Visibility

Abstract

Visibility is very important for evacuation during a fire and, therefore, a very important parameter for fire safety in a tunnel. There are different methods for estimating the visibility in smoke-filled spaces, using mass-specific extinction coefficient or the mass optical density. For both methodologies there are experimental values available for some materials of interest. First, the mass extinction coefficient methodology is presented and at the end compared and correlated to the mass optical density methodology. Values of these parameters for selected materials are presented and conversion of values for one of the parameters into the other is discussed. Finally, the effect on the walking speed during egress is discussed.

14.1 Introduction

Fire safety in tunnels relies to a large extent on the principle of self-evacuation. Visibility is one of the most important parameter affecting the possibilities for safe egress. Although reduced visibility in itself does not lead to incapacitation, visibility is an important parameter in tenability analysis. With the most common criteria used for visibility, the “tenability limits” for visibility are in most cases reached before similar limits are reached for other parameters of interest (gas concentrations, temperature, and radiation) as shown in Chap. 15. Therefore, good knowledge of visibility phenomena and the processes affecting it are very important for the safety of escaping people.

As with other parameters relating to perception, it is not easy to find a single mathematical equation describing the relation between visibility and smoke density. The situation is complicated by the fact that the typical size and shape of the particles in smoke from fires varies and depends on the burnt material and combustion conditions [1, 2]. This has led to different suggestions about how to calculate visibility, that is, how to relate a measurable (or estimated) physical parameter to visibility. In the next section different approaches are presented, compared, and discussed.

14.2 Different Methods of Predicting Visibility

One common way to express the smoke density is by the extinction coefficient, C _s (1/m):

$$ {{C}_{s}}=\frac{1}{L}\ln \left(\frac{{{I}_{0}}}{I} \right) $$

(14.1)

where I ₀ is the intensity of the incident light, I is the intensity of the light through smoke, and L is the path length of the light (m).

The relationship between the transmitted and incident intensities is a function of the mass-specific extinction coefficient of smoke σ (m²/kg), the mass concentration of smoke, ρ _sm (kg/m³), and L (m) as expressed by Bouguer’s law [3]:

$$ \frac{I}{{{I}_{0}}}=\exp (-\sigma {{\rho }_{sm}}L ) $$

(14.2)

Jin [4, 5] developed several relationships between the visibility (V _s ) and the extinction coefficient. For a light-emitting sign the relationship is given as:

$$ {{V}_{s}}\approx \frac{1}{{{C}_{s}}}\ln \left(\frac{{{B}_{EO}}}{{{\delta }_{c}}k\Pi } \right) $$

(14.3)

where,

B _EO :

brightness of the sign (cd/m²)

δ _c :

contrast threshold of signs in smoke at the obscuration level (-)

k  =:

σ_s/C _s

C _s =-σ_s + =-σ_ab :

extinction coefficient (1/m)

σ_s :

scattering coefficient (1/m)

σ_ab :

absorption coefficient (1/m)

Π:

1/π of mean illuminance of light radiating from all directions in smoke (m/m²)

The contrast threshold (δ _c) is in the range 0.01–0.05, and a value of 0.02 is often used (For example, ISO 13571). For reflecting signs the corresponding equation can be written as [4, 5]:

$$ {{V}_{s}}\approx \frac{1}{{{C}_{s}}}\ln \left(\frac{\alpha }{{{\delta }_{c}}k} \right) $$

(14.4)

where α is the reflectance of the sign.

Jin also showed that, at the obscuration threshold (for visibilities between 5 and 15 m) the visibility can be expressed as [5]:

$$ {{V}_{s}}=\frac{K}{{{C}_{s}}}$$

(14.5)

where K is a constant which is 5–10 for a light-emitting sign and 2–4 for a reflecting sign.

If the smoke is an irritant, the visibility is reduced and both the smoke density and the irritation affect the walking speed. There is a linear decrease in visibility as the extinction coefficient increases, in the same way as for nonirritant smoke for 0.1 ≤ C _s ≤ 0.25. For C _s ≥ 0.25 the visibility in irritant smoke can be written as [4, 5]:

$$ {{V}_{s}}=({K}/{{{C}_{s}}}\; )(0.133-1.47\lg {{C}_{s}}) $$

(14.6)

The experiments for which the correlation above was developed, showed that a value of K = 6 gave best agreement [5]. Note that those tests were performed with a lighted FIRE EXIT sign.

