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PDH Course M135

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HVAC made easy- Overview of Psychrometrics

Course Content

Introduction
Psychrometrics (derived from the Greek: psukhros = cold) is study of air-water vapor mixtures at different conditions. To quote the 1989 ASHRAE Handbook of Fundamentals, "Psychrometrics deals with the thermodynamic properties of moist air and uses these properties to analyze conditions and processes involving moist air." Take a note; it is not the same as psychometric, which your spell checker may offer you as an alternative! While the study of pure psychrometrics involves a number of different aspects, we shall restrict this course to the application of psychrometrics for use on human comfort in the air-conditioning system. In air-conditioning system, we use psychrometric properties for environment control.

Human comfort

The common notion is that as long as cooling or heating (in winters) takes place, the environmental conditions are comfortable or the air conditioning is effective. Over a period of time, experience as well as research has shown that there is much more to human comfort than just temperature. There are four major factors that determine comfort Air temperature (dry bulb temperature or DBT) Humidity (relative humidity RH) Air movement (velocity fpm or m/s) Internal Quality of Air
1. Air temperature (DBT) The dry-bulb temperature is the temperature of the air around us and is the most important of all of the above factors. The human body's primary response is towards the changes in temperatures and it is this temperature that we attempt to keep within comfort conditions while designing structures for habitation. 2. Humidity (RH %)
The atmosphere always contains moisture in the form of water vapor. The maximum amount of water vapor that may be contained in the air depends on the temperature;
higher the temperature of the air, the more water vapor may be contained. At high temperatures and high moisture contents extreme discomfort is experienced as the evaporation of moisture from the body into the atmosphere by the process of perspiration becomes difficult. Saturated air at 100% prevents any evaporative cooling.
3. Air movement (v) The air movement can produce different thermal effects at different air temperatures, in the following two ways: It increases convective heat loss, as long as the temperature of the moving air is less than the skin temperature. It provides cooling through evaporation at low humidity levels and at higher humiditys above 85%, air movement cannot help add vapor to the already highly saturated air. 'Pleasant' ranges of air movements induce skin evaporation, more significantly in medium (40%-50%) humiditys. 4. Air quality The air quality is important. In order to control the air purity the air supply to the space is filtered. The degree of filtration will depend on specified requirements for the environment within the room. In addition to the dust control, the air-quality demands precise temperature and RH levels. Too low RH irritates respiratory organs and dust populations increase rapidly at RH levels above 50% and fungal amplifications might occur above 65% RH. Standard is 30% to 60%. Other factors that influence comfort that are subjective, non-quantifiable individual factors include the metabolic rate of an individual, type of physical activity, clothing, body build, conditions of health, acclimatization to new environments, food and drink etc. Generally speaking, the thermal comfort is associated with the metabolism rate of an individual that led to the production of heat.

Comfort zone

It is an area plotted on the psychrometric chart that pertains to those conditions of drybulb temperature, wet-bulb temperature, wind speeds etc. in which most people wearing specified cloths and involved in specific activity will feel comfortable, i.e., neither too cold nor too warm. The comfort range of temperature varies between 70 to 76F dry bulb temperatures and 45 - 65% relative humidity. This applies mainly to summer airconditioning. During cold winters the comfort condition would be in the range of 65 to 68F dry bulb temperature and relative humidity of a minimum of 30%. Studies of personal comfort have shown that relative humidity ranges between 30% and 65% can be considered 'comfortable' depending on activity. However, from the standpoint of indoor air quality, upper ranges should be maintained below 50% (dust mite populations increase rapidly at relative humidity levels above 50% and fungal amplification occurs above 65%). Below 30% respiratory irritation occurs or static electric currents is a concern.

Enthalpy (E) is the heat energy content of moist air. It is expressed in Btu per pound of dry air (or kJ/Kg) and represents the heat energy due to temperature and moisture in the air. Lines of constant enthalpy run diagonally downward from left to right across the chart. Lines of constant enthalpy and constant wet-bulb are the same on this chart but values are read off separate scales. More accurate psychrometric charts use slightly different lines for wetbulb temperature and enthalpy. For air condition point (P) the enthalpy is read at point A. The sensible heat component can be read at point B, corresponding to the enthalpy of dry air at the same temperature. The remainder, i.e. A - B, is the latent heat content. Enthalpy Lines
The Psychometrics Processes
Psychrometric processes bring about changes in air-water vapor properties. The movement of the state point on the psychrometric chart represents changes. Common processes include: Sensible Heating and Cooling Cooling and Dehumidification Heating and Humidification Evaporative Cooling Air Mixing

1) Heating or cooling:

The addition or removal of heat, without any change in the moisture content (AH), resulting in the change in DBT. The status point will move horizontally to the left (cooling) or to the right (heating). Note that while the AH (represented on the y axis) does not change, the change in temperature means the relative humidity (RH) changes. The relative humidity increases if the temperature lowers and vice versa. Sensible Heating & Cooling Process
2) Dehumidification by cooling:
If, as a result of cooling, the status point moving towards the left reaches the saturation line, some condensation will start. The DBT corresponding to this point is referred to as the dew-point temperature of the original atmosphere. If there is further cooling, the status point will move along the saturation line and condensation will occur. The reduction in the vertical ordinate (on the AH scale) represents the amount of moisture precipitated, i.e., condensed out. This process will reduce the absolute humidity, but will always end with 100% RH. State 1 is warmer and humid. Cooling and dehumidification shall result in state 2. The total heat absorbed is shown broken into a sensible and latent heat portion. Dehumidification By Cooling

Dry-bulb temperature and wet-bulb temperature are relatively most simple to measure though relative humidity can also be found out easily.

Dry-bulb temperature

Dry-bulb temperature can simply and inexpensively be measured by an alcohol-in-glass or a common mercury thermometer. More sophisticated, hand-held thermistor, resistance bulb, or thermocouple thermometers can also be used. These are more expensive than a glass thermometer but are not necessarily more accurate. However these instruments provide digital reading and have advantages; for instance can be purchased with a probe allowing them to be used for measuring product or skin surface temperatures. When taking readings, the thermometer should be shielded from radiant heat sources such as motors, lights, external walls, and people. The reading must be taken in an area protected from these sources of radiation or thermometers must be shielded from radiant energy. The thermometers must be calibrated and in field situations, an ice-water mixture is an easy way to check calibration at 32F

Wet-bulb temperature

Wet bulb temperature (WBT) is usually measured with a sling or aspirated psychrometer consisting of two mercury thermometers, one of which is wrapped with a wick around the mercury bulb. The other is used to measure dry bulb temperature. To use this instrument, the wick is saturated with clean water and the psychrometer is whirled for approximately 10 to 15 seconds. The process is repeated two or three times until there is no further temperature drop on the wicked thermometer. 'Web bulb depression' is noted as the difference between the wet bulb and the dry bulb temperatures. The difference happens as the wet wick thermometer is cooled down by the evaporation on the wick. The greater the wet-bulb depression (Tdb - Twb), the lower shall be the RH. The amount of evaporation is a direct indication of the moisture carrying capacity of the atmospheric air at that temperature. 15
The key to accurate wet bulb temperature reading depends on: 1) Sensitivity and accuracy of the thermometer, 2) Maintaining adequate air speed past the wick, 3) Shielding of the thermometer from radiation, 4) Use of distilled or de-ionized water to wet the wick, and 5) Keeping wick saturated and use of a cotton wick. The thermometer sensitivity required to determine an accurate humidity varies according to the temperature range of the air. More sensitivity is needed at low than at high temperatures. For example, at 150F a 1F error in wet-bulb temperature reading results in a 2.6 percent error in relative humidity determination, but at 32F that same error results in a 10.5 percent error in relative humidity. Before wetting the wick of the wet-bulb thermometer, operate both thermometers long enough to determine if there is any difference between their readings. If there is a difference, assume that one is correct and adjust the reading of the other accordingly when determining relative humidity. The rate of evaporation from the wick is a function of air speed past it. A minimum air speed of about 500 feet per minute is required for accurate readings. An air speed much below this will result in an erroneously high wet-bulb reading. A buildup of salts from impure water or contaminants in the air affects the rate of water evaporation from the wick and results in erroneous data. Distilled or de-ionized water should be used to moisten the wick. Wick should be replaced if there is any sign of contamination. The wick material should not have been treated with chemicals such as sizing compounds that affect the water evaporation rate. Special care must be taken when using a wet-bulb thermometer in near freezing conditions. At temperatures below 32F, touch the wick with a piece of clean ice or another cold object to induce freezing, because distilled water can be cooled below 32F without freezing. The psychrometric chart must use frost-bulb, not wet-bulb temperatures, below 32F to be accurate with this method. Under most conditions wet-bulb temperature data is not reliable when the relative humidity is below 20 percent or when wet-bulb temperature is above 212F. 16

At low humiditys, the wet-bulb temperature is much lower than the dry-bulb temperature and it is difficult for the wet-bulb thermometer to be cooled completely because of heat transferred by the glass or metal stem. Water boils above 212F, so wet-bulb temperatures above that cannot be measured with a wet-bulb thermometer. In general, properly designed and operated wet- and dry-bulb psychrometer can operate with an accuracy of less than 2 percent of the actual relative humidity. Improper operation greatly increases the error.

