EPA/600/A-r9Z/?.29 cmaapm.cw4 RESIDENCE TIME OF CONTAMINANTS RELEASED IN SURFACE COAL MTNF.S -- A Wind-Tunnel Study Roger S, Thompson Atmospheric Characterization and Modeling Division Atmospheric Research and Exposure Assessment laboratory U.S. Environmental Protection Agency Research Triangle Park, NC August 1993 To be presented at the American Meteorology Society's Eighth Joint Conference on the Applications of Air Pollution Meteorology with the Air and Waste Management Association Nashville, TN January 23-28. 1994 ------- TECHNICAL REPORT DATA (Please read Instructions on the reverse before completi 1. REPORT NO. X FT'A /80 0/A -33/229 & 4. TITLE AND SUBTITLE RESIDENCE TIME OF CONTAMINANTS RELEASED IN SURFACE COAL MINES: A Wind-Tunnel Study 5. REPORT DATE 1993 6. PERFORMING ORGANIZATION CODE 7. AUTHOR(S) Roger S. Thompson EPA, Research Triangle Park, NC 27711 8. PERFORMING ORGANIZATION REPORT NO. 8. PERFORMING ORGANIZATION NAME AND ADDRESS Atmospheric Research & Exposure Assessment Laboratory Office of Research and Development U.S. Environmental Protection Agency Research Triangle Park, NC 27711 10. PROGRAM ELEMENT NO. 11. CONTRACT/GRANT NO. 12. SPONSORING AGENCY NAME AND ADDRESS Atmospheric Research & Exposure Assessment Laboratory-RTP, NC Office of Research and Development U.S. Environmental Protection Agency Research Triangle Park, NC 27711 13. TYPE OF REPORT AND PERIOD COVERED Extended Abstract 14. SPONSORING AGENCEY CODE EPA/600/09 15. SUPPLEMENTARY NOTES Preprint Vol: Eighth Joint Conf. on Appl. of Air Pollution Meteorology, Jan. 1994, Nashville, TN is. ABSTRAc't'he jyyu Clean Air Act Amendments direct the U.S. Environmental Protection Agency to evaluate and modify, as required, existing dispersion models for the prediction of dispersion of dust from surface coal mines. The application of mathematical air pollution dispersion models to the dispersion of dust from surface coal mines requires knowledge of not only the amount of dust generated in the mine, but the fraction of that generated that actually escapes from the mine. The escape fraction can be related to the residence time that released material will remain, on average, within the mine. A wind-tunnel study was performed to measure the residence time for a variety of rectangular mine shapes at a scale of 1:300. Although it is not possible to model the dispersion of dust particles at this model scale, the residence time of a neutrally buoyant gas can be measured. This determined residence time can then be used in algorithms that relate residence time and particle size to escape fraction. Twenty combinations of rectangular surface mine shape, source location and wind direction were studied in a simulated atmospheric boundary layer. For each case, a point source of a hydrocarbon tracer was placed at the floor level of the mine and a sample port was installed at the downwind lip of the mine. The sample port was connected to a flame ionization detector that was monitored with a personal computer. The source was turned on until the concentration at the sampler reached steady-state and then instantaneously turned off; the concentration was recorded as a function of time. Forty such realizations were performed and averaged for each case to obtain the mean residence time. In addition, a pulsed-wire anemometer was used to measure velocities on the centerplane for two of the cases. A recirculating flow with low mean speeds and large turbulent fluctuations was observed. The concentration in the mine was found to follow an exponential decay function from which an exponential decay time constant (or residence time) was computed for each case. A semi-empirical formula was found that related the residence time to the mine geometry and wind direction quite well. This formula can be used to estimate escape fraction in determining the source strength for the application of mathematical dispersion models. 