I V A TURBULENT SPOT IN A
LAMINAR BOUNDARY LAYER
c u m a . i iic eiiuaiiiiiiGiii ui yaiuuics uy a mrnuienï spoï in a laminar oounaary layer, page line replace hy
T 5 6 7 28 41 43 56 63 66 79 83 28 4 16 6 16 21 2 9 13 14 8 S= lira ƒ S(t)dt T P(n)= lim 1' [(S( T ^ o o - T looses qualificaton Figure 3.6.d decompositcd X = 0 mm underly dimension an grounded sheet theoratical 1 ' S = lim —- ƒ S(t)dt T-«*> -T ^T ( S ( t ) - S )n d t ] / S P(n) = lim T - K > 1
I T
T ƒ - T U S l O - S )n d t ] / Sn loses qualification Figure 3.4.d decomposed Z = 0 mm underlie dimensions a grounded sheet theoreticalm
rïi!m
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E
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1-3-1986 F.G.J. Absil•fc. 70
in S
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mi\ .
BY A TURBULENT B\P@Y IN A
LAMINAR BOUNDARY LAYEFa
Proefschrift
ter verkrijging van de graad van doctor in de technische wetenschappen
aan de Technische Hogeschool Delft, op gezag van de
Rector Magnificus, prof.dr. J . M . Dirken,
in het openbaar te verdedigen ten overstaan van
het College van Dekanen op 13 maart 1986 te 14.00 uur
door
FRANS GERTRUD JOZEF ABSIL
geboren te Heerlen
vliegtuigbouwkundig ingenieur
TR diss
1 4 7 5
Dit proefschrift is goedgekeurd door de promotor
prof.dr.ir. G. Ooms
TABLE OF CONTENTS
1 INTRODUCTION 1 1.1 The research project seen in a historical perspective 1
1.2 Particle entrainment force balance 2 1.3 Coherent structures in the turbulent boundary layer:
the turbulent spot 5 1.4 The influence of coherent structures in the turbulent boundary
layer on particle entrainment 11 1.5 Experimental research project 13
2 ENTRAINMENT VISUALIZATION STUDY USING HIGH-SPEED
PHOTOGRAPHY 15 2.1 Experimental set-up 15 2.2 Measuring program IS 2.3 Results and discussion 21 2.3.1 A qualitative description of the entrainment process:
bed entrainment forms 21 2.3.2 Classification of individual particle motions 30
2.3.3 Rolling and skimming 31
2.3.4 Direct entrainment 32 2.3.5 Entrainment after piling 33
2.3.6 Breaking 34 2.3.7 Entrainment starting time 35
2.4 Conclusions 38
3 TURBULENT SPOT STRUCTURE MEASUREMENTS 39
3.1 Experimental set-up 39 3.2 Probe calibration and data acquisition/processing (spot detection) 41
3.3 Measuring program 43 3.4 Results and discussion 46 3.4.1 The spot shape and growth 46 3.4.2 The ensemble averaged spot structure 49 3.4.3 Quadrant-hole analysis applied to the uv-signal within the
turbulent spot 56 3.5 Conclusions 60
SIMULATION MODEL FOR THE PARTICLE ENTRAINMENT
BY A TURBULENT SPOT 62 Model requirements 62 Description of the model 63
Calculation of the instantaneous 3-dimensional spot shape 63
The formation of the particle cloud 64 Calculation of the instantaneous concentration profiles 69
Calculation of the sampled weight distribution at a downstream
coordinate 69 Array limits and program options 69
Results and discussion: the main parameters 70
A model calculation 70
The influence of the spot origin: X0 , t0 72
The influence of the spot growth: UgLp. UgjE and O: 72
The influence of the entrainment time interval: Atg^ , AtSD 75 The influence of the entrainment coefficient, wind tunnel
speed and concentration gradient: Ac, Uoo and CG 75
The influence of particle size: Dp 77
Conclusions 7 7
PARTICLE SAMPLING EXPERIMENTS 79
Experimental set-up 79 Measuring program SI Results and discussion 83
Entrainment forms 83 Ensemble averaged collected weight distribution 85
Fitting the simulation model with the experimental results 92
Collecting experiments at different conditions 96
Conclusions 96
FINAL DISCUSSION AND CONCLUSIONS 98
LIST OF SYMBOLS 102 LIST OF REFERENCES ] 05 Samenvatting 1 12 Dankbetuiging 113 Levensbericht 1 14 SUMMARY
In a wind tunnel an artificial turbulent spot was generated using a tripping wire in a laminar boundary layer over a flat plate (Uoo = 7.0—8.5 m/s). This flow structure passed downstream over a particle bed (Dp = 1 - 2 0 0 urn), thereby initiating entrainment.
In a visualization study using high-speed photography particle trajectories were recorded. Two main entrainment motions were observed, called direct entrainment (for the larger particles) and entrainment after piling (for the smaller, more cohesive particles). For the types of particle motions average data were determined.
The structure of the turbulent spot was measured using hot-wire anemometry. An X-wire recorded the strcamwise and normal velocity components at several downstream, spanwise and vertical coordinates on the plate. From the ensemble averaged velocity signals the spot shape and growth were determined using a high-frequency spot detection criterium. The structure of the spot was found to be similar to that in other experiments. A quadrant-hole analysis was applied to the Reynolds-stress distribution in the spot core and this confirmed the similarity between the artificially generated turbulent spot and the naturally occurring structures in the turbulent boundary layer.
A computer simulation model was developed describing the entainment process by the turbulent spot using an entrainment criterium based on a particle force balance and assuming a regular turbulent burst size and spacing within the spot. Data from the high speed films and from the spot structure measurements were used as input into the model which then calculated the formation of the particle cloud due to the spot passage, the instantaneous concentration profiles and the sampled weight distribution in a vertical cross-section at a downstream coordinate.
Finally in the wind tunnel, using a frame with a set of electrostatic precipitators, collecting experiments were performed in order to measure the ensemble averaged lateral and vertical weight distribution and the downstream deposition characteristics. Thus the assumptions that were made in the simulation model could be verified and a choice of the free parameters could be determined. The total entrained mass and the sampled weight were highly dependent on the wind speed. The model calculated the deposition and the vertical weight distribution in an acceptable way but the lateral spreading of the particles in the tests was narrower than that of the spot. Also the decrease in particle entrainment that was observed as Uoo exceeds 7.5 m/s could not be predicted by the simulation model.
1 INTRODUCTION
1.1 The research project seen in a historical perspective
In nature the entrainment and transport of solid particles by an airflow may be observed in many situations. Examples of this phenomenon are: snowstorms, sand- and dust storms in desert areas, the forming of ripples and dunes in either desert or coastal areas and the blowing away of sou in agricultural areas.
Since human activity has interfered with nature other forms of particle entrainment have been introduced, of which to mention: dust annoyance due to wind blowing over a stockpile of ore or particle suspension due to traffic or the handling of materials (a combination of wind and human activity).
The human interest in the problem of entrainment of dense solid particles by the wind stems mainly from the negative aspects that accompany this phenomenon: economic loss (as is the case with stockpiles), ruin of fertile areas (in desert and agricultural areas), flooding by the sea (in coastal areas), health effects (respiratorial diseases) and environmental pollution effects (dirty windows and laundry etc.).
The quite recent interest in the dust annoyance due to the stockpiling of ores (to be a little more specific: the stockpiling of coal) may need a short historical introduction.
In our modem Western civilization crude oil has become one of the main energy resources. On earth there exists a geographical problem: the countries on earth where the oil is consumed are not the ones where mother nature offers her "black blood". This has caused an immense trade between the Western countries and the oil producing countries but this fact has also entailed a dependency in the relationship between these countries. During the 1970-s the oil producing countries got aware of their power and have started to use their resources as a political weapon. This has created a shock in the Western world and has made governments conscious of the one-sidedness of their energy policies and the limits that nature has put on its conventional energy resources. So they have started to consider and investigate the exploitation possibilities of new energy resources like nuclear or solar energy and the return to older natural resources like wind energy and coal.
It is this latter solution for the energy problem that our attention will be focused upon. Also the Dutch government has initiated a large research project on the re-introduction of coal as an energy resource (the National Coal Research Programme NOK). Industries, engineering companies, universities and other research and development organisations are carrying out research projects within the framework of this program. Items that are dealt with within the program are [Stork, 1984]: sampling/registration techniques, emission, dispersion models, concentrations, deposition, resuspension, abate ment techniques, annoyance and effects on human beings, nature, agriculture and horticulture.
