well hello everybody so we continue with our
ah discussions on the introduction on the
multiphase flow so i had already discussed
in my last lecture i had already discussed
the typical flow patterns which occur when
gas and liquid flows through a circular pipe
or through any particular semantics which
can be rectangular pipe more or less the same
flow patterns or a square pipe also the same
flow patterns as should seen now suppose instead
of air water i introduce may be an oil it
can be kerosene it can be towline it cane
be anything i introduce another oil do we
expect the same flow patterns to exist see
one thing is for sure gravity in this case
also will be trying to pull the lighter phase
towards the top heavier phase towards the
bottom right
so therefore at low flow rates we have the
satisfied smooth then as we increase the phase
velocity we have stratified waving now if
you remember in my last slide for did i get
sorry in my last slide from here if i an i
increased the phase fluorides we found that
the there was some points where the waviness
of the interface was so much that it was touching
the upper wall as a result of which plugs
were formed and it resembled the slug flow
pattern observed in vertical tubes although
it was an asymmetric slug now in this particular
case if you find we find that due to the highest
extension of the liquid it cannot assume the
shape of the elongated plugs as we observed
in gas liquid cases on the contrary when the
waviness is very much then it shreds the interface
and
therefore there is a large amount of droplet
of both the phases entrained at the interface
between a continuously kerosene phase and
continuous water phase this happens this did
not happen for horizontal air water flows
but in this case it happens because the liquid
tend to remain spherical and they cannot sustain
or they are not stable at an elongated shape
so therefore after stratified wavy instead
of slat flow we get a three layer flow pattern
and as we increase the velocity we find that
one phase gets disposed into the other now
here i have got a very important point to
tell while we were discussing gas liquid flows
repeatedly i had been telling you that well
when there is less gas large amount of liquid
we have bubbly when we have large gas less
amount of liquid we do not have droplet we
have annular why because the liquid phase
can wet the pipe wall the gas phase cannot
wet the pipe wall but when we are having two
liquids either of them can wet the pipe wall
it depends up on the hydrophobisity or the
hydrophilisity of the pipe like which phase
have a greater tendency to wet the pipe wall
but you must remember that either if them
can wet the pipe wall
so therefore just like we can have all droplets
in water we can also have water droplets in
oil therefore in a vertical pipe what do you
find a a pipe say of one inch diameter or
twenty five millimeters diameter then the
oil is in a smaller proportion compared to
water we have oil droplets dispersed in water
as we increase the oil velocity the oil tends
to take the several irregular shape but if
the pipe diameter is not very narrow it never
assumes the access symmetric bullet shape
which we observe for case of taylor bubbles
of fear they take some irregular shape and
finally increase the oil velocity of more
and more a time comes when the oil becomes
the continuous phase and water gets dispersed
in it now this the unique phenomena which
occurs for liquid liquid cases it does not
occur for any other phase flow situation and
this particular phenomena of the continuous
phase getting inverted to the dispersed phase
and vice versa this is known as phase inversion
so during phase inversion we find that one
phase it tends to become continuous from dispersed
and the other phase tends to get this from
continuous and this unique phenomena of phase
inversion since it is concerned or rather
since it is associated with the making and
breaking of large number of inter phases it
is usually associated with the large amount
of pressure drop and the high degree of turbulence
or mixer well this was for adiabatic condition
now suppose we go for a heated tube where
may be a single component say a liquid is
being introduced and heat is being supplied
from the walls and as it flows up change of
phase occurs now what happens in this particular
case the tube is heated maybe say sub cooled
water is coming in
so initially we have single phase liquid in
this particular case then as the liquid starts
getting heated bubbles start forming bubbles
will start at some nucleation at the wall
moment the bubbles start forming it will remain
attached for the wall for a very short time
and then it starts getting detached and it
rises due to as well as due to flow of the
liquid so therefore we get something like
the bubbly flow pattern now again as the this
particularly heated liquid or this particular
two phase mixture starts flowing up we find
that more and more bubbles are formed as more
and more bubbles are formed they get they
come very close they start collision moment
they start collision naturally the vapor bubbles
they will assume their stable shape which
is nothing but the access symmetric bullet
shapes sort of a thing or the taylor bubble
sort of a thing
so therefore this slug flow sets in and then
