C. H. Hunter
Westinghouse Savannah River Company
Aiken, SC 29808

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Historical data for wet bulb globe temperature (WBGT) were requested by WSRC Systems Engineering as part of an assessment of climate on loading operations to be conducted at the proposed Low Enriched Uranium (LEU) Loading Station in H-Area. This facility will have an insulated roof and partially enclosed sides to allow cooling inside the facility by natural convection. In 1996, the SRTC Atmospheric Technologies Group developed a computer algorithm to estimate WBGT using standard meteorological measurements. This algorithm assumes exposure to the ambient environment; consequently, modifications were necessary to simulate WBGT inside a partially enclosed structure such as the LEU Loading Station. To meet programmatic time constraints, these modifications, as described in this report, were kept simple and consistent with the overall framework of the existing WBGT algorithm. A brief field test and a qualitative review of results using meteorological data from the summer of 1999 suggest that the modified algorithm provides reasonable estimates of WBGT for the LEU Loading station environment.

Heat stress management at the Savannah River Site (SRS) utilizes a hierarchy of protective controls for outdoor work based on observed values of the wet bulb globe temperature (WBGT). Through the mid-1990s, routine measurements of WBGT were taken manually with a portable instrument, and the results disseminated to onsite workers via telephone. Subsequent workforce reductions adversely affected the ability of the WSRC Industrial Hygiene department to continue routine measurements. To ensure continued compliance with programmatic requirements, a computer algorithm was developed that calculates reliable estimates of WBGT using standard meteorological measurements from the Central Climatology facility near N-Area (Hunter and Minyard, 1999). This algorithm was configured to execute automatically every 15 minutes, with the results posted to the SRS ShRINE Intranet web site. In addition, the algorithm can be used with archived meteorological data to determine WBGT for investigations of heat-related occurrences or conducting long-term characterizations of heat stress potential.

The Highly Enriched Uranium (HEU) Blend Down Project will blend HEU feedstock from H-Canyon with offsite sources of natural uranium solution to produce low enriched uranium (LEU). The LEU will be shipped offsite for further processing and eventually will be used as fuel for the Tennessee Valley Authority’s Browns Ferry nuclear power plant. The LEU from H-Canyon will be transferred to a 20-gallon Measuring Tank, then drained to trailer mounted Type B containers for shipping. Loading operations for these containers are conducted within the LEU Loading Station. The LEU Loading Station is a clear-span, partially enclosed structure with roof and ridge vents. The structure is 25 feet wide, 60 feet long and 22 feet high. The sides of the building are partially covered by wall panels; a 3-foot section at the base of a side and a 4-foot opening along the eave will remain open to the environment. One end of the structure is open to allow trailer ingress and egress, and the other end is fully enclosed. The room consists of sheet steel exterior with a 4-6 inch layer of insulation and slopes slightly downward from the ridge center with a 3-foot overhand (WSRC, 2001).

The American Conference of Governmental Industrial Hygienists (ACGIH) threshold limit values (TLV) for heat exposure provide the basis for heat stress management at SRS (WSRC, 1995). The heat exposure TLV’s are based on observed values of wet bulb globe temperature (WBGT). The WBGT is defined as:

WBGT = 0.7T_n + 0_.2T_g + 0.1T_a (1)

WBGT = 0.7T_n + 0.3T_g (2)

for outdoor and indoor work, respectively, where T_n is a "natural" (static) wet bulb temperature, T_g is a "globe" temperature, and T_a is the ambient (dry bulb) temperature.

Unlike standard wet bulb temperature, T_w, which is typically used to quantify atmospheric moisture, ‘natural’ wet bulb provides a direct measure of the apparent temperature achieved by a moist, radiantly reflective body in equilibrium with the ambient environment. A natural wet bulb thermometer consists of a standard mercury thermometer covered with a wetted, white muslin wick and exposed to the atmosphere without ventilation or shielding, fully subject to gains and losses of heat through evaporation, solar radiation, and convection.

Similarly, T_g is used to approximate the temperature of a dry, radiantly absorptive body in the ambient environment. The globe thermometer consists of a thermally sensitive element placed at the center of a blackened, hollow copper sphere.

Neither T_n nor T_g represents perfectly the heat load on a clothed human body. Therefore, the WBGT heat stress "model" is expressed as a weighted sum of these apparent temperatures. The respective weights are based on correlations with observed deep body temperature and other physiological responses to heat (ACGIH, 1995). In practice, values of WBGT are used to determine one of six heat stress categories. Each category, in turn, defines a prescribed work/rest regimen for outdoor activities.

