Dear students, today we will be discussing about
fundamentals of solar concentrating collectors and analysis of parabolic trough collector.
Now, what is concentrating solar power technology? This concentrating solar
power technology utilizes focused sunlight. The concentrators increases the amount of
incident energy on the absorber surface as compared to that on the concentrator
aperture. And this CSP technology utilizes mirrors or lenses to concentrate Sun s energy
and convert it into high temperature heat.
So, the kind of collectors we were
discussing in the last classes, those collectors could be employed for generation of fluid temperature of about 100
or slightly more than 100 degree C. But if we have to generate high temperature, or we have to think
of application of high temperature application more than say 200, 300 or may be 400, so we need
to go for concentrating solar collectors.
So, how it will work? That is what, we have
explained here; and with the help of other slides, we will understand what is the importance of
this technology as far as high temperature application generation is concerned.
So, this concentrating solar power technology follows sun so that the beam radiation
are always focused on the absorber. So, as you can see here, a solar concentrator
generally consists of a reflector, there is a reflector or concentrator, we can say and this
is a receiver. So, solar radiation comes and strike on this reflector and it reflects to this
absorber. That is how it works and heat transfer fluid flow through this receiver and then that can
be collected in a collection unit and that can be applied or used as per the applications.
So, we need a focusing device, this is nothing but a focusing device, an absorber or
receiver. So, this is an absorber or receiver, so that may be with or without transparent
cover. Sometimes, so if we draw this tube through which heat transfer fluid flows, so this
may be steel or maybe copper, so material of construction is copper and just above it, will
have a glass transparent cover. This is glass, so this is glass, so that is why it is
said, with or without transparent cover.
And of course, we need a tracking device
for continuously following the sun. So, in case of flat plate collector, that kind of
systems are not required. So, that is installed in a location based on the phi value or latitude
value and that is fixed throughout the year. But in case of concentrating collector, we need to
rotate the device based on the solar radiation or to capture solar radiation
throughout the day.
So, there are some advantages of this kind
of technologies. So, first is, it is a better thermodynamic efficiency; because its operating
temperature is higher or range of temperature is higher. And less material requirement compared
to flat plate collector and reduced storage cost. So, these are the primary advantages of
these solar concentrating collectors.
And as we can say, or as we have said,
temperature as high as 3500 degree C have been achieved by using this kind of collectors.
So, these are high temperature collectors. These solar collectors are used for thermal
as well as PV conversion of solar energy. So, there are some drawbacks, like we cannot
employ diffused radiation for energy conversion, only beam radiations are applied in case of CSP.
And that is why, we need a clear sky or cloudless sky for installation of this kind of devices.
So, how this solar concentrator works if we have to see, this concentrating solar power system
generate electricity with heat, that we must know. This concentrating solar collectors use mirrors
and lenses to concentrate and focus sunlight onto a thermal receiver similar to a boiler
tube like conventional power plant.
The receiver absorbs and convert sunlight
into heat. The heat is then transported to steam generator or engine, where it is
converted to electricity. So, when we talk about solar PV system, so it converts sunlight
to electricity directly. But in case of solar concentrating collectors, we are utilizing
thermal energy to generate electricity. So, first we have to convert this solar energy to heat, then heat has to be converted to
electricity by using this generator.
So, CSP technology generate electricity
for a variety of applications, like ranging from remote power
systems as small as few kilowatt upto grid connected applications of
200 to 350 megawatt or more. A concentrating solar power system that produces
350 megawatt of electricity displaces the energy equivalent of 2.3 million barrels of oil,
so which is very-very advantageous.
And now let us pay more attention on
this thermo-mechanical system. How this heat energy is converted to electricity? So, as
we say thermo-mechanical system, which convert solar thermal energy to mechanical energy
through heat engine using Rankine cycle may be, maybe Stirling cycle, maybe Brayton cycle.
So, this mechanical energy produced may be used as shaft power such as water lifting.
And this mechanical energy produced may also be converted to electricity using generator.
So, what are the limitations of this conversion? This conversion efficiency is low. It
is about 9 to 18 percent. The efficiency of the collector system decreases as
the collection temperature increases, which is reverse in case of heat engine. The
efficiency of the heat engine increases as the working fluid temperature increases.