from slug flow as more and more amount of
liquid gets vaporized so large number of taylor
bubbles form so naturally they quails with
one another and when they quails they form
a continuous gas core and naturally they push
the liquid to the side it forms a annular
flow pattern if heat is continued and the
tube is long enough what happens the there
is annular flow the liquid film which is being
heated and the vapor core in the center region
now this liquid film it keeps on getting depleted
due to two reasons the first one is because
of vaporization some amount of liquid film
gets vaporized into the vapor phase and secondly
due to inter facial share which increases
as more and more amount of vapor is formed
as the vapor velocity increases
so therefore this inter facial share also
increases and it and the liquid from the film
gets sheered as droplets here possibly then
after that in a heated tube we get the droplet
flow pattern which we did not get for cases
and finally when all the liquid has vaporized
we get single phase vapor form
so therefore what we find when we are dealing
with the heated tube then we find that there
is departure from thermodynamic equilibrium
also there is a radial temperature profile
now due to these two reasons we find that
the flow pattern it changes inside the tube
which did not happen adiabatic case if all
the input parameters were kept constant
firstly the other things which we find is
that in this particular case if you observe
the flow patterns there are two new things
one is joint flow which was very prevalent
when we were discussing your vertical air
water flows is not present here the other
thing is droplet flow comes into picture
now this was the case of a vertical heated
pipe if simply make the pipe horizontal keeping
everything else constant and introduce water
here the factors which were there for a vertical
pipe namely radial temperature profile departure
from thermodynamic equilibrium will persists
along with that asymmetry due to the gravitational
affects sets in and the situation tends to
get much more complex with the possibility
of intermittent drying and re wetting of the
upper surface of the tube so in this way if
we keep on proceeding we find that more and
more complex phenomena or more and more interesting
phenomena i should say sets in as we deal
with other combinations of two phase flow
situation
so therefore from this you have understood
that what are the basic difficulties of analyzing
two phase flow the basic difficulties are
two number one the two phases can distribute
themselves in a number of ways as you can
see that depends as i have already discussed
it depends up on the condue geometry the condue
inclination the direction of flow phase physical
properties and so on and so forth and this
is not under the control of the experimenter
or the designer along with that what do you
find that difinitely the with the interaction
of the two phases changing the interfacial
shred changes and we have to remember the
most important thing that the two phases have
different densities as a result the lighter
phase tends to slip past the heavier phase
due to this if you have introduced the two
phases at a known composition the same composition
does not take place when the two phases are
flowing inside the pipe due to the existence
of the slip or in other words if we are talking
about air water mixture the inset to void
fraction will not be equal to the inlet fraction
of the two fluid or rather of the two fluids
so therefore what does it imply the first
thing that it implied is that the two phases
suppose for the time being we assume them
to air and water
so these two phases we find that while they
are flowing they have one particular void
fraction say alpha inside the tube how do
we define this alpha this is the say the proportion
of the gas phase or rather the volume occupied
by the gas phase divided by the total volume
of the pipe ok and this will not be equal
to the inlet volume fraction which we define
as beta so this is the inset to void fraction
and this is the inlet void fraction or the
inlet composition this will depend upon the
inlet flow dates if we denote q with the flow
rate then this is going to be q g by q total
which is nothing but where q total is equal
to q l plus q g right now due to [cough] this
several problems arise what are the problems
suppose we would like to analyze this two
phase flow situation the analysis will be
just the same as the single phase flow of
a of any particular fluid through a pipe
now if we go for a single phase flow say let
us develop the momentum equation i will be
not be going into the details of this suppose
we are having may be say we consider delta
z portion or delta z length of the pipe of
cross sectional area a and here we find and
may be the wetted perimeter as s so in this
particular case the pressure is going to or
the pressure force is p a and in this particular
case we find that the pressure force is p
del p del z into delta z into a right and
here we find that the gravity is acting and
there is a component in this particular direction
so if this is row g the component of gravity
will be row g sign theta and since flow is
occurring in this particular direction there
will be inter facial share so if we consider
these the forces which are acting on this
