Proceedings of the 51st Anniversary Conference of KSME PHYSICAL MODELING OF ATMOSPHERIC FLOW AND ENVIRONMENTAL APPLICATIONS B. R.

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1 Proceedings of the 51st Anniversary Conference of KSME PHYSICAL MODELING OF ATMOSPHERIC FLOW AND ENVIRONMENTAL APPLICATIONS B. R. WHITE Faclty of Mechanical and Aeronatical Engineering University of California, Davis, CA, 95616, U.S.A. Abstract - The philosophy of physical modeling of atmospheric flow is discssed with special emphasis on wind-tnnel simlation techniqes. The governing eqations of motion are analyzed for application of laboratory testing. Key similitde parameters sch as Reynolds, Frode, Rossby, and Richardson nmbers, as applied to wind-tnnel reqirements, are discssed. Prevalent bondary condition reqirements, i.e., Jensen s criterion and flly rogh flow, are presented. Physics of atmospheric bondary layers are presented in the context of practical laboratory applications. The stack dispersion process of plme rise and diffsion into the atmosphere are discssed for near-field and far-field wind-tnnel simlations. Stack downwash, boyant and non-boyant stack processes are examined throgh experimental testing of fll-scale cases and reslts are compared to wind-tnnel measrements made to simlate the reslts. Additionally, wind-tnnel reslts are compared to Gassian-based compter models (ISCSTII and INPUFF). Comparisons illstrate that sitespecific wind-tnnel reslts provide better assessment of the dispersion process than do the generic Gassian models. Wind-tnnel testing is strongly recommended for complex geometry and/or niqe topographic conditions. 1. Introdction The se of wind tnnels to stdy the effects of wind near the earth s srface began more than a centry ago when a scientist named Irminger [1] placed a model hose in a small wind tnnel to measre wind pressre against the model. Since then, many attempts have been made to develop sefl laboratory representations of the highly variable atmospheric winds. Early researchers employed tnnels derived from aeronatical wind tnnels that simlate steady wind flow sitations sch as the flight of aircraft throgh still air. In the last thirty years, wind engineering researchers have discovered that trblent bondary layer flow over the floor of a wind tnnel provides reasonable laboratory simlation of atmospheric bondary layer (ABL) flow. The ABL is a layer of air covering the earth, the thickness of which is determined by the height at which srface friction no longer affects the general flow of wind. Air in motion

2 2 can be divided into main flow, where viscosity (flid friction) plays a negligible part, and bondary layer flow where flid friction is inflential. The bondary layer is adjacent to a srface sch as the srface of a planet. Over large bodies of water the bondary layer height may be as low as 200 meters, while above large cities it may be as high as 600 meters. Within this layer of air, motion is generally gsty or trblent, with the wind changing speed and direction rapidly. Several factors affect this motion: distance from the earth, srface roghness, and temperatre. The average speed of the wind increases with the distance from the earth, while the intensity of the trblence or gsting decreases. Increasing the roghness of the srface across which the air moves increases the trblence. Srface roghness ths acconts for the differences in thickness of the layer for flow over water as opposed to flow over tall bildings. The temperatre differences within the atmospheric bondary layer affect both wind speed and intensity of trblence in complex ways and is classified by the stability of the atmosphere. The variables given above render the flow in a bondary layer difficlt to model mathematically and increase the desirability of simlating this flow in wind tnnels. The impets for designing special atmospheric bondary layer wind tnnels (ABLWT) came from the desire both to do basic research on trblence and trblent diffsion and to stdy the effects of wind on strctres (Irminger s hose, etc.). Dring the past twenty years, the stdy of diffsion of gases in the atmosphere has received increased attention. In 1979 the U.S. National Brea of Standards called attention to the need for stdying air flow at very low velocities sch as those that occr in stack dispersion. National concern with problems of the environment and occpational health and safety, the Brea elcidated, have imposed reqirements for instrmentation and calibrations that wold provide for more accrate air flow measrements at very low velocities. Facilities that can perform these measrements mst provide U.S. and world technology with needed data on low Reynolds nmber flows, bondary layers, flow stability, trblence, and flid mechanical modeling. Where wind engineers had previosly focsed on how winds affect strctres, they now increasingly concern themselves with calibrations, basic research, and applications to environmental sitation, to address health and safety concerns in the workplace. 2. Physical Modeling Philosophy Motivated by the desire to contribte to basic research on trblence, to the development of instrmentation to measre air flow at low velocities of trblence, and to applied research on environmental polltion, particlarly the dispersion of gaseos polltants in an atmospheric bondary layer, the UC Davis ABLWT was designed and bild in Since the ABLWT was specifically designed to simlate natrally trblent bondary layers, sch as wind flow near the srface of the earth, the ABLWT reqired a long flow