In literature coal handling emission factors are found ranging from 1 to 5000 g/m2s [Visser, 1984]. This means there is a large scatter and often the emission conditions are badly documented. So there is an interest for a better understanding of the entrainment phenomenon. On one hand emission factors need to be known differentiated towards entrainment source (form of the stockpile, handling activity, etc.) in order to make regulations (preventing or minimalizing the annoyance effects) or to have a better input into dispersion computer models. On the other hand research-workers in the field of two-phase flow phenomena are interested in the influence of turbulence on particle entrainment from a more fundamental point-of-view. It is in this latter perspective that the herein described research project at tiie Delft University of Techonology must be seen.
1.2 Particle entrainment force balance
A turbulent boundary layer flowing over a flat surface covered with particles is a gas-solid two-phase phenomenon. This phenomenon may be described by the following six parameters [Yalin, 1977]:
For the gas:
pg: the gas density [kg/m3 ]
fi; the dynamic viscosity [kg/ms]
For the particles:
pp: the particle density [kg/m3 ]
Dp : a characteristic particle size [pm] (1 pm = 10"6 m)
In the case of a mixture of non-spherical particles also information on the particle shape and size distribution is needed.
For the interaction between the flow and the particles: g: the acceleration due to gravity [m/s2 ]
u#: the bed shear velocity [m/s] (u* = \/r0jp, where r0 is the wall shear stress)
In general for dense solid particles in air flow we have: Dp = 0 . 1 - 1 0 0 urn; Uw = 1 - 1 0 m/s the kinematic viscosity v = ju/p„ = 14.61 x 10"6 m2 /s; pg = 1.2 kg/m3 \p^lp% = O ( 1 03) .
In the aerocolloidal system consisting of gas and particles the gas may be considered a continuum except for the smallest particle sizes while Brownian motion may be neglected to convective particle transport [Hidy, 1970).
Let us assume we have a particle bed over which the air is flowing at such a free-stream velocity Uoo that the forces induced by the wall shear stress on the particles are insufficient to move any of these. Then if the free-stream velocity is increased there is a critical stage where for the first time particle movement is observed.
The first one to derive a relation between two dimensionless mean quantities, one describing the flow field in the critical situation, one describing the particle characteristics was Shields [Shields, 1936]. This relation
2
|(pp py)Dpg |..r | v |.r
is known in the field of hydraulics and civil engineering as the Shields-curve, Figure 1.1, and has been experimentally determined for many flow and material conditions. The line in the graph indicates the critical stage and when the flow conditions are in the region above this line then particle motion will occur.
PP
$
^11
m
i~
- ~
u r mï'ilf... 'ïi
'T
. = » . . . C . „ . . . j l . 6 500gKD
1
Mi.lure+ L':°
: T. =,..., „;.r
-1! ~ T p W
,J «
~-m
■ s i a"—t
. !
t OS l a s 1 65 ; «.= 8 5 Alls 20M
lit
1
iFigure!.1: The Shields-curve. [Yalin, 1977}
The experimentally determined Shields-curve is not a unique function but shows much scatter depending on many factors of which to mention the bed geometry, inconsistency in describing the critical stage, the structure of the flow turbulence and interparticle forces [Grass, 1970;Mantz, 1973; Iversen et al., 1976 (2x); Fletcher, 1976 (2x); Fenton/ Abbott, 1977;Gilette, 1978; Yalin/Karahan, 1979; Willetts et al., 1982].
For a gas-solid system a critical curve analogous to the Shields-curve may be predicted using a force balance model [Phillips. 1980]. Consider a single spherical particle on a flat surface, Figure 1.2. There are two forces holding the particle to the surface: the adhesion force which, as long as the particle stays within one diameter distance from the wall (Y < Dp)
may be written as Fa d = Ci Dp. And secondly the particle weight Fz = c2 Dp 3. There exists a particle size where adhesion and particle weight are equal. This size is about 30 microns.
Figure 1.2: llxe forces acting o)\ a spherical particle on a flat surface.
For smaller sizes adhesion dominates over particle weight.
The first region to be considered is called the large particle region (Dp > 200 Mm). In this region particle weight is the holding force. This force may be counteracted by either the moment of aerodynamic drag FD about the contact point of a particle to its neighbouring particles (in the case of a bed of particles) [Iversen/Greeley/Pollack, 1976; Fletcher, 1976 (2x)] or by an aerodynamic lift force FLJ [Phillips, 1 9 8 0 ] .
Equating these forces (or moments) which is the definition of the critical stage, motion-no motion, these authors give for the large particle region (dimensions in Si-units):
Fletcher (1976): T0 = = 0.0169 (p„ = 2 6 5 0 k g / m3) (PP - P g ) g Dp
Iversen e t a l . (1976): T0 = 0.0121 ( pp/ pg = 2000)
Phillips (1980): T~Q = 0.014 (pp - 2500 kg/m3)
This means T0 *■ Dp or to say in words as the shear stress increases larger particles will
be entrained by the flow. This corresponds to the right side of the Shields-curve. For very small particles (Dp < 30 pm) embedded in the so-called viscous sublayer of the turbulent boundary layer (y+ = Y i u / f < 7), so when the flow regime may be considered turbulent smooth, other forces start playing a role in the entrainment process. Adhesion or cohesion now outweighes gravity and a lift-force F[_2 a s described by Saffman [Saffman, 1965] starts acting on the particle either continuously [Iversen, 1976] or intermittently during the so-called "updraft under a burst" [Cleaver/Yates, 1973; Phillips, 1980]. A more detailed description of this process will be given in the next two Paragraphs (1.3 and 1.4).
The force balance in this region leads to:
4
/ 1 + 0.055/pDgD 2\ iversen t al. (1 976,: r0 - 0 . 0 7I (pp - Pg >gDp ( i + 2J ^ U
Phillips (1980): T0= c3Dp-4 / 3 (c3 = 5 x 10"e)
Fletcher (1976): r0 = (pp - pg) 0 . 1 3 g Dp i / 2 + 0.057(—) f — j
(c4 = particle cohesion coefficient).
1
When plotting these results all authors lind r0 (with n > I); the critical wall shear Dp
stress is inversely proportional to the particle size which means that as the flow velocity is increased smaller particles that adhere stronger to the wall or to their neighbouring particles will be removed by the flow.
Looking at the two regions (large particles Dp > 200 pm and small particles Dp < 30 pm) one sees there has to be an intermediate region where the critical wall shear stress shows a minimum. For this region the authors give:
Fletcher (1976): u ,m i n = 14.2 cm/s (Dp = 80 pm). Iversen et al. (1976): u,.m m = 20.5 cm/s (Dp = 75 pm). Phillips (1980): uj m i n - 19.8 cm/s (Dp = 100 pan).
The resulting plot that is obtained showing the critical wall shear stress as a function of particle size is shown in Figure 1.3. There is an intermediate region (Dp = 30— 100 pm) where particles will first be removed by the flow and then when the wall shear stress is increased both smaller and larger particles will be removed.
1.3. Coherent structures in the turbulent boundary layer: the turbulent spot
In nature most Hows are turbulent: So for many years, starting from the end of the
19-th century people working in the field of aero- and hydrodynamics or related fields have been investigating turbulence and trying to describe it. (For a historical review of this research, see [Kunen, 1984]). In general there are two ways of approaching the study of turbulence.
In the first and more traditional way turbulence is considered a stochastic phenomenon where the timedependent flow properties S (velocity-components, pressure, etc.) at any point (X,Y,Z) in the flow may be separated into a mean (S) and a fluctuating part (s):
T S(t) = S + s, w i t h S = lim ƒ S(t)dt
T-+™ - T
Figure 1.3: Tlic critical wal! shear stress versus particle size for particles in an air flow. {Phillips, 19S0 ]
where S = U, V, W, P, etc.
The turbulence structure is then expressed in momenta of the turbulent velocities relative
to the mean value:
P(n)= Urn ƒ [ ( S ( t ) - S ) " d t ] / S , w i t h n = 1,2,3,
or spatial correlation techniques may be applied.
