator, version 6) is used to model the fire. Using the large-eddy turbulence model in FDS, as described in McGrattan *et al.* (2013), the temperature field inside the experimental room fire described in Sec. 3 was simulated. The simulated temperature field was sliced along a 2D plane and used as input to the ray trace model in Sec. 5.2.

The experimental burn structure fire was modeled in FDS. The fire was modeled as a planar surface with HRR = 150 kW. The walls, floor, and ceiling were modeled as 16 cm thick gypsum. The room volume was discretized in FDS using a grid resolution of 0.2 m, 0.16 m, 0.04 m in *X*, *Y*, *Z*, respectively. This resolution was sufficiently small to ensure model convergence.

### 5.2 Acoustic model

Ray theory is derived from the wave equation, and considers acoustic paths (or rays) that follow Snell's law (Blackstock, 2000; Jensen *et al.*, 2011). Due to its geometric nature, ray theory is computationally efficient compared to full-wave methods. Ray models used for room acoustics have traditionally been limited to isovelocity environments, primarily because typical room acoustics applications do not include wide temperature/sound speed variations (Savioja and Svensson, 2015). A room with a fire has significant sound speed variation and therefore we cannot use traditional room acoustics ray models. Ray models used in underwater acoustics typically do take sound speed variations into account, and have been shown to provide excellent comparison with measured data (Urick, 1983). Therefore, we used an existing open-source underwater acoustics ray trace software, bellhop (Porter *et al.*, 2007). bellhop uses a predictor-corrector scheme to model ray paths. bellhop can output ray paths, eigenrays and transmission loss at receiver locations. The version of bellhop used in this work is range-dependent and two-dimensional (Porter, 2011). The bellhop code was modified to add an additional constraint to ensure eigenrays always intersected with the receiver location within ±1 cm. The model is limited to specular reflections only.

It is important to note that our purpose in this modeling was understanding the acoustics of the room fire and to gain insight into the experimental results, not as a design or auralization tool. Therefore, in order to increase interpretability, reduce the model complexity and reduce computational load, we decided to limit the ray trace modeling to two-dimensional and frequency independent losses. We believe this is a step forward in modeling room fire acoustics. Future endeavors should include those effects.

Due to the two-dimensional nature of this modeling, out-of-plane acoustic paths are not present in the model and therefore comparisons between model and measurement may exhibit differences due to this approximation. It is useful none-the-less to test the degree to which this expedient approximation remains valid. Hence in this work we focus on trends in the results rather than a quantitative comparison. In the limiting case of a long narrow hallway the model and data would be more directly comparable.

Ray paths and delay times at the receiver were computed by providing bellhop with a sound speed field from the FDS model described in Sec. 5.1 at each 1-s interval. The ray trace field was a rectangular region representing a vertical slice in the burn structure, with length = 5.6 m and height = 2.1 m. A reflection coefficient of 0.9 was applied to all boundaries. The source is placed at range = 0 m and height = 10 cm, modeling a downed firefighter's alarm signal. The receiver is placed at range = 3.0 m from the source and height = 0.5 m from the floor. Five thousand rays were launched from the source, with launch angles equally spaced between ±90°. Multiple reflections, and backwards propagating rays were allowed in the calculation.

At each time step, the eigenray delays and amplitudes are computed. The amplitude of each arrival is considered frequency independent in this model. The frequency response was computed using the coherent sum of all arrivals. For each frequency, the time delays were used to compute the phase and the resulting complex amplitude of each arrival path. The sum of all arrival path amplitudes is the total amplitude at the frequency of interest. By assuming frequency-independent amplitude, we isolate the sound speed perturbations as the dominant mechanism for any changes in the impulse/frequency response.

## 6. Numerical results

Figure 2(a) shows a schematic diagram of the ray model, along with example ray traces before ignition (*T *=* *35 s) and while the fire was burning (*T *=* *207.9 s). The ray traces are presented for visualization purposes and the rays were truncated at the first intersection with the far right wall. The red × marks the location of the receiver. Before ignition, the environment is isovelocity, and the rays follow straight line paths. After ignition, the sound speed is downward refracting, and the rays curve down as they travel through the room.

Figure 2(b) shows the eigenray delay times at the receiver. These are time delays for rays whose path intersected with the receiver location. The trend in the delay times is very similar to that observed in Fig. 1(a). The earlier arrivals are least impacted and more stable. Later arrivals have a larger change in delay time. In addition to the decreasing delay time after ignition, there is also a random spread in the arrival times. The marker color indicates the elevation angle of the ray at the source (positive is towards the ceiling). Observe that the shallow rays arrive at the receiver earlier (direct path and shallow bottom reflection paths), and are impacted the least after ignition. The early arrivals being least impacted by the fire is consistent with the measurement data in Fig. 1(a).

Figure 2(c) shows the predicted frequency response based on the delays shown in Fig. 2(b). The calculation of this response is the same as that described in Sec. 5.2. Comparing the predicted frequency response with the experimental results presented in Sec. 4, we observe good agreement in the trends. After ignition low-frequency modes sustain their structure, but shift up in frequency, whereas higher-frequency modes attenuate. After extinction, low frequency modes return to the initial condition faster. The higher the frequency, the longer it takes for the system to return to normal. This is similar to the trends observed in Fig. 1(b).

## 7. Conclusions

The PASS alarm is an acoustic beacon used to locate and rescue downed firefighters. The acoustic environment in a room fire was examined in this paper using experimental and numerical methods. Impulse responses were measured and show that the fire creates a rapidly changing acoustic environment, with a strongly downward refracting sound speed gradient. Measurement and model results show that delay times between a source and receiver are impacted by the fire, leading to a change in the energy distribution over time. The fire increases room modal frequencies and attenuates higher-frequency modes.

The ray trace model, while incomplete, allowed us to gain further insight into the experimental results. The trend in the change of early arrival delay times is seen in both model and data. The difference in delay time change between earlier and later arrivals provides confidence in our understanding of acoustic paths in the room fire. The modeling also shows the loss of modal structure after ignition at higher frequencies, similar to that seen in the measured data, despite not accounting for frequency dependent losses. This let us conclude that a major factor in the loss of modal structure at the higher frequency is the random perturbations in sound speeds. The lack of frequency dependent absorption and reflection is a strength in this case, since we can isolate the effect of just the sound speed perturbations.

In order to create a comprehensive ray trace model that is reliable enough for PASS design, future modeling endeavors should be three-dimensional and include frequency dependent absorption, diffuse scattering, and temperature dependent material properties. We hope this paper is a step forward in understanding the physics of the environment.

These results should be considered in the design of future PASS alarms signals. For example, loss of modal structure at higher frequencies indicates that signals operating in that regime will be impacted by the fire. Future work should explore the effect of this signal degradation on alarm detection and localization by both human listeners and automated systems.