17 KEY WORDS AND DOCUMENT ANALYSIS a. DESCRIPTORS b. IDENTIFIERS/OPEN ENDED TERMS c. COSATI Field/Group 18. DISTRIBUTION STATEMENT RELEASE TO PUBLIC 19. SECURITY CLASS (Thu Report) UNCLASSIFIED 21. NO. OF PAGES 9 C U Ci 20. SECURITY CLASS (This page) UNCLASSIFIED 22. PRICE EPA Form 2220-1 (Rev. 4-77) previous edition is obsolete (fmf imitation) ------- INTRODUCTION Surface coal mining operations (blasting, shoveling, loading, trucking, etc.) are sources of airborne particles. The 1990 Clean Air Act Amendments direct the EPA to analyze the accuracy of the Industrial Source Complex model and the AP-42 emission factors, and to make revisions as may be necessary to eliminate any significant over-prediction of air concentration of fugitive particles from surface coal mines. A wind-tunnel study was performed at the U.S. Environmental Protection Agency's Fluid Modeling Facility to investigate dispersion from surface coal mines in support of the dispersion modeling activities. Although the dispersion of dust particles cannot be simulated at the reduced geometric scales of wind tunnel studies, some quite useful information on the dispersion process was found by measuring the concentration of a tracer gas. Described here is the portion of the study directed at determining the residence time that materia! released near the floor of a mine will stay within the mine. Twenty combinations of rectangular mine shape, source location and wind direction were studied in a simulated atmospheric boundary layer. Most mine models had terraced sidewalls to simulate the features of actual mines. A flame ionization detector was used to measure the time-dependent concentration at the downwind lip of the mine after rapidly turning off a point source located witnin the mine. For each case, forty realizations were obtained and averaged. From the average, an exponential decay constant was determined. A formula relating the residence time (exponential decay time constant) to the geometry of the mine is derived and evaluated with the experimental data base. The residence time computed with this formula can be used in algortihms that predict the retention (or escape fraction) of coal dust, as a function of particle size, in a surface mine- Additional details and a thorough description of the complete data set are contained in the project data report (Thompson. 1993). 1 ------- EX PERI MEN'FA L DETAILS All measurements were made in the EPA Meteorological Wind Tunnel (for specifications, sec Snyder, 1979) with a neutral boundary-layer approach flow. A freestream speed of 2 m/s was used for all diffusion measurements. A 2-m-deep boundary layer was generated with three triangular spires placed at the entrance to the test section according to the recommendations of Irwin (1981). The boundary layer was maintained over the length of the test section by covering the floor with SansprayS, gravel-coated plywood with a typical stone size of 10mm. A scaling ratio of 1:300 allowed fitting the models of actual coal mines into the wind-tunnel test section with a typical depth of the model mine of 15 cm (45m, full scale). The corresponding full scale boundary layer depth was 600 m. All models were rectangular, of various dimensions, and were from 10 to 25 cm deep. The bottom of the model was covered with a piece of Sanspray. Solid steps, constructed of plywood, were placed against all four side walls of the model (except for the few cases that did not have steps). The rise and run of each step was 5 cm with the top rise being the side of the model opening. These terraced sides simulated the access roads to the bottom of the mine and the layered mining of the coal. Source position and wind direction were varied. The details of each case are tabulated in Table 1 and shown in Figure 1. The tracer used for this study was high-purity ethane (C,II6; CP grade; minimum purity 99.5 mole percent) which, with a molecular weight of 30, is only slightly heavier than air. At a release rate of only 3000 cc/min into the highly turbulent flow within the mine models, the buoyancy of the tracer was negligible. The ethane was emitted from a perforated hollow plastic sphere of 10-mm diameter to minimize the momentum of the source. The source was located at the floor level of the mine at the positions shown in Figure 1 for each case. The concentration of the tracer in the air leaving the mine was measured. The sampler was located directly downwind of the source on the lip of the mine (at surrounding terrain level). ? ------- Measurement of the transient concentration after turning off the source required some special hardware. A flame ionization detector (FID) was modified to improve its response time by reducing the volume of the sampling line and pump. A pair of electrically operated solenoid valves to direct the flow of tracer gas or divert it was installed in the supply line as close to the plastic sphere as practicable to facilitate a rapid turn- off of the supply of ethane to the source. DATA COLLECTION AND REDUCTION Simulated Boundary Layer Vertical velocity profiles of the simulated boundary layer were measured and found to be representative of an atmospheric boundary layer over the portion of the lest section where the models would be located. A logarithmic