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II MA . te TUT 1 ORNI 8-1187 Sop CZN MASTER ./ 1966 سال کی - ام / AN ANALYSIS OF FISSION PRODUCT DEPOSITION AND CORRELATION WITH EXPERIMENTS* je, M. N. Ozisik North Carolina State of the University of North Carolina Raleigh, North Carolina *o. chest from that or coatrat contentor" becluded a M a plot A. Makes may uroly ur represenului.rep1#..... .....!'.. mury, complety, or watulson of the totornudoa coatated in wis report, or that we want of way toormation, uppuration method, or process dechowedba dhe report any hot latring D. Anda ay waduitor me mospect to the wol, or for deg med parte, c.chod, ar proceso ductoud b the report pernor setting on damall or a Colladon, or neployee of mucha contractor, to the act sployee or contractor of the COB INon, ar astoren al met contractor propers, dormitor, or promdes Accow to. way tutoriaattaa paret Cocosa, or No etapoyarat with sucha contrastor. petrately ownede; or ay taformation, As wood but the abom, Of contractor of o plor: back wd m F. H. Neill Oak Ridge National Laboratory Oak Ridge, Tennessee Prepared for the International Symposiun on Fission Product Release and Transport Under Accident Conditions, April 6, , 1965, Oak Ridge, Tennessee. PATENT CLEARANCE ORLAND. RELEASE TO THE PUBLIC IS APPROVLD. PROGEDURES 'ARE ON FILE IN THE RECEIVING SACTION, . . . *Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation. . . LE WWW AN ANALYSIS OF FISSION PRODUCT DEPOSITION AND CORRELATION WITH EXPERIMENTS M. N. Ozisik F. H. Neill ABSTRACT Radioactive species that enter the coolant stream of a gas... cooled reactor are carried in the stream and deposited on coolant passages and various system components. Analytical relations are presented for deposition of radioactive particles from isothermal gas streams to the walls of a conduit as a function of time, dis- tance, and variable source release rate. Effect of recirculation of the cool.ant gas on deposition is also included in the analysis. . In the physical model considered, particles are assumed to be trans- ported from the gas stream to the immediate vicinity of the walls of the conduit by diffusion; the resistance to mass transfer by diffusion is obtained by analogy from heat transfer coefficients . At the wall surface an imperfect retention scheme is assumed, that is particles striking the wall surface are not all deposited but some re-enters the gas stream. This imperfect retention scheme is characterized by a wall surface resistance to mass transfer in series with the stream resistance to mass diffusion. To simplify the presentation of the analysis this unknown wall surface resist- ance has been incorporated into a single factor, P, which enters the equations as a multiplier to the stream mass transfer coeffi- cient. The analysis is correlated with experiments for deposition of fission products from isothermal helium streams on the surface of a stainless steel tube. INTRODUCTION Recently interest has grown in the use of ceramic or graphite fuel elements in gas-cooled nuclear reactors because such fuel elements permit operations at higher surface temperatures. Advantages associated with high temperature operations are well known, but in such systems radioactive fission products produced in the fuel elements may have an increased release rate to the coolant stream since there is no metallic cladding to contain fission products. The question then arises how these radioactive particles are carried away in the stream and deposited on various system components. Experiments have been performed to investigate fission product depo- sition from gas streams.959394 A heat-mass analogy approach has been applied to obtain analytical relations for equilibrium concentration of radioactive particles from isothermal gas streams on the walls of a conduit, and for the effects of non-isothermal conditions and radial temperature gradients in the gas streams.",0,1,0 A tranεient analysis has been per- formed and a time dependent relation' has been derived for deposition from isothermal streams, for a source releasing fission products into the gas stream at a constant rate. An analytical model based on the analogy be- tween heat and mass transfer has been used to correlate the experiments. In the present paper the above mentioned terhniques have been used to derive an expression for the deposition of radioactive particles from 180- thermal gas streams on the walls of a conduit as a function of time and distance. în addition, the particles are assumed to be released into the gas stream from a source at a rate which may vary with time, and transported to the surfaces of the conduit by radial diffusion while they are carried in the stream. An imperfect retention scheme is assumed for deposition at the wall surface, because experiments performed on the deposition of radio- active iodine from gas streams have shown that effectiveness of surfaces in retaining the molecules varies for different surfaces. The stream re- sistance to mass transfer by diffusion is obtained by analogy from heat transfer coefficients. The imperfect retention of molecules at the wall surface is characterized by a surface resistance to mass transfer. 