3 3 development section to prodce a matre trblent bondary layer at the test section, and a flow that varies significantly from the test-section floor to the ceiling. In designing the ABLWT, se of previos research on trblent bondary layers were tilized. Using experiments condcted by Nikradse [2, 3] on flow in rogh-walled pipe, Stton [4] and Schlichting [5], among others, formlated a logarithmic wind profile law. Jensen [6] and other observed that a netrally stratified ABL also obeys the logarithmic law: z ( ) log z (2.1) = 1 k z0 where z ( ) is the time averaged velocity, a fnction of the height z ; z is the height above the srface; is friction velocity; k is von Kármán s niversal constant; and z 0 denotes the eqivalent roghness height. From this eqation and the work of Jensen one is able to determine what types of srface roghness shold be sed in the wind tnnel for proper simlation of varios types of natral wind flow. The strctre of the ABL is complex and difficlt to simlate. The inner layer, close to the srface of the earth, is two-dimensional in character, while the oter layer, frther from the earth, is three-dimensional since it is affected by the Coriolis force, a rotational force that creates a spiral effect, known as the Ekman Spiral [7], as the distance from the earth increases. This spiral effect cannot be modeled withot rotating the wind tnnel, which is impractical. Conseqently, only the first 100 meters adjacent to the earth can be modeled in a meaningfl manner. In the 1960 s, Cermak [8-13] and Davenport [14, 15] and their associates have shown that wind tnnels can model the ABL. Many have applied the problem of modeling the atmospheric bondary layer by laboratory simlation with some degree of sccess [16-18]. Arya and Plate [19] have shown that the Monin and Obkhov [20] similarity theory offers a good fondation on which to base modeling of a stable stratified atmospheric bondary layer. As a reslt there are a large nmber of stdies that have been condcted. Some good discssions of these classical cases are given in Monin and Yaglom [21], Lmley and Panofsky [22], and a basic review of the atmospheric layer in Monin [23]. From the similarity theory of Monin and Obkhov [20] the srface layer can be modeled if planar homogeneity exits. A detailed review of the implications of homogeneity to the similarity theory is given by Calder [24]. However, exact modeling of the entire ABL is not possible. By selecting certain similitde parameters that need not be strictly matched and relaxing these reqirements, one can obtain good laboratory reslts for special type atmospheric flows. The similarity criteria can be obtained from the eqations of motion for the particlar flow problem by nondimensionalizing the eqations. As a reslt the nondimensional eqations will yield similitde governing parameters as coefficients of the eqations of motion. If horizontal and vertical geometry is preserved it will reslt in an invariant nondimensional transformation of the conservation of mass 1 1 Cartesian tensor notation and Einstein smmation convention is sed.

4 4 k i i ( ) ρ ρ i = 0 and + = 0 (2.2) t x i Nondimensionalization of the time averaged trblent momentm eqation yields the criteria for dynamic similarity. The time averaged momentm eqation is 2 i i 1 p T ε δ ν t x ρ x T g + i j I + ijkω j k = i3 + + j i xk xk ( j i) x j (2.3) where the dependent variables are represented by mean (qantity represented by the bar over the variable and flctating vales. The Bossinesq density approximation is made ths limiting the application of the eqation to flows of T<< T where p is the deviation of pressre from the atmospheric pressre associated with ρ. Using, > = ; > ' = ' ; x> = x L i i i i i i > t t L ; > ; p> 2 = o o Ωj = Ωj Ωo = p ρo (2.4) (2.5) Τ > = Τ ( Τ) ; > = > ϕ g g g = o o; ϕ (2.6) ϕ to nondimensionalize the trblent momentm eqation yields: i t L + i ε j + ijk j k x j Ω 2 Ω 2 p T Lg ν j j = o o Tg δi + o i xi To L x x x o k k j 2 3 (2.7) Three dimensionaless parameters reslts as coefficients for the nondimensionalization of the momentm eqation. In order to maintain proper dynamics similarity these three similitde parameters mst be matched. These three parameters are known as (1) Rossby nmber: R ( L ) o = (2) Blk Richardson nmber: ( ) (3) Reynolds nmber: R L e = Ω ; (2.8) [( )][ ] R = Τ Τ L g 2 ; (2.9) i o o ν ; (2.10)

