Gas Cooling: Part 3

The first post in this series, Gas Cooling, began the process of providing a conceptual explanation of the fire control technique of gas cooling. As previously discussed, gas cooling reduces the hazards presented by the upper layer in a compartment fire by cooling hot gases and reducing the potential that they will ignite. Water is an effective fire control agent for this purpose because a tremendous amount of energy is required to raise its temperature and vaporize it at its boiling point.

Gas Cooling: Part 2 identified the amount of water that is theoretically necessary to cool the upper layer of a compartment containing 40 m3 (4 m wide  x 5 m long x 2 m deep) from 500^o C (932^o F) to 100^o C (212^o F). In addition, this post identified practical limitations with the efficiency of typical combination nozzles used and determined the duration of application necessary to cool the upper layer to 100^o C (212^o F) at different flow rates.

This raises the question, what would happen if you didn’t apply sufficient water to cool the upper layer to 100^o C (212^o F)?

What If?

Steam continues to absorb energy if its temperature is increased above 100^o C (212^o F). Some firefighters are under the impression that you cannot have steam at a temperature above 100^o C (212^o F) at normal atmospheric pressure. This is incorrect. Water (in liquid form) will not increase above 100^o C (212^o F) as this is it’s boiling point at normal atmospheric pressure, but steam acts as any other substance in the gaseous form and can increase in temperature beyond that which it changed phase from liquid to gas.

Figure 1. Properties of Water, Steam, & Smoke

1 100 kg/M³ =1 kg/l

2 Not applicable as smoke and steam are in the gas phase

3 TCC is based on heating water from 20^o C to 100^o C and conversion to steam

4 Steam will continue to absorb energy until reaching temperature equilibrium

As illustrated in Figure 1, a kilogram of steam (slightly under 1.69 m³ at 100^o C) will absorb 2.0 kJ of energy for each ^oC that the temperature of the steam is increased. The temperature of steam will continue to increase as long as the surrounding gases and/or surfaces that it is in contact with are of higher temperature. This process will continue until the steam, gases, and surfaces that the steam is in contact with reach equilibrium (i.e., the same temperature).

So even if insufficient water is applied to lower the temperature of the upper layer to 100^o C (as described in Gas Cooling: Part 2 [LINK]), the combined effects of heating and vaporizing the water (the major cooling mechanism) and heating the steam produced to a temperature higher than 100^o C (212^o F), can have a significant cooling effect. This effect is often sufficient to extinguish flames in the upper layer and slow or reduce pyrolysis caused by heating of fuel packages due to radiative and conductive heat transfer from the flames and hot gases in the upper layer.

Gas Laws

When water as a liquid is vaporized to form steam, it expands and becomes less dense. Fire service texts such as the 5^th Edition of the Essentials of Firefighting (IFSTA, 2008) commonly state that the volume of water expands 1700 times when it is converted to steam at 100^o C (212^o F). These texts state this as a fact to be memorized, but do not explain why this is the case or that if temperature is increased further, that the volume of steam will continue to expand. While having a number of different characteristics as illustrated in Figure 1, steam and smoke are both in the gas phase, they behave somewhat similarly. In chemistry and physics, the behavior of gases is described by a number of physical laws collectively described as the gas laws. Understanding the gas laws provides an explanation of why smoke and the steam produced during firefighting operations behave the way in which they do.

While gases have different characteristics and properties, behavior of gases can be described in general terms using the ideal gas law. This physical law describes the relationship between absolute temperature, volume, and pressure of a given amount of an ideal gas.

Figure 2. Temperature, Volume, Pressure & Amount

The concept of an ideal gas is based on the following assumptions:

• Gases consist of molecules in random motion
• The volume of the molecules is negligible in comparison to the total volume occupied by the gas
• Intermolecular forces (i.e., attractive forces between molecules) are negligible
• Pressure is the result of gas molecules colliding with the walls of its container

The ideal gas law is actually a synthesis of several other physical laws that each describes a single characteristic of the behavior of gases in a closed system (enclosed in some type of container). Of these gas laws, Charles’s Law provides the simplest explanation of the phenomena that occur during gas cooling.