A more recent description of the turbulence, starting from the end of the 1950-s (mainly at Stanford University, California) points at the deterministic elements that are contained within turbulent flow phenomena. This has evolved from visualization studies that were performed in turbulent flow situations (using smoke in wind tunnels and hydrogen-bubble or dye techniques in water tunnels). From these studies it was noticed that in turbulent flows orderly patterns (called coherent structures) could be discerned that, although occurring as a whole randomly in space and time, showed characteristic features within them, that occurred sequentially in each realisation of the pattern.
In the fully developed turbulent boundary layer coherent structures have been observed both in the wall layer (y+ < 100), see [Kline et al, 1967; Corino/Brodkey, 1969; Grass,
1971 ]) and in the outer, intermittent region of the boundary layer (see [Kovasznay et al., 1970]). For a survey of the literature on these structures see the reviews by [Cantwell, 1981] and [Kunen, 1984].
6
In the turbulent boundary layer near the wall energetic fluid motions were observed, distributed randomly in space and time, that are responsible for the main mass, impulse and heat exchange and that produce the major part of the turbulent energy [Corino/ Brodkey, 1969; Kim et al., 1971 ] . These fluid motions show a characteristic sequence of events that was called the "burst-cycle". Now it will be described in short what happens during one such cycle (see the meanwhile classical sketch from [Hinze, 1975] in Figure 1.4).
Figure 1.4: A conceptual model for the near wall structures. From {Hinze, 1975].
In the viscous sublayer (y+ < 7) counter-rotating pairs of longitudinal vortices may be
observed that are responsible for the streaky nature near the wall. Velocity measurements very close to the wall show alternating regions of low- and high-velocity (as compared to the local average value), called streaks. In the streaks due to the rotating movement, low-speed fluid is moved away from the wall. At a height of y+ = 1 0 - 1 5 within these fluid parcels oscillations start to occur, possibly oppressed by the outer flow field
(having an instantaneous adverse pressure gradient). These oscillations are amplified until at y+ = 30 the ejection (as the low-speed fluid parcel moving away from the wall is called)
looses its coherence and breaks up {the "bursting"). This is followed by an inrush movement at a velocity above the local mean value called the sweep. Both ejection and
sweep, due to their velocity-difference sign (during ejection u < 0, v > Q, during the sweep U > 0, v < 0. where u and v arc the fluctuating parts of the longitudinal and normal velocity components) have a considerable contribution to the production of turbulent energy in short time intervals [Willmarth/Lu, 1972; Eekelmann. 19741.
Research by [Head/Bandyopadhyay, 1981 ] shows that the structures in the outer region are in some way a continuation of the wall phenomena and that the fully developed turbulent boundary layer may be considered to consist of arrays of stretched hairpin vortices originating from the wall and inclined downstream at a preferred angle of 4 0 - 4 5 degrees.
Much effort has been spent on trying to study the development of a single structure by detecting and tracing it- But due to the random occurrence and the continuous interaction of the structures most existing detection methods have thus far failed in isolating a structure from its turbulent environment [Kunen, 1984]
This difficulty is avoided or at least reduced by considering not a fully developed turbulent boundary layer but what is called the "turbulent spot" in the laminar boundary layer. The turbulent spot is a How structure (crudely described as a pancake-shaped piece of turbulence) that occurs naturally when the How is in the transitional stage from laminar to turbulent (as was first observed by [Emmons, 195 1 ]) but that may also be generated artificially by introducing a disturbance at an appropriate position in the laminar flow.
The over-al! structure of the spot as determined by ensemble-averaging experiments [Wygnanski et al., 1976; Cantwell et al., 1978, Van Atta/llelland, 1980; Antonia et ah, 1981; Wygnanski/Haritomdis, 1979; Wygnanski et al., I9S2] shows a large vortex-like velocity defect region moving away from the wall, except for Y/H, < 0.1 (with H, the local spot height) where the velocity exceeds the local average. Its size and velocities at the outer edges are comparable to those of the large-scale structures in the intermittent region of the turbulent boundary layer (H8 Si o.US L I i = 0 . 9 Uoo, UST!: = 0 . 6 5 U » , where
USLE a n d USTE are the convection velocities of the spot leading edge and trailing edge respectively). The spot in side view (see Figure 1.5) shows a kind of rolling vortex with a steep leading edge, a maximum spot height at about 0.25 spotlength from the leading edge, and a considerably flatter back.
In plan view the spot is arrow-head shaped and followed by Tollmien-Schliehting wave-packets at its outer edges.
Visualization studies of the spot [Perry et al., 1981; Gad-el Hak et a!., 1981] show many features that are also characteristic for the turbulent boundary layer, to mention longitudinal streaks in the sublayer with an average lateral spreading equal to that in the boundary layer and accumulations of hairpin vortices similar to those observed by [ Head/ Bandyophadhyay, 1981] in the turbulent boundary layer (see Figure 1.6).
8
a) Spot in plan view; Bs/X, = 0.18 (X,, - 300 mm; U ^ = 9.4 m/s)
b) Spot in side view; H,/X, = 0.025. — , Z / B8- 0 ; , Z/B, = 0.118; _ __ , Z/B, = 0.471; - — , Z / B , : — x - , Z/B, = 0.824; — o — , Z/B, : ■• , Z/B, = 0.233; , 0.588; —v — , Z / BS = 0.706; 0.941
Figure 1.5: Vie ensemble-averaged spot shape (the contours in the graphs correspond to the lines where the instantaneous streamwise velocities deviate 2% from the local laminar value,
V = 0,98 UL)
Even in the ensemble-averaged spot substructures pointing towards hairpin vortex-like structures may be observed as shown by [Wygnanski, 1981] and [Itsweire/Van Atta, 1984].
In short, many spot feattircs give rise to the idea of a similarity between the spot (or at least the core of the spot) and the turbulent boundary layer. [Coles/Barker. 1975] have even suggested the creation of a synthetic turbulent boundary layer by summation and interaction of rows of spots intermittently generated in a laminar flow. And it is this similarity that has led to the idea of representing a structure in the turbulent boundary layer by a turbulent spot in the laminar boundary layer.
1.4 The influence of coherent structures in the turbulent boundary layer on particle entrainment
It was essential for the research project to assume that the near-wall structures in the turbulent boundary layer are the main activators in the entrainment process. Two arguments justify this assumption. At first when the flow velocity above a flat particle bed is increased, initiation of the particle pick-up occurs streakwise, showing "spots'1 of particle-entrainment, randomly distributed, like the wall structures. [Bagnold, 1954; Sutherland, 1967; Grass, 1970;Vanom, 1975; Fletcher. 1976;Yalin, 1979] Secondly, for very small particles embedded in the viscous sublayer, which according to older theories is a stationary flow region (thus dealing with spherical particles in a steady Stokes-flow at linear velocity gradient), theoretically no lift force is found [Cleaver/ Yates, 1973]. The presence of near-wall structures in the boundary layer may explain the pick-up of these very small particles either by pointing at the non-steady state of the sublayer (the occurrence of streaks, ejections and sweeps) or the non-negligible inertial forces close to the wall during certain stages of the burst-cycle.
Hence many authors have suggested a link between the wall structures and particle entrainment [Sutherland, 1967; Sumer/Deigaard, 1974;Vanoni, 1975; Jackson, 1976; Mantz, 1978; Sumer/Oguz, 1978; Sumer/Deigaard, 1 9 7 4 ] . Experiments of [Grass, 1974] showed that during sand-particle pick-up in a water channel the uv-velocity signal was in the ejection phase (u < 0, v > 0, the second quadrant in the uv-plane).
A model describing the entrainment/deposition process as linked to the wall-structures is presented by [Cleaver/Yates, 1973, 1975, 1 9 7 6 ] . An entrainment criterium is derived by considering a force balance on the particles while entrainment is calculated using mean burst size and spacing. Holding force on the particles is adhesion or cohesion: Fad B cad Dp. Next it is assumed that entrainment occurs under the burst (see Figure 1.7) and that during the ejection phase the flow field may be represented by a quasi-steady inverse axi-symmetric stagnation point flow (using [Laufers, 1954] pipe-flow data in order to estimate quantitative results). This leads to a lift-force:
called the "updraft under a burst"-lift force. Equating these two forces leads to the entrainment criterium T0 cr = p u# | C f 2 = &Dp~m where p1 is depending on fluid and particle properties and the type of adhesion. Experiments show values ranging for p1 from O(10"4) toO(10~B)Nm~2 / 3 as Dp is varied between 0 ( 1 0 ° ) and 0(10"3) /un, showing a scatter analogous to that in the experimentally determined Shields-curve.