11 ANALYSIS Consider a fully developed isothermal flow of gas in a closed conduit in the axial x-direction. A fission product source located at x = 0 releases radioactive particles into the gas stream at a rate which varies with time. Particles entering the stream are assumed to be electrically neutral and so small (less than 0.1u) that effects of electrical, inertial and gravi- tational forces on the motion of particles are negligible. As particles move with the stream, particle concentration in the gas stream of the species under study decreases because of deposition and radioactive decay. If the coolant stream is recirculating, as in most applications, particles that are left in the stream at the completion of one cycle are added to the particle concentration at the source at the beginning of the next cycle. The principal mechanism for the transport of particles from the gas stream to the surfaces of the conduit, for the conditions described above, is diffusion due to concentration gradient in the radial direction. Transport by diffusion takes place also in the axial direction, but this is very small in comparison to convection in the axial direction and therefore is neglected. To simplify the analysis a constant cross-sectional area, uniform temperature ụniform particle size, and a fully developed concentration boundary layer are assumed. Transport of particles from the gas stream to the surfaces of the con- duit is assumed to be by diffusion up to an interface at a distance of the order of a mean free path from the surface and then by free flight to the surface of the conduit. Diffusion of particles is characterized by a mass coefficient, h, which can be determined from heat transfer by analogy.° A mass transfer coefficient at the wall surface, h, is introduced for the effects of imperfect retention of particles at the surface, i.e., a value of h, equal to Infinity corresponds to a perfect sink condition, and a value of zero to no retention of particles at the surface. As illustrated in Fig. 1, particles are transported from the mean stream concentration, n, to the interface concentration n through a resistance 1/n, and from the interface concentration n. to the surface through a resistance i/n. The above assumptions are applied to derive two differential equations; one for the mean concentration of particles in the gas stream, and the other for the concentration of particles deposited on the surface of the conduit. The procedure is as follows. A material balance equation for the concentration of a given species of particles in the gas stream, n(x,t), for a control volume Ax about x may be written as (1) OX E (A ax n) = - (AUN) Ax – 1 A Ax n - a Ax h(n-nu) Storage Convection Decay Radial Diffusion where, A is the cross section area, a the deposition surface per unit length and U the mean stream velocity. - ---- www 3 1 TT . .. UNCLASSIFIED ORNL-DWG 64-6880R BULK STREAM = STREAM RESISTANCE TO MASS TRANSFER -- INTERFACE - = WALL RESISTANCE TO MASS TRANSFER WALL DISTANCE OF THE ORDER OF MEAN FREE PATH Fig. 1. The Stream and Wall Surface Resistance to Mass Transferi Defining, Equation I becomes, de + U V + a n) = 0 (5) A second differential equation for the particles deposited on the wall surface, c = c(x,t), can be obtained by writing a material balance equation for particle concentration on the wall surface. That is, de = new how - ac (6) A continuity equation for the interface where concentration of particles is ne is given by h(n - nw) = new (7) It is assumed that there is no storage in the interface. Substituting Eq. 7 into Eq. 6, and introducing the P factor as defined by Eq. 2, we obtain C = Phn - ac (8) The relation between the P factor and the mass transfer coefficients is obtained directly from Eq. 7, by making use of the definition of P as given by Eq. 2, P = 1+ h/h (9) Equations 5 and 8 become two linear coupled partial differential equations for the unknowns n and C, if we assume P constant, that is, the ratio n/h or n/n is independent of time and distance for a given set of conditions. It is to be noted that the assumption of P as constant implies that molecules re-entering the stream from