Prior to the summer of 1996, routine measurements of WBGT were conducted with a portable, manually operated instrument. This device consists of a natural wet bulb thermometer, a globe thermometer, and a dry bulb thermometer incorporated in a single hand-held unit. A processor within the device automatically interrogates each of the three temperature sensors every few seconds, processes the data, and outputs a WBGT value on a LCD display. Operating procedures required that WBGT measurements be taken with the portable instrument several times per day from May through September (WSRC, 1995). Workers could then phone, as needed, and obtain reasonably current WBGT information.

Workforce reductions at the SRS during the mid-1990s adversely affected the resources needed to support routine collection of the WBGT data. Consequently, the SRTC Atmospheric Technologies Group (ATG) was requested to develop an automated method for determining WBGT using standard meteorological data collected in real-time from ATG’s Central Climatology monitoring station near N-Area.

Meteorological monitoring at SRS is conducted from a network of nine 61-meter (m) towers. Eight towers are located adjacent to the primary operations areas at SRS: A, C, D, F, H, K, L, and P areas. These towers are equipped to measure wind speed, wind direction, temperature, and dew point at 61m and temperature and dew point at 2m above ground level. The ninth tower, the Central Climatology tower near N-Area, is equipped to measure wind speed, wind direction, temperature, and dew point at four levels (2m, 18m, 36m, and 61m), plus precipitation, pressure, and solar radiation at ground level. All data are recorded as 15-minute averages and automatically forwarded to the Weather Information and Display System computers in A-Area for archival in a relational database.

The two principal temperatures that comprise WBGT, natural wet bulb temperature, T_n and globe temperature, T_g, are specialized quantities that are not in standard meteorological monitoring programs. The following sections describe algorithms used to estimate T_n and T_g from a more conventional set of measurements (Hunter and Minyard, 1999).

An examination of WBGT data collected manually during the summer of 1995 provided several insights on the behavior of T_n. First, T_n was always bounded by the standard psychrometric wet bulb, T_w, and T_a. The effects of sunlight on T_n appeared to be relatively small, i.e., the white wick reflects much of the incoming solar energy. Furthermore, T_n tended to approach T_w if the wind speed was equal to or greater than the airflow across a standard ventilated instrument used to determine T_w such as an aspirated dew point hygrometer or sling psychrometer. Alternatively, if conditions were not conducive to evaporation (light winds and high humidity), the natural wet bulb depression, (T_a -T_n), tended to be less than that which occurs under breezy conditions, and, in some cases, appeared to approach values that were one-third to one-half a standard wet bulb depression.

The expression currently used to estimate T_n was developed from manual WBGT data collected on ten days during June and July of 1999. These days were selected to yield data for a representative range of conditions expected during a summer. An analysis of variance was performed to determine the relationship between measured values of T_n and 15-minute average meteorological data from Central Climatology. Nearly 70 percent of the variance in the difference between T_n and T_w was explained by wind speed and solar radiation. Multiple linear regression on the data resulted in the following predictive expression for T_n:

T_n = T_w + 0.021S - 0.42u + 1.93 (3)

Where S is solar irradiance (W/m²) and u is wind speed (m/s). The coefficients have units that are necessary to provide a result in Fahrenheit temperature.

The wet bulb temperature is calculated from the expression:

where P is pressure (inches of mercury), N = (T_a - T_d)/10, and coefficients have consistent units for Fahrenheit temperature.

Estimates of T_n are calculated from these equations using measured values of S, u, T_d, T_a, and P.

Globe temperature, T_g, is calculated explicitly using the expression

The two terms on the left side of Eq. (5) represent the sum of radiant energy absorbed by the globe in the visible (term [1]) and infrared wavelengths (term [2], respectively. Solar radiation, S, striking the earth’s surface consists of direct beam (db) radiation from the sun and diffuse (dif) radiation reflected by clouds and other atmospheric constituents. For high solar angles (midday) and cloudless skies, approximately 75 percent of the total incoming solar energy consists of direct beam radiation and the remaining 25 percent diffuse radiation (Oke, 1978). The contribution of diffuse radiation to the total solar load increases with increasing cloudiness and haze and with lower solar angles. Since summer afternoons at SRS are frequently hazy with some cloudiness, the average fractional contribution of direct beam radiation, f_db, and diffuse radiation, f_dif, were assigned values of 0.67 and 0.33, respectively.

Solar irradiance, S, is measured at Central Climatology by a radiometer that is level with respect to the horizontal plane (i.e. the earth’s surface). The spatially averaged direct beam irradiance on any three dimensional object can be related to measured values of S by determining a shape factor, s, for the object. The shape factor for a sphere (globe) is defined as the ratio of the area of a shadow projected on a horizontal plane to the surface area of the sphere, or

s_sp = p r²/(4p r²cos(z)) = 1/(4 cos(z)) (6)

where z is the solar angle to zenith.