formula, u(z) - u,/k ln[(z)/zj, was fit to each vertical profile. The equivalent full-scale roughness (at the 1:300 scale) was za 3.0 cm. This is representative of grassy fields. The ratios of friction velocity u.!: to freestream speed was 0.042. Fitting a power-law formula to the data gives u(z) « z0 :i. The exponent 0.11 — l/9,h is typical of fairly smooth rural terrain. Transient Concentration Data Transient concentration measurements were made with the modified FID system mentioned above. Two channels of an analog-to-digital (A/D) converter in the data acquisition computer were used. One channel recorded the signal from the FID. The other channel was connected to a known voltage source (1.5 volt battery) through a set of contacts on a relay that was operated by a switch near the computer. When the switch was turned on, the relay also actuated the pair of solenoid valves to direct the flow of the source gas to the mine. After a sufficient time to allow the concentration field in the mine to reach steady state, recording the FID's output was initiated. The switch was then turned off manually at an arbitrary time of about 4 seconds after starting the FID sampling. The contacts connected to the A/D converter recorded an instantaneous voltage ------- drop to mark the time that the source was turned oil. A 45-second record (at a sampling rate of 25 samples per second) was adequate for the concentration to decay to near background for all cases. Eight realizations as obtained for Case ! 1 are shown in Figure 2, as an example. The great variation from sample to sample and the need to average a large number of samples are easily seen. Forty realizations were recorded for each case. The forty "raw" data files for each case contain the output voltage of the FID versus the time from the initiation of sampling. These were put on the same time reference, averaged and scaled to produce a file containing normalized concentration at the sampling location as a function of time after the source was turned off, as follows. First, the time reference for each realization was adjusted to give time - 0 at the time the source was turned off (not yet accounting for sampling system lag). Then, the forty realizations for each case were averaged with the result stored in a single- file. Next, the sampling system lag time, determined as described below, was subtracted to give the FID voltage at the time the sample was entering the sample tube. The voltages were then converted to concentrations by multiplying by the calibration factor {as determined by calibration with a span gas prior to each scries of measurements) for the selected range of the FID. And finally, the concentrations were normalized by the steady- state concentration measured at the same location to give C(t)/C0. The normalized, lime-base-corrected result of the average of 40 realizations for Case 11 is shown ir. Figure 3. A Case 0 was added to evaluate the delay in the sampling system resulting from the pump volume and length of tubing between the sampling port and the FID burner. The porous ball source was installed at a height of 125 mm above Hat terrain. The sample tube was installed at the same height, 250mrn directly downwind. The source rate was reduced to 340 cm3/min to produce measurable concentrations at the sampling point. Forty samples were collected and processed as described above. The time interval between turning the source off and observing a drop in the concentration indicated by the FID was determined. By subtracting from this the estimated travel time between the source and the sample port, the sampling ------- system lag time was found to be 4.2 seconds. For comparison with Case 11, the instrument response (Case 0) is also shown in Figure 3. Formula derivation A simple derivation of an equation for the concentration in the mine after turning off the source can be made following that of Fackrell (1984) for a building wake. Assume that the concentration in the mine is uniform, or at least that it can be represented by an average value, C(t), and that the velocity field in the mine scales by a reference velocity, say the approach wind speed at a height of 10 m, Ur. Also assume that the material leaves the mine across the area of the top with a flux, F(t), that is proportional to the concentration and the reference wind speed. That is, F(t) = aU.C(t). The requirement of conservation of mass of the contaminant (or tracer) within the mine between times t and t—At after turning off the source can be expressed as: where At. is a small time interval and L, W, and V are the length, width and volume of the mine, respectively. (Note that the volume V is the true volume of the mine accounting for the terraced side walls.) By including the expression for '.he flux and rearranging, this gives: In the limit as At goes to zero, this becomes the differential equation C.'