the wall surface are independent of the concentration of molecules deposited on the wall surface. The solu- tion of Eas. 5 and 8 for the two unknowns n(x,t) and c(x,t) are presented in the next section for a given set of boundary and initial conditions. SOLUTIONS OF THE EQUATIONS The equations to be solved are n) = 0 de = Phn - ac where, a = } (at least in de With the boundary conditions for a closed loop defined as, n(0,t) = n(t) + n(1,t) $(t - 5) for all t lo for t where the step function is defined as, E(+: WIS HIS u 1 l fort for the and the initial conditions as, n(x,0) = 0 for 0 $(t - $ - $) $(T az - gth (ie. 6 = ent] (20-b) (20-c) X + Then Eq. 19 becomes, C = Ph e (21) Inverse transform of Eq. 21 is convolution integrals, given as ei cx,t) = 24 e ** [5* G6+ - +) @g(r) åt + } c{t - 1) @g(r) ao] (ee) Substituting the functions G from Eq. 20, we obtain c(x,t) = Ph eax (17 + Iz) (23) where, 1. * = $ - -) }(+ - $ –+) e* ar 12 * -O n(1,6 – 8 – 1) 81+ - – 1) e*** do If the functional form of n(t) is known, the concentration of particles deposited on the surfaces of the conduit can be evaluated from Eq. 23, with the aid of Eq. 17. Evaluation of particle concentration on the wall sur- face, c(x,t), for a constant source and on exponentially varying source is given in the next section. EVALUATION OF DEPOSITION FOR DIFFERENT SOURCE FUNCTIONS A Constant Source - If particles enter the gas stream at a constant rate, we have N(t) = No = constant (24) Equation 17 becomes, (25) O n(x,t) = (No f(t - #) + n(.,t - # $(t - 5 - 8) For times t» Eq. 25 becomes, n(x) = *** [$. + n(L)] (26) n(L) can be evaluated by substituting x = L in Eq. 26, n(L) = N e u Ice (27) Substituting Eq. 27 into I n(x) = N e Ox _1 (28) l- OL It is apparent from Eq. 28 that the term 1/(1 - e ab) is for the effects of recirculation. If the total length of the loop, L, is long or the value of a is high such that al >> 1, Eq. 28 reduces to n(x) = N e ax (29) no The relation for the concentration of particles deposited on the sur- face of the conduit can now be obtained from Eq. 23, by substituting Eqs. 24 and 28 into this equation and performing the integrations. For times e concentration of particles deposited on the surface of the con- duit is given by mit c(x,t) = N, Ph e Tax 1-2 * L- (30) (31) Two special cases of Eq. 30 are, (1) for it « 1 (and t » Ls C(x,t) = N, Ph e * , hai t (11) for steady state, 1.e., t * C(x,c) = N Phenox l - e M (32) -AL 1 - e Exact relation for concentration of molecules in the gas stream is derived in Appendix A. 10 It is to be noted that this steady state relation corresponds to the concentration of particles on the surface as limited by radioactive decay. There may be factors other than radioactive decay that may limit the maxi- mult number of molecules deposited on the surface before the limit given by Eq. 32 is reached. Therefore, Eq. 32 should be used with caution since no factors other than radioactive decay are included in the present analysis to limit the maximum amount deposited on the surface. An Exponential Source - If particles enter the gas stream from a source at a rate which vary exponentially with time, we may write, N(t) = N eBt (33) where N and B are constants, Eq. 17 becomes, n(x,t) = = = =(+ -( - ) + (Lạt -ử (-8 -8 (3%) for times t»Eq. 34 becomes, n(x,t) = 2* [16 23* + n(2,- # If we substitute x = 1 in Eq. 35 and assume that n(Lýt) = n(Lyt - 8 We obtain ni L, t - No e Bt - aL (37) Substituting Eq. 37 into Eq. 35, we obtain the relation for the concentra- tion of particles in the gas stream, n(x,t) = (N eBt) e ax 1 (38) 1- QL Comparing this equation with Eq. 28 for a constant source, it is apparent that both equations are similar in form, except the constant source term N of Eq. 28 is now replaced by the exponential source term N. e-Bt. Concentration of particles deposited on the surface of the conduit can now be obtained from Eq. 23, if Eqs. 33 and 38 are substituted in this 11 equation and Integrations are performed; for times t» , we obtain C(x,t) = N e-Bt Ph -ax 1 -e (A - B)t (39) 1 - B Two special cases of Eq. 39 are, (1) for B = 0, Eq. 39 reduces Eq. 30 for a constant source. (11) for |(– B)t/ «i, C(x,t) = N. e-Bt Ph e-3x - 1 (40) 1-2 at t Equation 40 is similar in form to Eq. 31 except the constant source term, No, of Eq. 31 is now replaced by the exponential source term. EVALUATION OF THE MASS TRANSFER COEFFICIENT The mass transfer coefficient, h, that enters the above equations can be obtained by analogy from the heat transfer coefficients. In applying the analogy the Prandtl number is replaced by the Schmidt number, and the Nusselt number for heat transfer by the Nusselt number for mass transfer. For turbulent flow inside closed conduits, for example, the mass transfer 12 coefficient may be evaluated from (41) and for fully developed laminar flow inside circular tubes, from hd = 3.66 (42) ***.