Annals of Occupational Hygiene Advance Access originally published online on May 22, 2007
Annals of Occupational Hygiene 2007 51(4):357-369; doi:10.1093/annhyg/mem016
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Published by Oxford University Press
Evaluation of a Proposed Velocity Equation for Improved Exothermic Process Control
1 National Institute for Occupational Safety and Health, Division of Surveillance, Hazard Evaluation and Field Studies, 4676 Columbia Parkway, MS-R14, Cincinnati, OH 45226, USA
2 Department of Work Environment, Universtiy of Massachusetts Lowell, One University Avenue, Lowell, MA 01854, USA
* Author to whom correspondence should be addressed. Tel: +1-513-841-4212; e-mail: JMcKernan{at}cdc.gov
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONEQUATIONS AND METHODSRESULTSDISCUSSION AND CONCLUSIONSAPPENDIX A: NOMENCLATURE AND...ACKNOWLEDGEMENTSREFERENCES |
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Exothermic or heated processes create potentially unsafe work environments for an estimated 5–10 million American workers each year. Excessive heat and process contaminants have the potential to cause adverse health effects in exposed workers. Owing to the potential hazards, engineering controls are recommended for these processes. Our understanding of heat transfer and meteorological theories, and their applications for engineering controls have evolved since seminal work was published by Hemeon in 1955. These refined theories were reviewed and used to develop a proposed equation to estimate buoyant plume mean velocity. Mean velocity is a key parameter used to estimate the plume volumetric flow required for controlling effluents from exothermic processes. Subsequent to developing the proposed equation, plume velocity data were collected with a thermal anemometer for a model exothermic process in the laboratory, and an actual exothermic process in the field. Laboratory and field results were then compared to solutions provided by the proposed, American Conference of Governmental Industrial Hygienists (ACGIH), and Hemeon mean velocity equations. To determine which equation most closely matched the laboratory and field data, either t-tests or Wilcoxon Signed Rank tests were conducted (based on examination of data normality) to determine the difference between collected data and solutions from the proposed, ACGIH, and Hemeon equations. Median differences and P-values from Wilcoxon Signed Rank tests (nonparametric) indicate that the ACGIH mean velocity equation provides significantly different estimates from the laboratory and the field mean velocity data. However, the proposed and Hemeon equation provided solutions that were not significantly different from the collected data. These results were unexpected due to the similar developmental backgrounds between the ACGIH and Hemeon equations. Findings indicate that radiant heat flux is an important consideration when using horizontal plate heat transfer equations to estimate plume mean velocity over the range of parameters investigated. Results indicate that the mean velocity equation currently recommended by ACGIH is not as accurate as either the proposed or Hemeon equations over the range of parameters investigated.
Keywords: engineering controls • hot process • local exhaust ventilation
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONEQUATIONS AND METHODSRESULTSDISCUSSION AND CONCLUSIONSAPPENDIX A: NOMENCLATURE AND...ACKNOWLEDGEMENTSREFERENCES |
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The current understanding of engineering controls for exothermic processes is based on a book chapter originally written in 1955 by W.C.L. Hemeon (Hemeon, 1955). Subsequently, Hemeon reissued a second edition in 1963, and a separate editor issued an updated, retitled third edition in 1999 (Hemeon, 1963, 1999). Hemeon developed Newtonian and empirical equations based on simplified heat transfer theory for vertical plates and meteorological theory to estimate buoyant plume mean velocity (
) and area (A) that are necessary to calculate volumetric flow (Q). The volumetric flow above a heated source is defined as the product of the plume mean velocity and area (ACGIH, 1998; Hemeon, 1999). The purpose of the currently accepted equations by Hemeon and the American Conference of Governmental Industrial Hygienists (ACGIH) is to estimate the plume volumetric flow (Q) at which heat and fine particle effluents are being introduced to the face of the engineering control (i.e. receiving hood). Determining the plume flow is of critical interest for two reasons: (1) it must provide adequate control of the effluent to prevent spillage back into the workplace air; (2) it should be calculated as accurately as possible to prevent overventilating the process, as this wastes conditioned indoor air. Accuracy of the flow estimation is important, as results from a laboratory study to determine the accuracy of Hemeon's flow equation indicated that this equation overestimates the flow above heated sources leading to excess process ventilation (Siebert and Fraser, 1973).