(t+At) • V = C(t)-V - P(t)LW At (1) AC/At - |C(t + At) - C(t)]/At (aU.LW/V) C(t). (2) dC/'dt = -(aUrLW/V) C(t) (3) which has the familiar exponential solution C(t) = Q, cxp[-t/(V/«U,LW)J = C0 exp(-t/Td). (4) 5 ------- The exponential decay constant is, therefore, xd - V/ocUrLW. (5) Because the sampler is located a finite distance from the source, there will be a delay in the response following the turning off of the source. Thus, a formula of the form C(t)/C(=exp(-(t-At)/xti) is used to approximate the average concentration at the sampler as a function of time, t. Td is the time constant determined from a straight-line approximation (on a logarithmic plot) of the concentration. At. the lag time, is determined as the time corresponding to the intersection of the straight- line approximation and a horizontal line at C/Cu=1.0. This is shown graphically, for example, in Figure 3 for Case II. The exponential decay constant for the instrument/sampling system, Case 0, was found to be 0.49 seconds. The lowest value observed for a coal mine model was 1.08 seconds for Case 16 which was more than double the instrument response. RESULTS Hand-drawn curve fits to the averaged results as described above were made for each case. The values of At and t(.;, for all cases, are tabulated in Table 2. Residence time A plot of all the values of xt! against V/U.LW, as suggested by equation (5), is shown in Figure 4. The outliers in the figure are identified as the cases included for evaluating the dependence of residence time on wind direction (Cases 13 - 16). The wind direction was the only parameter varied in these cases (Case 4 is the same mine with wind direction 0°). These cases are shown in Figure 5 where it is seen that the 6 ------- dependence of wind direction can be accounted for by an empirical factor including the cosine of the wind direction, o. That is. xd - (l/a)(V/U LW) [0.7cos(e) 4 0.31. (6) The residence times for all cases are shown plotted against equation (6) in Figure 6. A linear regression analysis of these data (assuming a y- iniercept of 0.0) results in a slope of 33.8 = 1/a and a correlation coefficient, r = 0.91. Using this value of 1/a, equation (6) becomes x, - 33.8 (V/IJ.LW) [0.7cos(o) -r 0.3]. (7) This is the suggested formula for residence time for rectangular mines. Castro et a/., (1993) found that for a neutrally buoyant gas in a shallow valley of triangular cross section, rd - 14.5 H/U0, where U0 is the approaching wind speed at z = H/4 and H is the depth of the valley (for a 40-m-deep valley, U() and Ur are equal, both evaluated at z — 10m). The volume of a triangular valley is V — 1/2 LWH. Thus, their formula can be written as Td - 29 V/IM W, which is quite close to that found above for rectangular coal mines. Lag rime. The lag time At defined above as the elapsed time between turning off the source and detecting a reduction in the concentration at the downwind lip of the mine is also related to the time a puff remains in the mine. The lag time can be thought of as the average travel time for a puff released at the source to get to the sampler at the downwind lip of the mine. This is the type of experiment that TRC Environmental Consultants, Inc. (1985) performed in the field using puffs of diesel smoke. That the lag time will be more dependent than the residence time on the geometric features of the particular mine can be seen by considering the How field within a mine. For the rectangular shapes considered here, '7 ------- with the wind perpendicular lo a side, a recirculating flow pattern exists. Mean velocities measured with a pulsed-wire anemometer (and computed streamlines) on a plane through the center of the Case 4 mine are shown in Figure 7. Details of the measurements are presented in Thompson (1993). The mean flow may be sin-ply described as a large vortex with the flow at the top of the mine in the direction of the flow aloft. At the downwind wall of the mine the flow is toward the mine floor. The flow moves upwind (that is against the direction of the mean wind aloft) along the floor of the mine and then upward at the upwind face of the mine. The mean wind speeds in the mine are quite small compared with the wind speed just above the top of the nine. Although the mean wind speeds within the mine are small, the turbulence