* * By similar analogies the mass transfer coefficient for other geometrical con- figurations can also be evaluated. The diffusion coefficient, D, in these equations may be evaluated from ..... . . ... D = 0.185 x 10-2 pe alte cm/sec (43) in K, M, and as the pressure of the where P is the total pressure of the system in atmospheres, T temperature in °K, M, and M, are the molecular weights, and o is the collision diameter in Ångstrom. 12 The dimensionless collision integral, s, is for deviation from the rigid sphere model for which it would be unity. The values of N are tabu- lated as a function of T/(€/k), and the values of 0 and () for a binary mixture may be evaluated from 0 = (0 + oz) (44-2) (V. De (44-6) 13 If the values of () for a given species is not available, an approximate value may be obtained from the relations based on boiling point, melting point or the critical point of the material. The mass transfer coefficient at the wall, h,, which has been corporated in the P factor, could not be evaluated by analytical means. Therefore, the P factor becomes the only unknown parameter in the present equations, and its value may be determined by correlating the experiments with the present analysis. Once the P factor is determined for a given set of experimental conditions, the value of h, can be evaluated from 1 (9) PI + n/hu The factors affecting h, however, are not known. It is expected that the type of surface material and the colliding particle, the surface condition, and the temperature level may be among the factors affecting it. In the present mode). molecules re-entering the stream from the wall surface are assumed to be independent of the concentration of molecules deposited on the wall surface. This condition is satisfied for small concentration of molecules deposited on the wall surface. CORRELATION WITH EXPERIMENTS Data obtained from experiments in the BMI and ORNL loops were applied to Eq. 31. The source release rate was unknown for the experiments conducted in both facilities. However, by rationing the surface deposition at differ- ent axial positions, the exponential portion of Eq. 31 can be evaluated. Let, C(x,,t) and C(xg,t) be the concentration of any given species deposited in the isothermal region of a tube at x, and xg, at any time t. From Eq. 31 for a constant source we obtain : 13 C(x,t) C(x, t= exp[- alxz - x)] (45) where, a = fra + au point if t» and at «1. The same result is obtained from Eq. 39 for an exponential source if we assume 11 - Blt «l. Equation 45 is further simplified to en prenos exp (- 42 st (46) (46) if we assume, The dimensionless Stanton number, St, in Eq. 46 is defined as st = Taking the logarithm of Eq. 46, and for convenience choosing, x, = 0, Eq. 46 becomes in alete = -2 (47) where, 2 = 48 st and P = 1+ h/h Equation 47 is applied to correlate the experiments performed for the Oak Ridge National Laboratory at the Battelle Memorial Institute and experi- ments performed in the fission product deposition loop at ORNL. The BMI. test facility consisted of a closed loop of one-half inch type 316 stainless steel tubing with a heater section, specimen heater, a 1200°F isothermal deposition section, a cooler section, a 600°F isothermal deposition section, and a circulator. Fission products entered the helium stream from a fuel specimen consisting of 100 mg of fully enriched UC, particles about 100 u in diameter each with a 4 u pyrolytic carbon coating. The fuel was irradiated to a burnup of 0.01 to 0.1 a/0 and allowed to decay for several weeks to reduce the activity level of the short lived fission products before use. ... 14 * t , N ik e W ": -Y - .. .. . . ... -..-.... -. . . . . . . .-.- . - . - . -. - . . The fuel specimen, when ins: rted into the test loop, was heated to about 1800°F to accelerate the diffusion of fission products into the gas stream. The test section consisted of a well-insulated hot isothermal zone where the gas temperature was about 600°F. The hellum stream was maintained at a pressure of about 300 psia. Fission products that entered the gas stream consisted of Cs-137, Ce-141, Ba-La-140, Ru-103, Zr-No-95, I-131, Te-129, Te-132 and Na-147. Total activity of the particles deposited on the sur- face was determined by measuring after each test the gross-gamma activity of tube sections with a multi-channel analyzer. A computer program was used to determine the relative magnitudes of the individual species from the measured gross activity. A check of the computer results with