particular feed element namely the pressure
force the body force and the wall force which
is given by the wall share is given by tow
w and if we equate it with the rate of change
of momentum then what do we get we get a pressure
drop relationships i leave it as a home assignment
to perform this particular balance and then
finally arrive at an expression to find out
the pressure gradient this expression is tow
w the s by a plus say row g pipe inclined
then have a sign theta component where theta
is the angle where horizontal plus this gives
you d d z of u into say g so g is the or rather
i will put is as w by a where g is the mass
flask which is equal to the mass flow rate
divided by area in other words w by a in my
set of
so this was for single phase flow now suppose
instead of single fluid say for example two
fluids are flowing here so what do we find
for this particular case what are the things
let there be any sort of distribution here
so what happens is this two fluids no matter
in whatever they are mixed they will be interacting
with the wall so therefore this is going to
become thou w two phase some sort of interaction
with all and instead of single density its
going to be a mixture density and this u is
going to be mixture rather mixture velocity
right if the two phases are completely mixed
then this equation is fine we have a g t p
here as well and if they are they are separate
then in that case the equation what it should
become they should be thou w one s one by
a plus thou w two s two by a plus row t p
g sign theta plus d d z of say one fluid is
g one one fluid is denoted by one the other
is two we get something of this kind
now when we try to evaluate the pressure of
using either of them what do we find first
thing we do not know is row t p on what does
row t p depends it depends upon the incite
void fraction mind it it depends upon the
incite and not on the inlet void fraction
inlet void fraction is a known fraction but
incite void fraction we do not know and row
t p it is a function it can be expressed as
if alpha is the void fraction and say for
a gas liquid system my phase two is gas phase
one is liquid then what do i get row t p should
be equal to alpha row two plus one minus alpha
row one so for finding out the gravitational
pressure drop you need to know alpha and alpha
is no way related in a straight forward fashion
with theta this is the first problem we face
what is the next problem we face how is thou
w t p related or how can it be evaluated can
be defined something like two phase friction
factor then in that case how is this two phase
friction factor related with a single phase
friction factor which we have so this is also
very much not known to us the other thing
is if you are defining u t p say so this u
it is function of say mass flow rate density
and area right so therefore sorry the for
single phase flow it is related in this particular
way if we are having two phases two phases
having different velocity and they are in
no way related to the velocity that the inlet
say one fluid has the velocity u one other
has the velocity u two so therefore what is
u two it is w two the mass flow rate it is
definitely measurable row two by a two where
a two is nothing but it can be written down
as a into alpha the void fraction so therefore
in order to find out how your u two is varying
with length you need to find out you need
to know alpha so therefore we find if alpha
cannot be determined from input parameter
which it cannot do it acts to the additional
complexity of two phase flow
just the way i was discussing till now so
therefore if you can write it in this particular
way we find that row has to be dis written
down or it has to be substituted with row
t p here of course i have defined as row m
the mixture velocity you can do whatever you
wish and we find that it is essential to have
an estimation of void fraction as i have already
said there is no obvious relationship between
wall shear in single and two phase flows we
also find that s it includes s one the wetted
perimeter for phase one s two the wetted perimeter
for phase two and apart from s one s two there
is also an inter facial inter facial area
where the two phases interact right
so therefore we find even for finding out
the simple pressure drop also it becomes difficult
why number one the two phase can distribute
in a large number of ways and unless we know
the distribution we cannot find out thou w
one thou w two we cannot find out s one s
two and again depending upon the distribution
the void fraction is going to be decided and
unless we know the void fraction we cannot
find row t p or row m so therefore this suggests
why the two phase flow becomes much more difficult
as compared to single phase flows the reasons
primarily being there is an existence of multiple
deformable and moving interfaces there is
multi scale physics of the flow phenomena
there is this significant discontinuities
of the fluid properties and complicated flow
field near the interface you can very well
understand that near the interface you suddenly
shift from liquid properties to the gas properties
in addition when we have one phase that is
the gas phase for example for gas liquid flows
vapor liquid flows or gas solid flows the
compulcibility of the gas phase also comes