Diffuse solar radiation is isotropic, that is, emitted (or received) equally in all directions. Therefore, the diffuse solar radiation measured by a radiometer is equal to that received by the upper hemisphere of the globe. The lower hemisphere of the globe will receive solar radiation that is reflected from the ground and nearby low structures. The albedo, a _es, for grassy surfaces ranges from 0.15 to 0.25. A value of 0.2 was assumed for this calculation (Budyko, 1974).

The second term on the left of Eq. (5) is the long-wave (thermal) black-body radiation emitted by (received from) a moist, cloudless atmosphere of temperature T_a and thermal emissivity e . Thermal emissivity, a nondimensional function of atmospheric water vapor, is calculated from the empirical formula

e _a = 0.575e_a^(1/7) (7)

e_a is atmospheric vapor pressure (Oke where, 1978). Real-time values of e_a are determined from the expression

Temperatures in Eq. 8 are Celsius and pressures (atmospheric and vapor) are in millibars. The Stefan-Boltzmann constant, s, in Eq. (5) is equal to 5.67 x 10^-8 (Wm^-2K^-4).

Imperfections in the black matte finish of the globe thermometer will cause small amounts of radiation striking the surface of the sphere to be reflected back to the atmosphere. Globe albedo for solar and infrared radiation, a _sps and a _spl, respectively, were assigned a value of 0.05 (Kuehn, 1970).

The two terms on the right side of Eq. (5) represent total radiant energy lost by the globe. The first term (term [3]) expresses long-wave black body radiation emitted from a globe at temperature T_g. The thermal emissivity, e , for a globe of black matte finish was assigned a value of 0.95 (Kuehn, 1970). The second term on the right (term [4]) is an empirical expression recommended by Kuehn (1970) for the net convective heat loss (or gain) from a sphere of temperature T_g (^oC) immersed in air of temperature T_a (^oC) moving at a speed u (meters/hr).

Equations (6) – (8) are evaluated using real-time 15-minute averages of S, T_a, T_d, P, and u from Central Climatology. An iterative procedure is used to determine the value of T_g that satisfies a steady-state equilibrium condition. Using Descartes rule of signs for polynomials, this result provides the only positive, real root that satisfies Eq. 5.

Computed values of T_n and T_g are used with observed 15-minute averages of T_a to determine WBGT according to Eq. 1. Field tests of the algorithm have shown that the estimates of T_n, T_g, and WBGT agree well with measured values (Hunter and Minyard, 1999).

The computer algorithm described above was copyrighted in 2000 as the WBGT Calculator (copyright SRS-00-511C.)

The WBGT Calculator algorithm applies to workers in the ambient environment. An individual inside a partially enclosed structure will receive little or no direct sunlight, but may be exposed to local sources of radiant heat such as a relatively hot roof or side panels. Consequently, modifications to the basic algorithm were necessary to calculate an adequate estimate of WBGT inside the LEU Loading Station. To meet the time constraints of the requesting organization, these modifications were purposefully simple and consistent with the overall framework of the WBGT Calculator algorithm.

The most significant modifications affect the determination of T_g. Two calculations prior to final determination of T_g were added:

1. Estimate the temperature of the outer surface of a flat roof.

To estimate of the equilibrium temperature of the outer skin of a flat (or nearly flat) roof, Eq.5 was modified to account for a different geometry and surface emissivity. The term s_sp is set to a value of one (1) since the irradiance on a flat roof (i.e. a surface nearly parallel to the horizontal plane of the earth) will be approximately equal to that measured by the pyranometer at Central Climatology.

Eq. (5) then becomes:

(1-a_rs)S[f_db+ f_dif] + e _a(1-a _rl)s T_a⁴
= e s T_roof ⁴ + 0.115u^0.58(T_roof-T_a) (9)

Albedo for the roof will depend on the type of material, the finish (i.e. polished, painted), and wavelength of the incident radiation. The LEU roof consists of sheet steel, and for the purpose of this study, was assumed to be painted with a relatively reflective coating, i.e., a light color oil paint. Albedos (a_rs and a _rl, respectively) for this surface are estimated to be about 0.7 in the visible wavelengths and 0.25 in the infrared wavelengths (Iqbal, 1983). Eq. 9 is solved iteratively and the resulting value for T_roof is applied in step 2.

2. Estimate the equilibrium temperature of the inner roof surface (ceiling).

The LEU roof will be insulated to achieve a minimum thermal resistance per unit are, R, of 19 W/K-m² (Chang, 2001). Heat energy transfer per unit area by conduction, Q (W/m²), from the outer roof surface (warm) to the inner surface (cool) was estimated using a simple steady state relationship (Kreith, 1973).

