MECHANTSM 0F RE-ENTRAINMENT OF SMALL PARTICLES FROM FLAT SURFACES IN TURBULENT FLOW Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY JAGJIT SINGH PUNJRATH 1970 OJ‘MIJ- __ T" [I' LIBL~:; an .,_ E Michigm Sane : 1Q Unix crslty ..,. mummmmuwmfiuuuun HTTFIH 10631 8409 This is to certify that the thesis entitled MECHANISM OF RE- ENTRAINMENT OF SMALL PARTICLES FROM FLAT SURFACES IN TURBULENT FLOW presented by Jagjit Singh Punjrath has been accepted towards fulfillment of the requirements for B, 6’. MAM“; Major professor Date 2/26/70 4. 0-169 J“ 26987 MRCILAM 3% rKR' flut tu’ l'v .. Claomif‘m ... 4'...“ (atom. ca ' o us nor“. u- ,. (tutu ~t 2*; t1... 8%? ' 2 ., .«V'a t“_l,_o ‘.V‘ 2‘ -crooxs9 : ~:~ ; t7 ”Amheenca ;~.'~m A v .. . 3 ~ A ”t 93.3.» ,-.s.‘. *-' ~:;' ' .' «f~ _-. =‘.ta.z.ace=; "Alec-tnzumm-~. :Lr . L ... L 7's '2, ucludeo an :a-v~t1;:'!nn ; r‘~ ‘» ABSTRACT MECHANISM OF RE-ENTRAINMENT OF SMALL PARTICLES FROM FLAT SURFACES IN TURBULENT FLOW by Jagjit Singh Punjrath The mechanisms of re-entrainment of small particles from flat surfaces are receiving increased attention due to the increasing importance in such diversified fields as sterile packaging rooms, sand dune movement, pneumatic transport of pow- der and grains and possibly bacterial warfare and space travel. ‘The objectives of this study were to investigate the mechanisms of re-entrainment from flat surfaces at zero angle of incidence. Classified small particles deposited uniformly over a thin flat surface were exposed to air flow at different velocities and intensities of turbulence in a low speed wind tunnel. The minimum distances from the leading edge at which re-entrainment initiated under different conditions of velocities and intensities of turbulence were observed. The varying degrees of turbulence were created by moving the experimental surface nearer or away from a turbulence producing grid placed upstream from the flat plate. A hot film constant temperature anemometer was used to measure instantaneous velocities. A different approach to calculation of re-entrainment velocities is suggested. The experimental analysis includes an investigation of the influence of turbulent intensity, particle size and location of particles. Jagjit Singh Punjrath Re-entrainment was observed to increase significantly as the intensity of turbulence increased. The force required to re- entrain particles of any size was found to be independent of the intensity of turbulence. The effect of turbulence on re-entrainment was observed to be analogous to the phenomenom of transition from laminar to turbulent flow in the boundary layer over a flat plate. It was concluded that increased re-entrainment due to higher inten- sities of turbulence was due to a shift of the point of transition from laminar to turbulent flow in the boundary layer over the flat plate. The particles with median diameter between 15 to 22.5 microns required the minimum velocities and force per unit area for re-entrain- ment. The location of particles on the flat plate was observed to be important in the re-entrainment process. Re-entrainment occurred more readily at greater distances from the leading edge than at locations near the leading edge. The location at which re-entrainment initiated moved nearer the leading edge as the intensity of turbulence increased. It was concluded that the re-entrainment process consists of a two-part mechanism: a. The particles start re-entrainment in the region where the flow in the boundary layer changes from laminar to turbulent and where the aerodynamic shear stress is sufficient to Overcome the force of friction between the particles and the surface. A Jagjit Singh Punjrath b. The particles set in motion at the transition point contact other particles while moving downstream, resulting in movement of particles due to momentum of particles set in motion at the transition point even when the aerodynamic force of shear stress on these particles may not be sufficient to overcome their frictional forces. Approved IQ K WW ‘7/“'/7O Major Professor Approved UVC Department Chairman .“b. » MECHANISM OF RE-ENTRAINMENT OF SMALL PARTICLES FROM FLAT SURFACES IN TURBULENT FLOW BY Jagjit Singh Punjrath A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 54.21/53 (. ~/ 0 «'70 Mr. & Mrs. I. S. Punjrath Miss Carmenza Meneses ACKNOWLEDGMENTS The author wishes to express his appreciation and thanks to Dr. D. R. Heldman, committee chairman, for his valuable suggestions and constant help during the course of this investiga- tion. It was a rewarding experience to work with him. His inspiration and advice shall always be remembered. Sincere appreciation is extended to Dr. F. W. Bakker- Arkema (Agricultural Engineering), Dr. C. W. Cooper (Chemical Engineering) and Dr. T. I. Hedrick (Food Science) for serving as guidance committee members and providing advice whenever needed. The author also wishes to thank Dr. C. W. Hall, Chairman, Agricultural Engineering Department for providing the financial assistance and also the members of faculty, staff and fellow graduate students for their interest and enc0uragement during the course of this investigation. Finally the author wishes to thank Messrs. P. Hock, G. Shiffer and L. Foster for their cooperation in assembly and fabrication of equipment. iii TABLE OF ACKNOWLEDGMENTS . . . . LIST OF TABLES . . . . LIST OF FIGURES . . . . LIST OF APPENDICES . . . NOMENCLATURE . . . . . Chapter 1. INTRODUCTION . . . 2. OBJECTIVES . . . 3. JUSTIFICATION . . 4. REVIEW OF LITERATURE . 4.1. The Re-entrainment Process 4.1a. Re-entrainment and Threshold Velocity 4.1b. Effect of Relative Humidity 4.1c. Influence of Particle Size on Re-entrainment 4.1d. Influence of Particle Shape 4.1e. Effect of Nature of Particle and Surface Material 4.1f. Influence of Surface Roughness 4.1g. Effect of Viscous Surface Coating 4.1h. Effect of Time of Contact 4.11. Effect of Static Charge 4.1j. Effect of Temperature 4.1k. Miscellaneous Studies 4.2. Turbulence Processes 4.2a. Turbulence 4.2b. Turbulent Boundary Layer along a Flat Plate iv CONTENTS on Adhesion Pa ii 12 13 13 14 15 15 15 16 16 16 19 ge i —-'-q w 5. THEORETICAL CONSIDERATIONS . . . . . . 21 5.1. Types of Forces between a Particle and a Flat Surface . . . . . . 24 5.1a. The Capillary Forces . . . . 24 5.1b. The Electrostatic Forces . . . 25 5.1c. Forces due to Molecular Interaction 27 5.1d. Forces due to Viscous Flow . . 28 5.2. The Forces for Re-entrainment . . . 29 5.2a. The Fluid Dynamical Force . . . 29 5.2b. The Inertial Forces . . . . 30 5.2c. The Direct Mechanical Contact Forces 30 5.3. The Re-entrainment Theory for Turbulent Flow 31 6. EXPERIMENTAL DESIGN AND PROCEDURES . . . . 37 6.1. Equipment . . . . . . . . 37 6.1a. The Settling Chamber and the Cloud Generator . . . . . . 37 6.1b. The Wind Tunnel and Turbulence Grid 41 6.1c. Measurements of Mean Velocity and Intensity of Turbulence . . . 43 6.2. Tests for Physical Properties of Particles 45 6.2a. The Particle Size Distribution 47 6.2b. The Test for External Friction Factor 47 6.3. Scope of the Tests . . . . . . 49 6.38. General Procedure . . . . . 49 7. RESULTS AND DISCUSSION . . . . . . 51 7.1. Effect of Turbulence on Re-entrainment 51 7.2. Effect of Particle Size 56 7.3. Effect of Particle Location . . . . 6O 7.4. Comparison of Predicted with Experimental Results . . . . . . . . 62 7.5. Comparison of Results with Previous Investigations . . . . . . . 68 7.6. Mechanism of Re-entrainment from a Flat Surface . . . . . . . . 69 7.7. Prediction of the Potential for Particle Re-entrainment . . . . . . . 72 8. SUMMARY AND CONCLUSIONS . . . . . . . 80 9. RECOMMENDATIONS FOR FUTURE WORK . . . . . 82 REFERENCES . . . . . . . . . . . 83 APPENDIX . . . . . . . . . . . . 89 vi Lab}; LIST OF TABLES Table 4.1. Influence of nature of particle and surface material . . . . . . . . A.l. Determination of external friction factor Page 13 92 E‘ LIST OF FIGURES Figure 3.1. Effect of Reynolds number on the drag coefficient for flow normal to a flat plate . . . . . Effect of percent turbulence on the drag coefficient for flow normal to a flat plate . . . . . Effect of relative humidity on adhesion . . . Schematic diagram of boundary layer . . . . Capillary force due to liquid layer . . . . Electrostatic Force . . . . . . . . Stefan effect . . . . . . . . . . Resistance formula for smooth flat plate at zero incidence . . . . . . . . . . Influence of intensity of turbulence on critical Reynolds number on flat plate at zero incidence Schematic of settling chamber . . . . . . Schematic of cloud generator . . . . . . Schematic diagram of the mounting of test plate in the wind tunnel . . . . . . . . . Schematic diagram of wind tunnel and related instrumentation . . . . . . . . . Wind tunnel and velocity recording instruments Settling chamber and cloud generator . . . . Cloud generator . . . . . . . . . Turbulence grid . . . . . . . . Effect of intensity of turbulence on Reynolds number at which re-entrainment started for particles of 15 microns diameter . . . . . . . . Effect of intensity of turbulence on Reynolds number at which re-entrainment started for particles of 22.5 microns diameter . . . . . . . viii Page 11 23 23 26 26 32 32 38 40 42 44 46 46 48 48 53 53 Figure Page 7.3. Effect of intensity of turbulence on Reynolds number at which re-entrainment started for particles of 30 microns diameter . . . . . . . . . 54 7.4. Effect of intensity of turbulence on Reynolds number at which re-entrainment started for particles of 5 microns diameter . . . . . . . . . 54 7.5. Effect of intensity of turbulence on the total force required to re-entrain particles . . . . 55 7.6. Effect of particle size on Reynolds number required for re-entrainment . . . . . . . . . 57 7.7. Effect of particle size on aerodynamic removal force per unit area . . . . . . . . . . 58 7.8. Variation of total force acting on a particle with particle size . . . . . . . . . 59 7.9. Variation of total force required for re—entrainment with distance . . . . . . . . . . 61 7.10. Comparison of experimental and the theoretical Reynolds numbers for re-entrainment for particles of 15 micron diameter . . . . . . . . 64 7.11. Comparison of experimental and theoretical Reynolds numbers for re-entrainment of particles of 22.5 micron diameter . . . . . . . . . 65 7.12. Comparison of experimental and theoretical Reynolds numbers for re-entrainment of particles of 30 micron diameter . . . . . . . . . 66 7.13. Comparison of experimental and theoretical Reynolds numbers for re-entrainment of particles of 5 micron diameter . . . . . . . . . 67 7.14. Effect of length of plate on degree of re-entrainment for particle, 10-20 micron in diameter . . . . 75 7.15. Effect of length of plate on degree of re-entrainment for particles 15-30 micron in diameter . . . 76 \l I H 0‘ 0 Effect of length of plate on degree of re-entrainment for particles 20-40 micron in diameter . . . 77 7.17. Effect of length of plate on degree of re-entrainment for particles 0-10 micron in diameter . . . 78 A.1. Calibration of hot film, constant temperature anemometer . . . . . . . . . . . 91 ix LIST OF APPENDICES Appendix Page A.1. Calibration of Hot Film, Constant Temperature anemometer . . . . . . . . . . 9O A.2. Determination of External Friction Factor . . . 