Next in the Cleaver/Yates model a monolayer of particles is considered with particle
0~)
Q
///77777ZW7ZZ7777? ~,"
essentially laminar How developing with time
particle itagnation point
Figure 1.7: The entrainment of small panicles underneath a bunt. {Cleaver/Yatcs, 1973]
sizes distributed according to a normal distribution (mean diameter Dp m. standard
deviation o). (10 2
Of these particles underneath a circular-shaped burst with average area I — 11—- I
per burst a fraction a is removed. In a control area (see Figure 1.8) based on mean burst spacing, and assuming a periodic burst occurrence, after time t. the percentage of cleaned
turbulent burst plan view area (ff/4) (20 ! ' / u , );
control area used to estimate rate of removal
Figure 1.8: Control area based on mean burst size and burst spacing.
surface is given by:
ƒ exp( - p:/ 2 ) d p ^
~s7
ƒ exp(-p3/2)dp
where Dp c = ( ra (fT3** >, the critical size above which particles are removed. Apart from
the difficulties in determining a, (3 and the mean burst data, this model gives a local and instantaneous prediction of the removal rate, this in contrast to previously derived equations that where based on mean flow parameters, not taking into account the boundary layer wall structures.
1.5 Experimental research project
In order to investigate the influence of a coherent structure in the turbulent boundary layer (as simulated by the turbulent spot in the laminar boundary layer) on particle entrainment a research project was started at the Delft University of Technology. Department of Mechanical Engineering.
No previous data existed on particle entrainment by an isolated structure and therefore several aspects of the turbulent spot and its interaction with a particle bed were investigated. At this stage a broad view at the subject was thought more appropriate than a detailed study of one of the aspects. This was realised by dividing the project into four parts that will consecutively be described in the following chapters.
i); Visualization of the particle entrainment using high-speed photography. ii): Measurement of the 3-dimensional turbulent spot structure using hot-wire anemometry.
iii): Development of a computer simulation model describing the particle pick-up process by the turbulent spot.
iv): Collecting of the entrained particles using electrostatic precipitators.
ad i): In a wind tunnel a high-speed camera was installed to rcgistrate the beginning of particle entrainment. Besides a qualitative image of the phenomenon also quantitative information was derived from these films using a motion-analyser. This gives data on: entrainment form, types of motion, trajectories (2-dimensional), instantaneous velocities and starting times.
ad ii): Although already literature exists on the turbulent spot a need was felt for a better understanding of this structure and a more thorough measurement of the 2-diniensional (U,V) velocity field throughout the spot. In a wind tunnel at several (X,Y,Z)-positions spot-realisations were measured using conditional sampling and processing these data on a
computer. This gives data on: spot shape (leading edge, trailing edge, lateral spreading, vertical growth), ensemble averaged U-, V- and uv-signals throughout the entire spot. Besides a quadrant-hole analysis was applied to the data in order to say something more definite about the similarity between the artificially generated spot and the naturally occurring structures in the turbulent boundary layer.
ad iii): In order to predict total entrainment (mass flux) and concentration profiles a computer simulation model was developed. As the spot is an instationary, bounded, inhomogeneous "piece of turbulence1' no effort was made to solve diffusion equations. So an integral model was developed using input on the spot geometry and growth and entrainment mechanism from both literature and own experiments.
ad iv): A set of electrostatic precipitators was used in order to collect the entrained particles. Thus the ensemble-averaged weight distribution at several streamwise positions downstream of the particle bed was measured. The data from these experiments were used to set the free parameters in the simulation model.
All experiments were performed at the Laboratory for Aero- and Hydrodynamics (Delft University of Technology, Department of Mechanical Engineering). Two wind tunnels were used hereafter called the particle-tunnel (for the filming and the collecting experiments) and the spot-tunnel (for the spot structure measurements).
14
2 ENTRAINMENT VISUALIZATION STUDY USING HIGH SPEED PHOTOGRAPHY
The purpose of these experiments is to gain information on: entrainment forms, particle trajectories and velocities, entrainment starting time.
The set-up and the experiments are described in [Zeegers, 1983] and [Beugeling, 1984]. Analysis of the films using the motion-analyser is reported in [BeugeUng, 1984], [Lorenz/ Rietveld, 1984] and [v.d. Kieboom, 1 9 8 5 ] .
2.1 Experimental set-up
The visualization study was performed in a low-speed (Uoo = 1 — 10 m/s) open-circuit wind tunnel, called the particle-tunnel. The wind tunnel has a 2m long rectangular test section (0.4 m wide, 0.3 m high) as sketched in Figure 2.1.
Figure 2.1: Particle-tunnel test section (dimensions in mm)
In this section a 1.5 m long horizontal flat plate having a sharp leading edge was mounted at 10 cm above the tunnel floor. At the downstream end of the plate an adjustable flap
was mounted while the plate itself could be rotated at small angles to the horizontal axis. This in order to obtain a laminar vertical velocity profile at zero pressure gradient. At a plate angle of 0.23 degree and a flap angle of I 2.4 degrees the longitudinal pressure
d / p — POQX
gradient was — ■ ■—- = -0,005 !/m while the measured profile corresponded well dX \ VipUov /
to the theoretical Blasius-profilc, sec Figure 2.2.
(line indicates Blasius profile)
Y/X^/Uoo X/c
Figure 2.2: Measured vertical velocity profile.
In order to generate a turbulent spot a 0.1 5 mm thick copper tripping wire was used. This was mounted at X, = 300 mm downstream of the flat plate leading edge ( R cx = 1.54 x 105 at Uoo= 7.5 m/s) across the section at a height of about 0.1 mm. The wire, embedded in a cellotape profile except for the central 1 5 mm. is on one side attached to the tunnel wall while at the other end a weight of 150 g hanging outside the section is keeping the wire under tension. Underneath the plate at X = 300 mm there is a row of permanent magnets with their magnetic field pointing in the main-flow direction The wire is part of an electric circuit (wire voltage/current 3V/1.65A) and when a current is sent through the wire this is pulled towards the wall thereby generating a point-like flow disturbance that grows downstream to a turbulent spot. After some experimenting with wire voltage/current, wire height above the plate and tension weight good reproducable spots could be generated.
At first some preliminary filming experiments were performed using a 150 x 150 mm2
particle bed consisting of cement powder with its leading edge (the upstream edge) at
16
XBLE = 616 mm (the way in which these beds were produced will be discussed below). The
laminar How velocity was fixed at Uco = 7.2 m/s (a velocity just below the entrainment limit). Then a turbulent spot was generated and while It passed over the particle bed a cloud of particles was moved. This confirmed the link between the presence of structures in the boundary layer and the initiation of sediment transport but so many particles were lifted over nearly the entire bedwidth that it was impossible to gain information en individual particles from the films.
Thus the set-up was changed from a large particle bed to a small 1 5 x 2 mm2 powder strip. But in order to simulate a large bed geometry (to prevent having a small strip in a Hat smooth environment) a 230 mm long, 280 mm wide sheet of emery paper was glued to the Hal plate with its leading edge at X = 606 mm. From this sheet at the required lateral measuring position (2 - 0. - 10, + / - 20. 30 mm) a 1 5 mm long, 2 mm wide strip of emery grains was scratched with its leading edge at X = 616 mm, see Figure 2.3.
-*r
. ,__, . particle strip ., ,. ttippmgwire section wall
Figure 2.3; Particle-strip configuration in the test section [dimensions in mm)
Particle beds were made by injecting the powder through the top of a 350 mm wide. 1 m long cylinder placed vertically on the plate. In the cylinder bottom there was a disk with an I 5 x 2 mm2 opening corresponding to the strip in the emery paper. Experimenting with blowing and settling times for the various materials used resulted in reasonably homogeneous particle beds with their top layer nearly flush with the surrounding emery paper.