Relative humidity

Direct relative humidity measurements can be achieved through an electric sensing hygrometers or a mechanical system. As the humidity of the air around the sensor increases, its moisture increases, proportionally affecting the sensor's electrical properties. These devices are more expensive than what computed by measuring wetand dry-bulb psychrometer. An accuracy of less than 2 percent of the actual humidity is often obtainable. Sensors lose their calibration if contaminated, and some also lose calibration if water condenses on them. Most sensors have a limited life. Electric hygrometers are based on substances that absorb or lose moisture with changing relative humidity and exhibit changes in electrical characteristics as a function of their moisture content. The electrical hygrometers are further classified as impedance/resistive hygrometers and capacitive hygrometers. Polymer film hygrometers are based on the fact that a hygroscopic organic polymer is deposited on a water permeable substrate. Both capacitance and impedance sensors exist with this technology. The advantages of polymer film hygrometers include: !" Small in size !" Low cost !" Low hysteresis !" Fast response ( = 1 to 120 sec) !" Long-term stability Mechanical or Hair hygrometer: Mechanical hygrometers usually employ human or animal hairs as a sensing element. Hair changes length in proportion to the humidity of 17
the air. The response to changes in relative humidity is slow and is not dependable at very high relative humidity. These devices are acceptable as an indicator of a general range of humidity. These require frequent calibration and are not suitable for instantaneous accurate measurements. A mechanical device known as Thermo-hydrograph measures and plots the temperature and RH with 2 colors tip pen on a paper for long durations. The instrument finds use in energy auditing surveys and is useful in recording the temperature/RH curves up to 7 days interval.

Dew point Measurements

Dew point products use chilled mirror hygrometers. These can measure dew/frost points from -80 C to 85 C that is obtained by cooling a solid surface usually a mirror, until condensation occurs on the surface. High accuracy (0.15 C) platinum RTD is embedded in the mirror surface to measure the reading. Various methods used to cool the mirror include ice, refrigerants (freon), thermoelectric cooling (Peltier device) etc. These are often used as a secondary standard to calibrate other humidity transducers. Performance largely defined by accuracy of temperature measurement. !" 1% RH from 40 % to 90% RH !" 0.5% RH from 1% to 40% RH

Sample Examples

Example Problem # 1: (Find air properties)
A sling psychrometer gives a dry-bulb temperature of 78 F and a wet-bulb temperature of 65 F. Determine other moist air properties from this information i.e. find Relative Humidity Dewpoint Temperature Humidity Ratio Enthalpy Specific Volume
Vapor Pressure Percentage Humidity

Solution

This example is shown in figure above, so you may check your work. Step#1: Find the intersection of the two known properties, dry-bulb and wet-bulb temperatures, on the psychrometric chart. Step#2: The dry-bulb temperature is located along the bottom horizontal axis. Find the line for 78 F, which runs vertically through the chart. Wet-bulb temperature is located along diagonal dotted lines leading to scale readings at the upper, curved boundary marked "saturation temperature". Step#3: The intersection of the vertical 78 F dry-bulb line and the diagonal 65 F wetbulb line has now established a "state point" for the measured air. Step#4: From this state point determine read all of the other values: Relative humidity as 50 percent (curving line running from left to right up through the chart) Follow the horizontal line, moving left towards the curved upper boundary of saturation temperature; Dewpoint temperature is 58 F Follow the horizontal line to the right until it intersects the humidity ratio scale. Read humidity ratio as 0.010 lb (~72 grains) of moisture per pound of dry air. Take a straight edge. Revolve it about the point until its edge intersects the same numerical value on the enthalpy scale at the bottom and the enthalpy scale outside of the 100% RH line. Read ~ 30 Btu per lb of dry air as the enthalpy. Interpolate between the specific volume lines. Read 13.7 cubic feet per pound of dry air. 19

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Follow the horizontal line to the right until it intersects the vapor pressure scale. Read ~ 0.48 inches of mercury. Percentage humidity equals actual humidity ratio found in step 4 c), divided by humidity ratio at saturation for same DB temperature. At 78F and 100% RH read W= 146 Percentage Humidity = 72/146 = 0.493
What might we conclude from this information? The relative humidity of 50 percent is acceptable for comfort. If we allowed the air temperature (dry-bulb) to decrease to 58 F (dewpoint) or below, the air would be 100 percent saturated with moisture and condensation would occur. The humidity ratio, as seen on the vertical, y-axis scale, is a reliable indicator of air moisture level since it reflects the pounds of moisture contained in a pound of dry air and does not fluctuate with dry-bulb temperature readings as does relative humidity.

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Lets put the above example in practical use. Imagine the outside air at 40 F dry-bulb temperature and 80 % relative humidity is heated to 65 F dry-bulb before it is distributed throughout a building shed containing material for drying say plantation leaves. From the results above, the heated air entering the building is dry enough to be useful in absorbing moisture from the interior spaces. The heated air, with its lower relative humidity, shall be mixed with moist, warm air already in the building.
As the air moves in indoor environment, it will pick up additional moisture before it reaches the ventilation system exhaust. We might measure the exhausted air conditions at 75 F (dry-bulb) and 70 percent relative humidity, represented by point C in the Figure. Note that in this exhausted air, the humidity ratio has tripled to 0.013 lb moisture/ lb dry air or in other words the exhaust air contains three times the moisture of fresh air. This means that a lot more water is ventilated out of the building in the warm, moist exhaust air than was brought in by the cold, high relative humidity incoming air. This is one of the major functions of a winter ventilation system: removal of moisture from the indoor environments.

Example Problem # 5:

Determine the amount of sensible heat needed to increase the temperature of air from 50F and 50% RH to 90F.
Enthalpy (50F, 50% RH) = 16 Btu/lb (HR = 0.0038 lb/lb da) Enthalpy (90F, same HR) = 26 Btu/lb Heat added = 26 - 16 = 10 Btu/lb
Example Problem # 6: (Evaporative Cooling)
Plot the following two cases on psychrometric chart and interpret your observations. Case#1: Air at 95 F dry-bulb temperature and 30 % relative humidity is passed through a water spray washer and leaves at 100% RH. Case#2: Air at 95 F dry-bulb temperature and 60 % relative humidity is passed through a water spray washer and leaves at 100% RH. 23
Solution: Refer the figure below:
Case#1: represented by points D and E. This can be categorized as Hot and Dry Air. Case #2: represented by points F and G. This can be categorized as Hot and Humid Air. Infer the following: For case#1 the temperature drops by 24 F from 95 F to 71 F and for case#2, the temperature drops by 12 F from 95 F to 83 F. The enthalpy of air for case#1 is 47 Btu per lb of dry air and for case#2 it is 35 Btu/lb of dry air. Observations: Greater evaporative cooling capacity occurs for the dry air as with case#1. The hot dry air (points D to E with a 24 F temperature drop) has more capacity for evaporative cooling than hot humid air (points F to G with only a 12 F temperature decrease). Evaporative cooling uses heat contained in the air to evaporate water. Air temperature (dry-bulb) drops while water content (humidity) rises to the saturation point. Evaporation is often used in hot weather to cool ventilation air. When the spray water temperature is the same as the WB temperature of the entering air, the evaporative cooling process is a constant WB process. The process moves upward along the line of constant enthalpy or constant web-bulb temperature, for example, from point D to point E.