92 NOMENCLATURE the projected area of the particle the amplitude of vibrations the radius of rotation the prOportionality constant the drag coefficient the total skin friction coefficient for smooth flat plate at zero incidence the local skin friction coefficient for flat plate the diameter of the particle the closest distance of separation between the particle and surface, cm. the fluid dynamic force the temperature in degrees fareinheit the centrifugal force the London van der Waals dispersion force, dynes the electrostatic force the gravitational force the external force the inertial force of removal the normal component of the force of capillary adhesion the sliding and rolling friction the forces due to viscous flow; Steffan force the frequency of vibration the acceleration due to gravity the Newtons conversion factor, 32.174 ft-lbm/lbf—sec2 xi WWWYW" * Re r exp Re r pre the distance from the surface the horse power the dielectric constant the roughness parameter the height (here diameter of particle) of grain for equivalent sand roughness length of the flat plate or surface measured in the direction of flow the mass of the particle the number of revolution per unit time the static pressure the time mean value of turbulence pressure the turbulent fluctuation of static pressure the number of atoms per cubic centimeter the maximum charge which can be carried by a particle of radius R the radius of the particle the radius of the disc the critical Reynolds number at which flow in the boundary layer over a flat plate changes from laminar to turbulent (U xc/v) the Reynolds number at which re-entrainment started (U xr/v) the Reynolds number (U x/V) the experimental Reynolds number at which re-entrainment started (U x /V) exp r exp the Reynolds number based on the velocity (UPr e) predicted by the equation 5. 34. (Upre xr exp/V) the radius of the particle, cm. the time — v-w‘.....e x r exp nary DI the intensity of turbulence G/_;f/U) the Eulerian velocity the time mean value of Eulerian velocity the wall friction velocity g/Fég) the time mean velocity observed in the experiments the time mean velocity predicted by the equation 5.34 the turbulence component the distance from the leading edge in the down stream direction the distance perpendicular to the wall or plate the critical distance from the leading edge in the down stream direction, where the flow in the boundary layer over a flat plate changes from laminar to turbulent the minimum distance from the leading edge in the down stream direction, where the re-entrainment initiated the minimum distance from the leading edge in the down stream direction, where the re-entrainment occured in the actual experiments the displacement from the median the contact angle between the liquid and the particle Von Karman's Universal Constant the surface tension of the liquid the time for moving from h1 to h2 A constant depending upon the composition of the particle the viscosity of the liquid 3.14159 density of the fluid the time mean value of density the turbulent fluctuation of density the density of the particles xiii - the wall shear stress the local drag on the flat plate angle of contact kinematic viscosity (%) 1. INTRODUCTION The mechanism of re-entrainment of small particles from flat surfaces plays an important part in nature and every day life. The phenomena of sand transport by wind in deserts, pneu- matic transport of powders and grain and possible role of re- entrainment in the air borne contamination in sterilized packaging rooms and the so called "Clean Room" are but a few examples of its daily application. According to Heldman and Punjrath (33) the Optimum contamination control condition in an enclosed space will not exist until all sources of contamination are eliminated, this being particularly true in food processing plants where dilution type ventilation systems are used predominantly. These systems tend to disperse any contamination which is generated until it is uniformly distributed within the space or room. The isolation and evaluation of sources of air borne contamination are very complex due to number of sources which normally exist and the different characteristics of the various sources. Horizontal flat surfaces appear to be a potential source of air borne contamination for several reasons: (a) they occur frequently in any enclosed space which contains equipment and machinery, (b) they are accessible to deposition of dust particles from the space and (c) there is likeli- hood that air flow characteristics may occur near the surface resulting in re-entrainment of the dust. It is well known that dust and microbial particles adhere to solid surfaces with great tenacity. Atmospheric dust particles cling to leaves, fabric, table tops, walls and other horizontal surfaces on equipment, etc. It is common observation that gravitational forces fail to overcome the adhesive forces of most particles. Similarly vigorous blowing on the surfaces dislodges only a few particles. Although these observations are common place, the quantita- tive aspects of these forces of adhesion and forces required for re-entrainment are not well defined and little is known of the mechanisms of re-entrainment and effect of flow characteristics such as degree of turbulence on the re-entrainment. Systematic theoretical and experimental study of the field, as a whole, is, however, still in an elementary stage due to the absence of reliable data on molecular forces, which oppose the separation of particles, uncertainty about the forces exerted by the air currents on the particles and of course the complexities of turbulent flow. ‘P‘V‘wwfi 2. OBJECTIVES The intent of this investigation is to: l. Elucidate the mechanisms of re-entrainment of small particles from flat surfaces at zero angle of incidence in turbulent flow. Investigate the effect of intensity of turbulence of the free stream on the re-entrainment process. Study the effect of particle size on the critical air velocity required to remove small particles from flat surfaces at zero angle of incidence. Investigate the effect of location of particle on the re-entrainment from the flat surface. Develop a correlation between different properties of particles and surfaces and critical velocity of air required to remove small particles from flat surfaces at zero angle of incidence. 3. JUSTIFICATION The re-entrainment of settled dust deposits depends upon a number of variable factors including the internal structure of air flow and composition and structure of the deposit (1). Most of the previous research conducted is limited to small scale experiments in which the surfaces have been glass microscope slides, cylinders or filter fibers (15). In most of these studies the objective has been to determine the forces required to remove the particles from the surface and relate these forces to the adhesion forces between the particles and the surfaces. As Bagnold (2) has stated the apparently simple question; "at what air speed will the re—entrainment of dust of specified size occur?" has not been answered. A great deal more information is needed both about the wind and about the dust deposits. The air flow needs to be defined in such a way as to enable an estimate to be made of maximum fluid impulse likely to be received by the least secure of the exposed particles. This means that the mean velocity measured elsewhere is not adequate. Previous studies have not accounted for the influence of intensity of turbulence in the air stream and the aerodynamic force coefficient used apply for a single sphere in an infinite fluid only (26). It is well known that all aerodynamics measurements are to some extent dependent on the magnitude of the small fluctuations of speed, collectively called turbulence, which are present in the air stream (19,21). The effects of turbulence are supposed to be related to the effect described by Reynolds number in that both are the Figure 3.1. Effect of Reynolds number on the drag coefficient for flow normal to a flat plate (From G. B. Schubauer and H. L. Dryden (48) ) O l 2 3 4 Percent turbulence Figure 3.2. Effect of percent turbulence on the drag coefficient for flow normal to a flat plate (FrOm G. B. Schubauer and H. L. Dryden (48) ) expression of the same basic phenomenon. Schubauer and Dryden (48), however showed that although there is no definite variation of the drag coefficient of a normally exposed flat plate with Reynolds number over the range 3x103- 6x104, there is marked change in the coefficient with turbulence (see figures 3.1 and 3.2). Further it is felt that for re-entrainment from flat sur- faces, use of a local skin friction coefficient which changes with location of particle rather than a free stream drag coefficient should give better results. In view of this and considering the practical aspect and numerous potential applications of particle re-entrainment data in air borne contamination control, adhesion studies, sand dune movement and pneumatic conveying of powder materials, the necessity of such a study need not be over-empha- sized. 4. REVIEW OF LITERATURE The history of investigations on re-entrainment of small particles is not a long one. Although Homo sapiens have been watching the wind take up huge quantities of dust and shift sand dunes from one place to another, it was not until recently when organized studies on re-entrainment were first started by Bagnold (1) and subsequently pursued by Gutterman and Ranz (27), Corn and Silverman (l4), Larsen (39), Orr and DallaValle (42), Deryagin and Zimon (18), Corn and Stein (13), Walker and Fish (53) and Heldman and Punjrath (33). This recent impetus and new interest in this field can be ascribed to results of developments and needs in other technologies such as "Clean Room", sterilized packaging, space travel and air pollution. The systematic theoretical and experimental study of the field as a whole is still in an elementary stage due to absence of reliable data on forces which oppose the separation of particles from surfaces and the uncertainty about the force exerted by the air current on the particles. In a broad sense the study of re- entrainment can be divided into two fields, (a) the re-entrainment process and factors effecting it and (b) the turbulence process. 