The films were recorded using a Strobodrum (F. Fruengel lnipulstechnik GmbH, Hamburg, Germany) high speed camera containing a 1.5 m long strip of 35 mm film
(Ilford HP5, 400 ASA). Shadowlight technique was used having a Fisher Nanolite high-frequency flash lamp (flash duration O(10~8} s) as light source. Two lenses focused its light to a parallel beam of 7 mm diameter, see Figure 2.4. Filming was done at a magnification factor of 3 resulting in a field of view of 6 x 8 mm2 from the particle bed
Front view
lense (f = 80 mm) test section high-speed camera
98 i 540^ j 90 i 250 I 267 I | 80Q
Figure 2.4: Camera and lense set-up. (dimensions in mm)
leading edge downstream (the X-Y-plane). The pulse generating the turbulent spot also triggered the camera system which after a delay time of 6 0 - 7 5 ms (the time the flow disturbance needed to reach the particle bed) produced a flash series (at frequency 2000 Hz, duration 2 0 - 3 5 ms). Simultaneously a hot-wire anemometer positioned at X = 616, Y = 3 mm recorded the longitudinal velocity-signal above the bed leading edge. The films consisted of 75—80 frames showing the initiation of particle movement during the passage of the spot.
Analysis of the films was done using a motion-analyser (a so-called X-Y-discriminator connected to a mini-computer system). Thus individual particle tracks were measured and presented in the form of tables and plots.
2.2 Measuring program
After experimenting with filmmaterial, lighting, particle bed size and position, magnification factor, camera delay time, flash frequency and duration the filming program started. The following parameters were kept constant during the experiments:
i): the undisturbed laminar flow velocity Uoo (average value 7.3 m/s, scatter +/— 0.3 m/s over the total number of films, turbulence intensity u ' / U0 0< 0.001 at Uoo = 7.5 m/s). ii): the spot arrival and duration time. The first is determined by the time the spot needs
18
to cross the distance from the tripping wire (at Xs = 300 mm) to the particle bed leading
edge (at XgLE = 616 mm). It is dependent on the air speed and cannot be regulated. The average spot arrival time was 60 ms, scatter +/— 5 ms. The spot duration can be regulated by changing the tension on the tripping wire or the voltage/current used. For each set of experiments at a specific lateral coordinate the spot duration was constant within 5 ms. Altering the lateral measuring position required an alteration of the test section and often caused a change in spot duration. So spot lengths from 20 up to 60 ms (as measured by the hot-wire anemometer a t X = 6 1 6 , Y = 3 , Z = 0 mm) were employed with an incidental spot-failure (less than 3% of the realisations) resulting in a much larger spot (of order 100 ms).
The following parameters were varied over the experiments:
i): the lateral position of the particle strip. Films were recorded at Z = 0, - 1 0 , 20, - 2 0 and —30 mm.
ii): the bed material. Two materials were used: cement powder (pp - 3.2 g/cm3 ,
Dpso = 65 fim, dried before the use in the wind tunnel) and Durcal (CaC03, pp = 2,75 g/cm3) a filler-material used in dye-industry. Of the latter five fractions were used with respectively Dpso = 60, 30, 15, 10 and 5 urn (hereafter called Durcal 65, 40, 15, 10 and 5 according to their industrial registration). A cumulative size distribution based on particle weight is shown in Figure 2.5.
Figure 2.5: Cumulative particle size distribution.
hi): the bed thickness. At Z = 20 mm for Durcal 40 several blowing times (from 20 to 200 s) were applied when producing the bed resulting in a thicker bed clearly protruding from its environment.
For each material and lateral position at least five films were recorded resulting in a total
number of about 150 films. The films at Z - 0 and Z - —10 mm (except for Durcal 5) were processed through the motion analyser thus obtaining about 400 particle trajectories.
2.3 Results and discussion
2.3.1 A qualitative description of the entrainmcnt process: Bed entrainme-nt forms
At first the films were analysed by over-all visual inspection (without the use of the motion analyser). In Table 2.1 the results of those observations are presented showing which type of entrainment occurred (differentiated towards two types; PA or i:P) and in what intensity (indicated by numbers between 0 and 5). Generally speaking two types of entrainment were observed which are named particle/lump-pick up (hereafter called PA) and piling/entrainment after piling (hereafter called EP). Examples of each of these types of entrainment are given in Figure 2.6 a and b.
Table 2.1: Observation of the films: Entrainment form plus the intensity of particle flux. (total number of films: 133) CE. Cement powder
D5 S: Durcal 65 D4 0: Durcal 40 D ,5: Durcal 15 DI 0: Durcal 10 D5: Durcal 5 Lateral measuring position Z [mm] 0 - 1 0 Bed material CE D65 D«) Dl5 D10 D5 CE D6 5 D40 Dl5 Dto D5 Numb r of films Nj Entrainment form: PA 10 3 3 6 4 4 4 5 4 4 0 0 EP 0 0 0
:
3 5 0 0 0 2 3 5 En 0 0 0 0 3 1 1 1 0 0 0 1 0 Num trainn 1 9 0 3 1 2 0 2 42
1 0 0 ler of him s NF ent intensity: 2 1 3 0 0 0 0 j 1 ] 1 2 0 3 0 0 0 0 1 2 0 0 1 1 0 1 4 0 0 0 3 0 3 0 0 0 2 1 3 5 0 0 0 0 0 0 0 0 0 0 1 1(continued on next page)
20 Table 2.1 (continued). - 2 0 - 3 0 Total Total CE D65 D4 0 D15 D,o D5 CE D6 5 D40 D,s D10 D5 CE D6 5 D40 Dis D10 D5 Z = 0 [mm] -10 -20 ■30 4 5 1 3 i 4 4 7 5 4 6 2 22 20 13 17 10 10 30 17 19 28 1 0 5 6 4 3 2 0 4 5 3 4 3 0 9 15 13 17 10 10 19 18 0 0 0 1 1 1 2 1 0 0 1 1 3 1 0 4 4 3 5 2 3 5 3 2 0 0 0 1 2 3 0 1 3 2 16 9 5 3 5 3 15 9 6 11 2 1 0 1 1 2 0 4 5 1 2 0 5 9 6 3 5 2 4 7 7 12 0 2 3 3 1 1 1 0 1 1 0 3 1 2 5 5 2 7 3 3 10 6 0 0 0 2 2 0 1 0 0 0 1 1 1 0 0 7 4 7 6 6 4 3 0 0 1 0 0 0 0 0 0 2 0 0 0 0 2 2 1 1 0 2 2 2
During the PA-entrainment type individual particles or lumps of particles (agglomerates of cohesive particles) are lifted from any position from the bed with a slight preference for pick-up near the particle bed leading edge. A sketch of the PA-type is given in Figure 2.7. Entrainment Into the flow occurs either directly or after an initial rolling stage. In the example given in Figure 2.6.a a phenomenon is shown that, though not occurring during all PA-motions is occasionally observed during both PA- and EP-motions and that is called breaking (BR). When an agglomerate of particles, lifted by the spot reaches a height of 0.3 to 0.4 mm, it breaks up into many particles or smaller lumps.
During EP-motion at first (after arrival of the turbulent spot) the particle bed leading edge is shifted downstream (see the sketch in Figure 2.8), at a velocity of about Q.05Uoo-While being shifted the bed height increases through piling of the particles. The bed keeps a more or less coherent shape until the top reaches a height of about 0.2 mm. From that moment on entrainment occurs from the top of the pile. An example of this type of motion is given in Figure 2.6.b.
Film 147 . U » - 6.9 m/s; Rex - 2.85 x 10s; Xs = 300 mm; XB L t = 616 mm; tSL t Bed material: cement ( p . = 3.2 g/cm3; Dp 5 c = 65 nm>
Figure 2.6.a (continued) Figure 2.6.a: Particle entrainmenl by the turbulent spot;
22
Figure 2.6.b (continued) Figure 2.6.b: Particle envramment by the turbulent spot
Figure'2.6.b (continued) 26
Y-■■\:i" <■*::■ ■•'• - ' . ^ W ' j *l * J
Film 130. Uoo = 7.19 m/s: «*X = 2-87 X^IO5; Xs = 300'mm; XB L I !
Bed material: Durcal 15 (pp = 2.75 g/cm'; D p 5 0 - « ( < " »
= 616mm:tSLE = 55 mm
Figure 2.6.Ö (continued)
flow direction particle 1: rolling particle 2: direct entrapment particle 1: lifted I ' o I particle 1: breaking
Figure 2.7: Schematkal PA-entrainmeni type.
flow direction
entramment from the top
Figure 2.8: Schematkal FP-entraiiiment type.