In calculating the volumetric flow (Q) present above exothermic processes, both the buoyant plume mean velocity () and area (A) continually change as the plume rises. As a first step in assessing the plume flow, the goal of this research is to ascertain the plume mean velocity at which heat and fine particle effluents are being introduced to the face of a receiving hood located above an exothermic process. Hemeon was the first to provide an estimation equation for this purpose (Hemeon, 1955, 1963, 1999). A slightly modified version of the original Hemeon plume mean velocity equation continues to be used, as it is the base on which the currently recommended equations in the US Public Health Service (USPHS) Air Pollution Engineering Manual, and the ACGIH Industrial Ventilation Manual are constructed (ACGIH, 1998; USPHS, 1973). In an attempt to generalize Hemeon's equation, the USPHS and ACGIH slightly modified Hemeon's original work by substituting a horizontal heat transfer equation in place of the vertical equation originally used by Hemeon. Beyond this modification of Hemeon's velocity equation, the U.S. Environmental Protection Agency (EPA), ACGIH, and Heinsohn have also implemented subjective safety factors in an attempt to address the uncertainty and inability to match empirical data to the solutions from the equations (ACGIH, 1998; Heinsohn, 1991; USPHS, 1973). However, improvements in the application of heat transfer and meteorological theories have occurred since the time of Hemeon's publications (Jaluria, 1980; Stewart et al., 1958; Sutton, 1950; USAEC, 1968). These improvements were used to develop a proposed mean velocity equation that utilizes heat transfer theory for vertical bodies (McKernan and Ellenbecker, 2007).
Observational experiments that could be used to validate Hemeon’s plume mean velocity equation have also been conducted. However, many were focused on determining the buoyant plume volumetric flow (Bender, 1979; Goodfellow and Bender, 1980; Siebert and Fraser, 1973). Issues with this research are that they do not consider the plume mean velocity and area variables separately, thereby introducing the potential to characterize inappropriately or oversimplify basic properties of the buoyant plume. Both parameters are important, and should be determined separately. For example, to construct an adequately sized and ventilated capture hood, information beyond the single flow solution is required. The plume radius or diameter must be known, as well as the average velocity of the plume at the height of the control device. These separate parameters ensure that the receiving hood is of the appropriate size and has sufficient face velocity to receive and contain the plume.
Earlier works that were focused on determining the rising plume velocity were conducted by Rouse et al. (1952), Morton et al. (1956), and Schmidt (1941). Rouse and colleagues used a gas burner as the point source for their experiments, which is not comparable to the work presented here, due to the changes in the properties of the air caused using a combustion source. Combustion sources are more closely related to forced convection (i.e. jets), which is not comparable to natural convection, since assumptions governing natural convection include minor fluid density changes and zero velocity at the point source. The addition of significant mass and drastic changes to the physical properties of the medium (i.e. air density) in Rouse and colleagues invalidates the balanced equations for volume, momentum, and density conservation required for solution of the governing physical equations. Therefore, the applicability of Rouses' plume mean velocity equation to processes with non-combustion sources is in question (Rouse et al., 1952).
Morton and colleagues gave the subject much consideration, and through differential equation development and limited experiments using a jet of dye in water, validated much of the previous meteorological research conducted on buoyant plumes (Morton et al., 1956). Morton and colleagues provided integral equations for balanced volume, momentum and density conservation required for determining buoyant plume velocity, density and temperature. In providing these equations, he also gave strong evidence based on his and Schmidt’s work, that the velocity and temperature characteristics of the buoyant plume cross-section is best described using the Gaussian distribution (Schmidt, 1941). Pitfalls of this work that have been repeated by Hemeon and Sutton are that the integrated equations invariably require the selection of a constant to obtain a useful numerical solution. Values for these integration constants have been hypothesized and experimentally derived; however, they always have caveats for their use. Although it may have been erroneous to do so, Morton and colleagues provided equations to describe characteristics of the buoyant plume using constant values extrapolated from the works of Schmidt, and Rouse and colleagues. The utility of his equations is limited by the use of these constants.