4.1 The Re—entrainment Process 4.13 Re-entrainment and Threshold Velocity Re-entrainment can be defined as flotation of settled dust dislodged from a surface or layer of dust when the removal force provided by the drag and lift of the air stream on the particles exceeds the force of particle adhesion or cohesion. According to .s ‘ Bagnold (2), a deposit of settled dust in static contact with one another or with solid surface under gravity constitutes a Vsolid body, the exposed surface of which has to be first disrupted i.e. the dust grain must be dislodged and set in motion by imparting a finite threshold of fluid force to overcome frictional forces due to gravity. This threshold velocity, i.e. the minimum velocity of air required to initiate motion of dust particle over the sur- face, is different than the pick up velocity used by Gutterman and Ranz (27). The letter researchers recorded their velocity measure- ments when particle movement occurred throughout the entire section. Bagnold (2) and later Heldman and Punjrath (33) noticed that movement of dust grains always began at the downstream end of the tunnel and was propagated upstream. This is evidently associated with the gradual development of turbulence in the bOundary layer as the air progresses down the tunnel. According to Bagnold (2) the threshold wind gradient at which the deposit surface is disturbed decreased with particle size to a minimum of about 50-80 microns and seems to increase as the size is further reduced. Jordan (36) measured efficiencies of removal of quartz and glass dust deposited on glass slides after exposure of deposits to high velocity air jet. However, because of ill defined aerodynamic conditions it is not possible to estimate particle removal forces from these data. Larsen (39) investigated the adhesion and removal of various diameter glass sphere from various diameter glass fiber and prOposed theoretical equations to explain the forces involved in adhesion. The air flow required for w-T~v'v the removal of isolated particles of various diameters from fibers of various diameters was determined and effect of fiber diameter was found to be negligible. Corn and Silverman (14) studied the removal of particles from screen. Air drag on particles submerged in the laminar boundary layer was calculated from a simple irrotational fluid flow model and compared to particle adhesion forces. Air drag calculated in this manner failed to account for observed particle re-entrainment. In addition re-entrainment velocity was observed to increase with the increase in the velocity of deposition of particles. Corn and Stein (13) investigated the adhesion of spherical glass particles and fly ash to glass and metal substrates using ultra-centrifuge and air at high velocity to achieve particle removal. Re-entrainment velocity was found to be influenced by particle size, ambient air relative humidity, surface roughness and electric charge. It was also observed that increased time of exposure did not increase particle removal in a centrifugal force field, but it did have this effect with high velocity air. This was also observed by Heldman and Punjrath (33). The result was interpreted on the basis of turbulent eddies penetrating the laminar sublayer to reach adhering particles or alternately due to turbulence created by the adhering particles in their immediate vicinity. 4.lb Effect of Relative Humidity According to Bowden £5 31 (7) there is increase of friction when the metallic surface films are removed. They found that admission of small amounts of oxygen, water vapor or other contaminants ‘n. ‘ 10 reduce this friction. Bowden and Tabor (6) cite work by McFarlane and Tabor (41) on the force of adhesion due to a small amount of liquid interposed between a glass sphere and a glass plane. For glass spheres from 133 to 500 microns diameter, the following equation was found to give quite good results. F = 2 U y Dp where: F = perpendicular force of adhesion, dynes Y = surface tension of liquid, dyne/cm. Dp = diameter of sphere, cm. This equation has been derived by Bradley (8), Bowden and Tabor (6), Larsen (39) and Walker and Fish (53) to give the maximum possible adhesion between perfectly smooth sphere and solid surface in a saturated atmosphere. The importance of relative humidity on force of adhesion is shown below in the figure (4.1) obtained by Bowden and Tabor (6). Larsen (39) working on removal of particles attached to air filter surfaces observed that ten times the air flow velocity head is required to remove particle at 40.0% R.H. as at 22.0% R.H. Similar results were obtained by Corn and Stein (l3) and Bagnold (2), however observations of Kordecki and Orr (37) were not consistant with above results. For sand on an unspecified surface, adhesion was stronger at 10.0% R.H. than at 50.0% R.H. while for glass on glass adhesion increased with R.H. It is evident from the above discussion that relative humidity of the ambient air greatly influ- ences the force of re-entrainment although the nature of the influ- ence is not clear. 11 100 S 90 w-l . m 0 s 80 < :1 7o :1 In "5 60 1% u, so 0 E m 40 30 30 40 50 60 70 80 90 100 Relative Humidity (%) Figure 4.1. Effect of relative humidity on adhesion (From F. P. Bowden and D. Tabor (6) ) . .-._ 12 4.1c Influence of Perticle Size on Re-entrainment According to Bagnold (2) the threshold of initial disturbance increases with the diameter of the particle above 100 microns and reduces to a minimum when the grain size is between 50 microns and 80 microns. Walker and Fish (53) postulated that, of the forces holding the particles, the capillary forces and Van Der Waal forces are prOportional to first power of radius, whereas electrostatic forces are proportional to the square of radius. Among the removal forces, vibrational and centrifugal forces vary as the cube of radius whereas fluid dynamic force is prOportional to the n power of radius (n ranging from 2 to 3 depending upon Reynolds Number). Removal forces therefore decrease more rapidly with particle size than do adhesive forces, consequently the smaller the particles the more difficult they are to remove or re-entrain. 4.1d Influence of Particle Shape The influence of particle shape on re-entrainment has not been studied so far perhaps due to extreme complexities involved. The nearest experimental approach to the influence of particle shape was by Larsen (39) who derived and experimentally confirmed the following equation for adhesion between sphere and cylinder in the presence of an intermediate liquid layer. F =2k1HYDp a __k_d___+_1____ 2 2. 2 o k =(kc+kd)05 -'ax +ax.(“dx.' j i J J puiuj)+Fi 5.7 Further approximations for the case of a horizontal flat plate at zero angle of incidence i.e. with‘U3 = 0 ;'%E = 0 ; Fi = 0 ; BZU 6U xi 1 = 0 and l = 0 lead to: x1 at a‘ 56' azu az‘fi azfi p(fi 1+5 1)=+u( 1 + 1 + 1)- 1 3x 2 35‘ 5x 5x 5x 5x 5x 5x 1 ,2 1 1 2 2 3 3 p ( 5 (u u ) + a (u u ) + a (u u ) ) 5 8 $1 11 $62 12 3213 13 ' An equation for the same situation, but with laminar flow gives: 2 U1E21+U OU1=V5U1 59 5x 2 5x 2 ' 1 2 3 x2 where: v =E 5.10 p 23 Boundary between Layer and Free stream Thickness .. ° . I f” “ . ———O/ .... 0 ' a.“ o '| 1 .’.I":ol’_ H r ——u O .:. . ‘ ’. 0....0 + ‘ __.’ Wall Figure 5.1. Schematic diagram of boundary layer Figure 5.2. Capillary force due to liquid layer (From R. L. Walker and B. R. Fish (53) ) 24 A comparison of equations 5.8 and 5.9 shows that it is the 4th, 5th and 6th terms on the left hand side of the equation 5.8 for turbulent flow which characterize the effect of turbulence for the situation under consideration. To describe the effect of turbulence, the correlation of these three terms on the re-entrain- ment process must be determined. 5.1 Types of Forces Between a Particle and a Flat Surface There are four basic mechanisms which act to retain particles on surfaces. These are related to capillary, electrostatic and molecular forces and a time dependent force due to a viscous flow phenomenon called "Stefan Flow". In each case the prOperties of the surface layer on both the particle and the surface can effect these forces. 5.1a The Capillary Forces Due to the prOperty of surface tension of the liquid, the presence of a liquid capillary layer between a particle and a sur- face results in a component of force normal to the surface holding the particle to the surface when both the particle and the surface are wetted by the liquid (Figure 5.2). \ In theory such a layer would be expected to form as a result of the lowering of vapor pressure over a concave liquid surface in comparison to that over a flat surface of the same liquid (17). Under the atmospheric environment this layer has always been found to exist consistantly even at very low humidity in the region sur- rounding the point of contact between the particle and the surface. 25 Only under very high vacuum and for particles and surfaces of high order of cleanliness can this layer be assumed to be non- existant. For a given size capillary layer, the normal component of this force is given by: FN = 2 U (R Sin) y Sin (0 +~a) 5.11 The maximum value of the normal force is: 2 FN(max) = 2 U y R Cos (a/Z) 5.12 i.e. for given surface and environmental conditions this force is preportional to the radius (R) of the particle. 5.1b The Electrostatic Forces Both deposition and adhesion of the particle to the surface can be affected by electrical forces. Allowing for charged, uncharged and polarized particles and surfaces and considering uniform and non-uniform fields, there are 50 combinations of conduc- tive and non-conductive particles and surfaces (53). Some of these cases are shown in the Figure 5.3. When a charged conducting parti- cle approaches a grounded conductive surface (figure 5.3a) there is initially an attractive force due to image charges before the particle comes into contact with the surface, however, after elec- tric contact is made the charge is grounded leaving no net effect on adhesion. In the case of positively charged conductive particles and surfaces (figure 5.3d) there is a repulsive force. On the other hand, for some surfaces, if the particle has a negative charge there will be an initial attraction before the surfaces come into contact but after electrical contact there will be a repulsive 26 + No effect + Repel + Both attract NON COND COND COND + NON COND COND\ (a) (b) (C) I \ / + Repel + Repel + Repel NON COND ’ COND + COND + NON COND + COND (d) (e) (D Figure 5.3. Electrostatic Force (From R. L. Walker and B. R. Fish (53) ) Disc of Radius Rd Liquid- hl Solid Surface \\\\\\\\\\\\\\\\\'\\\\ Figure 5.4. Stefan effect (From R. L. Walker and B. R. Fish (53) ) 27 force unless the particle charge and the surface charge just cancel. The three conditions shown in the figure 5.3(b), (e) and (f) all result in the same effect. These represent initially charged surfaces, under conditions in which no charge is exchanged between the particle and the surface. In the case of a non-con- ductive particle on a grounded conductive surface, (figure 5.3c); there is an image charge interaction yielding an attractive force. Similarly a charged conductive particle separated from a grounded conductive surface by a non-conductive layer would also experience an image-charge attractive force. For most of the cases involved, the force is directly prOportional to the charge squared and inversely prOportional to the square of the particle radius, i.e.: 2 FE S = 9.4% 5.13 ' ' 4K R 2 Since Q(R) a R 4 Therefore FE S = C R2 a R2 5.14 ' ' 4K R 5.1c Forces due to Molecular Interaction The most widely known of this complex group of forces of adhesion is that due to the London van der Waals dispersion forces resulting from the attraction between fluctuating electric dipoles and the dipoles that these induce in the adjacent molecules. This force is given by the formula: 112 21 FD = —32——--5 5.15 6 d 28 Thus for this case the force of adhesion is prOportional to the radius of the particle. Other examples of molecular forces include the interaction of dipoles with other dipoles or with polarizable molecules, hydrogen bonds, metallic bonds and image bonds (24). Whereas these forces may become dominant under high vacuum condi- tions and in some liquid systems, for ordinary atmOSpheric condi- tions, they appear to be minor compared to capillary and electro- static forces. 