When looking at the films an estimation of the particle flux was made (a rough classification: 0 = no entramment; 1 = few isolated PA-motions; 2 = PA + slight EP-motion; 3 = EP-motion; 4 = EP- + PA-motions; 5 = extremely intense flux). After each filming procedure the powder strip was inspected from above and the entramment described (individual holes in the bed; leading edge removed; first half of the bed removed; complete bed disappeared). The correlation between this bed qualificaton and the film particle flux classification is remarkably good.
Looking at Table 2.1 the following characteristics may be observed. As the average particle size decreases a gradual shift from PA- to EP-motion occurs. In those cases where
28
the EP-type is observed the particle flux is much intenser than for the PA-type. The influence of the lateral position of the particle strip on entramment type or intensity is negligible.
From the films the time when for the first time movement on the bed is observed was measured relative to the spot arrival time. These results are given in Table 2.2.
Table 2.2: Average time interval At between spot arrival at the particle bed leading edge and first particle movement.
Lateral Bed At coordinate material [ms] 0 mm D1 5 25 Dio 19 D5 15 - 1 0 mm CE 10 D6S 14 D4 0 10 Dis 9 Dio 18 D5 18 Lateral Bed At coordinate material [ms] - 2 0 mm CE 15 D6 5 13 D40 13 D15 14 Dio 13 D5 13 - 3 0 mm CE 16 D « 12 D40 12 D1 5 14 Dio 15 D5 18
This table shows no significant influence of either average particle size or lateral strip position on first entrainment as observed by over-all inspection of the films.
A remark must be made on bed geometry. If the bed is flat (and made flush with its surroundings) there is anyway a preferred entrainment near the bed leading edge. During PA-motion particles are lifted from all over the bed, but the intensity is greater near the leading edge. With the EP-type it is one of its main characteristics. If the bed is flat but protruding from its environment (as was tested in a set of experiments during which the blowing time and thus the bed thickness was varied) entrainment always occurs mainly at the leading edge. And finally if the bed shows a roughness, being cither a grain (or a lump of grains) lying on the bed or a "hill" in the bed, first entrainment is observed from that roughness element while only later the other types of entrainment are observed. The above described observations are in accordance with the experiments by [Fletcher, 1976].
2.3.2 Classification of individual particle motions
On the motion analyser 387 particle tracks were determined ( 1 72 for 2 = 0 mm and 215 for Z = - 1 0 mmj. The tracks were classified according to a scheme shown in Figure 2.9. To this some remarks may be made. Particle tracks are nearly two-dimensional. The depth of focus was 1 - 2 mm while particles, observed on the film, showed a constant clarity over the entire field of view (AX = 8 mm) thus indicating a constant lateral coordinate (Z = constant). The lower limit for the particle size to be observed is determined by the film-type used (film grain-size) and the optical apparatus (the number of lines per mm, expressing the resolution of the lenses). Thus a lower limit of about 10 microns is reached.
SK: skimming DE: direct entrainment • - ■ — • - — #— —• —
P
RO: rolling RO-EC: rolling-entrainment after collision
Figure 2.9: Types of particle trajectories.
Although the classification scheme shows mainly single types of motion, of course a combination may occur (to mention some examples: rolling-direct entrainment, direct entrainment-breaking, or even entrainment after piling-rolling-entrainment after collision-breaking). Those combinations may be found in the category Alternative. The classification thus obtained is presented in Table 2.3. From this table (assuming that a representative choice was made for the particles considered) it may be observed that as the-average particle size decreases the main type of motion changes from DE to EP. A great contribution is made by rolling being either rolling through the entire field of view (RO) or rolling followed by another form of entrainment (RO-DE or RO-EC). Skimming (SK) is the rapid movement over the bed at low altitude, while fly-over (FO) particles have no meaning in the entrainment process (they are lifted in the test section upstream of the particle bed).
30
Table 2.3: A classification of particle trajectories.
(as expressed by the percentage of particle motions per size fraction)
Type of motion DE EP RO SK FO RO-DE/EC ALT Number of particles Z - 0 mm Bed material CE D65 D4 0 D15 Dio D5 Total 62 33 50 34 50 24 45 0 0 0 45 12 44 15 11 43 50 10 12 8 17 2 12 0 4 26 4 6 2 0 0 0 0 0 1 13 12 0 0 0 12 10 10 0 0 7 0 8 6 73 29 8 29 8 25 172 Z = 10 mm Bed material D6 5 D4 0 Du D1 0 Total 25 29 28 0 26 27 31 25 79 37 2 4 5 6 4 5 3 5 0 3 14 11 10 9 11 25 11 14 3 12 2 11 13 3 7 44 75 61 35 215
Although the number of particles considered is not very great next some average properties of the types will be presented.
2.3.3 Rolling and skimming
Rolling and skimming are two types of entrainment characterized by a motion close to the bed and occurring mainly for agglomerates of particles. A distinction between both types is made by the average streamwise velocity during both types (after a short acceleration stage lasting less than 5 ms a nearly constant velocity is reached at a constant height). For the dimensionless average vertical position and streamwise velocity, see Table 2.4.
Table 2.4: The average rolling/skimming trajectory.
Lateral coordinate Z [mm] 0 - 1 0 Scatter Rolling Y/Scx 103 U p / U ^ x 103 Nf t l l 20 50 23 20 42 19 +10 ±10 Uooiav = 7.3 m/s; 5p av - 5.65 mm Skimming Y/5ex 103 U p / U ^ x 103 NP a I t 25 180 12 27 126 9 +15 +50 31
2.3.4 Direct entrainment
In order to determine the average DE-trajectory those particles were selected from the films, plots and tables that showed a sufficiently regular DE-motion. At four downstream points (as measured relative to the starting point of entrainment X]/) the dimensionless average vertical position above the bed Yav, the streamwise velocity Uav and the trajectory angle ^p were determined, see Table 2.5 and Figure 2.10.
Table 2.5: The average DE-trajectory.
X a v = ( X - XE) / 5 g x 103;Yav = Y/6fi x 103;Uav = U p / U ^ x 1 03; ^p = arctan ( Vp/ Up)
z
[mm] 0 - 1 0 Scatter Xav = 100 Yav Uav c?p 50 90 12 54 109 16 ±10 ±15 ±2 Xav = 200 Yav Uav ^p 65 135 9 77 164 11 ±10 ±20 +2 Xav = 400 Yav Uav <Pp 85 190 4 106 229 10 ±15 ±13 ±2 Xav = 600 Yav Uav ^p 100 245 4 144 305 9 +10 +30 ±3Uav = 7 . 3 m/s; 5 e , „ = 5.65 m m ; Np„ , = 29 (for Z = 0 ) ; Np a I, = 38 (for Z = - 1 0 mm)
From the instantaneous velocities an estimation was made for the horizontal acceleration during entrainment. The particles stayed within the field of view (AX = 8 mm) for about 5 ms. The range covered by the horizontal accelerations is d(Up/U0 0)/dt = 2 0 - 2 5 0 1/s. ( d Up/ d t = 146-1825 m/s2) with an average of d(Up/Uoo)/dt = 85 1/s
(dUp/dt = 620 m / s2) . The striking fact discovered was that after a short period (1 - 2 ms)
a nearly constant horizontal acceleration was achieved that lasted until the particles left the field of view. Apparently, although the particles are rising in a highly sheared velocity field, this velocity gradient has no influence on the horizontal particle acceleration during the first part of the trajectory. The vertical accelerations when plotted against time, showed too much scatter to detect a trend.
32
(Y/6g) x 103
Figure 2.10: Vie average direct entrainment trajectory.
2.3.5 Entrainment after piling
To this type of motion a procedure similar to the one described in the preceding section was applied (a kind of conditional averaging). For 3 downstream positions (as measured relative to XL , YE , the position where the trajectory starts at an angle tp% ) the characteristics are presented m Table 2.6 and Figure 2.11.
Table 2.6: The average entrainment after piling trajectory.