Since

$$ {{C}_{s}}=\sigma \cdot {{\rho }_{sm}}$$

(14.7)

one can write

$$ {{V}_{s}}=\frac{K}{\sigma {{\rho }_{sm}}}$$

(14.8)

where

$$ {{\rho }_{sm}}={{Y}_{s}}\frac{\Delta {{m}_{f}}}{V}\;{\rm or} $$

(14.9)

$$ {{\rho }_{sm}}={{Y}_{s}}\frac{{{{\dot{m}}}_{f}}}{{\dot{V}}}$$

(14.10)

depending on whether the object of interest is defined by a volume, V (m³; for example, a train without openings) or an air flow rate, $\dot{V}$ (m³/s; for example, a tunnel). Y _s is the soot yield (kg/kg) for the burning material under prevailing conditions. The change in mass of fuel can be given as a mass difference, Δm _f (kg) as in Eq. (14.9) or as a mass flow, ${{\dot{m}}_{f}}$(kg/s) as in Eq. (14.10). In Table 14.3 the soot yield Y _s is given for some selected materials in kg/kg. In Chap. 7 the soot yield and the effect of the equivalence ratio are discussed further.

The extinction coefficient, C _s, can be obtained either from measurements using Eq. (14.1) or from values of σ and ρ _sm using Eq. (14.7).

If one-dimensional smoke flow in a tunnel is assumed, the visibility can be calculated from

$$ {{V}_{s}}=\frac{Ku{{A}_{t}}}{\sigma {{Y}_{s}}{{{\dot{m}}}_{f}}}$$

(14.11)

where u is the velocity of air in the tunnel (m/s) and A _t is the cross section area of the tunnel (m²). The heat release rate, $\dot{Q}$ (kW), from a fire can be described as

$$ \dot{Q}=\chi \Delta {{H}_{c}}{{\dot{m}}_{f}}$$

(14.12)

where χ is the combustion efficiency and ΔH _c is the heat of combustion (kJ/kg). This means that

$$ {{V}_{s}}=\frac{Ku{{A}_{t}}\chi \Delta {{H}_{c}}}{\sigma {{Y}_{s}}\dot{Q}}$$

(14.13)

Note the difference between the optical density (OD), and the extinction coefficient (C _s ), where

$$ OD=\lg \frac{{{I}_{0}}}{I}=\frac{{{C}_{s}}\cdot L}{\ln 10}\approx \frac{{{C}_{s}}\cdot L}{2.303} $$

(14.14)

This is discussed in more detail below, when relating the specific extinction coefficient to the mass optical density, D _mass (m²/kg).

Both the mass-specific extinction coefficient and the soot yield depend on the type of fuel and therefore it is important to have data for different types of fuels. Note that there are different definitions and different ways of presenting this type of data.

Mulholland et al. [6, 7] have studied the specific extinction coefficient and presented an average value of 8700 m²/kg (wavelength = 632.8 nm) for postflame smoke production from well-ventilated fires. Table 14.1 and  14.2 summarize the mass-specific extinction coefficients for gases/liquids and solids, respectively, with values from different studies. The value 8700 m²/kg (with an expanded uncertainty of 1100 m²/kg and 95 % confidence interval) mentioned above is an average of all the included studies. One can note that for some fuels, for example, heptane there is some spread in the specific extinction coefficient between the different studies. This could be an effect of the experimental setup or the scale. However, for some fuels, for example, PS, PVC, and rubber, there are relatively good agreement between the different setups.

Table 14.1 Examples of mass-specific extinction coefficients (at 632.8 nm) for burning gases and liquids [6]

Table 14.2 Examples of mass-specific extinction coefficients (at 632.8 nm) for burning solids [6]

Note that the standard SS-ISO 13571:2007 suggests an average value of 10,000 m²/kg [8].