5.ld Forces due to Viscous Flow This time dependent force of resistance to the removal of particles from a surface is the result of visc0us forces. First studied by Stefan (53) in a liquid system, including the case of a capillary layer as a particle is pulled away from a surface, there is resistance to the flow of the liquid into the gap. This tends to retard the movement of the particle away from the surface. In short a given force must be applied for a finite time in order to separate the particle a given distance from the surface. For example for a disc shaped particle (figure 5.4) this force is: 4 3 n 11 Rd 1 1 FS _ -———-———- (-—2 - “—2) 5.16 4 9 h1 h2 Generally the closest distance of approach, h is negligible com- 1, pared to, h2, the distance at which the particle can be assumed to be removed from the surface. Consequently, the impulse required to remove the particle is: 3 U u R: 3.9 = --ir-- 5.17 4 h1 29 For this case, the force required to remove the particle is pro- portional to R4 and must be applied for a finite time. 5.2 The Forces for Re-entrainment In general these forces can be divided into three classes, (1) the fluid dynamical (liquid and air stream), (2) the inertial (centrifugal, vibration, gravitational) and (3) the direct mechanical contact (brushing or grinding). 5.2a The Fluid Dynamical Force Whenever a fluid moves past a solid body or a solid object is moved through a fluid, a force is required to maintain fluid flow past solid boundaries or around objects immersed in the stream. The force on the fluid is transmitted to the solid and by Newton's third law of motion, the force of the fluid on the solid is equal and Opposite to the force of the solid on the fluid. In the re- entrainment processes the fluid is moving past the particles on the surface and therefore the particles are subjected to the fluid dynamic force. For a spherical particle suspended in the fluid this fluid dynamic force is given by: _ 1 2 F - 2 A CD (p U ) 5.18 The drag coefficient is usually a function of Reynolds number. In the previous re-entrainment studies the value of drag coefficient has been computed assuming the particles to be immersed in a free stream of fluid, however a new approach to this is presented in section 5.3. 30 5.2b The Inertial Forces The inertial forces (vibration, centrifugal force and the gravitational force) depend directly upon the mass of the particles. The equation of motion of a vibrating surface is: Y = B Sin(2 U f t) 5.19 From equation 5.19 the acceleration is: d2 < 2 = - 4 U2 f2 A Sin ( 2 U f t ) 5.20 t 9.. Maximum force of removal of particles from the flat surface occurs when Sin ( 2 U f t ) = l and the removal force is: _43 22_1632 3 Fin - ( 3 n Rp pp) 4 n f B — 3 n f pp B Rp 5.21 Similarly the centrifugal force which tends to remove a particle from a surface under rotation about an axis is: 3b 3 4 n2 b N2 = 6W R 5.22 pp) -§1szpp 111 n ufls~ and the gravitational force on the particle is simply: _a 3 F ._ n R 5.23 s 3 pp p g 5.2c The Direct Mechanical Contact Forces Forces used to remove particles by direct mechanical contact are not easy to evaluate experimentally. Clearly, the probability of physically removing a particle from a surface depends upon the likelihood of contacting the particle and upon the effectiveness of the contact in transporting the particle off the surface. The 31 geometrical probability of contacting the particle is related to the largest linear dimension of the particle measured along a line parallel to the surface and perpendicular to the direction of brushing. For a bristle of a given stiffness the removal efficiency depends upon the length of the bristle which engages the particle, i.e., the average particle dimension perpendicular to the surface. Thus, removal probability depends approximately on the projected area, (R2), of the particle. For the case of particles on a rigid flat plate in an air stream, the only forces of importance are the aerodynamic forces. 5.3 The Re-entrainment Theory for Turbulent Flow The importance of degree of disturbance in the external stream was first recognized when measurements of the drag on spheres was performed in different wind tunnels. In this connection it was discovered that the critical Reynolds Number of a sphere, i.e. the value of the Reynolds Number which corresponds to the abrupt decrease in the drag coefficient depends very markedly on the strength of the disturbance in the free stream (46). This can be measured quantitatively with the aid of the time average of the oscillating turbulent velocities as they occur. Denoting this time average by 3?, u§,';§, the intensity or level of turbulence of a stream is defined as: T = _ 5.24 (U) LAN where: UI= the mean velocity of the free stream 1000 C Critical Reynolds number (Rec) 32 0‘0 La) 1.5 10 10 10 Reynolds number ( 26E.) Figure 5.5. Resistance formula for smooth flat plate at zero 5x10 4x10 3x10 2x10 1x10 O‘O‘O‘O‘ incidence (From H. Schlichting 42) ' Turbulent region T \ VLaminar ‘Transition region .Pregion . l L J l L 4_ L O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Intensity of turbulence (percent) (=100 fig/g) Figure 5.6. Influence of intensity of turbulence on critical Reynolds number on flat plate at zero incidence (From J. O. Hinze (34) ) 33 In general, at a certain distance from the screens or honeycombs the turbulence in a wind tunnel becomes isotrOpic, i.e. one for which the mean oscillations in the three components are equal: 77—2 111 — u2 = u3 5.25 In this case, it is sufficient to restrict oneself to the oscilla- tion u1 in the direction of flow and to let: vi T = -f:‘—- 5.26 U Measurements in different wind tunnels reveal that the critical Reynolds number of a sphere depends very strongly on the turbulent intensity, T. The value of critical Reynolds number increases rapidly as T decreases. Similarly if one considers the boundary layer along a rigid flat plate, several regions may be distinguished in the downstream direction. From the stagnation point on, the boundary-layer thickness increases in the downstream direction. The flow in the boundary layer is laminar initially, but at a certain location, the flow becomes unstable and transition into turbulent flow may occur if the disturbances are present. The location of this point along the surface depends on the velocity and on the intensity of turbulence in the free stream outside the boundary layer (see figure 5.6). After transition into turbulent flow the increase in thickness of the boundary layer occurs at a higher rate. For a flat plate placed in a uniform flow with zero pressure gradient in the flow direction, we have only a laminar and a turbulent region, separated by a relatively short transitional region. Since the 34 transport processes and the magnitude of forces in the laminar and turbulent region of the boundary layer are different, it is appropriate that prOper aerodynamic force coefficients be used in computing the re-entrainment forces. In the previous research, the coefficient used is that of a sphere in a free stream, assuming the presence of plate does not effect the flow regime. The observation of Gutterman gt 11. that particles roll or slide over a flat plate led to the conclu- sion that friction played an important role in resisting the drag force of the air stream. Since the skin friction changes along the length of the plate, the aerodynamic coefficient used must take this into consideration. In a completely rough regime it is possible to make use of the following interpolation equation for the coefficient of local skin friction in terms of relative rough- ness (46): — -2.5 Cfx - ( 2.87 + 1.58 log (x/ks) ) 5.27 According to Schlichting (46) this equation is valid for 102 < x/k8 < 106. The local drag on the flat plate due to turbulent air flow over the plate can be defined as: —2 U 19 2 gc T=C( o fx ) 5'28 The aerodynamic force is resisted by a sliding and rolling friction which can be written in terms of a combined friction factor, f*, and particle weight. The particle weight, in turn, can be written in terms of particle diameter and density: 35 3 111) 1* F = pp( P) R 6 5.29 The critical value of the local skin drag at which re-entrainment occurs should then be equal to this force of resistance, i.e.: U D2 T F = A T = .—-—E—-9 5.30 R o 4 01‘ TI D2 1 p 52 32 U D: f* 4 Cfx (2‘52"“) = 6 5'31 then: it ,_2 _ (4) (Disc D2,f U - 37 C 5.32 p fx or ._ 4 0 ac D f* 1/2 fx 0 Substituting the value of, C from equation 5.27 in equation fx’ 5.33 we get: 4 p 1/2 1/2 = L 3-52 1 (gc Dp f*) (2.87 + 1.58 log cl 5/4 (xr/Dp) ) 5.34 Since the critical Reynolds number at which flow over a flat plate in the boundary layer becomes turbulent, decreases as the intensity of the turbulence in the free stream increases, it is evident from the equation 5.34 that if intensity of turbulence has a similar effect on re-entrainment; xr, the distance from the leading edge at 36 which re-entrainment starts, should also decrease as intensity of turbulence increases at the same free-stream velocity. This decrease in xr with an increase in intensity would imply increased re-entrainment at the same velocity with higher intensity of turbulence. Conversely, for a constant intensity of turbulence, the velocity for re-entrainment should decrease with an increase in distance from the leading edge, i.e. the particles on the flat plate nearer the leading edge shall be more difficult to remove than those away from the leading edge. This has already been observed by Bagnold (2) and Heldman and Punjrath (33). Equation 5.34 also describes the effect of particle size, particle density and fluid density. It should be noted however that the effect of diameter should be coupled with the friction factor which varies with the size of the particles. 37 6. EXPERIMENTAL DESIGN AND PROCEDURES The relative humidity of ambient air has a profound effect on the force of adhesion between a particle and a surface and between particles themselves. It was, therefore, considered essential to perform all the experiments at practically the same relative humidity. As the amount of air required in each experi- ment was Quite large, it was not economically feasible to condition the air by artificial means. However, in order to achieve the same goal, all the experiments were conducted during that time of the year when the ambient relative humidity was in the range of 36-40 percent, the range in which the effect of small changes in relative humidity were not so significant. Except in the few cases the relative humidity remained in the range of 38-40 percent. 