levels are large. A puff released at the typical source position for this study, at the base of the upwind wall, will, on average, move slowly up toward the upwind lip of the mine until it reaches the lop of the mine. Then, it will be swept more rapidly across the top of the mine and past the sampling port. Since the larger amount of time is spent by the puff rising up along the upwind wall of the mine, the lag time could be expected to be directly related to the depth of the mine. The high turbulence levels in the mine rapidly diffuse the puff :u all directions. Thus, another possible measure, one that includes both the depth and the width of the valley, is the straight-line distance from the source lo the sampler. Linear fits to both of these relationships were evaluated with a linear-regression program; the computed correlation coefficients of 0.24 and 0.23, respectively, indicated little dependence. Another interpretation of the exponential decay time can be obtained by calculating the expected (or average) time that a puff will remain in a mine. Given that C(t)/C0 = exp(-t/rd), the average value of t, t, can be computed from t - t C(t)/C„ dt / ;ra C(t)/C„ dt - Tj (8) n o That is, the average lime a puff will remain in the mine is equal to the exponential decay time. Figure 8, relating lag time to decay time, shows 8 ------- this :o be the case. The dark line is a linear regression fit which has a correlation coefficient of 0.51. This is not a high correlation, but the lag time is seen to be roughly equal to the decay time. An "eyeball" fit of At = tcI, also shown on the figure as a lighter line, would appear to fit the data nearly as well as the linear-regression fit. APPLICATION TO PULL SCALE It is instructive to compute a full-scale residence time for a typical surface coal mine. Assume a mine with dimensions 450 by 225 meters that is 45 m deep. Given a reference wind speed of 2 m/s at a height of 10 m, we can find the residence time with equation (7). Also assume that the wind is perpendicular to one side of the mine and that the volume of the mine is about 80% (to allow for the stepped sides) of the product of its length, width and depth. This gives V = 0.80xLx\VxD = 0.8 x 450 m * 225 m x 45 m = 3.65*106 m3, and xd - 33.8<3.65>106 m3)/(2 m/s)(450 m)(225 m)(l) = 609 s = —10 min. The application of the residence time to the estimation of the escape fraction of coal dust from a surface mine can be made through an equation derived by Winges and Cole (1986) (their equation (65)). They derive the equation C - exp(-ud(Td)/H), (9) where c is the escape fraction of dust particles with settling velocity of u(i in a mine of depth II with a residence time of t(!. The residence time for a particular mine and wind condition can be computed with equation (7) above and used directly in their formula. 9 ------- SUMMARY A wind tunnel study was performed to determine an empirical formula for the residence time of contaminants released within surface coal mines. Twenty rectangular mine configurations were studied at a scale of 1:300. For each, the concentration at the downwind lip was measured as a function of time after turning off a point source of tracer; forty repetitions were made and averaged. For these mines, the concentration was found to follow an exponential decay with a residence time (exponential decay time) of t, = 33.8 (V/U..LW) [0.7cos(o) -i 0.3J. This can be used in computing escape fraction of dust from surface coal mines. 10 ------- KEFERENCES Castro, I.P., Kumar. A., Snyder, W.H. and Arya, S.P.S. 1993 Removal of Slightly Heavy Gases from a Valley by Crosswinds, to appear in J. Hazard. Mar. Fackrell, J.H. 1984 Parameters Characterising Dispersion in the Near Wake of Buildings, J. Wind Eng. Indus. Aerodyn. 16, 97-118. Irwin, H.P.A.H. 1981 The Design of Spires for Wind Simulation, J. Wind Hng. Indus. Aerodyn. 7, 361-366. Snyder, W.H. 1979 The HP A Meteorological Wind Tunnel: Its Design, Construction, ar.d Operating Characteristics. U.S. Envir. Prot. Agcy. Rpt. No. EPA-600/4-79-051, Res. Tri. Park, NC, 78p. Thompson, R.S. 1993 Wind-tunnel Simulation of Dispersion from Surface Coal Mines, Internal Data Report. U.S. EPA Fluid Modeling Facility, RTF, NC, March. TRC Environmental Consultants, Inc. 1985 Dispersion of Airborne Particulates in Surface Coal Mines, Rpt. No. EPA-450/4-85-001, U.S. Environmental Protection Agency, Res. Tri. Pk., NC, 81 p. Winges, K.D. and Cole, C.F. 1986 Continued Analysis and Derivation of a Method to Model Pit Retention, Rpt. No. EPA-450/4-86-003, U.S. Environmental Protection Agency, Res. Tri. Pk., NC, 