Schmidt provided seminal research in the area of empirical equation development for the characterization of buoyant plumes (Schmidt, 1941). Major limitations of his work include a lack of details regarding his experimental apparatus and conditions. The physical characteristics of the heated source used in his experiments are not described in any detail, and there is no information regarding heated source or environmental temperatures for his experiments. These limitations do not allow for comparison of his work to that provided here, since physical characteristics and excess temperatures of the source are necessary to solve the proposed equation. Therefore, the historical research does not include a detailed investigation of buoyant plume velocity for conditions with a non-combustion heat source in steady-state, producing a constant buoyant plume.
Mundt conducted research into the behavior of buoyant plumes (Mundt, 1996). Mundt utilized Morton and colleagues differential equations, and provided generalizable integrated solutions. The most applicable aspect of Mundt’s research is the point source model developed to describe buoyant plume characteristics, including velocity. Limitations of the point source model developed by Mundt include the use of the same constants as Morton and colleagues, and the use of an empirically derived convective load term.
This paper presents: (1) an overview of the current mean velocity estimation equations, and proposed equation development; (2) description of the laboratory and field work conducted; (3) statistical comparison of the laboratory and field results to solutions from the proposed and current mean velocity estimation equations. The latter provides an evaluation of the accuracy of the current and proposed mean velocity estimation equations. With this information, ventilation engineers and practising industrial hygienists will be better equipped to design ventilation systems for adequate control of buoyant plumes and any contaminants within them.
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EQUATIONS AND METHODS |
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TOPABSTRACTINTRODUCTIONEQUATIONS AND METHODSRESULTSDISCUSSION AND CONCLUSIONSAPPENDIX A: NOMENCLATURE AND...ACKNOWLEDGEMENTSREFERENCES |
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A review of heat transfer and meteorological theories provide the basic differential, partial differential, and integral equations to evaluate velocity in the boundary layer close to a vertical heated source, and in the buoyant thermal plume (McKernan and Ellenbecker, 2007). However, since a secondary objective of this work was to provide simplified equations for use by practitioners, integrated correlation equations are presented in lieu of complex equations with exact solutions. Results from the laboratory and field were compared statistically with solutions from the proposed, ACGIH, and Hemeon plume mean velocity equations.
Plume Mean Velocity Equation Development
To develop the proposed mean velocity equation, two equations must be introduced. The first provides the boundary layer thickness, and the second provides the total heat flux from the source. For air at 296 K, the boundary layer thickness (
[m]) equation from heat transfer theory provides (Jaluria, 1980; McKernan and Ellenbecker, 2007):
 | (1) |
T = Excess temperature; Ts – T
(K)
Ts = Surface temperature of heated source (K)
T = Ambient temperature (K)
By definition, the velocity at the outer edge of the boundary layer is 1% of the maximum velocity inside the layer.
Meteorological theory described by Sutton translates excess temperature between the heated source and ambient environment into power per unit area (Sutton, 1950). The power per unit area, or total heat flux from the source (P [W m–2]) is expressed as the sum of the radiant (PR) and convective (PC) heat flux based on Stefan-Boltzmann’s law and Newton’s law of cooling (Lide and Frederikse, 1996; McKernan and Ellenbecker, 2007).
 | (2) |
= Emissivity of heated material; 0.95 (dimensionless) (Lide and Frederikse, 1996)
' = Stefan-Boltzmann constant; 5.67 x 10–8 (W m–2 K–4)
hP = Natural convection heat loss coefficient for horizontal plates; 1.52(T)0.33[W m–2 K–1]
The last parameter required to develop the proposed equation for plume mean velocity is the vertical height (H) above the virtual point source. H is the sum of the determined distance between the top surface of the heated source and the virtual point source (Z' [m]), and the distance between the top surface of the heated source and a point of interest on the plume centerline (Z [m]). Figure 1 provides a visual representation of this concept, and the characteristic equation for vertical height is:
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 | (4) |
(m)
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RS = Physical radius of heated source (m)
For comparison, the respective ACGIH and Hemeon equations for Z' and H are (ACGIH, 1998; Goodfellow, 1985; Hemeon, 1999):
 | (5) |
 | (6) |
) is an application of compiled meteorological theory outlined by Sutton (Stewart et al., 1958; Sutton, 1950). The proposed equation relates gravitation, power per unit area, and the physical properties of the heated medium to provide a plume mean velocity (m s–1) at a given height (HP) (McKernan and Ellenbecker, 2007):
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 | (8) |
AS = Projected area of source; 
(RV)2 (m2)
P = Total heat flux from the source (W m–2)
CP = Specific heat of ambient air at T; 
1000 (J kg–1 K–1)
= Density of ambient air at T; 1.20 (kg m–3)
C = Diffusion coefficient for stable environments; 0.12 (dimensionless) (Stewart et al., 1958).