5 5 The time averaged conservation of trblent energy eqation is, neglecting radiation and assming constant flid properties, ( θ i ) Τ Τ κ Τ φ + i = 2 > > + + t xi ρcp xk xk xi ρc ρ (2.11) where φ is the dissipation fnction. Nondimensionalizing, as for the momentm eqation, it becomes: Τ Τ + i = t x i ( θ i ) κ ν 2 Τ φ ν ϕ ρ cp ν L xk x k xi ρ cp 2 L cp ( Τ ) 4 5 (2.12) Here two additional similarity parameters reslts: (4) Prandtl nmber: Pr =νρ cp κ (2.13) 2 (5) Eckert nmber: Ec cp ( Τ ) (2.14) = If these two parameter criteria are satisfied then thermal similarity exists. For wind-tnnel simlation in air the Prandtl nmber criterion is atomatically satisfied and the Eckert nmber is only important in compressible flow. For correct simlation of the ABL pressre distribtion (on varios objects), in windtnnel modeling, Jensen [6] observed that the roghness height ratio in the wind tnnel to that of the planetary bondary layer mst be eqal to a characteristic length of each, i.e., z z = L L (2.15) m Ths the geometric scaling of the bondary condition also mst be satisfied as stated by Jensen. If the other similitde parameters are also satisfied then dynamic similitde will prevail. Accordingly, geometric similarity is sally maintained between fll-scale and model flows. Also, since the atmospheric flow over the srface of the earth has negligible pressre gradients over short horizontal distances, the wind tnnel also mst have zero-pressregradient flow in the flow direction. This is obtained by having a false flexible ceiling in the wind tnnel and adjsting it to different heights for different floor roghnesses, which in trn m

6 6 model different srface topography, sch as oceans, rral areas, and rban areas, to maintain the zero-pressre-gradient condition. In addition to meeting these desirable similitde criteria, it was also necessary to develop a matre trblent bondary layer within the tnnel. This is sally accomplished by one of two methods. The first method involves bilding a long test section to develop a bondary layer of matre trblent strctre. The second method is to se trblent tripping fencing and roghness elements at the entrance of the wind tnnel to artificially create a bondary-layer -like velocity profile. The latter method sally does not prodce matre trblent flow becase basic flow variables change fairly rapidly with distance downstream from the pertrbating devices. Therefore, the UC Davis ABLWT facility has a long flow development section. The geostrophic wind is the wind above the ABL and it is not analogos to the freestream velocity in the wind tnnel de to the three-dimensional aspect of the ABL. Windtnnels stdies are only valid for simlation of the srface layer of the planetary (or atmospheric) layer. Since this layer is essentially independent of the geostrophic wind and the Ekman spiral effect, it can be modeled withot matching Rossby nmber. For netral ABL srface layers, Monin and Obkhov [20] developed a theory which ses only variable parameters defined at the grond srface, i.e., the srface roghness height, z and friction speed,, to entirely describe the layer. The srface layer extends p to a height of approximately 100 meters. Effects de to a nonnetral atmosphere (stable or nstable) can be simlated to some extent by cooling and heating the wind tnnel floor and/or ceiling. 3. Facility and Eqipment The ABLWT Facility The facility is an open-retrn type with fan blades plling air throgh the tnnel. The tnnel, which has an overall length of 22 meters, is composed of for sections: the entrance, the flow developing section, the test section, and the diffser section, as shown in Fig. 1. The entrance section is elliptically shaped to provide the incoming flow with a smooth contraction area for minimizing the freestream trblence. To redce large-scale pressre flctations of the flow and limit the size of airborne particles entering the wind tnnel, the contraction area is followed by a commercially available air filter. After the air filter, a honeycomb flow straightener is sed to redce large-scale trblence.