6.1 Equipment 6.1a The Settling Chamber and the Cloud Generator Preliminary experiments showed that the method of deposition of powder on the flat surface had significant influence on the re-entrainment studies. It was essential that a uniform reproducible procedure for deposition of test powder evenly over the surface of the test plate be develOped. In order to do this, a settling chamber 1 feet x 3 feet x 6 feet was constructed out of wood and plexiglass (see figure 6.1) in which a uniform cloud of dust could be generated for uniform settling (adibatically) on the test surface. As shown in the figure 6.1, it was a box with an inlet at the t0p 38 Ac our rasqrdotr Rscower tube . |'-«"'l "' Oulot ofcloud 1‘7\\ generator r_'b Slldll‘lg door Figure 6.1. Schematic of settling chamber 39 through which an outlet of a cloud generator could be introduced. The outlet for the air used for cloud generator was provided near the bottom on the two side ends to keep the cloud as uniform as possible. A sliding door was provided on the front side of the chamber to facilitate the easy handling of the test plate. The test plate used in the studies was an aluminum plate, eight inches wide, twenty three and one-half inches long and one-eighth inch in thickness. It was painted black with a glossy black enamel to give a sharp contrast between the portion covered by the powder and the portion from.which powder was removed. Lines were drawn with a red glass marking pencil both parallel to the leading edge (eight inch side) and perpendicular to it. The lines parallel to leading edge were placed at a distance half an inch apart, whereas those normal to the leading edge were one inch apart; the first line was one-half inch from each edge. There were a total of forty-six lines parallel to leading edge and eight lines normal to leading edge. The dust cloud generator system was used to create a uniform cloud of the test powder near the t0p of settling chamber so as to allow a uniform settling of the test powder over the test surface. The test surface was placed in the settling chamber on two wooden supports about one feet above the bottom. The cloud generator was constructed out of plexiglass. As shown in the figure 6.2, it is a modification of converging-diverging nozzle in which regulated com- pressed air passing through the inlet section created sufficient vacuum on the powder receiver tube outlet to cause entrainment of the powder in the air stream.and create a uniform cloud due to very high degree of turbulence in the air stream. 40 Regulating value Powder receiver tube 155— ~‘-" Compressed air ——-T _. 'EIKR 13+:- -- Powd e r C: -—— » I’~..O. O I .go.’: 53-4.. ’1‘ 0".“ ?.'¢ .II. . ,' ‘3‘. '1’! .~- . 9 . . ’0‘ -‘ o - ‘ "1 Powder receiver aJ .1;; tube outlet 3~n'1‘; '\3 r: (r- I T . . h ‘ - cloud o ~O Mixing chamber Figure 6.2. Schematic of cloud generator 41 The rate at which test powder was drawn into the system could be controlled by a regulating valve which controlled the air velocity in the nozzle. As shown in the figure 6.1 the cloud leaving the cloud generator was directed upward and settled due to gravity only. Using this method it was possible to obtain a very uniform layer of powder on the test plate. The amount of powder deposited was prOportional to the amount of powder intro- duced in the receiving tube. 6.1b The Wind Tunnel and Turbulence Grid The re-entrainment studies were performed in a low speed, open return wind tunnel manufactured and supplied by Integron, Inc., Burlington, Mass. This model is approximately twelve and a half feet long and has a round cross section with test section diameter of eighteen inches. It has an all electric drive system, driven by a 5.0 H.P., 440/220 volts, 3 phase electric motor and will provide mean velocities between 7 to 60 feet per second. The test plate was mounted on a support fixed to the remov- able mounting pad provided at the bottom of the tunnel, below the observation window. A tripod type mechanism was constructed at the base of the support to keep the plate level (see figure 6.3). A grid (see figure 6.8) with one inch spacing between two consequ- tive rod was constructed from five-eighth inch diameter iron rod to generate turbulence in the wind tunnel. The grid was placed after the honey comb straighter section of the wind tunnel i.e. in the test section and different levels of turbulence were obtained by moving the plate closer or further from the grid. 42 ‘ Wall Test table Screw knob Leveling tripod Wall Removable test pad Figure 6.3. Schematic diagram of the mounting of test plate in the wind tunnel 43 The support fixed to the removable mounting pad could be shifted to different positions on the mounting pad and also the test plate itself could be moved independently by a screw type mechanism over the support (see figure 6.3) to expose it to different level of turbulence. The test plate was mounted in such a manner that it was practically in the center of the tunnel and not effected by the wall. It was possible to remove the plate, together with support and the removable mounting pad as one unit, from the tunnel without disturbing the distribution of powder deposited on the test plate. The mean velocity in the wind tunnel could be adjusted to thirteen different levels with the help of a manually Operated lever. 6.1c Measurements of Mean VelocityAand Intensity of Turbulence The instrumentation used for measurement of mean air velocity and intensity of turbulence is shown in the figure 6.4. The instru- mentation includes a hot film, constant temperature anemometer supplied by Thermo-System Inc., St. Paul, Minnesota. The sensor used had an Operating resistance of 7.19 ohms. The sensor was fixed on the probe support and was mounted on a clamp, which could be moved over a graduated iron rod supported in the tunnel with the help of two circular rings pressing against the walls of the tunnel. Thus it was possible to move the sensor up and down stream and position it at any location over the test plate. The signals from the sensor were routed to an analog-to- digital converter via the output jack on the anemometer module. The analog-to-digital converter, when in continuous mode, scanned the 44 cowuwucmEDHumcw wmumamp pom Hmccsu wcw3 mo Emuwmflv owumesom .q.o mpswfim w 0 a? , kuwEUHO> kuhm>GOU kuamao HmuHmHu ou QOHHHU LU -monE‘ _ a : uwumEoEmc< NU saga uom hp .fi kl o .IIIIIIIIIILFII\ \ O dwum «IUOQAHH lull” ““ ummu mfinw>oamm m llllllllll use .32 W m E 44] \ 3me anon. m pomcom cw mm 11‘ «M nuuuunu ousumuoosma uH< com \\ \nI‘ . 14w ”w \d .IIMWII was muawaasm \ a J MW: waamfio poacmm vauu mumuswgwuum um>wA wcwumaswom «onwaannae auaoon> ua< 45 output of anemometer every five-hundredth of a second and placed the digital values on punched paper tape. The paper tape output was in terms of voltage values and a library program was used to transfer the data to a magnetic tape and get a punched card output. A computer program was deve10ped to convert voltage output to air velocities and calculate the mean air velocity and intensities of turbulence. The hot film sensor was maintained at an overheat ratio of 1.5 as recommended by the manufacturer. It was calibrated against a highly sensitive pitot tube (manometer sensitive to 0.001 inch of water) in the wind tunnel at the lowest level of turbulence i.e. with the turbulence producing grid removed. A calibration curve was drawn by plotting voltage against air velo- city. To facilitate an easy use of this curve by the computer for calculation of air velocities and intensities of turbulence, a six degree polynomial equation was fitted to this curve and was used in all the calculations of velocities and intensities of turbulence from the perforated tape data. A comparison of the experimental results and curve fitting is shown in the figure A.1. 6.2 Tests for Physical Properties of Particles The test particles used in this study were spherical glass shot supplied by Microbeads Div., Jackson, Mississippi. These glass beads had a specific gravity of 2.99, crystal color and were free from surface films. In addition, they were reasonably free from sharp angular edges, the quantity of which did not exceed one percent. The foreign matter (including iron particles) did not exceed one-half percent. 46 Figure 6.5. Wind tunnel and velocity recording instruments. Figure 6.6. Settling chamber and cloud generator. 47 6.2a The Particle Size Distribution The glass particles supplied by Microbeads Div. ranged from five to forty-four microns in diameter. These particles were then classified in an air classifier (Alpine Model 100 MZR: manufactured by Alpine American Corporation, Natick, Mass.) and divided into four fractions: 0-10, 10-20, 15-30, and 20-40 micron size ranges. A median diameter for each size range was computed and this value was then used in the studies on effect of size distribution on re-entrainment. 6.2b The Test for External Friction Factor The external friction factor, f*, was measured by the method used by Gutterman and Ranz (27). An aluminum block was pulled across a mono-particle layer of test powder resting on a smooth aluminum plate by adding water to a container until the block began to slide. Additional weight was added to the aluminum block and the force required to move the additional weight was determined. The experiment was repeated with additional weight and a relation- ship between weight of block and force required for movement was established. The experiments were continued until a linear relation- ship between weight and force was obtained. This method of deter- mining a friction factor gives a combination of sliding and rolling friction which according to Gutterman and Ranz (27) is very similar to conditions existing in a wind tunnel when particulate matter is picked up or moved by fluid motion. 48 Cloud generator. Figure 6.7. Turbulence grid Figure 6.8. 49 6.3 Scope of the Tests The primary objectives of the experiments were to determine all the required values needed to verify equation (5.34). In this equation the mean velocity, 6, the intensity Of turbulence, T, and the distance, xr, were Of primary importance and were evaluated for various independent parameters. The values of 'f', T and U were determined as described earlier and determination of 'x; is described in the section 6.3a below. 6.3a General Procedure In a typical experiment the test plate was dismounted from the support and after wiping clean with a dry piece of cloth, the plate was placed in the settling chamber. About 20.0 grams of test powder was placed in the receiver tube Of the cloud generator and the cloud generator was started by Opening the valve supplying regulated compressed air from a compressor. After all the powder taken into the system had settled, the plate was removed from the chamber very carefully to avoid disturbing the distribution of the test powder. The plate was then mounted on the support inside the wind tunnel and with the assistance Of the screw knob was located at the position which resulted in least turbulence at the leading edge Of the test plate. For an initial set Of experiments the leading edge was at the greatest distance from the turbulence pro- ducing grid. The plate fixed on the removable test pad was then placed in the tunnel very carefully avoiding sudden motion. The anemometer sensor then moved over the leading edge and the experiment was 50 started. The velocity control lever was positioned at ”minimum re-entrainment velocity position" for the given size of particles. The tunnel was then started and particles exposed to air flow for three minutes. After identification data was manually entered into the analog-tO-digital convertor, the convertor was changed to con- tinuous scan mode and velocity data collected for one-half minute. The analog-to-digital convertor was reset, the tunnel was stOpped and the distances from the leading edge at eight different locations (on the eight lines normal to the leading edge) where the removal took place were measured. The mean Of eight distances at a given intensity of turbulence was then used in the various computations. After initial measurements were completed, the