A case study illustrating the use of this proposed plume mean velocity equation is provided in Appendix A. For comparison, currently accepted equations to determine plume mean velocity from the ACGIH (
) and Hemeon (
) are (ACGIH, 1998; Hemeon, 1999):
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(RS)2 (m2)
T = Excess temperature; (Ts – T) (K)
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T)0.25 (BTU hr–1 ft–2 °F–1)
AB = Area of entire cylinder emitting heat; (3.28RS)2 + 21.5LRS (ft2; L and RS in m)
T = Excess temperature; (Ts – T) (°F)
Experimental Design and Equipment
Experimental data were collected from three facilities:
- University of Massachusetts (U. Mass) Lowell, North Campus in the Pinanski building, Lowell, MA
- National Institute for Occupational Safety and Health (NIOSH), Hamilton Building Ventilation Laboratory, Cincinnati, OH
- An art glass facility in Cincinnati, OH
At U. Mass Lowell and NIOSH, a vertical cylinder was selected to represent the basic shape of an exothermic process container, such as a reactor or furnace. This model heated source was constructed of round galvanized steel ductwork, 0.15 m in diameter and 0.30 m high. The cylinder was painted matte black to better approximate the predictable radiant and absorptive properties of a black-body ( = 0.95). The heated vertical cylinder was placed 0.30 m above the floor on an electrically grounded platform in a 7.62 by 9.14 by 2.43 m room at Lowell, and a 3.65 by 4.57 by 2.43 m room at NIOSH. The cylinder was placed away from objects that could potentially disturb the buoyant flow around and above the cylinder. An attempt was made to control room drafts by sealing air supply and return ducts, as well as gaps around doors and windows.
For the low-temperature (TS < 343 K) experiments, the vertical cylinder was filled with sand. It was heated internally with heat tape capable of 800 W output (Model EW-36050-30, Cole Parmer, Vernon Hills, IL) spiraled from top to bottom in the cylinder, suspended in the sand. A proportional voltage controller with thermocouple probe (Fisher Scientific, Model MC240X1, Pittsburgh, PA) was used to regulate the heat output of the tape to ensure uniform heating of the cylinder throughout the experiments. Surface temperatures were collected using a thermocouple attached to the proportional voltage controller, and ambient temperatures were collected in the center of the room using a sling psychrometer (Dwyer Instruments Inc., Model A-525, Michigan City, IN).
Alternatively, for the high-temperature (TS > 343 K) experiments conducted at NIOSH, the interior of the same cylinder contained heavy-gage aluminum stock with air space between the stock and exterior walls of the cylinder. The apparatus was heated at the bottom with a 1100 W (maximum output) 0.15 m diameter electric heating element with a built-in proportional voltage controller (Durabrand, Model SBS110-B, Bentonville, AR). Surface temperatures were measured with a high-temperature immersion mercury thermometer (Fisher Scientific, Model NC9262583, Pittsburgh, PA). Ambient temperatures were measured using a mercury thermometer positioned at 1.50 m above the floor in the center of the room (Fisher Scientific, Model 15-041-1A, Pittsburgh, PA).
Data collected at the art glass facility were an extension of the high-temperature experiments. Velocity measurements were conducted above a custom-constructed rectangular melting furnace with dimensions of 2.31 by 1.33 by 1.66 m. Rectangular or cubic geometries were converted to cylindrical dimensions using the source height and hydraulic diameter. The furnace walls and the interior were constructed of refractory brick with a heavy-gage steel insulated top. The internal temperature of the melting furnace was maintained at 1273 K using a thermocouple monitoring system and two internal gas burners that were fired as necessary to provide uniform heating. Surface temperature measurements for the steel top were collected using a non-contact infrared (IR) pyrometer (3M Co., Model IR-16EXL3, Austin, TX). Ambient temperature measurements were collected using a mercury thermometer mounted on a wall 2 m from the floor and 5 m away from the source (Fisher Scientific, Model 15-041-1A, Pittsburgh, PA). Here, an attempt to minimize drafts was made through closing doors and windows, and exhaust fans were set to the lowest setting since they could not be deactivated.