into picture and definitely there can be different
wall interactions for the different fluids
so therefore we find that when there is one
phase present and we just introduce the second
phase the situation becomes much more complex
because the two phases interact not only with
the wall but also among themselves accordingly
they distribute in a wide variety of ways
and since the two phases have different density
the lighter phase tends to slip past the heavier
phase as a result of which the incitive void
fraction is different from the inlet composition
inlet composition we can manipulate but incitive
composition we there is no straight forward
way of finding out the incitive composition
again this incitive composition depends upon
the distribution definitely if you have some
or a if you have devised some particular way
of finding alpha in bubbly flow you cannot
use the same relation you cannot use the same
relation to find alpha for annular flow or
if you have some particular relationship to
find alpha for gas liquid fluid bubbly flow
there is no guarantee that the same relationship
can be applied for oil and water disposed
flow
so therefore with these things i i thing we
have got clearly good introduction of multi
phase flow but before i start i would just
like to show you i would just like to discuss
in very brief the terms which we will be coming
across frequently my reason for discussing
these terms are see you have come across these
terms but may be not the same nomenclature
if all of us use the same nomenclature or
in other words suppose if i have a unified
nomenclature then at every point i dont need
to define those things for example as far
as i am concerned for me the mass flow rate
will be denoted with w and now let me clarify
one this at this point you are free to use
any other nomenclature but in that case you
have to define your nomenclature normally
as chemical engineers or mechanical engineers
we define mass flow rate as m dot but for
this class i prefer to keep it as w volume
flow rate as q there is one particular term
we do not come across much when we are discussing
single phase flows but will be coming across
wide frequently into phase flows that is the
mass flux just like heat flux mass flux it
is the mass flow rate per unit area pipe diameter
d cross sectional area a wetted perimeter
s these are all fine de equip corresponding
terms in two phase flow are naturally we have
got two phases
so there are two ws and a total w we have
two qs and a total q we have two mass fluxes
and definitely a total mass flux also along
with the cross sectional area we need to know
the area occupied by phase one and phase two
we need to know the wetted perimeter which
is rather the perimeter which is off the valve
which is contact with phase one s one which
is in contact with phase two s two and of
course there is an inter facial area as well
as a consequence what do we find we find that
there are four velocity terms instead of two
because u one u two they are the local or
the incite velocity
so therefore incite velocity of phase two
and this is the incite velocity of phase one
so by definition u two should be equal to
q two by a two this should be q one by a one
now what now what are this a one a two they
are the cross sectional areas occupied by
phase two cross sectional areas occupied by
phase one so naturally this is this can be
defined in this particular way this can be
defined in where alpha is the void fraction
or fraction of phase two so therefore along
with these two just because we refer to velocity
of the fluids very frequently so therefore
what we will prefer to do will also prefer
to define two the other velocities which are
known as the superficial velocity where this
is the velocity which the fluid will have
if it were flowing alone in the pipe
so therefore these are measurable parameters
they are just your volumetric flow rates divided
by the cross sectional area because they define
the velocities which would have if they were
flowing alone in the pipes so therefore these
are inputs while u one and u two are outputs
so therefore just as i have mentioned the
additional terms are definitely incitive void
fraction the inlet volume fractions and the
other important thing which i forgot to tell
you is the quality which is the weight fraction
of these two in the flowing mixture this x
varies in a heated tube and it is a constant
for an adiabatic condition
right now before i end i would also like to
specify one particular thing that by convention
might lighter phase or the dispersed phase
i denote it as phase two and all the properties
including void fraction inlet volume fraction
quality we define with respect to this phase
that means for an air water flow my air is
phase two and water is phase one for kerosene
water flow may be if kerosene is in a smaller
proportion or it is the discontinuous phase
kerosene will be phase two and water will
be phase one and most of the properties we
define in terms of phase two right
so therefore with i complete my particular
introduction of multi phase flow and in the
next lecture i will be discussing the ah rather
these uniqueness or the specialties its not
the uniqueness exactly the specialties of
two phase flow through miniaturized systems
thank you very much