7 7 Fig. 1 Schematic diagram of UC Davis ABLWT showing cross-sections of entrance (Section A-A), test section with three-dimensional traversing mechanism (Section B- B), and the diffser-power drive system (Section C-C) The flow development section is 12.2 meters long and is sed to prodce a matre trblent bondary layer at the test section. For spires placed at the beginning of this

8 8 section and srface roghness elements placed throghot its length are sed to enhance the thickening of the bondary layer to a height of abot one meter at the test section. The flow developing section has an adjstable false ceiling and diverging walls, to provide zeropressre-gradient flow. The test section is three meters in streamwise length by 1.7 meters high by 1.2 meters wide. A framed Plexiglas door provides access to and allows observation of the test section. The test section ceiling also is adjstable to permit zero-pressre-gradient flow over its length. A three-dimensional probe traversing system provides accrate and fast sensor placement and can be moved over a large portion of the test section volme. To minimize flow distrbances the traversing mechanisms is aerodynamically shaped with aerofoil strts. Centerline wind speeds within the test section can be varied from 1 to 10 m/s. The 2.44 m diffser section allowed a continos transition from the rectanglar cross section of the test section to a circlar cross section for the fan. The eight-blade, fixed-pitch, 1.83 m-diameter fan is driven by a 56 kw (75-hp) DC motor with controller. The facility is described in White [25]. Velocity Measrements A Dantec Low Velocity Flow Analyzer and Thermo-Systems, Inc. (TSI), hot-wire anemometary are sed for all velocity and trblence measrements. The Dantec sensor was factory calibrated; additionally, a single hot-wire probe (TSI-1210, T1.5) was sed to verify the Dantec calibration. Dantec probe and hot-wire anemometer measrements were fond to have an inherent ncertainty of 5%, based pon laboratory calibrations sing a TSI model 1125 calibrator nit. Three-dimensional Traversing Mechanism The probe was vertically monted on the platform of the three-dimensional traversing mechanism in the test section. The electronic otpt of the probe-traverse mechanism was connected to three potentiometers, one for each of the three directions, x, y, and z. As the traverse wold change position, the voltage differential across the potentiometers wold vary. By sing a digital voltmeter, it was possible to identify the position of the probe in all three directions. The Dantec probe was positioned at specified locations (i.e., exhast fan heights), and the flow was digitally sampled over a 60-second period for velocity and trblence measrements. The mean velocity and trblence data were atomatically analyzed on line. The Dantec low velocity analyzer displayed the mean and root-mean-sqare (rms) velocities digitally averaged over the 60-second period. The ncertainty associated with these measrements and sbseqent calclations are specified by Dantec to be 5%. Concentration Measring Eqipment Wind-tnnel experiments are an effective means by which to evalate the dispersion of efflents from bilding stacks or exhast fans. Experimental analysis of plme dispersion cases for the present work was carried ot by two methods: i) flow visalization sing smoke composed of brned mineral oil; and, ii) gasconcentration-measrements made by a hydrocarbon analyzer sing ethane as a tracer gas. Flow Visalization Smoke visalization tests were sed to establish the location of the recirclation zones, or cavities, formed at the leading edge of bilding srfaces (see Fig. 2). Smoke was horizontally injected to follow a streamline near the leading edge and a