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Example Problem # 7:
How much moisture is added to 20 lb of air going from 50 F, 50% RH to 80 F, 60% RH?
HR (50 F, 50% RH) = 0.0038 lbm/lb da HR (80 F, 60% RH) = 0.0132 lbm/lb da Water added = 20 lb * (0.0132 - 0.0038) lb/lb = 0.188 lb-m

Example Problem # 8:

The air in a swine nursery building has a dry bulb temperature of 80 F and is at 70 percent relative humidity. How warm do the walls have to be to prevent condensation? Solution: In this example, we need to know the dew point temperature. Locate the intersection of the 80F dry bulb temperature line and the 70 percent relative humidity line. Proceed horizontally to the left until the dew point temperature scale is intersected. This gives the dew point temperature as 69F. The wall temperatures must be warmer than this to prevent condensation.

Example Problem # 9:

A swine producer is considering installing evaporative cooling in a breeding herd building. What is the lowest temperature that can theoretically be obtained from the air coming off the cooling pads if the outside air has a 90F dry bulb temperature and 35 percent relative humidity? Solution:
Locate the intersection of the 90F dry bulb temperature line and the 35 percent relative humidity line (which is not shown on the chart, but is mid-way between the 30 and 40 percent lines). Since evaporative cooling is the same process that determines wet bulb temperature, follow the wet bulb temperature line upward and to the left until the wet bulb temperature scale is intersected. The lowest possible temperature for these conditions would be the wet bulb temperature of 69F. However, due to the inefficiency of evaporative coolers, the temperature of the air coming off the cooling pads will be 3 to 5 degrees F above the wet bulb temperature. This producer can probably expect to obtain air at about 73F from the evaporative cooler under these conditions. This air would also have a relative humidity of approximately 85%.

Example Problem # 10:

Find the other properties of air at 73F dry bulb temperature and 20% RH Solution:
Figure above illustrates properties of air. Wet-bulb temperature is 52F; Enthalpy is 21.3 Btu/lb; Humidity ratio is 0.0035 lb/lb; Dewpoint temperature is 30F and Specific volume is 13.5 ft /lb.

Example Problem # 11:

7500 CFM of chilled air at 57F DB and 56F WB mixed with 2500 CFM of outside air at 96F DB and 78F WB. Find the properties of mixture. Solution 1) Locate points for re-circulated and outside air on the chart.
2) Connect with a straight line. 3) Read specific volumes of air at each point
4) Convert CFM of air to pounds of air and find total wei ght of m i xture Wei ghtof Mixture : 7500 13.14.37 = = = 567.3 lbs / mi n 173.9 lbs / min 741.2 lbs / min

5) Dry Bulb of Mixture :

567.2 741.2 173.9 741.2
= 43.6 deg F = 22.5 deg F = 66.1 deg F

The given design conditions are shown in figure above (Not to scale). For the first part of the question A system is designed with a coil that cools and dehumidifies air from 80 F db and 67 F wb to 51.5 F db and 90 % RH for supply to the space. The space is to be maintained at 75 F db and 50 % RH. 30
The process 1-2 is for the cooling coil: (Note that the path for the cooling coil process depends on coil design and temperature of cooling medium. However for thermodynamic analysis only the end points are relevant and straight line from points 1 and 2 is sufficient) The process 2-4 is for the space. (Note that extending this line to the north to hit the sensible heat factor line shall provide the space SHF reading) The space SHF is about 0.71 for the design condition. (obtained by extending line 2-4 to cut the SHF line, refer ASHRAE psychrometric charts showing SHF scale)
STATE TEM PERATURE (DB / WB, deg F) 80 /67 51.5/49.9 61/54 75/62.50 RH (%) Enthalpy ( h ) (Btu / lb) 31.5 20.3 22.6 28.2 Specific Volume ( v) (Cu ft/lb) 13.85 13.0 13.3 13.7
When the SHF is 0.6 indicating that the space sensible heat is reduced, Process 3-4 for the off-design period is laid out from state 4 for a SHF of 0.6. Then the reheat process is 2-3 (sensible heating). Read space temperatures as 61F db and 64 % RH determined by the intersection of processes 2-3 and 3-4. (a) The amount of reheat per unit mass of dry air is Q23 Q23 = Cpt (t3 t2) = 0.244 (61 51.5) = 2.32 Btu/ lb
(b) The design-cooling load is Q24 Q24 = (h4 h2) = (28.2 20.3) = 7.9 Btu/lb
(c) The cooling load for off design period Q34 Q24 = (h4 h3) = (28.2 22.6) = 5.6 Btu/lb
The cooling load for the off-design period is about 29 % less than the design-cooling load.

Example Problem # 16:

How much heat must be removed to cool X amount of air at 90 F dry-bulb and 85 F dewpoint to 70 F dry-bulb and 100% RH? How much moisture is removed from the air? What is the Sensible heat factor in this process? Solution:
Sensible heat removed Latent heat removed Total heat removed Sensible heat factor Moisture removed
= 39.3 34.2 = 50.8 39.3 = 50.8 34.2 = 5.1/16.6 = 0.0266 0.016
= 5.1 Btu/lb = 11.5 Btu/lb = 16.6 Btu/lb = 0.307 = 0.0106 lb /lb

Example Problem # 17:

Outside air at 95 F dry-bulb and 88 F wet-bulb is mixed with conditioned air at 55 F drybulb and 50 F wet-bulb. If the mixing ratio of outside air to the conditioned air is 10:1, what is the dry-bulb temperature and relative humidity of the resulting mixture? Solution: Plot the two state points on the psychrometric chart. Join the two state points and divide the line in 10:1 ratio as shown in the figure Read dry bulb temperature as 91F and RH as 80% on the resultant state point.
Psychrometric Examples (in SI UNITS)
The psychrometric chart in SI metric units is shown below:

Example Problem # 18:

Use a psychrometric chart to determine the following air-water properties: Given: tdb = 27 C; RH = 50%; and the atmospheric pressure is 101.3 kPa (standard barometric pressure at sea level) Solution:
Dewpoint temperature, tdpt Wet-bulb temperature, twb Humidity Ratio, W Specific Volume, v Enthalpy, h
= 16C = 19.5C = 11.4 g/kg of dry air = 0.866 m /kg = 55 kJ/kg

Example Problem # 19:

a) A dry-bulb thermometer reads 25C and a wet-bulb thermometer reads 18C. What is the relative humidity? The vertical 25C dry bulb (db) line and the diagonal 18C wet-bulb (wb) line intersect at point (state point), which falls on the 50% relative humidity (rh) line. b) What is the dew point temperature of the air in problem a)? If the air is cooled without changing its moisture content, it will follow a horizontal line until it reaches 14C. At that temperature, it has 100% relative humidity. Any further cooling will cause water to condense out of the air (dew forms). The dewpoint (dp) temperature is 14C.
c) What is the humidity ratio? Find the humidity ratio of the air by reading horizontally across to the vertical axis on the right side of the psychrometric chart. The humidity ration (hr) is 0.01 kg/kg. d) If the air is passed through a 100% efficient evaporative cooler, what will be its temperature after it leaves the cooler? Evaporative cooling (and spray humidification), follow the diagonal wet-bulb lines. As air passes through the cooler, it will move from state point along the 18C wet bulb line until it reaches 100% relative humidity (saturation). At this humidity it is saturated; will not accept more water vapor, and will cool no further. It will leave the cooler at a temperature of 18C, its wet-bulb temperature. e) When air represented by state point (db= 25C, wb=18C) enters a storage room with a temperature of 0C and a relative humidity of 95%, will it add moisture to the storage room or dry it out? The air has a dew point temperature of 14C (from b). When this air is cooled to just less than 14C it will begin to lose water and will continue to do so until it reaches the storage room temperature. In fact, air will lose about 0.006 kg/kg of dry air as it cools down to 0C. Thus, air at state point will add moisture to the room. f) If air leaves a wet-coil evaporator at 0C and 100% relative humidity and is heated 2C by the circulation fan before it reaches a stored product, what is the relative humidity of the air to which the product is exposed? Sensible heating processes follow horizontal lines on the psychrometeric chart. Air will leave the coil at point say B represented by 0C and 100% and move horizontally to the right on the chart until it reaches 2C. At that point, the relative humidity will be about 87%.