Charles’s Law: In the 1780s, French scientist Jacques Charles studied the effect of temperature on a sample of gas at a constant pressure. Charles found that as the gas was heated, the volume increased. As the gas was cooled, the volume decreased. This finding gave rise to Charles’s Law which states that at a constant pressure the volume of a given amount (mass or number of molecules) of an ideal gas increases or decreases in direct proportion with its absolute (thermodynamic) temperature. The symbol  is used to express a proportional relationship (much the same as = is used to express equality), so this relationship can be expressed as:

Where:

V=Volume

T=Temperature

When two values (such as volume and temperature in Charles’s Law) are proportional, one is a consistent multiple of the other. For example If one value was consistently eight times the other, the values would also be proportional. In the case of Charles’s Law when the absolute temperature of a gas doubles, the pressure doubles. Figure 3 illustrates the relationship between absolute temperature in Kelvins (K) and volume in cubic millimeters (mm³).

Figure 3. Charles’s Law

This relationship can also be stated using the following equation:

Where

V=Volume

T=Temperature

Subscript of 1 refers to initial conditions

Subscript of 2 refers to final conditions

It is important to remember that absolute temperature is measured in Kelvins (K), not degrees Celsius or Fahrenheit, because the Kelvin scale places the zero point at absolute zero, so that doubling the temperature in K, is actually doubling the temperature. As illustrated in Figure 4, the same does not hold true when using the Celsius scale (the Fahrenheit scale presents the same problem).

Figure 4. Absolute Temperature

Application of Charles’s Law provides a simple approach to examining the question of why application of water into the upper layer does not necessarily result in an increase to upper layer volume (by adding steam) and increasing its thickness (with the bottom of the layer moving closer to the floor). This requires the assumption that while the higher temperature inside the fire compartment results in increased pressure, this increase is fairly small and does not have an appreciable outcome on volume changes during gas cooling.

As a first step in answering the question, consider what is known at this point (as illustrated in Figure 5):

• The initial volume of the upper layer (V_u1) is 40 m³.
• The initial temperature of the upper layer (Tu1) is 500^o C (932^o F)
• The ending temperature of the upper layer (T_u2) is 100^o C (212^o F)

The answer we are in search of is the ending volume of the upper layer (V_u2), the volume of fire gases (V_fg) plus the volume of steam produced (V_st) during application of water for gas cooling.

Figure 5. Compartment Temperature and Volume

Expanding Steam

As discussed in Gas Cooling: Part 2 [LINK], 4.35 kg (4.35 l) of water must be vaporized in the upper layer in order to lower the temperature to 100^o C (212^o F). The volume of water in liters must be converted to cubic meters (the same units of measure used for the volume of the compartment and upper layer). A liter is 0.001 m³, so 4.35 l equals 0.00435 m³. For now, we will accept that conversion of water to steam results in a 1700:1 expansion ratio (a later post in this series will explain why). With an expansion ratio of 1700:1, 0.00435 m³ of water expands to 7.395 m³ of steam at 100^o C (212^o F) (see Figure 6)

Figure 6. Expansion of Steam at 100^o F

Figure 7 illustrates the volume of steam produced when 4.35 l of water is vaporized in the upper layer of the example compartment relative to the initial volume of the upper layer.

Figure 7. Steam Expansion in a Compartment

Contracting Upper Layer

Why doesn’t the 7.397 m3 of steam that results from vaporization of the 4.35 liters of water applied for gas cooling simply increase the volume of the upper layer by 7.397 m³? Charles’s law provides the key. Charles’s Law indicates that as a gas is heated its volume will increase in direct proportion to the increase in its absolute temperature. However, the reverse is also true. The volume of a gas will decrease in direct proportion to the decrease in its absolute temperature.

Cooling the upper layer from 500^o C (932^o F) to 100^o C (212^o F) results in a 52% decrease in absolute temperature from 773 K to 373 K. The volume of the upper layer which was initially 40 m³ is reduced in direct proportion to the reduction in absolute temperature.