9 9 recirclation bbble eight was determined from the observation of the smoke streamline patterns. Knowledge of the extent of recirclation is considered important since any stack enveloped by the recirclation zone wold release efflent that wold not be properly dispersed into the atmosphere, or, more seriosly, may be drawn into the air intakes. Fig. 2 Flow patterns arond a rectanglar bilding Flow visalization proves valable in predicting average plme dispersion trajectories and characteristics of the maximm plme envelope. This is achieved throgh the se of a video camera (COHU, model 4815) and a video-cassette recorder (Panasonic, model AG- 1950) as a means of videotaping the dispersion of smoke in the wind tnnel. The taping is condcted over a long enogh period of time (i.e., several mintes) to give a good representation of the flctating plme. Data are redced by taking large nmber of plme trajectories and positions (i.e., fifty or more) directly from the screen of a Sony Trinitron color video monitor (model PVM-2030). These data otlined the area where smoke is observed to be present. Hydrocarbon Analyzer A Beckman 400A Hydrocarbon Analyzer is sed to measre qalitatively the dispersion of bilding exhasts. The hydrocarbon analyzer system (see Fig. 3) is composed of: (1) a tracer gas injection; (2) a three-dimensional traversing sampling mechanism; (3) a flame-ionization hydrocarbon analyzer; and, (4) an analog-to-digital data acqisition system. All lines in the system that carry either the tracer gas or the air and tracer-gas sample mixtre are 0.63 cm (1/4 in) refrigeration grade copper tbing, since copper does not absorb or prodce significant qantities of hydrocarbons. The tracer gas injected throgh the modeled exhast stacks is 97.5% ethane for netrally boyant emissions. The air and ethane mixtre, or simlated exhast plme, downstream of the stack

10 10 in the wind-tnnel test section was sampled at specific critical locations (bilding entrances, air intakes, etc.) to determine the level of dispersion. Fig. 3 Schematic diagram of Beckman 400A Hydrocarbon Analyzer System connected to the ABLWT to measre concentration of trace amonts of ethane gas in air. Downstream of the stack, the ether-air mixtre is sampled isokinetically at specific critical locations called receptors, e.g., air intakes, bilding entrances and cortyards, etc. The sample is then brned in the hydrocarbon analyzer with a mixtre of pre air and 40%

11 11 hydrogen and 60% nitrogen. An analog-to-digital acqisition program samples the flctating otpt voltage from the analyzer with a freqency of 300 samples per second for a total of 27,000 individal voltage measrements to prodce one averaged vale (i.e., a sampling time of 90 sec). The time-averaged voltage is then converted to parts per million (ppm) concentration of ethane in air. Calibration of the analyzer, with two known samples of ethane-air mixtres, prodces a linear relationship between the otpt voltage and the concentration. For each location, between two and three samples generally are taken to prodce an average vale of concentration at that location. The continos injection of ethane into the wind tnnel cases the backgrond level of concentration of hydrocarbons to increase with time. To accont for this effect the increase was considered to be linear over time and conseqently backgrond concentrations are taken at the beginning and the end of each testing session. Then, each sample vale is corrected by sbtracting the appropriate backgrond hydrocarbon concentration, determined from the linearly increasing backgrond concentration. 4. Similitde Criteria To model plme dispersion in an ABLWT the most important similarity criteria mst be met. Additionally, it is necessary to model the characteristics of natrally occrring wind, and the dynamic and thermal properties of the exhasted plme. Since some parameters sch as gravity, g, or the kinematic viscosity of air, v, can not be scaled, similarity criteria are often conflicting in some sense or can not be simltaneosly matched for all fll-scale parameters. Therefore, it is necessary to identify certain similarity criteria that are considered less inflential than other more important ones. Local Wind Characteristics Wind-Tnnel Trblence An accrate simlation of the ABL can be achieved only if the wind-tnnel bondary layer is also trblent. To create a trblent bondary layer the srface has to be aerodynamically rogh; i.e., the roghness Reynolds nmber, Re z, has to be greater than 2.5, or z Re z = 0 > 25. (4.1) ν The UC Davis wind tnnel satisfies this condition. For a freestream wind-tnnel velocity of U =3.8 m/s the following vales have been measred: friction velocity = 024. m s and roghness height z0 = m. Ths, the calclated roghness Reynolds nmber is 40, well above the 2.5 criterion. Mean Velocity Profile The relationship for the mean velocity,, verss height, z, in the wind-tnnel bondary layer flow also shold be represented by the power-law, known to exist in fll scale, which is given by:

12 12 z = α, (4.2) δ where δ is the bondary-layer height, is the inviscid speed (at height δ ) and α is the power-law exponent. The wind-tnnel flow can be conditioned sch that the exponent α will closely match the fll-scale vale of α. For the present case stdies, Fig. 4 displays a ABLWT mean velocity profile, and α is eqal to approximately 0.3, the tnnel vale is approximately the same. In the lower 20% of the bondary layer the velocity profile mst also agree with the logarithmic mean velocity relationship, 1 = n z 1, (4.3) κ z0 where κ is von Kármán s constant, which is eqal to abot 0.4. The scaled model is desirably contained within this layer. For a bondary layer height of approximately one meter in the test section, the depth of this layer is 0.2 meter and corresponds to a fll-scale height of 30m to 50m depending on the scale of the model. The maximm stack height considered in the crrent case stdies is 40m (above grond level), i.e., within the logarithmic layer region. Also, this region of the ABL is relatively naffected by the Coriolis force, and is the only region that can be modeled accrately by ABLWT. Trblence Intensity Profile Trblence intensity profiles, verss z, provide an indication of the variation of streamwise trblence throgh the shear layer. The profile for the wind tnnel shold agree reasonably well with the fll scale, especially within the lower 20% of the bondary layer where testing is carried ot. Maximm vales of the UC Davis wind-tnnel trblence intensity range from 35% to 40%, similar to those vales fond in fll scale in the srface layer as shown in Fig. 5. Similarity of Scaled Model Geometric Scale Depending on the size of the wind tnnel, the roghness height and the power-law index α, the scale ratio for geometric dimensions of the model may be determined. If possible, the integral scale length ratio, fll scale to wind tnnel, shold be matched, ths setting the scale. Typical geometric scales vary from 1:100 to 1:1000. The model sed in this analysis was scaled 1:360 for the first case stdy and 1:300 for the second case stdy, which match the estimated fll-scale integral length scale.

13 13 Fig. 4 Theoretical mean velocity profile of fll-scale case with srface roghness, z eqals 5 cm (solid line). Experimental data are taken from UC Davis ABLWT 1:192 simlation for a geostrophic wind speed of 40 m/s. Fig. 5 Theoretical longitdinal trblence intensity profile of fll-scale case with srface roghness, z, eqals 5 cm (solid line). Experimental trblence data are taken from UC Davis ABLWT 1:192 simlation of fll-scale for geostrophic wind speed of 40 m/s.

14 14 Scaling of Wind Speed Fll-scale wind speeds of interest in diffsion stdies are sally in the range form 3 to 20 m/s. Depending on specific test conditions, scaling of the natral wind may be based on eqality of stack momentm or densimetric Frode nmber. Both qantities will be discssed later in this section; however, matching either similitde parameter reslts in wind-tnnel speeds in the range of approximately 1 to 7 m/s. Also, regardless of the method chosen to establish a velocity scale, some mechanical limits imposed by the windtnnel facility itself may frther redce the range of operating speeds. Most wind tnnels have a minimm operating speed that gives satisfactory performance. At very low speeds, inlet flow conditions can introdce small pertrbations. The reslting flow instabilities may effect the velocity spectra. The minimm operating speed for the UC Davis ABLWT is considered to be 0.5 m/s. The maximm operation speed of wind tnnels is governed by the physical limits of the electric motor that drives the fan to introdce flow. The 56 kw (75 HP) motor at UC Davis prodces a maximm operating speed of 10 m/s. Bilding Reynolds Nmber The bilding Reynolds nmber Re H, represents a ratio of inertial to viscos (or frictional) forces over the srface of the bilding. It is often sed as a similarity parameter that shold be matched between the fll scale and the model to insre similitde. The Reynolds nmber is given by: Re H HH = ν, (4.4) where H is the bilding height, H is the wind speed at that height, and ν is the kinematic viscosity of air. Since wind-tnnel simlations se the same flid, air, as in fll scale, the fll-scale Reynolds nmbers exceed those of the model by several orders of magnitde de to scale redctions; therefore, it is impossible to exactly match the bilding Reynolds nmber. However, for the prpose of concentration measrements, flow above a critical bilding Reynolds nmber vale of 11,000 is known to be Reynolds nmber independent and will accrately model fll-scale bildings and strctres. It can be shown experimentally that the critical vale for flow independence is conservative and smaller bilding Reynolds nmbers may be acceptable. Past wind-tnnel simlations at UC Davis involved a series of tests to establish Reynolds nmber independence. In the case of dispersion stdies, this was achieved by making concentration measrements for what represents high and low wind-tnnel speeds relative to stack exhast speed, and showing that grond-level concentrations were relatively naffected by the extremes of this ratio for vales of bilding Reynolds nmber as low as Scaled Plme Characteristics Internal Stack Reynolds Nmber Stack emissions in fll-scale are sally trblent, while modeled internal stack flows might be laminar. Matching the fll-scale stack Reynolds nmber in wind-tnnel simlations is not always possible. However adeqate similarity is