Air Conditioning Processes (moisture control)
Before commencing on the design phase, it is important to look at the ambient conditions you are going to be designing for and assess the required indoor thermal comfort conditions throughout the year. Outdoor air creates the baseline for indoor humidity levels, besides numerous indoor activities such as occupancy (people exhale moisture and perspire), cooking, cleaning, etc. add moisture to air. We typically apply the psychometric process to design the desired indoor conditions. As we have seen in the first part of this tutorial, the process of conditioning /changing the temperature of air shall alter the indoor relative humidity.
In the air conditioning process the moisture content of the air may be reduced by the use of a cooling coil or added by the use of a humidifier. Most refrigerant-type or chilled water air
conditioning systems, by design, remove moisture from the air during the cooling cycle through condensation at the evaporator coil. This moisture is removed from the interior using a condensate drainage network. In certain applications, dehumidifiers may be necessary if indoor relative humidity levels get too high.
Lets check out other practical applications of psychrometric analysis in equipment duty estimation or performance evaluation:
Performance Evaluation of Cooling Coil
Plotting a process on the psychrometric chart allows you to calculate the total duty, sensible duty and humidification rate. Once you have calculated the heat load and done the psychrometrics, you will need to select air-conditioning plant equipments. The most fundamental of these is the cooling/heating coil. The most common psychrometric analysis made by HVAC contractors involves measuring the dry and wet bulb temperatures of air entering and leaving the cooling coil. If these temperatures are measured along with the CFM airflow rate, the performance or cooling capacity of a unit can be verified. Procedure: Step # 1: Measure entering air-dry bulb and wet bulb temperature of the coil in degrees F and locate this state point 1 on the psychrometric chart. Step # 2: Measure the leaving air-dry bulb and wet bulb temperature of the coil in degrees F and locate this state point 2 on the psychrometric chart. Step # 3: Read the corresponding enthalpy values (h1) & (h2) against the state point 1 and 2. 36
Step # 4: Measure the volume of air passing through the coil in CFM across the coil through an Anemometer. Step # 5: The total energy output or cooling capacity of the coil in BTU/hr can than be worked out by multiplying 4.5 times the CFM value times the enthalpy difference of the two air state points i.e. Q = 4.5 x CFM x (h1 h2)

Humidity ratio is expressed as lb of water vapor per lb of dry air. Older references used grains of vapor per pound of dry air (7000 grains equal 1 lb) 2) Specific Humidity (q): Specific humidity is the ratio of the mass of water vapor to the total mass of the moist air sample: q = Mw / (Mw + Ma) where, Mw = mass of water vapor of the sample of air. Ma = mass of dry air contained in the sample. 3) Absolute Humidity (dv): Absolute humidity (alternatively, water vapor density) dv is the ratio of the mass of water vapor to the total volume of the sample of air: dv = Mw / V where, Mw = mass of water vapor of the sample of air V = total volume of sample air 4) Density ( ):
The density of a moist air mixture is the ratio of the total mass to the total volume. = (Ma + Mw) / V = (1 / v) (1 + W) where, Mw = mass of water vapor of the sample of air Ma = mass of dry air contained in the sample V = total volume of sample air v = the moist air specific volume, ft / lb (dry air) W = Humidity Ratio
5) Relative Humidity ( ):
The humidity of air in any condition can be expressed relative to the amount of moisture the air could support at that temperature, i.e., as a percentage of the saturation humidity. This is the relative humidity RH = (AH/SH) x 100 (%), where RH = Relative humidity AH = Absolute humidity SH = Saturation humidity Or Relative humidity, RH, is defined as the ratio of the mole fraction of water vapor in a moist sample of air to the mole fraction in an saturated sample at the same temperature and pressure. Relative humidity is expressed as a percentage. RH% = 100*pw/pws where: pw = actual water vapor pressure pws = vapor pressure of saturated air
6) Degree of Saturation (u): Degree of saturation, u is the ratio of the actual density of water vapor in the air to the density of saturated water vapor at the same dry-bulb temperature. u = W/W s = (Pw/Pws)*[(P-Pws)/(P-Pw)] where: W = actual humidity ratio W s = humidity ratio at saturation
7) Specific volume (v): The specific volume (v) is a mixture per pound of dry air (inverse of density) v = V / Ma where, V = total volume of the mixture Ma = total mass of dry air Empirical relation.
v = V/Ma = V/(28.9645*na) = (nRT/P)/(28.9645*na) Since RT/V = Pa/na, then Pa = P*na/n, and: v = RT/(Pa*28.9645 = RT(1 + 1.6978*W)/(28.9645*P)

Where;

n= Number of pound-moles
= Weight of gas divided by its molecular weight
na = Mw / 28.9645 for air Mw = mass of water vapor of the sample of air. R = Universal gas constant = 1545.32 ft-lb / (lb-mole- R) [8314 J/kgK-mole] T = Absolute temperature, R P = Absolute pressure, psf [Pa]
8) Dry-bulb temperature, (t db): Temperature as read from a common thermometer 9) Wet-bulb temperature, (t wb): Temperature indicated by thermometer covered with a wicking material saturated with liquid once the system has reached equilibrium. Wet bulb temperature decreases as rate of evaporation of water from the wick increases. 10) Wet-bulb temperature depression: Wet bulb depression is a difference between the dry-bulb and wet-bulb temperatures. The temperature is depressed by evaporative cooling of the wet bulb. The greater the difference between the amounts of water in the air and the saturation water capacity the more rapid the evaporation and thus the greater the temperature depression. The greater the wet bulb depression, the lower is the RH. 11) Dew-point temperature (tdp) Dew point is the temperature of moist air saturated at the same pressure p, with the same humidity ratio W as that of the given sample of moist air. It is defined as the solution tdp(p,W) of the equation. Ws (p, tdp) = W If you slowly reduce the temperature of moist air while holding p and W constant, then the temperature at which the saturation is reached tdp. The terms derives from the phenomenon of the formation of dew-drops, which are formed when the air at a high temperature and absolute humidity cools down so far that it can no longer hold the moisture as vapor and has to relinquish the excess moisture for that temperature. 12) Enthalpy: Enthalpy is the heat energy content of an air-water mixture. The enthalpy of a mixture of perfect gases equals the sum of the individual partial enthalpies of the

The terms sensible heat and latent heat are used to distinguish how air has gained heat. Sensible heat can be thought of as "dry" heat since a sensible heat gain involves gaining heat with no increase in the moisture content of the air. On the other hand, latent heat can be thought of as "wet" heat since a purely latent heat gain results from adding moisture to the air with no increase in the air temperature.
Located at 78F db and 50% RH is an Alignment Circle. This is used in conjunction with the sensible heat factor to plot the various air conditioning process lines for instance in estimating the coil dewpoint temperatures.
Standard psychrometric charts are based on a sea-level condition. Precise calculations of psychrometric variables require an adjustment for barometric pressures different from those listed on a standard chart. Consult the ASHRAE handbook for more information on this.
Humidity ratio is not affected by a temperature change unless it drops below the saturation temperature. Humidity ratio is useful in calculating the amount of moisture involved in a process, such as the amount removed by ventilating a stable or the amount added by an evaporative cooler used in a greenhouse
Note that cooler air (located along lower, left region of chart) will not hold as much moisture (as seen on the y-axis' humidity ratio) as warm air (located along right side of chart). A rule of thumb, during winter conditions, is that a 10 F rise in air temperature can decrease relative humidity 20 percent. When air is cooled, relative humidity increases.
Moist Air Properties Units o o o o o o o Dry bulb temperature ( F or C) Wet bulb temperature ( F or C) Dew point temperature ( F or C) Relative humidity (%) Humidity ratio (lb H20/lb dry air, or kg H20/kg dry air) Enthalpy (BTU/lb dry air, or kJ/kg dry air) Density (lb/ft , or kg/m )