The volume of the upper layer (fire gases) after cooling from 500^o C (932^o F) to 100^o C (212^o F) can be calculated by solving for Vu₂:

Reduction in temperature from 500^o C (932^o F) to 100^o C (212^o F) results in reduction of the volume of fire gases from 40m³ to 19.3 m³ as illustrated in Figure 8.

Figure 8. Contraction of the Upper Layer

Putting it All Together

If the water applied to cool the upper layer expands to form 7.395 m³ of steam and the final volume of the cooled upper layer is 19.3 m³, the total upper layer volume is 26.95 m³.

Figure 8. Total Upper Layer Volume

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Dividing the Total Upper Layer Volume (Vu2) of 26.95 m³ by the area of the compartment (20 m²) determines the depth of the upper layer as being 1.347 m. Therefore, cooling the upper layer from 500^o C (932^o F) to 100o (212^o F) C will cause the bottom of the upper layer to rise 0.6525 m (2.1’).

The Short Answer

The following points summarize the last three posts dealing with gas cooling as a fire control technique:

• The volume of water required to cool the upper layer is quite small due to its specific heat and latent heat of vaporization in its liquid form and the specific heat of steam.
• The expansion ratio of steam at 100o C (212o F) is 1700:1, but as the volume of water used to cool the upper layer is small, the expanded volume is still relatively small (in comparison to the contraction of the upper layer).
• In the process of reaching equilibrium, the temperature of the upper layer is reduced to a greater extent than the temperature of the water increases due to the cooling capacity of the water and the relatively low specific heat of fire gases and air.
• The large temperature drop in the upper layer results in a proportional reduction in volume (which works out be greater than the increase in volume resulting from the expansion of steam from water vaporized in the hot gas layer for cooling).

Based on each of these factors, a small amount of water can cool the upper layer and reduce its volume, resulting in the lower boundary of the upper layer rising as its depth decreases.

A Few Little Wrinkles!

The preceding example may conflict with your personal experience. Many of us have been in a hot, smoke filled compartment and had steam and smoke bank down on top of us after application of water. Why might this be the case?

The outcome of the preceding example depends on all of the water being vaporized while traveling through the upper layer. In this case, energy to vaporize the water is transferred from the hot gases in the upper layer, cooling the layer and causing it to contract. If the water passes through the upper layer without vaporizing, the temperature of the upper layer is not reduced and it does not contract. Water vaporizing on contact with hot compartment linings results in the steam produced being added to the volume of the upper layer. This steam cools the upper layer to some degree, but far less than using the energy of the hot gases to vaporize the water as it passes through the upper layer (compare the specific heat of steam to the specific heat and latent heat of vaporization of water in Figure 1).

When applying water fog into the upper layer, some of the water vaporizes as it travels through the hot gases and some reaches the compartment linings. Determining changes in the volume of the upper layer under these conditions is a bit more complex and requires a deeper examination of the gas laws.

Continuing the Discussion

The next post in this series will examine the other gas laws that lead to the development to the Ideal Gas Law and how this law can be used to answer questions about changes in upper layer volume as a result of gas cooling under a variety of different conditions.

Spanish Translation of Effective and Efficient Fire Streams

Thanks to Firefighters Tomá Ricci and Martín Comesaña from San Martín de Los Andes, Argentina for translating the series of posts on Fire Stream Effectiveness and Efficiency into Spanish. They can be downloaded in PDF format:

• Efectividad y eficiencia de los chorros de ataque: Parte 1
• Efectividad y eficiencia de los chorros de ataque: Parte 2
• Efectividad y eficiencia de los chorros de ataque: Parte 3

Ed Hartin, MS, EFO, MIFireE, CFO

References

International Fire Service Training Association (IFSTA). (2008). Essentials of firefighting (5^th ed). Stillwater, OK: Fire Protection Publications.

Tags: 3D firefighting, Fire Control, nozzle techniques, practical fire dynamics