133p. DISCLAIMER: The information in this document has been funded by the U.S. Environmental Protection Agency. It has been subjected to the Agency's peer and administrative review and approved for publication. Mention of trade names or commercial products does not constitute endorsement or recommendation for use. ------- table 1 .cw4 Table 1. Cases modeled. (Both model, mod., and full scale, f.s., dimensions are given.) Case Pit Steps L, length W, width D, depth Wind Source* Comments No. Shape mod. f.s. mod. f.s. mod. f.s. dir. Location (cm) (m) (cm) (m) (cm) (m) (deg) 1 Square Y 75 (225) 75 (225) 15 (45) 0 u ] 2 Square V 75 (225) 75 (225) 25 (75) 0 u [¦simple shape, basic source position 3 Square y 150 (450) 150 (450) 15 (45) 0 u J vary size and depth 4 2x 1 Rect. y 150 (450) 75 (225) 15 (45) 0 u 1 more typical aspect ratio, 5 2x1 Rect. y 150 (450) 75 (225) 15 (45) 0 s i-vary source position 6 2x1 Rect. y 150 (450) 75 (225) 15 (45) 0 d J 8 Square n 75 (225) 75 (225) 15 (45) 0 u ' remove steps from side walls to 9 2x1 Rect. n 150 (450) 75 (225) 15 (45) 0 u find influence J 10 2x1 Rect. y 150 (450) 75 (225) 10 (30) 0 u 1 11 2x1 Rect. y 150 (450) 75 (225) 20 (60) 0 u [¦ variation of mine depth 12 2x1 Rect. y 150 (450) 75 (225) 25 (75) 0 u J for 2x1 Rect. 13 2x 1 Rect. y 150 (450) 75 (225) 15 (45) 22.5 s 14 2x1 Rect. y 150 (450) 75 (225) 15 (45) 45 s ¦variation of wind angle 15 2x1 Rect. y 150 (450) 75 (225) 15 (45) 67.5 s 16 2x1 Rect. Y 150 (450) 75 (225) 15 (45) 90 s 16A 2x1 Rect. y 150 (450) 75 (225) 15 (45) 90 u J 17 2x1 Rect. y 150 (450) 75 (225) 10 (30) 90 u smaller mine depth for 2x1 Rect. at 90° 18 4x1 Rect. y 200 (600) 50 (150) 15 (45) 0 u additional aspect ratio - 4x1 Rect. 19 Jacob's y 200 (600) 100 (300) 15 (45) 0 u idealizations of some 20 Rosebud n 150 (450) 15 (45) 15 (45) 0 u actual mine shapes * u = upwind edge; s = side; d = downwind edge (see Figure 1) ------- Table 2. Mine volume, straight-line distance from source to sampler, residence rime xd and lag time At for each mine, in model units. source to Case volume sampler Td At No. cm3 distance, cm sec sec 0 0.49 1 64375 66.7 3.58 3.7 2 80625 60.4 4.67 3.5 3 295000 140.8 3.45 3.5 4 137500 66.7 3.58 2.6 5 137500 40.4 3.68 2.3 6 137500 18.0 3.53 0.8 8 84375 76.5 5.21 3.8 9 168750 76.5 5.04 5.2 10 101750 65.8 2.95 1.5 11 164500 68.0 3.75 2.7 12 183750 69.6 3.95 3.2 13 137500 71.9 3.14 1.8 14 137500 93.1 2.78 2.7 15 137500 170.1 2.11 2.8 16 137500 76.5 1.08 1.8 16A 137500 140.8 3.53 3.7 17 101750 140.4 2.83 3.0 18 115000 42.7 3.49 2.5 19 257500 91.2 3.75 2.5 20 33750 140.8 4.00 1.6 ------- ~w (I) ' i © 2 (D = 25) 4 7FT <15- (no steps) 9 (no steps) 10 (D = 10) 1 1 (D = 20) 12 (D = 25) 13 (22.5 deg.) 14 (45 deg.) 15 (67.5 deg.) (s* © © 18 I (0 I 16A 17 (D = 10) (no steps) © 19 Figure 1. Details of mine models by case number; top view. D=15 cm, model has 5 cm steps on sides, and source is at mine-floor level unless otherwise noted. Wind direction is from top to bottom of page. © indicates source location. cmnfigl .Urw ------- cmnfig2.drw 0.10 t q 0,08 - X5 0.06 ra 0.04 O 0.02 30 0 15 45 Time from start of sample, sec. Figure 2. Eight realizations of the concentration measured at the downwind lip of Case 11 mine as a function of the time after turning off the source. ------- cmnf;g3.drw At - 2.7 sec. -A - \ exp[-(t-2.7)/3.75] 0.1 O u o Case 0 Case 1 exp[-t/0.49] 0.01 0.001 28 32 20 24 4 8 12 16 0 4 Time, sec Figure 3. Transient concentration for Case 11. Average of 40 records. t = 0 when source turned off, adjusted for instrument response lag. Instrument response, Case 0, on left, shown for comparison. ------- 0 7 I- 1 + 0 +- H r i- A A 4 + aa A A A 4 A A - A r a Case 13 3 T A (0=22.5°) A A Case 14 1 ( 0 _ 45°) i a Case 15 2 t ( © = 67.5° ) a Case 16 ( © = 90° ) _j i i j ; i 1 » —i f— 1 i i i 0 0.05 0.1 0.15 V/UrLW, sec Figure 4. Residence times for all cases ------- . Case 4 0.9 Case 13 Case 14 0.7 Case 15 0.6 0.7 cos(e) + 0.3 0.5 0.4 -- 0.3 •- Case 16 60 70 80 90 10 20 30 40 50 0 Wind Direction (©}, degrees Figure 5. Residence time as a function of wind direction. ------- slope = 33.8 0.1 0.05 0 (V/UrLW)[0.7cos( 0J + O.3], sec Figure 6. Residence time versus equation 7. ------- o o CD c ro o o CD > o -O ra E £ "•00 2 m/s f ' —r >" . r^, ... &-5>— -> > r -2»-- y~> &-> > > ¦>- -j: z\ru x, mm from coal mine center Figure 7. Centerplane velocity vectors and streamlines for Case 4 as computed from pulsed-wire anemometer measurements. ------- 6 f u c to c D) re 3 -• 1 - A A 0 ¥—>•—1—1—1—f 2 3 4 residence time (Td), sec Figure 8. Lag time versus residence time. ------- |