The solar collectors are generally more expensive than engine, and a part of
thermal energy is lost during the transportation of the working fluid from the collector to
the heat engine. That has to be considered. A very large area is required to
install the solar collector system. And due to intermittent nature of solar energy,
storage of thermal energy is also important.
Now, let us see this picture how this high
temperature heat which is generated in the receiver system. So, as we can see thermic
fluids are used in the tube through which heat exchange takes place. Solar radiation, so may
be this is the collector, so radiation falls here, beam radiation falls here and strikes in the
receiver system; so heat transfer fluid flows.
So, here this heat will be very-very high, if
we talk about parabolic trough, may be 350 to 400 degree C. It is a very high temperature, so
the thermic fluid will be heated up. And then that will move to thermal generator or maybe
heat exchanger, so that heat will be utilized, and then that heat will be used for heating
the secondary fluid. And then it will pass through the steam turbine. Because once that
fluid what is used in this Rankine cycle will be expanded in the turbine, and that mechanical energy can be converted to
electrical energy by using this generator.
So, of course, heat rejection will be there from
the turbine. So, this will work in a closed loop. So, this heat transfer fluid or
say the fluid what is used in this cycle may be different from the fluid
what is used in this concentrator cycle. So, this is how from thermal collectors to
the electricity generation takes place.
Now, let us learn some of the parameters
which characterizes solar concentrators, like aperture area. So, if we talk about
this tube and this is the reflector part, so this area is nothing but aperture area. The
area through which solar radiation is incident, is nothing but aperture area. And this absorber
area is something like that, it is a very long tube if we talk about parabolic trough.
The total area of the absorber surface that receives the concentrated radiation, it is also
the area from where useful energy can be obtained. And then acceptance angle, which is
represented by 2 theta s, which defines the angular limit to which the incident ray may
deviate from the normal to the aperture plane and still reach the absorber or receiver. So,
this is the aperture angle, what you can see here. So, this is sun and this is
the receiver, earth surface.
And also, we need to know what is intercept
factor, which is defined as the ratio of energy intercepted by the absorber
of a given width to the total energy redirected by the focusing device. So, the amount
of radiation which is striking onto this absorber. So, some of the radiations may not be striking
here, so it may goes off or maybe it is coming in that way and then it might not be striking
this absorber. So, that is why, this factor need to be considered. Of course, we are looking for
unity, but always you will not get this unity.
And also, we need to know what is optical
efficiency. So, this optical efficiency defines the energy absorbed by the absorber to
the energy incident on the concentrators aperture. It includes the effect of mirror or lens surface, shape and reflection transmission losses, tracking
accuracy, shading, receiver cover transmittance, absorptance of the absorber and solar beam
incident or solar beam incidence effects.
So, let us define concentration ratio.
So, how we can define concentration ratio? Concentration ratio is the ratio of aperture area
to the absorber area. So, as I am writing this again and again, so this is an aperture area, so
maybe A I can write and this is the absorber area, so this Aa by Ap is nothing but C which is
concentration ratio. The local concentration ratio can also be defined which is the ratio of solar
radiation at any point on the absorber surface to the incident radiation at the
aperture of the solar concentrator.
So, we can see the definition of C here. And this
is very important point like a concentrator with large acceptance angle, needs
only seasonal adjustment; while a concentrator with small acceptance angle
is required to track the sun continuously. So, this is very very important, so sometimes we need
to design the concentrator in such a way that it has to operate continuously and sometimes
intermittent adjustment is also fine. So, this defines acceptance angle is
important for deciding this adjustment.
Now, let us see the radiative exchange between
the sun and the receiver. So, if we consider a black body, sun is always considered
as a black body having temperature Ts and the radiation from the sun on the aperture or
receiver is the fraction of the radiation emitted by the sun which is intercepted by the aperture,
which can be represented by this expression Q s to r is equal to Aa r square by capital
R square sigma Ts to the power of 4.
So, sigma is known to us, it is Stefan s
Boltzmann s constant and a perfect receiver such as black body radiates energy equal to Ar Tr
to the power 4. This is the receiver temperature and the function of this reaches the sun, and the
fraction of this reaches the sun. So, this can be expressed by using this expression.