the chemical 14 analysis showed that the agreement was reasonably good. The fission-product deposition facility at the Oak Ridge National Laboratory is an isothermal loop fabricated from 1 1/2 in. diam type 304L stainless steel pipe. A heater section, an 8 ft long deposition section, an injection system, and a circulator constitute the major components of the loop. The facility is designed to operate isothermally up to a tempera- ture of 600°F and up to a maximum pressure of 300 psig. The radioactive material are injected into the helium stream in the solution form using a small positive displacement pump. A typical solution consisted of about 5 millicurie of radioactive 1-131 in 5 mg of stable iodine dissolved in either 10 or 20 ml of cyclohexane. The solution is injected into the helium stream at a constant rate over a period of about 2 hr. Activity deposited on the surface of the tube is measured by scanning the tube during experi- ments with a traveling scintillation crystal encased in a lead shield with a suitable slit for monitoring a l-inch long section of pipe activity at any given location. Figure 2 shows a plot of the ratio of c rfission prod- juct deposition from laminar and turbulent helium streams on stainless steel tubes as obtained in BMI experiments. The mass transfer coefficient, b, 1.s calculated from Eqs. 41. and 42 for turbulent and laminay flows respectively, and the diffusion coefficient from Eq. 43 by assuming molecular size (or atomic size depending on the species) particles. The experimental points shown on Fig. 2 are evaluated by assuming a perfect sink condition at the -all surface (1.e., P = 1.). It is apparent that all the experimental datid, -. - . - . -. TH ' * . ,! * Lib ra . .. " :- : * * . ZA . . anier . y i T . A . • 7 . id * - 1 . ' 7 - 1 : m ' . - . + . '" -..comer 1 . . i . . UNCLASSIFIED ORNL-DWG 64-6882R2 . . . 0.5 0.2 G 0.1 F -2 VALUE CALCULATED A LAMINAR FLOW FOR P = 1.0 • TURBULENT FLOW 0.37-in.-ID SS TUBE GAS = HELIUM ISOTOPES: Cs-137, Ce-141, Ba-La-140 Zr-95, Te -129, Te-132, Nd-147 1 TEMPERATURE: 600-1200 °F ' TTTTT 0.4 0.8 1.2 1.6 2.0 2.4 2.8 2 = 4 p.st.com 0.04 0 . Fig. 2. Relative Deposition vs 2 for Deposition on Stainless Steel Surfaces. 16 with the exception of a few laminar flow tests, fall above the theoretical solid line. This indicates that P values for the experiments under consid- eration are less than unity. The experimental data in Fig. 2 can be made each experiment. Figure 3 shows the P. values thus evaluated for each experimental point as a function of, h, the stream mass' transfer coefficient. Included on Fig. 3 are four dotted lines calculated from Eq. 9 for the constant values of the wall mass transfer coefficient, h, equal to 2, 3, 6 and 8 cm/sec. It appears from Fig. 3 that substantially all the experimental data under consideration are reasonably well bracketed by the two dotted lines evalua- ted for h = 2 and 8 cm/sec. No attempt has been made to differentiate between the wall coefficients, h, for different species because of limi.- tation in the accuracy of the experimental data. Included in Fig. 3 are the experimental data obtained from ORNL-FPD Loop for deposition of I-131 on stainless steel tubes, which also fall in the region bracketed by the dotted lines for H = 2 and 8 cm/sec. CONCLUSION An important factor that affects deposition from gas streams is the behavior of molecules upon colliding the wall surface. Correlation of ex- periments with the present simple model shows an imperfect sink condition at the wall surface. The exact mechanism of interaction between the wall surface and the colliding molecule is very complicated, and our understand- ing of this mechanism is still insufficient to formulate a rigorous theory. The model in the present analysis is a simple one; it does not provide for the effects of build-up in wal.l. concentration on the rate of evaporation of molecules from the wall surface. In physical reality, as the concentra- tion of molecules builds up on the wall surface, the molecules are evaporated from the surface at a rate which is some function of wall concentration. Therefore, the present model is strictly applicable for a small concentra- tion of molecules deposited on the wall surface or for small evaporation rates of the molecules deposited. In correlating the experiments with the present analysis the validity of these assumptions could not be checked; - I - - UNCLASSIFIED ORNL-DWG 64-6883RA TUBE: STAINLESS STEEL GAS: HELIUM ISOTOPES: Cs-137, Ce-141, Ru-103, Bo-L0-140 Zr-95, Te-129, Te-132, Nd-147, 1-137 , O EXPERIMENTAL, TURBULENT FLOW, ORNL-FPD DATA A EXPERIMENTAL, LAMINAR FLOW Bro BMI DATA • EXPERIMENTAL, TURBULENT FLOWS - CALCULATED FROM DEFINITION OF P FACTOR P-FACTOR how = 8 cm/sec hw=6 cm/sec + t 17 - how =3 cm/sec- hw = 2 cm/sec + 011 TEMPERATURES: 600-1200 OF O 1 2 8. O 3 6 . 