plate was removed from the tunnel and the leading edge moved by two inches to a location with higher intensity Of turbulence. The test plate was then reinstalled in the tunnel, taking precaution not to dis- turb the distribution Of test powder during re-installation. The air velocity sensor was again moved directly over the leading edge and the wind tunnel was Operated at the same mean velocity but with a higher degree Of turbulence at the leading edge. The velocity signals were once again recorded on the analog-tO-digital convertor and tunnel was stOpped after three minutes exposure to measure the distances from the leading edge at which removal occurred for the new intensity Of turbulence. This procedure was repeated for higher intensity Of turbulence and four sets of data were collected for each particle size. 51 7. RESULTS AND DISCUSSION 7.1 Effect Of Turbulence on Re-entrainment The effect Of intensity of turbulence Of the free stream on re-entrainment from a flat surface is illustrated in Figures 7.1, 7.2, 7.3, and 7.4 for different particle sizes. As shown in these figures, the intensity Of turbulence (100 /‘u2/Um) has been plotted against Reynolds Number (Uexpxr/v) where, xr, is the distance from the leading edge at which re-entrainment initiated. Each point on the distance scale is a mean Of eight Observations and the intensity of turbulence has been computed from two hundred and forty velocity readings taken five hundredth Of a second inter- vals. All data were taken under similar conditions of relative humidity (35-40%) and temperature (75-80°F) thus minimizing the influence of these parameters. It is evident from these figures that the Reynolds Number (Rer exp) at which the re-entrainment starts decreases as the inten- sity Of turbulence increases, i.e. for a given mean velocity which is adequate to start re-entrainment from any location ”xr" on the plate, the distance "xr" from the leading edge where re-entrainment starts decreases as the intensity of turbulence increases. As a result Of this decrease in "xr" with an increase in the intensity Of turbulence, the total re-entrainment of particles from the sur- face also increases with an increase in the intensity of turbulence. This effect of increased re-entrainment due to increased degree of turbulence is more marked on the lower level of turbulence and 52 decreases as the intensity Of turbulence increases, becoming less evident as the intensity Of turbulence is increased beyond 12-15%. In general, the shapes Of curves for different sizes are similar indicating similar phenomenon at work for all the sizes tested. Mention should be made of the effect Of intensity Of turbulence on critical Reynolds number (Rec). Schubauer and Skramstad (49) reported that the critical Reynolds number (Rec) at which flow in the boundary layer over a flat plate changes from laminar to turbu- lent decreases with an increase in intensity Of turbulence (see figure 5.6). A analogy between critical Reynolds number (Rec) and Reynolds number (Rer) at which re-entrainment starts seems quite plausible. Both parameters decrease as the intensity of turbulence increases. It would appear that a possibility of a close analogy between the two phenomena exists, i.e. the phenomenon Of transition of laminar boundary layer to turbulent and process Of re-entrainment over a flat plate. A detailed discussion Of this shall be given in a section devoted to mechanisms of re-entrainment. Figure 7.5 shows the effect Of intensity Of turbulence on the total force required tO re-entrain particles. It is Obvious that the total force does not vary with degree Of turbulence i.e. although the increase of turbulence increases the total amount of re-entrainment, the force required tO re-entrain particles of a given size remains independent of the degree Of turbulence. This is quite logical because the forces Opposing the re-entrainment i.e. forces holding the particles on the surface are not expected to be function Of turbulence. It can, therefore, be concluded that only effect Of increased turbulence is to shift the point of re—entrain- ment closer to the leading edge. Intensity Of turbulence (%) Intensity Of turbulence (%) 53 13 ._ 12 .. 11 a 10 ._ C) 11 6 L2 i L. L ¥ 1 vol 30,000 50,000 70,000 90,000 110,000 e r exp Figure 7.1. Effect of intensity Of turbulence on Reynold number at which re-entrainment started for particles of 15 micron diameter. 13 _. 12 - 11 r— 10 L- 5 1 1 1 1 1 1 1 1 1 11 10,000 30,000 50,000 70,000 90,000 110,000 Re r eXp Figure 7.2. Effect of intensity of turbulence on Reynolds number at which re-entrainment started for particles of 22.5 mi ('1'an (H nmnfpr 15 14 13 8 12 1: G) H :3 '2 11 :3 4|.) “—1 ° 10 >3 «U 0H m 8 9 U c: H 8 7 6 54 O )— 1 1 1 1 1 1 1 1 1 1 J 20,000 40,000 60,000 80,000 100,000 120,000 Re r ex Figure 7.3. Effect of intensity of turbulenge on Reynolds number at which re-entrainment started for particles Of 30 micron diameter. l4. _ 13 _. Q m 12 - U C Q) '3 .o 11 ,— § O U ‘8 10 t >. u ”.1 2 9 - Q) U I: H O 8 _ 7 1 11 i 1 1 1 1 1 1 1 50,000 70,000 90,000 110,000 130,000 150,000 Re r exp Figure 7.4. Effect Of intensity Of turbulence on Reynolds number at which re-entrainment started for particles of 5 micron diameter. 55 Theoretical 1.5x10-5" Experimental ---------- €> (D O O ...O O O “‘“U'O“"6;\ —"0000""'“ o. -o \ - 1x10-5.— ‘(///,’ Particle dia — 30 microns 9 P 3 3 - E. 'o 7 _ I O on 2 5 r Nbo' :- 4 _ Particle dia = 22.5 microns NM :> O O ,. a—wm—mo ——————— G—O—-- U 3 00 Q P" t: m H .3 fl 2 '- m D. m g 1.5 ”’ Particle dia = 15 microns 00 .5 § “06° 990-Ooo----—o—qy%-———-—— § 1x10'6_— O U-d c; 1 JJ .2 5 _ J l 1 1 1 1 I 1 1 5 6 7 8 9 10 11 12 13 14 1 Intensity Of turbulence (%) Figure 7.5. Effect of intensity Of turbulence on the total force required to re—entrain particles. 56 7.2 Effect Of Particle Size The influence Of particle size on re-entrainment is illus- trated in figures 7.6, 7.7, and 7.8 in which the median size Of the particles classified in an air classifier is plotted against Reynolds number (Rer), force per unit area and total force acting on particles, respectively. In figure 7.6 the Reynolds number (Rer) at which re-entrainment occurred is plotted against median size of the classified particles. The results indicate the influ- ence Of intensities Of turbulence, also. In addition, it is Obvious that particles with median diameter between 15-22.5 microns require minimum Reynolds number (Rer) for re-entrainment i.e. for a given distance 'xr' from the leading edge the re-entrainment velo- cities are minimum for particles sizes between 15-22.5 microns. It follows that particles between 15-22.5 microns require minimum force per unit area for re-entrainment. This is shown more expli- 2/> citly in figure 7.7 where force per unit area (Cfx p Uexp 2 gc required for re-entrainment is plotted against the corresponding size on a semi-log scale. It is evident from this figure that force per unit area required to re-entrain particles is minimum for 15-22.5 micron particle sizes and increases rapidly for sizes outside this range. It is interesting to note in figure 7.7 that the force per unit area required for re-entrainment correSponding to different intensities of turbulence fall on the same line at random indicating that force for re-entrainment of a given size of particle is inde- pendent Of intensity Of turbulence. Figure 7.6 however shows that Reynolds number (Rer) decreases as the intensity Of turbulence 1H,.llllllilllllllii 57 ucchfimuu:O1wp pom wouflavou umnEDG mwfioc>om :0 Oman mHoHuumo mo uowwwm .o.n muswwm mcouofiE ow mofiofiuuma mo Mouwamfio 0m mm 0N mH 0H m 0 1 08.8 1 08.3 I 000.00 1 08.8 I 000.00H 1 80.8: I 08.0.: dxa 1 38 Cfx/ch) dynes per square centimeter 2 exp Force Of removal (0 U U1 0‘“ mVOO b 0.2 0.1 I fr! 11" Figure 7.7. 58 I I l l J I l l I 10 15 20 25 30 DIAMETER OF PARTICLES (MICRON) Effect Of particle size on Aerodynamic Removal Force per unit area. 59 -5 5x10 _ 4 _ Experimental Results 0 3 Theoretical Results ——— 2 .— 1x10”5 5 9 '3' m 8 _ 6 — 'T 5 r A 4 " a? 3 F 2'; N 2 ‘- :1 No. 6 g “,3 1x10 _ o g _ 1: 7 I: C). 6 I- v 5 p- :2 4 - o 12 3 - o a 2 _ 3. m c o -7 2.? 1:10 _ :3 8 I n g ” s . .2 4 - H m U 5 J, l 1 I 1 1 I 1 1 11 11 2.5 7.5 12.5 17.5 22.5 27.5 Figure 7.8. Particle diameter in microns Variation Of total force acting on a particle with particle size. 60 increases. It can be concluded that an increase in the intensity Of turbulence does not result in increased force acting on the particles, instead the location at which the re-entrainment initiates is shifted tO a point further upstream, resulting in lower Reynolds number (Rer). The results in Figure 7.6 illustrate that the influence of particle size on Reynolds number (Rer exp) between 15 and 22.5 micron becomes less evident with increased intensity Of turbulences. In figure 7.8, the total force required to re-entrain dif- ferent size particles is plotted against median size on a semi-log scale. The solid line is the force predicted theoretically by equation 5.34 based on the distance 'xr exp. Observed in the experi- ments. The experimental results Obtained in the actual experiments are illustrated also. Again total force acting on the particles is independent Of intensity of turbulence and increases with size Of particles. 7.3 Effect Of Particle Location Figures 7.1, 7.2, 7.3 and 7.4 also describe the effect of particle location on the flat plate. It should be noted (see figure 7.9) that although the force required to remove the particles from the surface should be same at all locations along the length of the plate, in actual practice the velocities required for re- entrainment near the leading edge (smaller 'xr') are different than those required for the particles down stream from the leading edge indicating that the aerodynamic force Of removal acting on the particles may vary along the length Of the plate. This supports /8 gc) in Dynes N “-1 C U2 2 P Total force acting on the particle ( p U D 61 4x10.S - 3 *' Theoretical ---------- Experimental *- 2 1— o O .000 9 O 0 ° O O *61"’ *o O O 0 O 5 30 microns 1x10 -. 9 +- “““““““““““““““““““ 8 1— 7 - 6 h— 5 _. Particle dia, 22.5 microns 4 .. ' "‘"“';‘6"""“"""""‘ 3 L 2 _ O O o 0‘00 7 0 av 9:15 -g ‘° 0 o 0 Particle dia. 15 microns -6 _..-...-..-_--___..__......__.___.______......_._..__.__._--.. X10 1- 0.9 - 0.8 ' .7 b , L- l I L l I I I i L l J 1 2 3 4 5 6 7 8 9 1 10 11 Distance from the leading edge ( x ) in inches r exp Figure 7.9. Variation of total force required for re-entrainment with distance. 62 the contention that the use of an aerodynamic drag coefficient dependent only on mean velocity is erroneous. In other words, computation of an aerodynamic coefficient for re-entrainment from a flat plate assuming the particles to be immersed in a free stream of fluid does not reflect the real picture of the process. It is evident from these figures that for any given particle the removal of particles near the leading edge is much more difficult than for locations away from leading edge. This Observation is in line with the results obtained by Bagnold (2) and Heldman and Punjrath (33). 