15 15 achieved by ensring that the tnnel stack flow also is trblent. Stack flow will be trblent as long as the stack Reynolds nmber, Re s, is above a critical vale, or sds Re s = > 2300, (4.5) ν where s is the stack exit velocity and D s the stack inside diameter. The stack flow shold be tripped to enhance trblence if the stack Reynolds nmber is less than Plme Boyancy The sqare of the densimetric Frode nmber, 2 Fr d ( ) = ρ a U 2 w ρ a U 2 w s a gd = ρgd s s ( ρ ρ ), (4.6) represents the ratio of inertial to boyancy forces, where w is the wind speed at stack height, ρ the density difference between exhast gases and the ambient atmospheric air density, ρ a, and g the gravity. If emissions are netrally boyant, the densimetric Frode nmber similarity will not be considered. The standard Frode nmber is relatively straight-forward to dplicate in a windtnnel model; however, strict adherence to it can reslt in difficlties de to extremely low velocities if the critical vale of the Reynolds nmber for Reynolds-nmber-independent flow also is to be met. For example, in order to match large fll-scale Frode nmbers for a model scale of 1:300, it is necessary to decrease the wind-tnnels mean flow speed. As shown previosly, lower mean speeds reslts in smaller Reynolds nmbers and, possible, laminar flow, which is nacceptable. Therefore, the se of the densimetric Frode nmber rather than the conventional Frode nmber, 2 2 U ( Fr w d ) =, (4.7) gds can reslt in model wind speeds of approximately 50% higher. This is directly related to the fact that for boyant plmes, the ratio of stack gas density to ambient air density is not nity. Recent stdies at UC Davis examining boyant heated exhasts have modeled plme rise by matching fll-scale and wind-tnnels boyancy length scales, L B [26], the boyancy length scale also may be represented as: L s ρd 2 s g B = 4ρa U 3, (4.8) w

16 16 D L s s 1 B = 4 U 2 w ( Fr ), (4.9) d ths factoring in both the densimetric Frode nmber and the plme velocity ratio, s /U w. Plme Velocity Ratio To maintain a correct ratio of plme exhast velocity, s, to that of the ambient flow, U w, the following reqirement has to be met: s U w = constant. (4.10) Taking into accont the limited wind-tnnel operating velocities, the wind speed at stack height, U w, and/or the stack exit velocity, s, in the tnnel can be varied, sch that their ratio remains eqal to that of the fll-scale case. Plme Momentm Ratio The plme momentm ratio represents the ratio of vertical to horizontal momentm. Maintaining of a correct ratio in the wind tnnel to the one fond in the fll-scale case reqires that: ρs D 2 s 2 s ρa LU 2 2 w = constant, (4.11) where ρ s and ρ a are the gas densities of the stack and airflow, and L is a vertical length scale. For a non boyant stack exhast, ρ s is eqal to ρ a, and therefore : DSS DSS = LU w FS. (4.12) LU w WT With length scale λ, defined as, LWT LFS = 1 λ, (4.13) this relationship redces to: If exact scaling of stack diameter is maintained then this expression redces to ( ) ( ) s U w = FS s U w which is often sed as a similitde parameter; however, this is only the wt case when exact geometric scaling is sed.