Now, if I am interested for estimation of maximum concentration ratio, then
we need to do something. Like when Tr and Ts are the same or fixed values of this Tr and Ts,
the second law of thermodynamics requires that heat transfer from source to the receiver or sun
to the receiver should be equal to receiver to the sun. So, if we use this expression, then
what we will get, this kind of expression.
Now, since the maximum value of E r to s is unity,
the maximum concentration ratio for circular concentrator is found to be 1 by sin square
theta s, this is for circular concentrator. So, geometry of the concentrator may be different,
so this is for circular concentrator. And for linear concentrators, the maximum concentration
ratio is found to be 1 by sin of theta s.
So, if we know this theta s
which is equal to 0.257 degree, the maximum possible concentration ratio for
circular concentrator is calculated to be about 46000 and for linear concentrator,
it is found to be about 215.
Now, let us pay attention about the different
configurations of concentrating collectors. As you can see these are tubes and one reflector
is placed at the bottom of the tubes. And this is one more configurations,
which is nothing but tubular absorber with specular cups reflectors. So,
this kind of configurations are there to increase the concentration ratio.
So, normally what happen in case of flat plate collector will have concentration ratio
is equal to 1. So, if we can increase the concentration ratio, so we can increase the
operating temperature of the collector. So, these are different attempts. And this is a
compound configuration, so where we can have more radiation exposure and then we can get
slightly higher concentration ratio.
And this configuration is, for say, parabolic
trough. So, receiver is here, this is a reflector, so these rays are focused on this axis,
because this is a long tube not a point. And this configuration is for Fresnel reflectors
and this configuration is for arrays of heliostats with central receiver system.
So, we will learn details with time.
So, as we understand for point focus system,
this concentration ratio can be defined as 1 by sin square theta and for line focus
system, this is 1 by sin theta. So, if we know this theta value, then we can
straight away calculate what will be the maximum concentration ratio for a point focus
system and for a line focus system.
And as I said, so these are the attempts
to increase the concentration ratios, though this first three, the maximum
concentration ratio can be achieved is 4. And the other configurations, of
course, concentration ratios are quite high. The actual value of this concentration ratio, C is
much lower since the acceptance angle is usually greater than 0.267 degree. This
includes tracking errors, imperfections in the reflecting or refracting components of
the concentrator, mechanical misalignments, et cetera. So, these are the causes of
reduction of this actual concentration ratio.
And this slide shows the collector type based
on concentration ratio. So, as we can see this planar and non-concentrating type, which
provides concentration ratios of upto 4 and are of flat plate type. So, if you see
this figure, this vertical axis shows concentration ratio and horizontal axis shows
receiver temperature. So, these are the lower limits and this is the band. Normally, this is
the band at which the concentration ratio falls, when temperature increases.
And the ranges of operation, or ranges of concentration ratios are shown. So, this is for
paraboloid, you can see the range of operation, of course that can be adjusted by using
different means. And for conical configurations, we can see this is the range and for cylindrical,
this is the range. So, for line focus system, we can have concentration ratio up to 10 and for
point focus system, it is very-very high.
So, this slide shows about the comparison of flat
plate collector and concentrating collector. As already we are aware that this flat plate
collectors are normally used for low temperature applications. So, maximum may be 100, 110
degree C. For this kind of configurations, for concentrator, it may go up to 3500
degree C, starting from 260 degree C.
And here, in case of flat plate collectors,
what primary advantage is, we can employ both normal and diffuse radiation,
but in case of concentrator, only normal radiations are applied
for energy conversion. So, diffuse radiation cannot be employed.
Or even though diffused radiation falls on these devices, contribution of these
radiations are very-very less.
And here no tracking is required but in case
of concentrating collectors, tracking is must. And because of this, mechanically, it is
unstable and then it requires maintenance, but in case of flat plate collector,
maintenance is very-very less.
So, let us classify the concentrating collectors,
there are different modes of classification. So, based on the aperture type, it s a reflecting type utilizing Fresnel
lens or refracting type utilizing mirrors. So, if we have to use mirrors then refracting
surface may be parabolic, spherical or flat; that may be continuous or segmented.