7 h, MASS TRANSFER COEFFICIENT (cm/sec) . Fig. 3. The P Factor as a Function of h for Deposition of Fission Products on Stainless Steel Surfaces. 18 however, the concentration of molecules deposited on the wall surface is considered to be small. Presence of larger size particles in the gas stream such as those resulting from agglomeration of molecules or dust particles entering the gas stream tend to lower the diffusion doefficient for the mixture. No estimate could be made for the effects of larger size particles on diffusion coefficient. Agglomeration of molecules is considered negli- gible for the weak concentration of molecules under consideration, but the effects of dust particles, if such particles existed in the stream, could not be included in the correlation of experiments with the present analysis. If the diffusion coefficient is evaluated by assuming particles exist in the gas stream only in molecular (or atomic) sizes while some larger size particles exist in the stream, then the value of he determined from experi.. ments will be effected. There fore, values of h, estimated as a result of correlating the present analysis with experiments is considered affected both by the imperfect sink condition at the wall surface and by the presence of larger size particles, if such particles exist in the gas stream. In the present model, the total resistance to the transport of molecules from the gas stream to the wall surface is considered composed of two resist- ances in series; stream resistance to diffusion, 1/h, and the wall resist- ance to deposition, 1/h. If experiments are devised to reduce the stream resistance to diffusion, such as by using very small diameter tubes on very high flow rates, the wall effect on deposition can be determined more ac- curately. NOMENCLATURE > , a small error will be involved if this relation is used for small values of t. In order to estimate the amount of error involved at any time, t, the exact relation is derived for the closed-cycle concentration of molecules in the gas stream. In the following analysis, concentration of molecules in the gas stream at any location, x, is evaluated for each consecutive cycle and the results added to obtain the total concentration. Consider a closed loop of length L, and a constant source N, at x = 0. 1. The concentration of molecules in the gas stream at x for the first cycle is, n(x,t) = No e as $(t - 다 ​for os (A-1) 2. The concentration of molecules in the gas stresin at x for the second cycle is, n(x,t) = N, e ax + No e Alx * L)g(t - 5 - 1) for 1/4 < t < 2 / 2 (A-2) 3. The concentration of molecules for the third cycle is n(x,t) = N e-CX + N 4(x + 1) + N e A(x + 21) $(t - L - ) for 2 1 < t < 3 (A-3) O Continuing in this manner, concentration of molecules in the gas stream at x for the (k + 1) cycle is n(x,t) = No e ax + N e Alx + 1) + N e Alx + 2L) + . (continued next page) 22 ... + N. *(x + kt) $(t - - A) OL KO N e JO for k < t < (k 1) (A-4) The summation in this relation can be expressed as, (A-5) to 1- Hence the concentration of molecules in the gas stream at x for the (k + 1) cycle is given by -OKL 11 - e - - te 17e R(,4) – Y, 2-per estat (* =* -51 for < t < (x + 2) . (A-6) It is now apparent that for large enough values of k, that is for a large number of circulations emakl « 1 Equation A-6 reduces to x 1 n(x,t) = N, ex a (A-7) 1 - e which is the same as Eq. 28. The error involved in Eq. 28 at any time t can be estimated by comparing it with the exact relation given by Eq. A-6. *** 3 . " ! .. . 03 1.. . UGA DATE FILMED 16 / 8 /65 . .. TRI. * ** * . . . . . -# . LEGAL NOTICE *!! ! r. - - -- - . This report was prepared as an account of Government sponsored work. Neither the United States, nor the Commission, nor any person acting on behalf of the Commission: A. Makes any warranty or representation, expressed or implied, with respect to the accu- racy, completeness, or usefulness of the information contained in this report, or that the use of any information, apparatus, method, or process disclosed in this report may not infringe privately owned rights; or B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or process disclosed in this report. As used in the above, "person acting on behalf of the Commission" includes any em- such employee or contractor of the Commission, or employee of such contractor prepares, disseminates, or provides access to, any information pursuant to his employment or contract with the Commission, or his employment with such contractor. . - . . . . END