17 17 ( ) s = 1 WT λ ( D ) ( D ) S FS S WT ( U ) ( U ) W WT W FS ( ) S FS. (4.14) Let ( s ) FS be the critical stack speed for minimm, crit, and the flow-rate be Q WT = ( s A s ) WT, with A = π 4 ( D ) S S WT 2 (4.15) then, the reqired trace gas flow-rate in the wind tnnel, Q wt, becomes: ( U ) W QWT = π 1 ( DS) WT ( D WT S) 4 λ FS crit ( ) S FS. (4.16) Therefore, different fll-scale wind speeds may be simlated in the ABLWT by adjsting the tracer gas flow rate, flow-rate. For testing prposes, adjsting the trace gas flow-rate is more convenient than changing the wind-tnnel velocity. Concentration Measrement Scaling Under similar atmospheric conditions, measred wind-tnnel concentrations may be related to those in the fll-scale case by the following relationship: CUw CU = C A λ 2, (4/17) C A W S S S FS S S S WT where λ is the scaling factor and C s is the concentration of the sorce. In this case, the concentration nits are in mass of polltant per volme of air. To convert volmetric concentrations (ppm), C vol, as sed in the present stdy, to mass per volme concentrations, the following relationship is sed: ( ) = vol ( ) 3 g 3 C g m C ppm M M a pa 10. (4.18) R T Since the exhast gas mixtre has a moleclar weight close to that of air and the exhast temperatre is close to the otdoor ambient temperatre, volme fraction and mass concentration diltion s are assmed to be eqal. d a 5. Discssion of Selected Case Stdies Plme dispersion stdies sing mineral-oil-based smoke for flow visalization have been condcted in the UC ABLWT since Concentration measrements of plme dispersion began in More than twenty stdies have been carried ot since then, and two selected cases of particlar interest are presented here. Case 1 addresses far- and near-

18 18 field effects, sch as those seen at roof level and close to the strctre of interest. Reslts from this test are compared to Gassian-based calclations generated by the U.S. EPAapproved Indstrial Sorce Complex Short Term (ISCSTII) model, that predicts concentrations by Gassian techniqes. Case Stdy 2 addresses both the near vicinity of the stack, as well as a range over 800 meters arond the stack. In this case stdy, the efflent is highly non-boyant and reslts from these tests are compared to the U.S. EPA-approved Integrated Pff-dispersion model (INPUFF) that predicts polltant concentrations at distances greater than 100 m form the sorce. In the evalation of stacks and exhast fans, the local wind-speed distribtion is very important, since the expected near-maximm wind speed at the stack height is issed to estimate the reqired stack exit velocity. Local wind characteristics are presented in a wind rose. The wind rose for Case Test 2 is shown in Fig. 6. This figre represents wind speed, direction, and freqency of occrrence. In its present sage, a west wind direction implies that the wind was from the west to the east. The wind-tnnel flow was conditioned to represent the atmospheric bondary layer semi-rban area and vales of roghness height, z o, and velocity profile exponent α, are similar to sbrban settings which is the sistation for both case stdies. In each of the two cases presented, an objective of the test will be stated, the appropriate analysis will be presented identifying those critical parameters to be simlated, and the reslts will be given, inclding a discssion of interesting findings and other points of interests. 6. Case Stdy 1: Near- and Far-Field Air Toxics Stdy of a Large Indstrial Complex Wind-tnnel stdies and wind engineering calclations for polltant dispersions from roof exhast fans were carried ot for a large proposed commercial-research indstrial complex to be located near San Francisco, California. Wind-tnnel stdies inclded flow visalization to establish qalitative characteristics of the bildings sites and stack plmes, and ethane tracer gas tests to establish qantitative polltant concentrations at specific downwind locations. The ASHRAE model [27] was sed analytically to predict concentrations (or diltion factors) in the near vicinity of the stack. Assessing Risk from Toxic Air Contaminant Emission An analytical model is commonly sed to estimate the health risk de to toxic air contaminant emissions and also to estimate the potential for other (non-cancer) acte or chronic health effects. For analytical steps are reqired: (1) hazard identification - determining the hazardos emissions reslting from a project; (2) dose-response assessment - evalating the health effects of exposre to these emissions; (3) exposre assessment - estimating the possible level of exposre; and, (4) risk characterization - integration of the first three steps to estimate risk. Each step involves making assmptions, and each assmption involves inherent ncertainties.

19 19 Fig. 6 Annal meteorological wind rose for Lawrence Livermore National Laboratory, Livermore, California.