All measurements to determine buoyant plume velocity and centerline air stream temperatures were collected using a hot-wire anemometer (Velocicalc Plus Model 8386A, TSI Inc., Shoreview, MN). Calibration was conducted by the manufacturer prior to the collection of laboratory and field data. The instrument allows for the measurement of air velocities in the range of 0–50 m s–1, with an accuracy of ±0.02 m s–1 or ±3% of reading, whichever is greater. Additionally, the instrument can measure air stream temperatures in the range of –263 to 333 K, with an accuracy of ±0.30 K. Velocity measurements were collected along the plume axisymmetric centerline at various heights above the heated source, providing maximum velocity data. Thirty minutes was given between each change in temperature to provide time for the source to achieve steady state conditions. Between each change in height (Z), the probe was moved to the next height of interest in the plume, and 5 min was given to provide the anemometer probe time to equilibrate to that plume temperature. Horizontal plume traverses were not conducted due to the inability to measure a sufficient number of points accurately across the diameter of the plume. The edges of the plume are known to have low or unstable velocities far from the centerline (Mundt, 1996). The instrument collected velocity data every 20 s, and logged the mean every 120 s. These data were then downloaded into a spreadsheet application for organization and initial analyses (Microsoft Inc., Excel 2003, Redmond, WA). Five height (Z) and six excess temperature (T) combinations were included in the experiments (see Table 1). A minimum of three repetitions were conducted for each unique combination.
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Maximum centerline velocity data from the laboratory experiments were transformed to a mean velocity value (
), since the proposed, ACGIH, and Hemeon velocity equations provide estimates of the plume mean velocity. To transform the measured maximum centerline velocity data (UMax) collected in the laboratory and field to a mean velocity, a transform factor was used. The transform factor was based on those used to describe the mean of turbulent velocity distributions with a parabolic profile (Bird et al., 2002; Ligget and Caughey, 1998).
 | (11) |
Statistical Analyses
A comparison was conducted between the data from the laboratory and field work, and the estimated mean velocity values provided by the three equations. The data from the laboratory and field were considered the reference values in these comparisons. Examinations to determine the normality of the data distribution were conducted for the difference between the mean measured data and the three estimation equations within unique Z and T combinations (i.e. 30 data pairs) using the CAPABILITY procedure in SAS (SAS Institute, Version 9.1.3, Cary, NC). If the data were approximately normally distributed, separate paired t-tests were conducted for the difference of means between the measured data within unique Z and T combinations and solutions from each of the three estimation equations using the UNIVARIATE procedure in SAS. If the data were not approximately normally distributed, three separate nonparametric Wilcoxon Signed Rank tests were conducted using the UNIVARIATE procedure in SAS.
The statistical tests conducted regarded the difference of means (or medians) as uncorrelated between unique Z and T combinations. Ideal results would be that there were no differences between the calculated solution from each of the three estimation equations and the values (i.e. P-values > 0.05). The three t-tests, or Wilcoxon Signed Rank tests, provided an overall assessment of the agreement between the and estimated mean velocity solutions from each of the three equations. If the individual estimation equation analysis fails to reject the null hypothesis, then that equation can be used to estimate the plume mean velocity with insignificant difference from the data. Adjusted coefficients of determination (R2) values are provided as a measure of association between data, and excess temperature or height parameters.