Course Summary

A psychrometric chart graphically describes the relationship of seven air properties under variety of conditions and illustrates how these properties change as the heat and moisture content of the air changes. The psychrometric chart graphically represents the interrelation of air temperature and moisture content. This aspect of psychrometrics is very important when it comes to analyzing indoor conditions as temperatures and humidity levels within our environments are very dynamic. In air-conditioning applications the knowledge of psychrometrics is essential to design the system for optimal thermal comfort. Thermal comfort is that condition of mind that expresses satisfaction with the thermal environment. The air conditioning engineer uses the

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Proceedings of the Combustion ~nstitu; 31 (2007) 2547-2555
Experimental study and large eddy simulation of effect of terrain slope on marginal burning in shrub fuel beds

Xiangyang Zhou

Shankar Mahalingam

David Weise

Department of Mechanical Engineering, University of California, Riverside, C A 92521, USA Forest Fire Laboratory, Pacific Southwest Research Station, Forest Service, US Department of Agriculture, 4955 Canyon Crest Drive, Riverside, C A 92507, USA

Abstract

This paper presents a combined study of laboratory scale fire spread experiments and a three-dimensional large eddy simulation (LES) to analyze the effect of terrain slope on marginal burning behavior in live chaparral shrub fuel beds. Line fire was initiated in single species fuel beds of four common chaparral plants under various fuel bed configurations and ambient conditions. An LES approach was developed to model fire spreading through a fuel bed with a subgrid scale turbulent combustion model based on a flame surface density concept. By examining two fuel bed slope configurations, it was found that upslope fire spread depends not only on the increased radiant heat transfer but also on the aerodynamic effect created by the interaction of the flame with the inclined surface. Under certain conditions, the convective heat transfer induced by this interaction becomes the dominant mechanism in determining fire spread success. Seventy-three (or 42%) of 173 experimental fires successfully propagated for slopes ranging from -70% to 70%. It was found there exists a critical slope above which fire spread in these live fuel beds was successful, and below which fire spread was unsuccessful. This critical slope for marginal burning varied widely with fuel moisture content and fuel loading. A stepwise logistic regression model was developed from experimental data to predict the probability of successful fire spread. It is expected that this model may be helpful in providing guidelines for prescribed fire application. O 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
Keywords: Marginal burning; LES; Slope; Chaparral; Flame spread

1. Introduction

Wildland fire commonly occurs in Mediterranean climates that are characterized by cool, moist winters and hot, dry summers [I]. Fuel complexes of various shrub species prevalent in these
* Corresponding author. F a : +255 4024.
E-mail address: (X. Zhou). ,f*
xiangyang.zhou@fmglobal.com
areas exhibit significant fire behavior. The shrub complexes are known by various names such as fynbos (South Africa), mattoral (Chile), garrigue (France), and chaparral (California, US). Approximately 85% of the vegetation area burnt during the 2003 fires in southern California was in chaparral, indicating the importance of managing chaparral vegetation. Prescribed fire is one of the alternative strategies used by land management agencies to reduce wildland fuels and prevent wildfires [2]. Because of the fire risk in
1540-7489/$ - see front matter The Combustion Institute. Published by Elsevier Inc. All rights reserved doi: 10.1016lj.proci.2006.07.222

X Zhou et

a1 I Proceedings of the Combustion Institute 31 (2007) 2547-2555
chaparral and other living fuels, prescribed fires are often conducted under marginal burning conditions. These conditions occur when environmental variables such as wind speed and direction, air temperature, relative humidity, and topography, and fuel conditions such as type, moisture content, and continuity result in low-intensity fire that may or may not spread successfully. However, even when all variables are seemingly within the prescribed conditions, often ignition results in little, or no fire spread, due to undesired extinction. Consequently, the cost of prescribed burning increases as significant equipment and personnel allocation costs are incurred prior to ignition. It is thus desirable from both an economic and scientific perspective to gain a better understanding of marginal burning conditions. Chaparral grows extensively on hilly terrain, indicating the importance of understanding marginal burning in live fuels occurring on flat and sloped (up and down) terrains. The literature review reveals that only a limited number of experimental studies have investigated slope effects in dead fuels and virtually none have studied wildfire spread in live fuels under marginal burning conditions [3-91; most of our previous laboratory experiments were limited to zero slope conditions [10,11]. Towards this end, a dual approach including experimental and numerical modeling was adopted to study the effect of terrain slope on marginal burning. Over the last forty years, a significant amount of interest in numerical modeling of wildland fire spread has been generated within the scientific community. Operational models [12-141 refer to computer-based, semi-empirical models that are currently utilized in the field for decision support systems. They do not include a two-way coupling between the fire and the fire-induced fluid flow in the atmosphere. Furthermore, they were designed primarily for dead, not live, fuels. Coupled atmosphere-fire research models [15-181 on the other hand focus on improved methodologies, often limited in scope and designed to better understand specific physical processes. Research models for fire spread at intermediate length scales (typically laboratory scale fire spread experiments through fuel samples) have included simple gas-phase turbulent combustion models and an appropriate form of the Reynolds-averaged Navier Stokes (RANS) equations, including transport equations for gaseous chemical species arising through pyrolysis of solid fuel [19-221. These research models are appropriate to overall length scales of the order of a few meters. In this paper, a three-dimensional large eddy simulation (LES) approach to model a fire spreading through a fuel bed is developed. In LES, the super-grid scales are accurately resolved, while the subgrid scales (SGS) are modeled through

appropriate closure models. A recently proposed SGS turbulent combustion model, based on the well-known concept of flame surface density, was applied to model finite rate chemistry effects [23]. This LES approach is motivated by our desire to develop a physically more accurate method to simulate fire spread through a porous shrub fuel bed, compared to previous approaches [20,22]. When fire spreads upslope, it is observed that propagation depends not only on the increased radiant heat transfer rate [24-271, but it is also influenced by the complex aerodynamic flow created by the interaction of the flame with an inclined surface [28]. By obtaining instantaneous and detailed data on turbulent flow, heat transfer, and fuel combustion, LES is a promising tool to model this complex, dynamic two-way coupling between the fire and the fire-induced fluid flow. Given the obvious difficulty with large scale fire spread, the current LES is restricted to model fire spread through shrub fuels at laboratory scales.

2. Experimental setup

Fuel beds (2.0 m long and 1.0 m wide) were prepared with one of four live chaparral species: manzanita (Arctostaphylos spp.), chamise (Adenostoma fasciculatum), hoaryleaf ceanothus (Ceanothus crassifolius), and scrub oak (Quercus herheridzfolia) that are typical of the chaparral found near Riverside, CA. Fuel was cut in the morning in the North Mountain Experimental area at an elevation of 1160 m, bagged, and transported to the laboratory. The test bed was prepared and ignited early in the afternoon of the same day to reduce moisture loss from the cut material. The shrub fuel bed holder was constructed with an aluminum frame, 2.12 m long, I. 1 m wide, and 0.4 m high, and placed on an experimental platform that is 6.2 m long, 2.4m wide and 0.6 m high. The surface above the frame was covered by steel mesh with grid size 5 x 10 cm. A known mass of fuel (L, kg/m2) made up of a single species with branches with diameter less than 6.3 mm and including foliage was spread uniformly on the mesh to the final fuel bed depth 6 = 20 cm (or 6 = 40 cm). Because the foliage and branches in most chaparral shrubs are elevated above the ground, the fuel bed was elevated 0.4 m (stem space) above the platform. Thus, air could be entrained from the bottom of the fuel bed into the flame zone. The first 50 cm length of the fuel bed was designated as the ignition zone. Between 300400 g of excelsior and a small were added amount of isopropyl alcohol (C3H80) uniformly in the ignition zone to initiate and sustain a line ignition. Air entrainment from the lateral sides of the fuel bed was prevented by metal sheeting. It was found that most of the experimental
X Zhou et al. I Proceedings of the Combustion Institute 31 (2007) 2547-2555