7.4 Comparison of Predicted and Experimental Results In order to test the validity of the equation 5.34 which predicts the minimum mean free stream velocity (U) required for re-entrainment, the Reynolds numbers (Rer exp) observed in the experiments were plotted against the theoretical Reynolds numbers (R ) predicted by the equation. The results of these compari- er pre sons are shown in the figures 7.10, 7.11, 7.12 and 7.13 for dif- ferent particle sizes. The Reynolds number (Rer exp) was obtained from the mean of the values of distances and velocities actually Observed in the experiments, whereas the theoretical Reynolds numbers (Rer pre) were computed from the velocities obtained from equation 5.34 based on particle size, friction factor, densities of particles and air, local skin friction coefficient and the mean distance 'xr exp. from the leading edge where the removal initiated. In general, in all these comparisons, the observed Reynolds number (Re ) formed a straight line inclined equally to both axis, r exp when plotted against predicted Reynolds number (Rer pre) indicating 63 that the values of velocities predicted by equation 5.34 are in good agreement with experimental data. The only major exception to this Observation is figure 7.13 for smallest size particle. The straight line in this case indicates that the Reynolds number (Rer exp) observed in the experiments were consistently higher than those predicted by the equation 5.34. The difference may be due to lack Of accuracy in the measurement of friction factor where inability to preserve a mono-layer of particles presented significant difficulties. It is evident that, in general, close agreement exists between the actual data and the values predicted by the equation 5.34 throughout the entire range of Reynolds number tested. The total force required to re-entrain particles of dif- ferent sizes in the actual experiment is compared with the total force predicted by the equation 5.34 in the figure 7.8. The solid line is the total force predicted by the equation. It is evident that there is a close agreement between the experiments and theory. The close agreement between the predicted and the experimental results is also evident from the figure 7.5 where total force required to re-entrain particles is plotted against intensity of turbulence. Again the solid lines are the values computed using equation 5.34 based on 'xr exp. while experimental data were com- puted from the velocities Observed in the actual experiment. It is clear from this figure that intensity of turbulence does not effect the total force required for re-entrainment of a given size particles and this force can be predicted with a reasonable degree of accuracy using velocities predicted by equation 5.34. .umqume :OHOHE mH wo mmHoHuumo mo ucoEchpucmumu new amassc mwfiocmmm HooHuouoozu Ono can Hmucoewuooxm mo sewapmano .ofl.n muswwm 64 , a o u oxm axe u A: x x 3 mm 000.00fi 000.0NH 000.00H 000.00 000.00 000.00 000.0N 0 m a _ a q a a o 000.0N 000.00 000.00 mcouofie ma 000.00 woumeww OHOguumm 000.00H 98 and 1 n) d (A/ xa 1x and 65 machoqfi m.- .umuoEmHv couOgE m.~m we mmHowuumo mo ucmEcfimuucmuou MOW muonEDC mwfloczom HmoHumuoonu 0cm HoucmEHuoaxm wo conflumnEoo .Hi.a ...wut oxm u oxw oxm a A; x 8 mm 000.00H 000.00 000.00 000.00 000.00 a q q 11‘ 111 _ . _ q umumEm«c macauumm +Imuasmmu Hmsuo< oOaumHouuoo uommpoo we mafia l 000.0N 000.00 000.00 000.00 000.00H 38 31d J 31d 0) dxa J (0/ 66 .uwu08000 mcouowe 0m 00 mmflowupma 00 ucmEcfimpucmumu How muansc mvaocxmm Hmowuouoosu 0cm Hmucmewpm xw mo comwpmanv .NH .m opswwm oxm u oxo oxo u n>\ x :0 00 000.000 000.000 000.00 000.00 000.00 000.00 0 11 0 _ _ _ _ q d _ _ w 0 .\j 0 \ \ \ 1 \ \. \ 1 000.00 IL I 000.00 muasmmu Hmsuo< I \ V \ .1 000.00 0000006 on pooosmfiv wHofiuumm \ \. _I \ \ \ \\ 1 000.00 \ATI‘ cOHumHopuoo uoowuoa mo mafia \ \ \ \ 1 000.02 9 31d 1 0) 31d dxa J (A/ 67 .uouoEwwc mcouOHE 0 mo mofiowupmo mo ucoEchuucmuou 000 mquEDC mwaooxmm HmOHumuomSu 0cm Hmucmewuwaxm mo cowaumoEoo .mH.n muswflm oxo u oxm axm u A; x B 00 00oH000 000.000 000.000 000.00 000.00 000.00 000.00 0 _ 4 0 _ _ a 4 a a _ _ \a 000.00 .\ \. .11 \. .\ \ . \ 1 000 00 \ \. o l muasmmu Hmouo< \. 1 000.00 \ \ \ .1 \ \. \ \ I 000.00 \. \.API1co«umHmquo uommuoo mo mafia I \\. \ . x 1 000 00H wcouows m n wou05000 wHoHuumm 1L 000.000 91d 1 n) 311 and dxa J (A/ 68 7.5 Comparison of Results with Previous Investigations Unfortunately very little research has been conducted on the re-entrainment process and on the role of turbulence in re- entrainment. Most of the investigation reported have emphasized the complexities of the process or assisted in defining the various parameters involved qualitatively. Strictly speaking the present results cannot be compared with the previous works because of the differences in the type of particles, surface and lack of data on intensities Of turbulence in previous investigations and hence the forces involved in the process. Nevertheless it is possible to discuss the results of the present investigation in the light of previous research to provide some indication of the order of magni- tude of different values. Gutterman and Ranz (27) have observed velocities ranging from 17.0 to 32.5 feet per second for re-entrain- ment Of glass, tin and carborundum particles ranging in size from 28 to 200 microns. These values compare favorably with those obtained in this investigation. The present investigation also con- firms the earlier observations of Bagnold (2) and Heldman and Punjrath (33) regarding the effect of the location of particles on the flat surface. It was Observed that an increase in intensity of turbulence has an effect similar to an increase in the velocity of flow. In both investigations, the distance 'xr' downstream from the leading edge at which re-entrainment started decreased with an increase in intensity Of turbulence or velocity of the free stream. Bagnold (2) observed that forces required to re-entrain the particles 69 decreased with the decrease in size to a minimum until the diameter was 50-80 microns and started increasing as the size decreased further. In this study the minimum force was Observed at 15-22.5 microns. This is maybe due to higher intensity of turbulence in the present investigation which decreased the thickness of viscous sublayer over the surface. 7.6 Mechanisms for Re-entrainment of Particles from a Flat Surface According to Prandtl (44) the motion in the boundary layer will be either laminar or turbulent. It is common practice to characterize the motion of a fluid in the boundary layer by a non- dimensional number Rex. For values of Rex below a certain critical limit, the motion is ordinarily laminar, whereas when Rex surpasses this limit turbulent motion begins, provided the flow in the boundary layer is subjected to disturbances of sufficient magnitude. The smaller the disturbing effects acting on the motion in the boundary layer, the greater is the value which Rex must attain before turbulence will appear. In the case of thin flat plate and for small values of "x", the number Rex will be less than the critical limit and the motion will be laminar. However as "x" increases Rex will increase and eventually depending on the magnitude Of the disturbing effect, the critical limit will be reached and turbulent motion will exist. It is assumed that the plate is of sufficient length to deveIOp turbu- lence. Hence in general the first part of the boundary layer will be laminar and the trailing part will be turbulent. 70 The transition from laminar to turbulent flow in the boundary layer is accompanied by a sudden and large increase in the shearing stress near the surface (46). It is clear from the figure 5.5 that skin friction coefficient is different for laminar and turbulent regions. In the laminar region, the skin friction coefficient is highest at the leading edge and decreases as the distance from the leading edge increases. Similarly, all the pre- vious work (38,46) revealed that the local skin friction coefficient for turbulent flow is also highest at the location immediately downstream from transition and it decreases as the distance along the length of the plate increases. If the re-entrainment is to start in the laminar region of the boundary layer, it should start at the leading edge where the aerodynamic force is highest. If the re-entrainment does not begin at the leading edge, it should not start at any location in laminar region of the boundary layer because the drag forces continue to decrease with distance down- stream until reaching the point of transition. In the transition region there is a jump in the aerodynamic friction on the particles and the force acting on the particles is highest. The aerodynamic forces of removal begin to decrease as the distance from the leading edge increases because of the decrease in local skin fric- tion coefficient. It is logical therefore to expect that maximum probability of re-entrainment is in the transition region i.e. in the region where flow in the boundary changes from laminar to turbulent. 71 One test of this hypothesis is to move this transition region and observe the effect of this movement on re-entrainment. For example, if the transition region is nearer the leading edge, the distance at which re-entrainment starts should also be closer to the leading edge. According to Dryden (22,23) and Schubauer and Skramstad (49) the location of the transition region along a flat plate can be varied by changing the intensity Of turbulence (see figure 5.6) without changing the mean velocity of the main stream. Thus if the re-entrainment process follows a similar pattern, the validity of this hypothesis can be verified. The influence of the intensity of turbulence is shown in the figures 7.1, 7.2, 7.3 and 7.4 and has been discussed under section 7.1. It was illustrated that an increase in the intensity of turbulence increased the re-entrainment by decreasing the Rey- nolds Number (Rer); the Reynolds Number at which re-entrainment started on a flat plate. The point at which the re-entrainment initiated moved toward the leading edge as the intensity of turbu- lence was increased, thus establishing the analogy between the re-entrainment process and transition of flow from laminar to turbulent over a flat plate at zero angle of incidence. Based on the observations of this investigation, an explana- tion of re-entrainment from the flat surfaces can be develOped. There are two mechanisms involved in the re-entrainment process. First, at a certain distance from the leading edge the flow in the boundary layer over a flat plate changes from laminar to turbulent resulting in increased aerodynamic shear stress on the particles 72 deposited on the surface. If this force is enough to overcome the resisting force, the particles are set in motion. The second mechanism is responsible for re-entrainment of particles deposited downstream from the region of transition. Under this mechanism, the particles set in motion by the aerodynamic shear stress at the beginning of turbulent region by the first mechanism, contact particles as they move downstream causing movement of other particles because of their momentum even if the aerodynamic forces are not adequate to cause re-entrainment at downstream locations. This explanation of particle re-entrainment accounts for the fact that re-entrainment does not occur until certain distances from the leading edge and introduces phenomenon of rolling and sliding of particles as Observed by Chepil (10, ll, 12) Sokolov (50) and Gutterman ££.El (27). This explanation accounts for the effect of turbulence on the re-entrainment mechanism and the reason for the re-entrainment of particles near the downstream edge although the aerodynamic forces acting on these particles continue to decrease as the distance from the leading edge increases. 