Tewarson [9] presented data for many different types of fuels. There the information is given as

$$ {{D}_{mass}}=\frac{OD\cdot {{Y}_{s}}}{L\cdot {{\rho }_{s}}}$$

(14.15)

Using Eqs. (14.7), (14.14) and (14.15), a relationship between the specific extinction coefficient and D _mass can be found:

$$ \sigma =\frac{\ln 10\cdot {{D}_{mass}}}{{{Y}_{s}}}$$

(14.16)

In Table 14.3 and 14.4 Y _s and D _mass for a number of fuels and building materials are listed. Equation (14.16) is then used to calculate the mass-specific extinction coefficient. In the table, there are two columns with soot yield. The reason for this is that, the more recent version of the SFPE handbook has somewhat different values compared to the 1st edition. The 1st edition version is included since those values correspond to the reported values of D _mass.

Table 14.3 Soot yield, D _mass and specific extinction coefficient for selected materials

Table 14.4 Soot yield, D _mass and specific extinction coefficient for selected building materials

For some materials there is a large variation in the values of the specific extinction coefficient calculated from D _mass in Table 14.3 and 14.4 compared to the measured values listed in Table 14.1 and 14.2. The specific extinction coefficient depends on the experimental setup and the size of the fire as shown by the values in Table 14.1 and 14.2. In some cases there is a good correlation between the values in Table 14.1 and 14.2 and Table 14.3 and 14.4.

Table 14.5 shows the difference in soot yield for some fuels at different fire sizes. It can be seen that the mass-specific extinction coefficient depends on the fuel type, but does not seem to depend on the flame conditions (laminar or turbulent) [3].

Table 14.5 Yield of soot for different fuels and different HRR [7]

Using Eqs. (14.13) and (14.16) one can derive an equation for visibility based on D _mass:

$$ {{V}_{s}}=\frac{K\cdot \chi }{\ln 10}\frac{uA\Delta {{H}_{c}}}{{{D}_{mass}}\dot{Q}}$$

(14.17)

If a combustion efficiency of unity is assumed, Eq. (14.17) reduces to:

$$ {{V}_{s}}=\frac{K}{2.3}\frac{uA\Delta {{H}_{c}}}{{{D}_{mass}}\dot{Q}}$$

(14.18)

and if a value of K = 2 is assumed, one obtains the following expression:

$$ {{V}_{s}}=0.87\frac{uA\Delta {{H}_{c}}}{{{D}_{mass}}\dot{Q}}$$

(14.19)

which is the same equation presented by Ingason [11]. Ingason also summarized mass optical densities for different vehicles. These are given in Table 14.6.

Table 14.6 Mass optical densities (D _mass) for different types of vehicles [11, 12]

In a test series in the Runehamar tunnel in Norway, Ingason et al. [13] performed tests simulating fires in heavy goods vehicle (HGV) cargos. Except for a pool fire test using diesel, different mixtures of cellulosic materials and plastics (18–19 % plastics in each test) were used as fuel to simulate the cargo. During these tests the extinction coefficient was measured. The mass optical density estimated from the measurements for different types of materials (cargo) is presented in Table 14.7. The values correlate well with the values given for “truck” in Table 14.6. The values for diesel are similar to those given for benzene and styrene in Table 14.3.

Table 14.7 Mass optical densities (D _mass) for different types of HGV cargo materials [13]

For the estimation of the visibility in a tunnel either Eq. (14.13) or Eq. (14.17) can be used depending on which information is available on the involved parameters. If the visibility is to be determined for a line of sight having a distance x m downstream of a fire with a nonconstant HRR, it is important to take the transport time into account and relate the transient visibility to the relevant HRR. This was discussed also in Chap. 8 on gas temperatures, where a relation for the actual time and its dependency on a nonconstant velocity was presented. If for simplicity, a constant velocity, u, is assumed, the actual time τ (s) for the fire development at the distance x from the fire can be calculated as

$$ \tau =t-\frac{x}{u} $$

(14.20)

where t (s) is the measured time from the ignition of the fire.

For estimation of the soot yield, the $\dot{Q}(\tau)$is used in Eq. (14.13) or Eq. (14.17), that is, the transportation time should be accounted for in this case.