fires maintain a rectilinear shape, and reached a quasi steady state after approximately half of the total length of the fuel bed. From a marginal burning perspective, an experiment resulted in a successful fire spread if the live brush fuel ignited from the ignition zone and then propagated the remaining length of the fuel bed. The experiment was considered unsuccessful if the fire, once ignited, failed to propagate. All fire tests were video recorded by a digital video camcorder for post fire spread analysis. The effect of slope was simulated by raising one side of the fuel bed assembly. The slope angle is the angle 0, between the fuel bed bottom plate and the horizontal plane. Topographic slope is defined as the ratio of vertical rise and horizontal distance expressed as a percentage: slope = 100 tan(@).Positive slope indicates uphill fire spread; negative slope indicates downhill fire spread.
3. LES methodology applied to fire spread
In a LES, the instantaneous, time-dependent, three-dimensional governing transport equations for various field quantities such as density, velocity components, species mass fractions, etc. are spatially filtered using a characteristic filter-width A [23]. This results in a set of transport equations for the filtered or resolved field. They include new terms that characterize sub grid scale (SGS) phenomena, occurring at scales below A. These SGS terms are modeled in terms of resolved quantities, to ensure closure of the system of filtered transport equations. The filtered conservation equations are expressed as
where $(x,t) stands for a filtered generic fluid property which represents density (p, in Eq. (I), in which case 4 is unity), three velocity components (u,), enthalpy ( h ) , species mass fraction (Y, of moisture, oxygen, carbon dioxide, and pyrolysis fuel gas), and soot volume fraction. The quantity Td is the molecular transport coefficient, and the fourth term M, is the unresolved SGS convective fluxes of momentum, energy and species that need to be modeled. In this work, M, is modeled via an eddy viscosity model in which the eddy viscosity coefficient is given by the generalized Smagorinsky formula [29]. In the case of fire spreading through a fuel bed, taking into account water vaporization, pyrolysis fuel gas release, combustion in the gas phase, and char combustion within the preheating and burning process, the last source term Sg,,, of Eq. (1) represents the mass exchange between gas and solid phase for density, drag force for momentum, convective and radiative heat exchange of energy between the two

phases, and physical and chemical source terms for species, respectively. Further details of modeling M, and s+,, can be found in references 122.231. One major challenge in introducing LES to wildland fire i ~ t h proper modeling of the filtered e , reaction rate & of gas species a, where the computational mesh size is generally very large whereas the flame thickness is generally very thin (<l mm) so that the detailed reaction structure cannot be resolved. Here, the filtered reaction rate & of species a is estimated as the product of the , consumption rate per unit surface area m, and the filtered FSD C whichjs the flame surface area per unit volume, i.e., &,(x, t) = riz,C(x, t) [23]. This approach is attractive since it decouples the complex chemical problem (m,) from the descrbtion of the turbulence combustion interaction (C). For wildland fuels, the composition of the pyrolysis products is complicated and temperature dependent. To simplify the problem, the pyrolysis gas is modeled as a mixture of CO, CH4, HZ,and C [30]. The governing equations of mass, momentum, energy, and species mass fractions were discretized in a three-dimensional (3D) Cartesian coordinate system. An explicit (quadratic upstream) third order accurate scheme in space and time, QUICKEST [31] was employed to numerically integrate the governing equations. Including the contributions from gas (COz and H20), soot, and solid phases, a 3D Discrete Ordinates (DO) method [32] was developed to calculate the radiative heat transfer within the flame and solid fuel. A 3D computational domain 1.2 m long, 1.2 m high and 1.2 m wide with a uniform grid system of 62 x 62 x 62 cells was designed. The computational time on a Unix workstation (CPU 2.0 GHz) was about three weeks for 2 min of simulated fire spread time. Given the current computational capability, the experimental geometrical domain was not fully modeled and the boundary of the computational domain was not extended too far away after examining the effect of numerical boundary conditions. The modeled fuel bed was shortened to 0.8m allowing us to focus on the initial ignition and subsequent propagation. The fuel properties of chamise measured by Countryman and Philpot [33] were used in computation. For two solid phases (foliage and small branch) considered in the model, they have different values of density (p,, dry wood mass per unit green volume) and surface-to-volume ratio (a, foliage has a, = 3687 m p l and p, = 376 kg/m , and branch has 0 ,= 1308 m-' and p, = 744 kg/ m3. The fuel heat content is 20.1 MJ/kg and the moisture content (M) changes with season and environment. Ambient temperature (T,) and relative humidity (RH) are known to play important

X Zhou el aProceedings of the (:ombustion Institute 31 (2007) 2547-2555
roles on wildfire spread. These environmental effects were considered in the current model.
4. Results and discussion 4. I. Aerodynamic effect induced by jire and slope
Each test bed was placed on a large platform that is designed to tilt up to an angle of 45" (slope = 100Y0)to the horizontal to model a terrain slope. This configuration is designated setup A as illustrated in Fig. l a and models the actual arrangement of wildland fuels in mountainous terrain. Because of safety concerns involving use of the large tilting platform, another slope setup B was designed to lift one side of the fuel bed to different angles (see Fig. lb) while keeping the heavy platform horizontal. Setup B is significantly easier
Fig. 1. Illustration of (a) slope setup A, and (b) slope setup B, with instantaneous 3D gas phase temperature contours in one half of the computational domain and a velocity vector field along the center section (x-y) calculated by LES at t = 25 s.
to arrange and is not representative of actual fuel arrangement; however, setup B led t o unexpected, yet insightful experimental results. Using setup B and chamise as fuel, a series of experiments was completed for three slope levels: zero slope, 40% upslope ( Q = 21.go), and 60% upslope ( B = 3 1"). At zero slope, slope setups A and B are equivalent. Other experimental conditions were essentially unchanged. Each case was repeated two times and the experimental sequence was random. At zero slope setup, the fuel ignited from the burning zone and then propagated the length of the fuel bed. The fire spread rates approximated from video were 0.143 m/min and 0.171 m/min, respectively. For marginal burning analysis, these fire tests were described as successful. For other upslope fire spread cases with slope 40% and 60%, it was anticipated that fire would spread successfully and with faster spread rate in comparison with the zero slope case. However, experiments using setup B showed a contrary result that all fires did not spread, and extinguished within about 2 min after ignition. As analyzed by many researchers [24-271, upslope fires are closer to the unburned fuel, thereby increasing the radiation heat transfer rate incident on the fuel, the preheating rate, and thus the rate of spread. For slope setup B, these factors still affect the burning of chaparral fuel by increasing the radiative heat transfer to the fuel ahead of the flame front. However, this did not promote vigorous fire spread. In our limited marginal burning tests using setup A, it was found that the upslope conditions enhanced fire spread. In wildland fire behavior studies, much attention is often devoted to radiation from the flame front as the dominating process in fire spread. Because of the complexity of turbulent flow induced in fire and modified by terrain, the role of convection for heat transfer is sometimes overlooked, making it difficult to explain some features that are observed in fire propagation in complex terrain, such as the above case. By comparing the fire behavior observed in experiments using setups A and B, it is seen that the main difference is due to the aerodynamic effect created by the inclined platform. The detailed flow field in the fire is currently unavailable because of our limited measurement capability. As an auxiliary research tool, the 3D LES approach was used to model chaparral fuel ignition process under the conditions close to experimental setups A and B as 6 = 0.2 m, M = SO%, L = I.2 kg/m2, T, = 27 "C, RH = 30%, and slope 40%. By analyzing the numerical results for flow velocities, temperature, and heat transfer, it is possible to understand the aerodynamic effect induced by fire and terrain slope on marginal burning behavior. At time t = 25 s, Figs. l a and b display the instantaneous 3D gas phase temperature contours