And classification based on image formation, may be non-imaging system or non-imaging type
or maybe imaging type. So, under imaging type, again we have two classes; like line
focusing type or point focusing type. And based on operating temperatures, may
be low temperature, medium temperature and high temperature.
And then fourth category of classification is based on tracking
system. So, single tracking system or two axis or double tracking system. Sometimes
we need double tracking system to track the sun in order to capture more beam radiation.
Now, let us see different CSP technologies what is available. So, first
technology is parabolic trough, then dish stirling, central power receiver system,
then Fresnel collector. So, what we can see here, so this is a concentrator, this part is
concentrator and this is receiver system. So, solar radiations falls here and is reflected to
this focal axis. So, reflector, then absorber tube, then this is solar field piping.
So, here as we can see, this is an absorber tube, then over it, this is
a glass cover. So, this is maintained vacuum, so this is vacuum, in order to reduce
the heat losses. So, in case of dish stirling system, so reflector is something
like this and it will focus on this system. So, engine is placed, normally stirling engines are
attached here. It is a external combustion engine, so heat is supplied here and then expansion
of fluid will be there and from that, electricity can be generated directly.
And this is central power receiver system. So, here lot of heliostats are there, so these
are heliostats, mirrors. Solar radiation falls and it is reflected to this receiver system. So,
normally molten salt and oils are used so that may be collected and later on, will have powerhouse
here. So, this heat exchange will be there to the secondary fluid of this Rankine cycle
and then from that if we have generator, we can generate electricity. This is solar
tower and Fresnel collectors are something like, these are segmented pieces of mirrors, solar
radiation falls here and strike on this absorber tube and then heated fluid
can be taken out for applications.
And we can compare those technologies
with different aspects like for parabolic trough collectors whether
possibility of storage systems are there or not, or what are the other advantages, we can
list it out. So, if we talk about possibility of integration of storage system, it is yes, it
is possible and advantages includes relatively low installation cost and large experimental feedback
is there in case of parabolic trough collector.
And disadvantages are relatively large area
occupied, low thermodynamic efficiency due to low temperature. So, since this temperature
difference is low, because of that, will have lower thermodynamic efficiency. And in case of
linear Fresnel reflectors, storage is possible and advantage is relatively low installation
cost and disadvantages include low thermodynamic efficiency due to low operating
temperature, which is primary.
For solar power tower, it is highly
desirable, that kind of storage system because that has to be stored. Huge amount of
heat is generated and that has to be stored for night use or maybe when demand is very-very
high. And its thermodynamic efficiency is high as the operating temperatures are
high, but it requires large space area and relatively high installation
cost and high heat losses are taking place for this kind of technologies.
And in case of parabolic dish, it is difficult to install storage system. Advantages are relatively
small area occupied and high thermodynamic efficiency, but disadvantages are relatively
high installation cost and little experimental feedback. So, this slide shows about the
comparison of four different CSP technologies.
Now, let us pay attention about thermal
analysis of concentrating collectors. So, under steady state condition, the energy
balance on the absorber plate can be written as something like this. So, this qu is the useful
heat gain and Aa is the effective area of the aperture of the concentrator and S is the
solar beam radiation per unit effective aperture area absorbed in the absorber and ql
is the rate of heat loss from the absorber.
So, if we write ql, that is, rate of heat loss in
terms of overall loss coefficient, so we can use this expression. So, ql is Ul Ap Tpm minus Ta.
So, Tpm is average temperature of the absorber surface and Ul is overall loss coefficient.
So, if we use it here, qu is Ap into S minus Ul then Ap Tpm minus Ta. And if
we ,so this is Aa, so if we take out Aa S minus Ul Ap by Aa Tpm minus Ta.
So, we can define concentration ratio now. Already we know what is concentration ratio,
the aperture area to the absorber area. So, this will be 1 by C. So, qu
will be Aa S minus Ul by C Tpm minus Ta. So, this is l, so this will be useful
heat gain. So, that is how we can write this expression, Ap multiplied by S minus Ul by C Tpm
minus Ta and C is the concentration ratio.