Q_c= (T_roof-T_a)/R (10)

The equilibrium temperature of the inner roof surface (T_ceil) will depend on the sources of radiant heat within the structure and the heat gained from conduction. Assuming no local radiant sources are present other than the surrounding air, T_ceil is determined by solving the expression

(1-a _cel)s T_ceil⁴ = Q_c+(1-a _cel)s T_a⁴ (11)

where a _cel in this calculation is the albedo of the ceiling to thermal wavelengths. This albedo is assigned a value of 0.35 (Chang, 2001).

Given T_ceil, an estimate of the globe temperature at ground-level inside the LEU Loading Station was determined from a modified form of Eq (5):

(1-a_sps)S[0.1(1 + a_es)f_dif)] + e _a(1-a _spl)s T_ceil⁴ = e s T_g⁴ + 0.115u_i^0.58(T_g-T_a) (12)

This expression assumes that radiant heat from the ceiling is isotropic, i.e., the ‘hot’ ceiling is a sphere symmetric with respect to the globe thermometer. Generally, this assumption should be conservative since, on average, the sides of the structure will be cooler than the ceiling. A small contribution to T_g will come from diffuse sunlight through the open sides of structure. For this calculation, the value of S was assumed to be one-tenth the value of the diffuse component of ambient solar irradiance. In addition, wind speed inside the structure, u_i, was assumed to be 20 percent of the ambient wind speed. Globe albedos for both solar and thermal wavelengths were assigned values of 0.05, as before.

The natural wet bulb temperature within the LEU Loading Station was based on Eq. (3) with two adjustments: (1) the solar irradiance, S, inside the structure was assumed to be 10 percent of the measured ambient value and (2), the wind speed, u, was assumed to be 20 percent of the measured ambient value. The adjustments assumed for S and u are qualitative estimates; site-specific measurements are needed to define more certain values.

Final calculation of WBGT inside the LEU Loading Station was based on Eq. (2).

Results from a brief informal field test and a review of WBGT data for May-September 1999 were used to demonstrate the adequacy of the modified algorithm. The field test was conducted October 24, 2001 in and around 643-43E, a structure very similar in design to the LEU Loading Station. Weather conditions during the time of the test were partly cloudy with unusually warm temperatures, light wind, and relative humidity around 50 percent. A manual WBGT instrument was used to measure T_a, T_n, T_g, and WBGT over a 20-minute interval in the early afternoon. These measurements are summarized in Table 1. This table also shows (in parenthesis) calculated values for T_n, T_g, and WBGT using the modified algorithm for a partially enclosed structure. For this test period, calculated values show good agreement with the measurements.

In addition, measurements were collected in a well-exposed area outside of 643-43E. These data illustrate the significant effect of solar radiation on T_g and on the final WBGT result.

A modified algorithm for calculating WBGT in a partially enclosed structure such as the LEU Loading Station in H-Area, using readily available standard meteorological data, has been developed. A brief field study suggests that this algorithm can provide users acceptable results for use in heat stress evaluations. Further evaluation over a wide range of meteorological conditions is warranted prior to more general applications.

In general, the data demonstrate that the shade provided by a partially enclosed

structure gives a significant reduction in WBGT, as long as the structure utilizes materials with low thermal emissivity and/or high thermal resistance to minimize sources of radiant heat.

1. American Conference of Governental Industrial Hygienists (ACGIH), 1995-1996 Threshold Limit Values (TLVs) for Chemical Substances and Physical Agents and Biological Exposure Indices (BEIs).
2. Budyko, M. I., Climate and Life, p. 54, Academic Press, New York (1974).
3. Chang, Information Regarding LEU Loading Station, e-mail communication dated October 22, 2001.
4. Hunter, C. H. and C. O. Minyard, Estimating Wet Bulb Globe Temperature Using Standard Meteorological Measurements, WSRC-MS-99-00757, Westinghouse Savannah River Company, Aiken, SC (1999).
5. Iqbal, M. An Introduction to Solar Radiation, Academic Press, New York (1983).
6. Kreith, F., Principles of Heat Transfer, 3^rd Edition, Intext Educational Publishers, New York (1973)
7. Kuehn, L. A., et al., Theory of the Globe Thermometer, Journal of Applied Physiology, Vol. 25, No. 5, pp 750-757 (1970).
8. Oke, T. R., Boundary Layer Climates, pp 339-390, Methuen & Co., New York, New York (1978)
9. Westinghouse Savannah River Company (WSRC), The SRS Heat Stress Management Program, Procedure Manual 4Q, Procedure 502, Revision 2 (1995).
10. WSRC, LEU Production Time-Motion for the HEU Blend Down Project, G-ESR-K-00006 Rev. A (2001)