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RESULTS |
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TOPABSTRACTINTRODUCTIONEQUATIONS AND METHODSRESULTSDISCUSSION AND CONCLUSIONSAPPENDIX A: NOMENCLATURE AND...ACKNOWLEDGEMENTSREFERENCES |
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Two-hundred and twenty-six laboratory and field data points were collected for analysis. The numbers of data points collected at each facility were as follows: 67 from U. Mass Lowell, 126 from NIOSH, and 33 from the art glass facility. Table 1 provides the number of samples collected at each unique experimental height (Z) and excess temperature (
T) combination. The data, height above the heated source (Z), and excess temperature (T) data are presented in three dimensions in Fig. 2. Figures 2 and 3 suggest an association between increased T and increased velocity values (adjusted R2 = 0.44). Figures 2 and 4 indicate no linear association between increased Z and increased velocity values (adjusted R2 = –0.25), although there may be a more complex mathematical relationship present. data and solutions from the proposed (
), ACGIH () and Hemeon () velocity equations for the model exothermic process are provided in Figs. 5–9. Each figure depicts data from one of the five Z values investigated. The figures provide the six T investigated in the left column, with and the three equation solutions at each T. The number of samples collected and mean velocity values are also provided in columns on the right of the figure. Confidence intervals (95% C.I.) are provided for the data.
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The difference of means between
and each of the three estimation equations were plotted individually, and were not normally distributed. Therefore, significance for the three estimation equations was determined using the P-value from the Wilcoxon Signed Rank test. The Signed Rank test results indicated that the ACGIH mean velocity equation provides significantly different estimates from the data (mean difference = 0.07 m s–1, = 0.12, P-value < 0.01). However, the proposed (mean difference = –0.03 m s–1, = 0.15, P-value = 0.26) and Hemeon (mean difference = –0.001 m s–1, = 0.14, P-value = 0.44) equations provided solutions that were not significantly different from the measured plume mean velocity data. |
DISCUSSION AND CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONEQUATIONS AND METHODSRESULTSDISCUSSION AND CONCLUSIONSAPPENDIX A: NOMENCLATURE AND...ACKNOWLEDGEMENTSREFERENCES |
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It is notable that although
T ranged 100 K, the data changed gradually with increasing temperatures and did not exceed 1 m s–1. The difference between the estimates provided by the three equations and the data is on the order of ±0.05 m s–1 (±10 FPM). This magnitude is small due to the narrow temperature range (100 K) investigated in this research. Wider temperature ranges (i.e. high-temperature processes) may lead to larger discrepancies between the plume mean velocity values and the estimates provided by the equations. Overall, the absolute difference between the data and solutions from the three estimation equations was larger at increased T.
Figures 2 and 3 illustrate a positive association between and T (adjusted R2 = 0.44). However, Fig. 4 indicates low velocities at Z < 0.40 m. These results were surprising, because on first inspection it would appear intuitive that the plume velocities should be greater closer to the source, and decrease steadily as the distance from the source increases. These decreased velocities close to the source can possibly be explained by differences in the behavior of air in laminar and turbulent flow. The height where the acceleration occurs is likely the point in the plume where flow transitions from laminar to turbulent. Calculating Reynolds numbers (Re) to characterize the flow regime at the various heights above the two sources indicated that this conclusion is likely correct.
 | (12) |
K = Kinematic viscosity of air evaluated at TF (m2 s–1)
TF = Film temperature; 0.50 (TS + T) (K)
In practice, flow is laminar at Re <2000, or in transition from laminar to turbulent flow at Re values between 2000 and 4000 (Burgess et al., 2004). Calculations indicate that 108 data points correspond to Re that are either laminar or in the transitional region between laminar and turbulent flow. A great majority (80%) of these occur at Z <0.40 m.
Signed Rank test results indicated that the proposed and Hemeon equations provided solutions that were not significantly different from the data. Solutions provided by the ACGIH velocity equation were significantly different from the data. Results indicating a difference between the ACGIH and Hemeon equation solutions were unexpected due to the similar developmental backgrounds between these equations. The ACGIH equation is drawn directly from the Air Pollution Engineering Manual (USPHS, 1973). This equation from the Air Pollution Manual is an application of Hemeon's equation with two key assumptions. First, Hemeon's natural convection heat loss coefficient at the source is simplified by characterizing all heated sources as horizontal flat plates. Second, the Air Pollution Manual recommends the use of a subjective 15% ‘safety factor’ with Hemeon's equation. There is no reasoning provided for the selection of 15% compared to any other value. With these substitutions, the ACGIH equation appears to provide less useful solutions than the Hemeon equation over the range of excess temperatures (T), heights (Z), and source characteristics examined.