7.7 Prediction of the Potential for Particle Re-entrainment The present study discusses the mechanisms of re-entrainment of small particles from horizontal surfaces. The effect of turbu- lence and size of the particles on the re-entrainment process are investigated, also. Equation 5.34 predicts the velocities required to initiate re-entrainment of different sizes of particles from different types of surfaces to a reasonable degree of accuracy, given the distance, xr, at which re-entrainment occurs. Thus if 73 we know the distance at which the boundary layer changes from laminar to turbulent flow as a function of degree of turbulence and surface roughness (particle size), it is possible to predict the extent Of re-entrainment from the various prOperties of the surfaces and particles. Unfortunately there is complete lack of data on the effect of intensity of turbulence on transition from laminar to turbu- lent motion in the boundary layer on a flat plate, particularly when the intensity of turbulence is more than three percent. In this situation the only approach to prediction of re-entrainment is to refer to figures such as 7.1, 7.2 and 7.3 which relate the effect of intensity of turbulence, diameter Of particles and Reynolds number. The process shall be tedious due to the need for relationships for various particle sizes and surface charac- teristics. However, after such figures are available for most common particles and surfaces, the process of prediction becomes relatively easy. By knowing the diameter of the particles and the intensity of turbulence the Reynolds number for re-entrainment can be determined from these figures. As an example, if the average particle diameter is 15 microns and intensity of turbulence in the main stream is 8 percent, from figure 7.1, the minimum Reynolds number (Rer) required to start re-entrainment is 50,000. If we assume the kinematic viscosity of air to be 1.615x104 square feet per second then the mean velocities of the main stream to start re-entrainment at distances of 5, 4, 3 and 2 inches from the leading edge shall be 19.4, 24.2, 32.4 and 48.5 feet per second, respectively. 74 If however, we know the distance, xc, at which the motion in the boundary layer changes from laminar to turbulent as func- tion of intensity of turbulence and particle size, then equation 5.34 can be used directly to calculate the minimum velocity to start re-entrainment at the given distance, xc. For example let the distance, x, be equal to 11.0 inches when the intensity of turbulence is 6.3 percent and mean diameter of particles is 15.0 microns. Assuming the friction factor between the surface and particles equals 0.2052 and densities of air and particles to be 0.0735 and 186.576 pounds mass per cubic feet respectively, equa- tion 5.34 indicates a minimum velocity of 17.759 feet per second; a value which compares favorably with the experimental value of 19.792 feet per second. It should be remembered that equation 5.34 has an implicit assumption regarding the type of flow at distance, x, where re-entrainment occurs. It applies only if the flow has changed to turbulent. Hence this equation cannot be used to cal- culate the distance, x, at which re-entrainment occurs for a given velocity, because, x, is also a function of intensity of turbulence in the free stream. The extent of re-entrainment or the percent re-entrainment defined as the percentage of particles re-entrained when compared to the number initially distributed uniformly over the entire plate can be observed from figures 7.14, 7.15, 7.16 and 7.17. In these figures the percent re-entrainment is plotted against Reynolds num- ber (p L U/u), L, being the total length of the plate in the flow direction. It is evident from these figures that percent re-entrain- ment increases as the length, L, increases, approaching hundred 75 .nmumfimfiw CH mcopoda 0N10H mmHOHuumo pow unmanamuuoo1wh we oohwmw co mumfio mo suwcoa mo uoowmm .0H.n muswwm 1 D A Q x ofixon 00Hx00 00Hx0m quxoq «OHxOm qofixON 00H 0H _ _ _ _ _ _ _ 0 ON 1.). E uu\ AH 050.00H u NO0N.0 m oucmflsnuae N n t .. 0 \ L 00,0 nuamuialnue-ag uuaoaad 76 .00008000 :0 0000006 0m1m0 mmHOHuumn pom uooE:0m0ucouou wo mouwww so woman 00 LuwcwH mo uoowwm .m0.n mpswwm :\ p 0 0 x x x x x x x mofi m 00H 0 00H m mOH 0 00H m 00H N 00H H 0 0 _ 0 _ 0 0 0 0 I 0m I c I!) quamuielnua-ag 3u9318d E 000\ 00 000.000 1 0 0000.0 1 0 77 .uoueEaav =0 0:00005 0010N mmfiowuuwn gem ucosc0muuconou we oeuwew do madam we :uwaeH we uowmwm .0H.n ouswam E0 000 x x x x x x x 00H m mOH 0 00H m 00H 0 00H m 00H N 00H H 1 0 - 0 _ _ _ q _ 0 _ _ A _ C Nu n N0 n NHH n NmH n om H H H H l E _ muw\ 0H 0mm.0wa u 0 mo-.0 u m nuamulelnua-aa nuaOJad 78 x 000 w OHXN 00x0 _ m m H m :\0 D 0 oflxm 0 m 0Hx¢ 0 x moa n 0 m , .uoquM00 :0 mcouoaa 0010 moaowuuma you ucoEGHMuucmuwu we nonwov do mumHa we pumcefi we uowmwm 00x0 0 m E muu\ AH 0nm.0wa mem.0 00x0 .00.0 000000 cm 00 00 00H nuamurslqua-au Juaelad 79 percent re-entrainment level asymptotically. It is significant to note that even low velocity may result in significant amounts of re-entrainment due to greater plate length. These figures also depict the effect of intensity of turbulence on the extent of re- entrainment. It is clear that higher intensity of turbulence result in higher re-entrainment levels. In summary, equation 5.34 can be used to predict the minimum velocity required for re-entrainment from flat surfaces. However, knowledge of friction factor between the particle and the surface, the critical distance, x, at which flow in the boundary layer changes from laminar to turbulent as affunctien of intensity of turbulence in the free stream, surface roughness (particle size), the densities Of particles and air and the size of the particles must be available. 80 8. SUMMARY AND CONCLUSIONS 1. When computing the aerodynamic forces of re-entrainment acting on a particle on a flat surface, the use of local skin friction coefficient provides a better description of the process and provides more reasonable results than the use of a drag coef- ficient Of a particle immersed in a free stream of fluid. 2. The critical velocity at which re-entrainment begins can be predicted by the use of the following equation: 1/2 1/2 1/2 5/4 0 43c ,0. = -—2 -—-——-—— U (Q ) ( 3 ) (DP) [2.87 + 1.58 Log (x/Dp)] where "x" is the distance from the leading edge at which re-entrain- ment starts and which is a function Of intensity of turbulence and type of the particles. 3. The re-entrainment along a flat surface starts near the downstream end Of the surface and proceeds upstream as the velocity increases. 4. The increase in the intensity of turbulence decreases the distance "x" at which re-entrainment starts thereby increasing the total re-entrainment from the surface. 5. The aerodynamic force per unit area, for re-entrainment from flat surface is function of size of particles and was minimum for 15-22.5 micron size particles. 6. The total aerodynamic force acting on a given sized parti- cle at the location where re-entrainment initiated was found to be constant and independent of intensity of turbulence or distance from the leading edge. 81 7. The re-entrainment of small particles from a flat surface can be described by two mechanisms: 3. The initiation of particle re-entrainment occurs in a region where the flow in the boundary layer changes from laminar to turbulent and where the aerodynamic shear stress is sufficient to overcome the force of friction between the particles and the surface. The particles set in motion at the transition point contact other particles while moving down- stream, setting these particles in motion by their force of momentum, even when the aerodynamic force of shear stress on these particles may not be suf- ficient to overcome their frictional forces. 82 9. RECOMMENDATIONS FOR FUTURE WORK During the course of present investigation it was felt that there is need of further investigation in the following area: Investigation of the effect of intensity of turbulence on transition of flow from laminar to turbulent in the boundary layer over a flat plate especially at higher levels of turbulence. Studies on the effect of surface roughness on the transition of flow in the boundary layer. Investigation Of the effect of temperature on the re-entrainment process from a flat plate. Additional investigations on the role Of surface density of particles, surface roughness (relative humidity and electrostic charge) on the re-entrainment process. 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New York) Stone, W. 1930 Some phenomena of the contact Of solid. PhilOSOphical Magazine and Journal of Science. 9:610 Taylor, G. I. 1935 Statistical theory of turbulence. Part 1. Proc. Roy. Soc. A151:444 Walker, R. L. and B. R. Fish 1965 Adhesion of particles to surfaces in liquid and gaseous environments. Oak Ridge National Laboratory, Tech. Memo. 1228 Zimon, A. D. 1963 Adhesion of solid particles to a plane surface II. Influence of air humidity on adhesion. Kelloidn Zn. 25:317. (translation by the Consultants Bureau Chicago.) 89 APPENDIX 90 APPENDIX A.1 Calibration of Hot Film Constant Temperature Anemometer A hot film constant temperature anemometer was used for measurement of mean velocity and intensity of turbulence. A pitot tube (sensitive up to i 0.0001 in. of water) was used to calibrate the hot film anemometer. The hot film anemometer sensor and pitot tube were mounted side by side in the wind tunnel having a uniform velocity profile. Care was taken to see that the presence of sensor did not effect the flow regime around pitot tube and vice versa. The bridge voltages of the anemometer were plotted against the velocities indicated by the pitot tube for various levels of velocities in the wind tunnel. A six degree polynomial was then fitted to this curve. To get a good accuracy the seven simultaneous equations so obtained were solved on a computer (MATHATRON 4280 T D; using program T-Ml4) The result of this curve fitting is shown in the figure A.1. The equation obtained from this curve fitting was then programmed to calculate mean velocity and intensity of turbulence etc. on the Control Data 3600 digital computer at the Michigan State University Computer Center. 91 on umquoEmcm musumumaEwu ucmumcoo .anw 005 we ceHuMMLHHmo vceomm you poem CH >u0oeam> 00 00 00 0m 0m .0.< 000000 4 — q q _ 0 0m mmmmmm0.0 + m hmwwmm.0 1 m Hummm0.0m + m m 0 m mommm0.omm 1 mm nnmmm.fi0om + m Hw~.0mmNH 1 Hmm0.HmHmH u > 0.0 0.0 (SJIOA) andnno aBsnIOA OBPIJQ Janamomauv 92 NONN.0 0.000 0000 00~N.0 0mm o000 ~0-.0 0.00m m000 mo-.o 00-.0 mm0 m0n om mmm0.0 mom 0000 0000.0 nnm m0m0 nmm0.o ¢0N 0000 0m¢0.o 0000.0 000 000 m.- n00~.0 00m m0m0 0m0~.o n.0wu m0m0 000~.o mNN 0000 ~m0~.o 0m0~.0 000 m0n m0 0000.0 000 a0m0 0m0m.0 0~0 m0M0 000m.0 own 0000 0m0m.o 0000.0 omm 005 0 060001 mammm. 0:00008 neuomm oe0ue0um nououm 00000 neueam0v 0aoueuxm c002 oe0u00um 0aeumuxm 00000 00 u£0003 m0u0uuwm neuomm oe0uo0um 0ocuouxe we de0uma0suwuea .0.< 00049 "‘7'16@Wflfljflfi'flfiililfiflfwmfiflfl“