Xav = ( X - XE, / §Cx 1 03; Y a v = ( Y - YE)/6fix 103: Uav = Vp}Uo0 x 1 03: ^p = arctan <Vp/Up )
z
[mm] YE ^ E 0 85 8 - 1 0 41 10 Scatter ±10 +3 Xav = 200 Yav Uav yïp110 200 7 70 172 8 +10 +25 +3 Xav = 400 Yav Uav ipp 130 250 4 96 246 6 + 15 ±40 ±2 Xav = 600 Yav Uav ^p 140 270 3 115 298 5 +22 ±60 ±2 I V a v = 7.3 m/s;5{_„= 5.65 m m ; Np a n = 22 (Z = 0 > ; Np„ , = 37 ( Z = - 1 0 mm) 33
Horizontal accelerations for the EP-type arc nearly equal to those for the DE-type (the range now is d Up/ d t = 1 4 6 - 1 4 6 0 m/s2 and an average value of d l ip/ d t = 730 m / s2) . Here also nearly constant horizontal accelerations occur over the entire field of view.
( Y / 6 £ ) x i o3 200 100 I l
' *
'
z
I I - 0 mmA - [
Z = - 1 0 mm i ( X - XL) / 5 v . x 1 03Figure 2.11: Vie average entrainment after piling trajecton'.
2,3.6 Breaking
As was already mentioned in Section 2.3.1 for airborne agglomerates of particles breaking may occur. For Z = — 10 mm average conditions during breaking were determined, see Table 2.7.
Table 2.7: Average conditions during breaking.
[mm] - 1 0 72 Scatter ±15 UOOJK = 7.3 m/s 10J .6s,av = Up.ta/U^x 103 117 +25 5.65 m m ; Np a r t = 26 Vp,b 20 +7 /U«,x 103 Dp (microns) 196 ±45 34
2.3.7 Entrainment starting time
For the particles a dimensionless starting time tS P L was determined. The idea behind this is: there is a certain time interval between spot arrival at a certain position X1 (t = il)
and the beginning of entrainment (t = tE ). During this interval At = tL - t , the wall shear
stress increases to a certain level within the spot at which particles are lifted. At may be a function ol" Z, the type of motion and the bed particle size fraction used. We have t, = ( X ' / XB L E) tSL E , w i t h
XBLL - longitudinal position of the particle bed leading edge.
tS L E = the arrival time of the spot at the bed leading edge las measured by the hot-wire anemometer) X' ~ XB L E + X i 82/1000 So we have At = tE XBLE + X I 6 £ / 1 0 0 0 At tL f Xjög and tSpE = - —
tSEJE ^LE VlOOOXttLE
with XBL E = 6 1 6 mm; tS L E = 53 ms (for Z = 0 mm); tStE = 55 ms (for Z = - 1 0 mm) and X, and tg from the particle trajectory tables. The results are presented in Figures 2.12, 2.13 and 2.14.
From these figures one may conclude that the entrainment starting time is hardly dependent on the lateral position of the powder strip. The times fall within the same range (mainly between tS P E = 0.23 and 0.78, corresponding to time-intervals between 12.4 and 42.1 ms) and show a maximum at At = 20 ms.
For the DE-type the peak in tSpE lies in the range 0.23—.45 (At = 1 2 - 2 4 ms) while for
RO and EP it is in the range 0.34-0.45 (At = 1 8 - 3 0 ms). This means that for the latter two types of motion entrainment starts about 6 ms later than for the DE. With the EP-type this time is needed to obtain a sufficiently high and rough hill from which entrainment may occur. With the RO-type usually larger agglomerates of particles are entrained so within the spot a larger wall shear stress must be achieved before motion will start, thus leading to a longer time than with the DE-type.
Figure 2.12: Tiie entrainm<
a ) : R o l l i n g
nt starting time distribution (for the total number of particles considered).
b): Direct Entrainment Np.RO Np.DE Np.EP r - , Z = 0 [mm] 44 68 23 1 - 1 Z = - 1 0 [mm] 34 56 72
c): Entrainment after Piling
rrrmsT
Figure 2.13: Tiie entrainment starting time distribution,
aj: for rolling particles: b}: for direct entrainment; cj: for entrainment after piling.
3 6
%
40 20 ; ) : D4C"
—|
1
-_J~
- i p p o p p o p S ts%
4 0 20 n s): 010—|
-p -p -p o -p 2 t p p p p p a SPE 1 Number of particles Np.,0,
&
CE D65 D40 D15 D10 D5s
z = 1 a co = - l O m r r I 1 33 56 38 33 ÏSPE 2 = 0 mm r — i 56 21 7 26 8 17Figure 2.14: Tiie entrainment starting time distribution,
a}: for Cement, b): for Durcal 65. c): for Durcal 40, dj: for Durcal 15. e): for Durcal 10. f): for Durcal 5.
2.4 Conclusions
The general picture one gets when observing the pick-up of particles from a flat strip by a turbulent spot is that there are two entrainment forms. When the particles are large (covering the range 3 0 - 3 0 0 u) the entrainment form is the one described as Direct Entrainment. Particles or agglomerates of particles are lifted by the aerodynamic forces and follow a nearly parabolic trajectory during which they are accelerated. For the smaller particles (the range 1—50 fim) which are strongly cohesive a much different entrainment form prevails which is called Entrainment after Piling. Here after an initial stage (lasting about 5 ms) during which the particle bed more or less as a whole is shifted downstream and being piled, entrainment occurs from the top of a 300 /jm thick hill. When the EP-form occurs the particle flux is considerably greater than for the DE-typc. The trajectory that the particles follow after being entrained from the pile is nearly equal to the one for the DE-type.
Horizontal accelerations are nearly constant (dUp/dt = 675 m/s2) over the entire field of view. Of course these accelerations will have to decrease after some time because else the particle velocities will exceed the undisturbed flow velocity after about 10 ms. But somehow during the first stage of their flight (the first 5 ms, when the particles stay within the zone Y = 0 - 0 . 7 5 mm) the horizontal force balance results in a constant acceleration.
Entrainment starts 12—20 ms after arrival of the spot leading edge and then continues during the entire spot passage. Over the lateral range considered within the experiments (Z - 0 - 3 0 mm) no influence of the lateral position of the powder strip was observed.
Except the mentioned difference in over-all entrainment form no influence of the average particle size could be determined. The spot apparently is a turbulent structure, whose intensity over a great part of its area is sufficient to lift all particle sizes within the range 1—300 fim.
A parameter of major influence on the entrainment process is the bed geometry (bed roughness). If on a flat bed a type of roughness occurs (being a thick bed leading edge or a grain/hill lying on the bed) entrainment will start from the roughness element. In fact the entire EP-entrainment form is based on a large-scale roughening of the particle bed.
38
3 TURBULENT SPOT STRUCTURE MEASUREMENTS
The purpose of these experiments is to gain information on spot growth, ensemble-averaged spot structure and Reynolds-stress distribution m the spot. The experimental set up and the results are reported in [Bosveld/van Haren, 1984], [Vonk, 1986] and [Martens, 1986],
3.1 Experimental set-up
The spot structure measurements were performed in the spot tunnel, a closed circuit low-speed wind tunnel, having a rectangular test-section 40 x 60 cm2 of length 2.7 m, see Figure 3.1.
Figure 3.1: The spot-tunnel.
In the test-section a 1.7 m long glass flat plate was mounted vertically, having a sharp leading edge, an adjustable trailing edge flap and leaving a height of 0.28 m on the working side. The airflow velocity during the experiments was 8.35 m/s (longitudinal turbulence intensity u ' / U » < 0.001, pressure gradient dCp/dX < 0.004 1/m) while heater elements could bring the tunnel temperature above ambient temperature (and keep it constant within an accuracy of +/— 0.1 °C).
At Xs = 295 mm there was a spot-generating equipment similar to that in the particle tunnel (see Paragraph 2.1). The wire thickness now used is 0.12 mm while the central gap
is 20 mm. The electric circuit was different. In rest position the wire was attached to the wall (wire voltage 2 V, current 0,5 A). A device could periodically interrupt the current for a pre-determined time-interval tu n l ( 0 , 5 - 2 s) during t, ( 7 - 3 5 ms) (see Figure 3.2) letting the wire vibrate in the flow before being pulled towards the wall again. At the same time a trigger signal (a 25 ms square wave) started the computer sampling (see
computer sampling trigger pulse
Figure 3.2' Spot-generating electric signal.
Paragraph 3.2). A value for ts was chosen by inspecting on the oscilloscope the quality of the spot velocity signal as measured by a hot-wire anemometer.