These research findings provide valuable information necessary for researchers and practitioners to determine critical design parameters to assist in the design and evaluation of engineering controls for exothermic processes. Findings indicate that the ACGIH mean velocity equation does not provide accurate estimates of the mean plume velocity over the range of parameters investigated. This may be due to the number of assumptions that were made in the development of this equation. The horizontal plate heat transfer coefficient used in developing the ACGIH equation applies to convective heat, and does not consider radiant heat. The proposed equation considers the sum of the convective and radiant heat flux for horizontal plate heat transfer. If the radiant heat flux is excluded from the total heat flux (P) in the proposed equation, then the outcome of the statistical test is nearly identical to the results for the ACGIH mean velocity equation (mean difference = 0.06 m s–1, = 0.12, P-value < 0.01). Additionally, the ACGIH equation implements a safety factor that does not appear to add a margin of safety in determining the plume mean velocity. In this evaluation, the proposed () and Hemeon () equations for plume mean velocity provided estimates that were not significantly different from the measured data over the source dimensions and range of parameters investigated.
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APPENDIX A: NOMENCLATURE AND CASE STUDY UTILIZING THE PROPOSED VELOCITY EQUATION |
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TOPABSTRACTINTRODUCTIONEQUATIONS AND METHODSRESULTSDISCUSSION AND CONCLUSIONSAPPENDIX A: NOMENCLATURE AND...ACKNOWLEDGEMENTSREFERENCES |
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Nomenclature:
Boundary layer thickness (
)—Thickness of the air layer in contact with the heated source that experiences conductive heat transfer (m). Convective heat flux (PC)—Heat energy per unit area transferred to the surrounding air by convection currents (W m–2).
Diffusion coefficient (C)—Coefficients that are dependent on the meteorological condition (i.e. stability) of the atmosphere. In the ambient environment, temperature decreases as height increases. This condition in meteorology is defined as neutral, or unstable, and is associated with a diffusion coefficient of 0.27. In indoor environments, temperature increases as height increases. This condition is defined as stable, and is associated with a diffusion coefficient of 0.12 (Stewart et al., 1958; Sutton, 1950; USAEC, 1968).
Emissivity ()—The ratio of energy radiated by the material to energy radiated by a theoretical ‘black-body’ at the same temperature. Emissivity is a measure of energy absorbtion and radiation by a material. A theoretical ‘black-body’ has an emissivity of 1, while real objects have emissivities <1 (dimensionless).
Laminar flow—Flow in which layers of air move smoothly over one another in the direction of movement.
Natural convection—convective air currents that arise due to the temperature difference between air near the heated source with lower density (warmer air), and air in the ambient environment with higher density (cooler air).
Newton's law of cooling—The rate of heat loss by a heated source is proportional to the difference in temperatures between the body and its surroundings (W m–2 K–1).
Radiant heat flux (PR)—Heat energy per unit area transferred to the surrounding air by radiation (usually in the infrared radiation range) (W m–2).
Specific heat (CP)—The heat energy required to raise the temperature of a given amount of air by one degree (J kg–1 K–1).
Stefan-Boltzmann's law—The radiant heat transfer from a heated source is proportional to the fourth power of the absolute temperature (W m–2 K–4).
Total heat flux (P)—Sum of the heat energy per unit area transported by radiation and convection currents emanating from the surface of a heated source (W m–2).
Turbulent flow—Flow in which the layers of air are perturbed, and mix freely with one another in the direction of movement
Case Study:
Given: 1.20 m melting pot diameter (D) [RS = 0.60 m]
2 m melting pot height (L)
600°C melting temperature = 873 K (Ts)
70°C ambient temperature = 343 K (T)
Circular canopy hood located 3 m above pot (Z)
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Calculate the plume mean velocity () at the hood face:
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONEQUATIONS AND METHODSRESULTSDISCUSSION AND CONCLUSIONSAPPENDIX A: NOMENCLATURE AND...ACKNOWLEDGEMENTSREFERENCES |
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The author gratefully acknowledges the contributions of Rafael Moure, G. Scott Earnest, James Bennett and Robert Hughes for their support, review, and guidance. The authors also greatly appreciate the technical contributions, as well as laboratory and equipment support provided by Paul Baron and Gregory Deye. The authors also recognize and appreciate the statistical assistance provided by Misty Hein.