Example 14.1

An HGV loaded with polypropene (ΔH _c = 38.6 MJ/kg) is burning in a tunnel with the cross section W = 9 m and H = 6 m. The air velocity in the tunnel is 2 m/s. The HRR of the fire increases linearly at 210 kW/s for 12 min. What is the visibility after 6 min at a distance of 500 m downstream of the fire? Assume nonirritant smoke.

Solution: Start with calculating the actual time using (14.20): τ = 360−500/2 = 110  s. This gives $\dot{Q}(\tau)$  = 210 × 110 = 23100 kW. From Table  14.3 the D _mass  = 240 m ² /kg for polypropene can be found. Using Eq. (14.18) and assuming K = 2 gives

$$ {{V}_{s}}=\frac{2}{2.303}\frac{2\cdot 9\cdot 6\cdot 38600}{240\cdot 23100}=0.65\text{ m}. $$

In this solution we used K = 2 (lower end of the interval for reflecting signs), which often is used, but note that in many cases other values are used, for example, K = 3, that is, the centre of the interval for reflecting signs.

14.3 The Influence of Visibility on Egress

One of the most well-known and used relationships between visibility (extinction coefficient) and walking speed is presented by Jin [4]. The values are presented in Fig. 14.1 and also included in Fig. 14.2. These tests were performed with a limited number of participants.

Fig. 14.1

Relationship between the walking speed and the extinction coefficient for irritant and nonirritant smoke after Jin [4]

Fig. 14.2

Relationship between the walking speed and the extinction coefficient for irritant and nonirritant smoke [15]. The graph is based on several different sources [16, 14, 17]

Frantzich and Nilsson [14] performed tests in a tunnel with these dimensions: 36.75 m long, 5.0 m wide and 2.55–2.70 m high. In total 46 persons participated in the study, with an average age of approximately 22 years. The extinction coefficient was measured using a 5 mW diode laser with a wavelength of 670 nm. The measurements were performed at a height of 2 m in the tunnel with a sight distance of 1 m.

In their tests, Frantzich and Nilsson used the value K = 2 in Eq. (14.5) for calculating the visibility, that is, at the lower end of the interval reported to be valid for reflecting signs. One aim of the study was to verify the results by Jin. However, the extinction coefficient in the tests by Frantzich and Nilsson was found to be between 2 m^− 1 and 8 m^− 1, while in the tests by Jin it was below 1.2 m^− 1. Another difference between the tests was that Jin used black fire smoke while Frantzich and Nilsson used white artificial smoke with addition of acetic acid. It is difficult to say what these differences mean for the results. Frantzich and Nilsson have, however, shown that the equation for visibility is valid both for black fire smoke and for white artificial smoke [14]. The results from the walking speed tests are included in Fig. 14.2.

Based on the tests, Frantzich and Nilsson found the following relation [14]:

$$ {{u}_{w}}=-0.057\cdot {{C}_{s}}+0.706 $$

(14.21)

when the general lighting (normal lighting inside the tunnel) was used, where u _w is the walking speed. When the general lighting was not used, there was no statistically significant influence of the extinction coefficient on the walking speed. Furthermore, Frantzich and Nilsson showed that there was an influence on the walking speed of the choice of walking along a wall or not [14].

The walking speeds registered by Frantzich and Nilsson were lower (varied between 0.2 and 0.8 m/s) than those measured by Jin. This is expected since the visibility was higher in Jin’s test series. Frantzich and Nilsson also argued that the measured walking speed should be multiplied by a factor lower than 1 to get an effective walking speed, taking into account both stops on the way and the fact that the persons did not take the closest way to the escape route. There was a large variation in this factor between the people participating in the tests with an average value of approximately 0.9. Also, the dependency of the extinction coefficient has a high uncertainty. Furthermore, it was concluded that the walking speed was in general higher for those walking along the tunnel wall for at least two thirds of the walking distance studied in the tests. The dependency on the extinction coefficient was also more evident in the cases where the test participants walked along the wall. The choice of route, therefore, seems important for determining the effective walking speed and there might also be other properties or conditions affecting the walking speed such as a person’s height and gender.