(ts too short produced only a sinus-wave disturbance, ts too long produced a series of spots)
The free stream velocity was measured using a Pitot-tube, the spot signal was rcgistrated using two hot-wire anemometers hereafter called the X-wire and the reference-wire. The reference-wire (5 ^m tungsten, length: 2 mm) was attached to the wall 4 cm behind the X-wire at Y = 7 mm, Z = 5 mm and was used for time-aligning of the spots (due to variation in arrival-time) in the computer data processing.
The X-wire probe consisted of two perpendicular 5 urn thick tungsten wires (each at an angle of 45° to the main flow direction), with a measuring length of 1 mm and a spanwise separation of 1 mm. The probe was inserted into the flow through a slot in the front wall and could be translated in X-, Y- and Z-direction (X = 0 . 7 - 1 . 2 5 m, Y = 0 - 2 8 mm, Z = 0 - 9 0 mm) and rotated in the X-Z-plane (for probe aligning) and X-Y-plane (for yaw calibration). The probe could measure the longitudinal U- and normal V-velocity to a closest distance 0.7 mm from the wall. The probe design is shown in Figure 3.3.
40
Figure 3 3: T/ie X-wire probe.
3.2 Probe calibration and data acquisition/processing (spot detection)
To the X-wires a velocity and a yaw calibration were applied. Velocities were calculated from the anemometer output voltages using a third-order polynomial function. Yaw-calibration was performed by placing the X-wire at 5 angles (0°; ± 1 2.5°; ± 25°) to the undisturbed flow and using 3 velocities ( U » = 2.8, 5,3 and 8.4 rn/s).
The three velocity signals (2 from the X-wire plus the Reference-wire) were sampled using a 1 2-bits A/D-convcrtor and processed by a DEC PDP 1 1/34 minicomputer. Sampling started at a variable time interval after the spot-generating trigger pulse. The data were stored on magnetic disk each channel at a sampling frequency of 5 kHz during about 200 ms (1152 samples, encompassing the entire spot plus part of its surrounding laminar flow).
For detection of the spot leading edge (hereafter called LE) and the spot trailing edge (hereafter called the TE) at a measuring station <X,Y,Z) a detection scheme analogous to that of [Wygnanski, 1976] was used. The signal of one of the X-wires, after substracting the laminar undisturbed velocity component (see Figure 3.4) was high-pass filtered at a cut-off frequency 500 Hz (Figure 3.4.b) obtaining a ?.ero signal outside the spot. Next squaring (Figure 3.4.c) and smoothing using an exponential filter (Figure 3.6.d) were applied.
Finally two spot detection criteria were used. At first a level criterium. Working from two sides (forward and backward in time) an approximate LE' and TE' were determined by satisfying the criterium U > k ! (Figure 3.5.a). Secondly going from LE' and TE' into the spot a gradient criterium was applied AU/At > k2 (Umax/Ls) (Figure 3.5.b) leading to the
a): original velocity signal a): level criterium
U
m
%
t
b): high-pass filtered D): gradient-cr terium
u
1
- /
i1 1
[lA
V
tJIL
Figure 3,5: The turbulent spot e detection criteria
Figure 3,4: The velocity signal processing.
42
final LE and TE. The choice of the cut-off frequencies, kj and k2 (k2 being 1 at the LE and 0.5 at the TE) was determined by comparison with visual detection of the spot on the video terminal.
As said in the Introduction the ensemble-averaged spot was to be measured. Therefore a number of spot-realisations was sampled on disk. An individual spot-realisation was rejected if its reference wire spot length crossed a certain minimum or maximum limit. Sampling continued until a preset number of realisations N passed the test (average rejection percentage < 10). Then after LE- and TE-detection two ensemble-averaged spots were determined by respectively aligning LE-s and TE-s. These were combined into a single ensemble-average at an average spotlength Ls a v using a weight-function (see Figure
3.6) favouring the LE-ensemble near the leading edge and the TE-ensemble near the trailing edge thereby retaining most of the spot-characteristics near its edges. By ensemble-averaging high-frequency information is lost. The number of spot realisations N within the ensemble average is then determined by how well the low-frequency part of the structure is represented. Two approaches were used: N = 60 plus a low-pass filtering (at a cut-off frequency 200 Hz) [Bosveld/van Haren, 1984] and N = 150 without filtering [Martens, 1 9 8 6 ] . The second approach shows more details of the ensemble-averaged structure but requires considerably longer measuring times, memory space and data processing time.
3.3 Measuring program
The instantaneous velocities may be decomposited as follows (analogous to [Antonia et al., 1981]), see Figure 3.7:
U = U L + <LJS > + u in streamwise direction
V = V L + < VS> + v , normal to the plate, where U L , VL : the laminar velocity components ( V L = 0 m/s)
< US> , < VS> : the ensemble-averaged velocity signals within the spot, relative to the laminar values
u, v: the fluctuations to the ensemble-averaged signals « u > = < v > = 0). The following quantities were measured during the experiments i): the ensemble-averaged spot velocity signal
< US> = « U - UL) > and < VS> = < ( V - VL) >
ii): the Reynolds stress - p < u v > distribution within the spot, with
< U V > =!< ( U - UL- < U5> ) ( V - VL- < VS» = < ( U - ULX V - VL) > - < US> < VS> The X-wire plus the Reference-wire (placed 4 cm behind the former) were placed at longitudinal positions X = 0.7, 0.85, 1.05 and 1.25 m. Vertical traverses were made at the lateral positions Z = 0, ±15, ±30, ±45, ±60, 75 and 90 mm. Each traverse contained about 15 Y-positions (between 0.7 and 25 mm). At each (X,Y,Z)-position <US>-, < VS> - and <uv>-distributions throughout the spot were measured using conditional sampling for
a): t h e L E - e n s e m b l e - a v e r a g e .. ( , . ( a l i g n i n g t h e l e a d i n g edges) b | : t h e T E - e n s e m b l e - a v e r a g e ( a l i g n i n g t h e t r a i l i n g edges) L _ _ L _ _ L _ _ 1 _ L - _ _ L — L _ _ J _ — L _ _ J L _ _ L J L I 1 L . J — — L _ _ l Ü 100 2D0 300 400 500 600 700 800 Q 1 DO 200 300 400 500 BOO 700 BOO 900 — > S a m p l e n u m b e r d ) : t h e TE-ensernble-average m u l t i p l i e d b y i h e c ) : t h e L E ensemble-average m u l t i p l i e d b y t h e T E - w e i g h t - f u n c t i o n ( b e i n g 0 a t t h e L E a n d L E - w e i g h t - f u n c t i o n ( b e i n g 1 at t h e L E a n d 0 at t h e T E ) 1 at t h e T E ) J _ 1 _ L-0 1L-0L-0 2L-0L-0 3L-0L-0 4L-0L-0 5L-0L-0 BOO 7DL-0 0 100 200 300 400 500 600 700 800 300 e)'. t h e f i n a l c o m p o s i t e d e n s e m b l e - a v e r a g e d s p o t w i t h l e n g t h Ls ( t h e a d d i t i o n o f c) a n d d ) 0 10D 200 300 400 500 600 700 BOO 900
Figure 3.6: The composited ensemble-averaged velocity signal.
44
X - 1 2 5 . 0 mm U Y" 0 . 7 0 mm U Z - 0. 0 r
1BD 200 220 240 260 2B0 300 320 340 360 — > T i m e Cms)
Figure 3. 7: Decomposition of the instantaneous velocity signal.
N = 60 spot-realisations. From the positions of LE and TE at the measuring positions the spot growth was determined.
Ai X = 1.25 m the spot was sampled for N = 1 50 in order to study the structure of the Reynolds stress within the spot, using a quadrant-hole analysis analogous to [Lu/Willmarth, 1972; Kunen, 1 9 8 4 ] . The quadrant-hole analysis sorts the instantaneous uv-signal into the four quadrants of the u-v-plane, depending on the sign of u and v (see Figure 3.8) and thereby reveals the relative importance of ejection- and sweep-type of motions that occur during the near-wall phenomena (see Chapter 1).
For the i-th sample point in the j-th spot realisation (where the index i is indicating the time-dependency) the instantaneous (UVJJ) is compared with a level;
if It K H u i V with u.'
then it is assigned to the hole, else it is sorted into one of the four quadrants. The fractional contribution of any of the quadrants is defined as the ratio
2 (uv^ hi 2 (uvy) with k = I, I ,111 or IV.