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FOOTNOTES |
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The findings and conclusions in this report are those of the authors and do not necessarily represent the views of the National Institute for Occupational Safety and Health. 
Received December 19, 2006; in final form February 22, 2007
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REFERENCES |
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TOPABSTRACTINTRODUCTIONEQUATIONS AND METHODSRESULTSDISCUSSION AND CONCLUSIONSAPPENDIX A: NOMENCLATURE AND...ACKNOWLEDGEMENTSREFERENCES |
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ACGIH. (1998) 21–3. Chapter 3: Local exhaust hoods. In Industrial ventilation: A manual of recommended practice (Metric Version). 23rd edn. Cincinnati, OH: American Conference of Governmental Industrial Hygienists.
Batchelor GK. Heat convection and buoyancy effects in fluids. Quart J R Met Soc (1954) 80:339–58.[CrossRef]
Bender M. Fume hoods, open canopy type—their ability to capture pollutants in various environments. Am Ind Hyg Assoc J (1979) 40(2):118–27.[Web of Science][Medline]
Bird RB, Stewart WE, Lightfoot EN. Transport phenomena. (2002) 2nd edn. New York: John Wiley & Sons.
Burgess WA, Ellenbecker MJ, Treitman RD. Ventilation for control of the work environment. (2004) 2nd edn. Hoboken: John Wiley & Sons.
Goodfellow H. Design of ventilation systems for fume control. In Advanced design of ventilation systems for contaminant control. (1985) New York: Elsevier. 359–438.
Goodfellow H, Bender M. Design considerations for fume hoods for process plants. Am Ind Hyg Assoc J (1980) 41(7):473–84.[Web of Science][Medline]
Heinsohn RJ. Canopy hoods for buoyant sources. In Industrial ventilation: Engineering principles. (1991) New York: John Wiley & Sons. 314–24.
Hemeon WCL. Plant and process ventilation. (1955) New York: Industrial Press Inc.
Hemeon WCL. Chapter 8: Exhaust for hot processes. In Plant and process ventilation. (1963) 2nd edn. New York: Industrial Press Inc. 160–96.
Hemeon WCL. Chapter 8: Exhaust for hot processes. In: Hemeon's plant and process ventilation—Burton DJ, ed. (1999) 3rd edn. New York: Lewis Publishers. 117–47.
Jaluria Y. Natural convection heat and mass transfer. (1980) New York: Pergamon Press.
Lide DR, Frederikse HPR, eds. CRC handbook of chemistry and physics. (1996) 76th edn. New York: CRC Press.
Ligget JA, Caughey DA. Fluid mechanics. In: An interactive text (1998) Reston, VA: ASCE/AIAA.
McKernan JL, Ellenbecker MJ. Ventilation equations for improved exothermic process control. Ann Occup Hyg (2007) 51. (In Press).
Morton BR, Taylor G, Turner JS. Turbulent gravitational convection from maintained and instantaneous sources. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences (1956) 234(1196):1–23.
Mundt E. (1996) The performance of displacement ventilation systems: Experimental and theoretical studies. [Ph.D.]. Stockholm: Royal Institute of Technology.
Rouse H, Yih CS, Humphreys HW. (1952) Gravitational convection from a boundary source. Tellus; 4 201.
Schmidt W. Turbulent propagation of a stream of heated air. Z Angew Math Mech (1941) 21:265–351.[CrossRef]
Siebert GW, Fraser DA. Exhaust ventilation for hot processes. Am Ind Hyg Assoc J (1973) 34(11):481–86.[Web of Science][Medline]
Stewart NG, Gale HJ, Crooks RN. The atmospheric diffusion of gases discharged from the chimney of the Harwell reactor BEPO. Int J Air Pollut (1958) 1(2):93.
Sutton OG. The dispersion of hot gasses in the atmosphere. J Meteor (1950) 7(5):307–12.
USAEC. (1968) Meteorology and atomic energy. Oak Ridge, TN: Division of Reactor Development and Technology, U.S. Atomic Energy Commission.
USPHS. Design of Hoods for Hot Processes. In: Air Pollution Engineering Manual—Danielson JA, ed. (1973) Cincinnati, OH: US Department of Health, Education, and Welfare, Public Health Service, Bureau of Disease Prevention Environmental Control, National Center for Air Pollution Control. 34–43.
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