To increase the number of data points, Fridolf et al. performed tests similar to Frantzich and Nilsson with a span in extinction coefficients between 1.2 m^− 1 and 7.5 m^− 1. The results are included in Fig. 14.2. They then combined their results with those of Frantzich and Nilsson and derived a new relationship for walking speed:

$$ {{u}_{w}}=-0.1423\cdot {{C}_{s}}+1.177 $$

(14.22)

or if visibility is used as the independent parameter:

$$ {{u}_{w}}=0.5678\cdot {{V}_{s}}+0.3033 $$

(14.23)

where K = 2 was used when calculating the visibility. The correlation with the extinction coefficient is statistically somewhat better (R ² = 0.4132) than the correlation with the visibility (R ² = 0.3612). Using the extinction coefficient directly also avoids the use of the constant K. In Fig. 14.3 the walking speed is shown as a function of visibility for the test series mentioned above [15]. Note that K = 3 was used when producing Fig. 14.3.

Fig. 14.3

Walking speed as function of visibility [15]. The graph is based on several different sources [16, 14, 17]. Note that a value K = 3 was used to produce these results

In the guidelines to the Swedish building code there are suggestions for walking speeds to be used in performance based design of means for evacuation [18]. Note that these guidelines are for buildings rather than tunnels. However, the basic unhindered walking speed is set to 1.5 m/s. Note also that the influence of visibility is not discussed in these guidelines, probably since high visibility (10 m for areas > 100 m²) is one of the design criteria. For children or people with disabilities (in mobility or orientation) the walking speed is set to 0.7 m/s. There is also a decrease in walking speed in stairways (0.6 m/s up and 0.75 m/s down) in relation to the basic unhindered walking speed.

Frantzich [19] has also shown an effect of people getting used to the surface and the conditions. In tests with evacuation of metro trains the walking speed near the train was 1.0–1.4 m/s while further away (130 m from the train) it was 1.0–1.8 m/s. The tests were run without smoke and with emergency lighting, but Frantzich argues that this adaption effect should exist also during evacuation in fire smoke or darkness. When the tests were performed in darkness (without smoke) the walking speed varied between 0.5 and 1.0 m/s.

Example 14.2

What is the walking speed in Example 14.1?

Solution: Using the equation proposed by Fridolf et al., Eq. (14.23) gives ${{u}_{w}}=0.568\cdot {{V}_{s}}+0.3=0.568\cdot 0.65+0.3=0.47\text{ m/s}$ . One should here again note that this is based on K = 2 and that a value K = 3 is used to derive the graph in Fig.  14.3 . One can still see that the visibility in this case is in the lower end of the graph and that the resulting walking speed is not very much higher than the constant value given by Eq. (14.23).

Example 14.3

At what time has the fire in Example 14.1 reached a point where the walking speed is 0.9 m/s at a position 150 m downstream of the fire?

Solution: The heat release rate $\dot{Q}(\tau)=210\cdot \tau$ and τ = t – 150/2. Using this together with Eq. (14.18) give after some algebraic steps:

$$ t=\frac{1}{210}\cdot \frac{K}{2.3}\frac{uA\Delta {{H}_{c}}}{{{D}_{mass}}{{V}_{s}}}+\frac{150}{2}=\frac{1}{210}\cdot \frac{2}{2.303}\frac{2\cdot 9\cdot 6\cdot 38600}{240\cdot 0.9}+\frac{150}{2}=155\text{ s} $$

14.4 Summary

Visibility is very important for evacuation during a fire and, therefore, a very important parameter for fire safety in a tunnel. In this chapter different methods to define and describe visibility have been presented and discussed. The main methods for estimating the visibility in smoke-filled spaces are to use either the mass-specific extinction coefficient or the mass optical density. For both methodologies there are experimental values available for some materials of interest. The focus has been on the mass extinction coefficient methodology, but at the end this method was compared and correlated to the mass optical density methodology. Values of these parameters for selected materials were presented and conversion of values for one of the parameters into the other was discussed. Finally, the effect on walking speed during egress was discussed and some methods for estimating walking speed were presented.