X Zhou et al. I Proceedings of the C:ombustion Institute 31 (2007) 2547-2555
in one half of the computational domain for setups A and B, respectively. The velocity vectors in a vertical section (x-y) along the center of the fuel bed denote the direction and speed of fluid flow. A fire plume is formed above the ignition zone of the fuel bed, and large vortical structures appear at the center and the edge of the fire plume. Ambient air is entrained into the fire plume. Inside the plume the gas undergoes an upward acceleration and the maximum instantaneous vertical speed reaches 4.3 m/ s. Within the fuel bed the flow speed (<0.07 m/s) is strongly reduced due to drag force induced by shrub fuel. When the time evolution of temperature contours is examined, it shows a classic Rayleigh-Taylor instability in which large vortical structures are semi-periodically shed from the burning zone and rise above in the fire plume as coherent structures. The fire plume displays a strong pulsation in flame height. The fire puffing frequency approximated from numerical results is roughly 1.6 Hz that is very close to experimental observations. Because most of burning occurs in the large vortical structures, the pulsation of these structures is believed to play an important role in determining the rate of entrainment, heat transfer rate, and also in determining the flame geometry. In setup B (Fig. lb), air is entrained from both upslope and downslope sides by passing through the bottom of the fuel bed before entering the fire plume. In this case, the air entrainment from both sides is almost balanced, and the fire plume is vertical. Beneath the burning zone, the velocity vectors show an opposed flow induced by the aspired air and the velocity magnitude is very small. For setup A (Fig. la), however, air entrainment into the fire plume from the upslope side is restricted by the inclined platform; entrainment from both sides is thus not balanced. Figure l a shows most of vortical structures appear at the upslope side of the fire plume. By averaging temperature contours in time, it is found that the flame is tilted toward the fuel bed. Under the burning zone in the stem space, the velocity vectors show a local 'wind' that blows upslope at about 0.5 m/s. In our experiments using setup A, the local wind was observed by tracing smoke that moved upward along the inclined platform. To identify aerodynamic effects induced by fire and slope on heat transfer processes, we evaluated the accumulated value of various heat transfer variables integrated through the burning time as QA(t) = Q(t')dt'. Figure 2 illustrates the time evolution of solid phase temperature (T,), and accumulated heat absorbed or released by solid particles through convective heat transfer between gas and solid (QA,,,,) and radiative heat transfer (QArad,,).A solid particle requires sufficient energy from QA,,,, and QArad,to reach its ignition temperature. For a solid particle located at the bottom of the fuel bed, Fig. 2 shows that in the

50 time (s)

Fig. 2. Time evolution of solid phase temperature (T,) and accumulated heat (QA,,,, and QArad,,) absorbed or released by solid particle located at the bottom of the fuel bed for slope setups A and B.
case of setup A, it is ignited successfully due to increased energy from QArad,s and QA,,,,, however, in the case of setup B, it is not ignited because of the cooling effect (negative value) from QA,,,, although QArad,,is still strong. These calculations agree with the ignition results observed in experiments. The calculated fire spread rate for setup A was 0.42mJmin which is in the range of 0.23-0.44 m/min measured from repeated experiments. The contrary results obtained from setups A and B demonstrate that the aerodynamic effect created by the interaction between the flame and the inclined platform became the dominant mechanism in determining burning success. Steeper the slope, the more rapidly the fire will burn upslope (and more intensely) because of both enhanced convective and radiative heat transfer rates. This was verified by our experimental results and by wildland fire behavior.
4.2. Effect of slope on marginal burning
To maintain the fire behavior of setup A, setup B was modified by attaching a piece of steel plate underneath the fuel bed, while maintaining the 0.4 m stem space between the bottom of the fuel bed and the steel plate. A series of fire spread experiments was completed using this modified setup. All experiments were conducted under no wind conditions. The natural changes in live fuel moisture content, ambient temperature, and relative humidity were considered by collecting fuels and conducting experiments over the course of an annual cycle (2003-2004). Moisture content (M) of hoaryleaf ceanothus samples burned on the day of collection was 68% on 11/18/2003, 88% on 5/17/2004, 61% on 7/9/2004, and 54%
X Zhou et a1 / Proceedings of the Combustion Institute 31 (2007) 2547-2555
on 9/10/2004, which indicated that new growth on May and drying out by September - a typical annual moisture trend in chaparral. Other fuels exhibited the change in moisture content similar to ceanothus. The dry fuel loading (L) was 1.24.9 kg/m2 changed with depth (6 = 0.2 m or 6 = 0.4 m) and fuel type. The environmental temperature (T,) ranged from 16 to 39 OC, and the relative humidity (RH) ranged from 17% to 96%. In the experiments, the slope percent was a static value that could be controlled accurately. Experimental uncertainties arise from the heterogeneous nature of the fuel samples and fuel bed, and variations in the ambient temperature, and relative humidity. Uncertainty would be reduced by averaging across repetitions for the same nominal values of all variables. Seventy-three (or 42%) of 173 tests resulted in successful fire spread for different slope percent, fuel moisture content, fuel loading, and ambient conditions. To quantify marginal burning, we define a "marginal burning index" (MBI) that is indicative of a fire's proximity to a successful spread. By excluding the ignition zone, MBI was calculated as the area fraction of fuel burned in the fuel bed after initial ignition. A successful fire spread had MBI = 1.0, and fires that went out had MBI value in a range of 0 < MBI < 1. Near the marginal slope percent, the MBI value was observed to be close to 1.0. Figure 3 illustrates the MBI values obtained from a group of marginal burning experiments for a range of slopes and various burning conditions. For chamise with 6 = 0.2 m, it is found that all MBI values increased with upslope percent. Over a narrow range between 30% and 40%, there

was a sharp increase in MBI values from 0.25 to I. The data suggests that there exists a critical slope (40% for chamise for the conditions in Fig. 3) above which fire spread in these live fuels was successful, and below which fire spread was unsuccessful. This result is consistent with other researchers' observation [4,28] that there is a critical inclination angle for the change of fire behavior and fire spread rate. The convective heat transfer rate would be greatly enhanced around the critical slope leading to a successful fire spread. It is well known that high moisture content can hinder the burning of cellulosic fuels. For manzanita with M = 82%, Fig. 3 shows that the critical slope increases to 50%. This indicates that the marginal slope percent varies with fuel moisture content. Fuel bed depth (or fuel loading) also increases the probability of fire spread success. For chamise with doubling of 6 to 0.4 m, Fig. 3 shows that all fire spread cases were successful even in downslope condition. Another important factor that affects marginal burning is the ambient wind [lo,] I]; however, this is not considered in this paper. Figure 4 illustrates the MBI obtained from marginal burning experiments with ceanothus and scrub oak. For upslope fire spread, there is a critical slope of 40% for ceanothus and 50% for scrub oak. For downslope fire spread, as expected, the effect of slope on marginal burning was not as sensitive as in the case of upslope fire because of decreased heat transfer rate from convection and radiation. Figure 4 illustrates that all fires went out. For ceanothus the MBI decreased with slope from 0 to -70%. However, for scrub oak, the MBI increased to a maximum value of
+Chamise (S=O2 m) Chamise (S=0,4 m) +Manzanita ( M. 2 m)

slope percent

Fig. 3. Marginal burning index obtained from experiments for various burning conditions: chamise (6 = 0.2 m, M = 58%, L = 1.7 kg/m2, T, = 23 "C, RH=49%);chamise(6=0.4m,M=59%,L=3.4kgl m2, T, = 29 "C, R H = 42%); and manzanita (6 = 0.2 m, M = 82%, L = 2.7 kg/m2, T, = 25 "C, R H = 43%).
Fig. 4. Marginal burning index obtained from experiments for various burning conditions: ceanothus ( 6 = 0. 2 m , M=57%, L=2.1kglm2, Ta=34"C, RH = 32%), and scrub oak (6 = 0.2 m, M = 65%, L = 1.8 kglm2, T, = 34 "C, RH = 33%).
X: Zhou et a1 / Proceedings of the C:ombustion Institute 31 (2007) 2547-2555
0.5 with slope from 0 to -100%. It was observed from downslope experiments that some tiny fire brands fell to the unburnt fuels due to gravity. These fire brands might act as igniters to aid burning, but this contribution was hard to judge. Based on 173 marginal burning tests for no wind and different slopes, fuel moisture content, fuel loading, and ambient conditions, a statistical model was developed to estimate the probability of fire spread success. It is expected to provide guidelines for prescribed burning success. Because the response variable (spread success) was binary, a stepwise logistic regression method was used. The result of this model is

40%, the fire spread rate increases greatly because convective heat transfer rate increases greatly around the critical slope. This result is consistent with our analysis in Figs. 3 and 4 on the effect of slope on MBI, and agrees with the results obtained by other researchers [4,8,28].

5. Conclusions

In examining two fuel bed slope setups, the large eddy simulation approach is useful in analyzing the detailed fire structure and the coupled physical processes. Upslope fire spread depends not only on the increased radiant heat transfer rate but also on the aerodynamic effect created by the interaction of the flame with the inclined platform. Under our experimental conditions, the convective heat transfer induced by this interaction becomes the dominant mechanism in determining fire spread success. Experimental results demonstrate that there exists a critical marginal slope below which fire spread is unsuccessful, and above which it is successful. This varies with fuel moisture content and fuel loading. Using a stepwise logistic regression method to analyze these 173 fires, a logistic model was developed to predict the probability of fire spread success. It is clear that the combined effects of wind and slope are not adequately modeled. Further work is still needed to improve the current LES approach, and to obtain more detailed experimental data to validate the numerical model.
The probability P r of fire spread success was set equal to the function of parameters SI (slope percent, %), L (kg/m2), T, ("C), and M (%). The fitted model correctly classified nearly 86% of the 173 fires in the data. This equation is different from our earlier equations [lo,111 because a different subset of the entire data set was used for estimation. When the data set is better balanced, a logistic model will be developed from the entire data set. The slope of the fuel bed influenced not only the marginal burning characteristic, but also the fire spread rate. Fire spread rate is an important variable in wildfires since it is indicative of the potential fire intensity and fire danger. For successful fire spread tests, Fig. 5 illustrates fire spread rate in chaparral fuel beds as a function of slope percent from -70% to 70%. Fuel moisture content, fuel loading, and ambient conditions vary between data points. Figure 5 shows that the effect of slope over the range -70% to 30% on fire spread rate is relatively minor. For slopes above

Acknowledgments

The funding source for this research is the USDAIUSDI National Fire Plan administered through a Research Joint Venture Agreement No. 01-JV-11272166-135 with the Forest Fire Laboratory, Pacific Southwest Research Station, Riverside, CA. We appreciate the efforts of Joey Chong, David Kisor, Lulu Sun, and Watcharapong Tachajapong in assisting with the experimental bums.

References

[I] J.M. Moreno, W.C. Oechel (Eds.), The Role of Fire in Mediterranean-type Ecosystems, Springer, 1994, p. 201. [2] L.R. Green, USDA Forest Service, Gen. Tech. Rep. PSW-51, 1981, pp. 1-36. [3] T. Hirano, S.E. Noreikis, T.E. Waterman, Combust. Flame 22 (1974) 353-363. [4] D.D. Drysdale, A.J.R. Macmillan, Fire Safety J. 18 (1992) 245-254. [5] J.L. Dupuy, Int. J. Wildland Fire 5 (3) (1995) 153164.

Slope percent

Fig. 5. Fire spread rate plotted as function of the slope percent.
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Meteorology, Orlando, FL, November 16-20, 2003. [I91 B. Porterie, D. Morvan, J.C. Loraud, M. Larini, Phys. Fluids 12 (7) (2000) 1762-1782. [20] X. Zhou, J.C.F. Pereira, Fire Materials 24 (2000) 37-43. [21] D. Morvan, J.L. Dupuy, Combust. Flame 127 (2001) 1981-1994. [22] X. Zhou, S. Mahalingam, D. Weise, Combust. Flame 143 (2005) 183-198. [23] X. Zhou, W. Pakdee, S. Mahalingam, Phys. Fluids 16 (10) (2004) 3795-3807. [24] P.J. Pagni, T.G. Peterson, Proc. Combus2. Inst. 14 (1973) 1099-1 107. [25] F.A. Albini, Proc Combust. Inst. 11 (1967) 553560. [26] F.A. Albini, Combust. Sci. Technol 45 (1986) 10. [27] P.A. Santoni, J.H. Balbi, Fire Safety J 31 (1998) 201-225. [28] Y. Wu, H.J. Xing, G. Atkinson, Fire Safety J. 35 (2000) 391403. [29] J. Smagorinsky, Mon. Weather Rev 91 (1963) 99164. [30] X. Zhou, S. Mahalingam, Combust. S c i Technol. 171 (2001) 39-70. [31] B.P. Leonard, Comp. Meth. Appl Mech. Eng. 19 (1979) 59-98. [32] M.F. Modest, Radiatiue Heat Transfer, McGrawHill, New York, 1993. [33] C.M. Countryman, C.W. Philpot, USDA Forest Service Res. Paper PSW-66, 1970, Berkeley, CA, 16 p.
[6] C.E. Van Wagner, Can. J. For. Res. 18 (1988) 8 18820. [7] J.M.C. Mendes-Lopes, J.M.P. Ventura, J.M.P. Amaral, Int. J. Wildland Fire 12 (2003) 6784. [8] D.X. Viegas, Int. J. Wildland Fire 13 (2) (2004) 143156. [9] D.R. Weise, G.S. Biging, in: Proceedings of the Fourth International Symposium on Fire Safety Science, 1994, Ottawa, pp. 1041-1051. [lo] X. Zhou, D. Weise, S. Mahalingam, Proc Combust. Insl. 30 (2005) 2287-2294. [I I] D. Weise, X. Zhou, L. Sun, S. Mahalingam, Int J. Wildland Fire 14 (2005) 99-106. [I21 P.L. Andrews, USDA Forest Service Gen. Tech. Rep. INT-194, Ogden, UT, 1986, 130 p. [13] M.A. Finney, USDA Forest Service Res. Pap. RMRS-RP-4, Ogden, UT, 1998, 47 p. [I41 Forestry Canada Fire Danger Group, Inf. Rep ST-X-3, Ottawa, ON, Forestry Canada, Science and Sustainable Development Directorate, 1992, 65 p. [15] A.M. Grishin, in: F. Albini (Ed.), Mathematical Modeling of Forest Fires and New Methods of Fighting them, Publishing House of the Tomsk University, Tomsk, Russia, 1992. [16] T.L. Clark, M.A. Jenkins, J. Coen, D. Packham, J. Appl. Meteor. 3 (1996) 875-901. [17] R.R. Linn, J. Reisner, J. Colman, J. Winterkamp, Int, J Wildland Fires 11 (2002) 1-14. [I81 R. Rehm, D. Evans, W. Mell, S. Hostikka, K. McGrattan, G. Forney, C. Bouldin, E. Baker, in: 5th Symposium on Fire and Forest

Comments

Juan de Dios Rivera, Universidad Catolica de Chile, Chile. 1. How did you ignite the fuel bed? 2. Did you notice any effect at the side walls on quenching or reducing the flame propagation rate in its vicinity? 3. Did you weigh the remaining char, in order to determine the percent of the fuel that actually burned? 4. Have you considered any re-radiation of the ground into the fuel bed? Reply. The ignition of the fuel bed was described in detail in the experimental setup, section 2. For numerical modeling, the ignition of the fuel bed was simulated by introducing a volumetric heat source over the entire fuel bed depth and This heat supply is maintained until along a length of 20 cm. 70% of fuel in the ignition zone is burned out. Because air entrainment from the lateral sides of the fuel bed was prevented by metal sheeting, it was found that most of the experimental fires maintain a rectilinear shape. The effect of the side walls on quenching or reducing the flame propagation rate is minor. We did not measure the unburned residue after each experimental fire. When the fire spread successfully, virtually all of the fuel was consumed. The marginal
burning index describes the percent of the total fuel bed that was unburned. Because the fuel was elevated 40 cm above the ground, the re-radiation of the ground into the fuel bed was not considered. The ground surface under the fuel bed in the experiments was composed of white, insulating fire brick. While the brick did heat up somewhat due to radiant heat transfer, the amount of energy re-radiated was minimal given that the brick did not reach 100 "C for the duration of the experiment.
Carlos Fernandez-Pello, University of California Berkely, USA. Heat transfer by conduction and radiation in the porous fuel bed can be an important mechanism of fire spread. Have you considered these effects in your analysis? Reply. Heat transfer by conduction might be minor but radiation is important. The term QArad,,represents the radiative heat transfer received by a particle in the fuel bed. By virtue of the particle's location, all radiative heat transfer is through the porous fuel bed-

X Zhou et al. 1 Proceedings of the Combustion Institute 31 (2007) 2547-2555
either from the flame above the fuel bed or from the flame zone within the fuel bed. At this point in time, the model does not distinguish between these two
sources. Due to the fuel bed porosity in this experiment, the mean free path for radiant heat transfer is about 16 cm.