And this slide shows the efficiency versus
receiver temperature. So, this is the system efficiency and this is the receiver temperature
at different concentration ratios. So, these are different concentration ratios. So, it goes
maximum and then it come back to 0. So, it shows the variation of efficiency
with respect to receiver temperature at different concentration ratios.
So, for flat plate collector concentration ratio is 1, for parabolic trough it is about 80, for
solar tower it is 500, parabolic dish about 2000. So, this overall efficiency of a CSP plant can be
expressed something like this, eta system is eta collector multiplied by eta Carnot. So, if we know
the Carnot efficiency and collector efficiency then straight way, we can calculate what will
be the system efficiency of the plant.
So, with increasing temperature, this collector
efficiencies decreases but Carnot efficiencies increases, so that is how we can get
higher system efficiency if Carnot efficiency is significantly higher.
And this slide shows the applications of CSP in commercial scale and domestic level. So,
for commercial scale, the CSP can be applied for power generation in stand alone mode or maybe
grid connected system or maybe hybrid system or maybe to meet the demand of thermal requirement;
hot water and steam generation, air conditioning, absorption chillers, desalination
of seawater by evaporation.
Solar chemistry, manufacture of metals
and semiconductors, hydrogen production may be water splitting or material testing under
extreme conditions like, design of materials for shuttle reentry. Or as far as domestic
applications are concerned, it may be applied for hot water generation or maybe HVAC or
air conditioning system and solar steam cooking, solar oven or cookers, then solar food drying.
And also, we can compare these technologies with different parameters. So, like relative cost,
then land occupancy, thermodynamic efficiency, operating temperature, solar concentration
ratio and then improvement potential. So, as far as parabolic trough is concerned, it is a
relatively low cost but large land is required.
But thermodynamic efficiency is lower and
operating temperature ranges from 20 to 400 degrees C and concentration ratio varies from
15 to 45 and improvement potential is limited. So, for solar power technology or solar power tower,
so it is a very high cost and occupancy is medium, so not much land area is required. Thermodynamic
efficiency is higher and operating temperature is also higher, concentration ratio we can see,
it varies from 150 to 1500 and improvement potential is very-very significant.
In case of linear Fresnel reflector, it is a relatively low cost and land occupancy
is medium, thermodynamic efficiency is low, operating temperature may go up to 300 degrees
C and concentration ratio varies from 10 to 40 and there are a lot of scope for
improvement. And parabolic dish collector, so it is a very high cost, land requirement is
small, thermodynamic efficiency is high because operating temperatures are high and you can see
the operating temperature 120 to 1500 degree C and concentration ratio varies up to 1000 and it
has got a lot of potential for improvement.
So, now let us pay attention about the analysis
of parabolic trough collector. So, let us consider this configuration. So, we will have solar field,
then you have absorber tube and then reflector. So, if we take a section, so it appears
like this, so this is concentrator and this is the receiver system. So,
when we call receiver system, it includes absorber tube plus this glass cover, which is
placed concentrically and vacuum is maintained in between this.
So, if we consider a section, so this is the tube through which heat transfer
fluid flows and if we take the length of the tube, this is the length of the tube and start from is
x is equal to 0, maybe x equal to 0 here and it moves something like this and take a section dx,
so fluid is flowing from this tube, so maybe at this point, fluid temperature is Tf and at this
point, this fluid temperature is Tf plus dTf.
So, we will assume some parameters or some of
the information like radiation flux is same along the length. So, it is assumed that this
radiation flux which is falling in the absorber is same. Of course there will be some differences
in actual case but what we will consider is same. And temperature drop across the absorber
tube and the glass cover are neglected. So, this is absorber tube, this is a glass cover, so
temperature drop is neglected, it will be same.
So, this aperture of the concentrator is W
which is represented here and length is L is the length of the tube is L, so this length or we
can say this is the length, so this length is L. So, I can write this way also, this length will
be L along the length, so length of this tube and rim angle is phi r and it should be here,
so rim angle is phi r, so this is the phi r.
And this absorber inner diameter is Di and
outer diameter is Do and concentric glass cover, inner diameter is Dci so here so thickness will
be here. So, it has got some thickness and outer diameter is Dco. And the fluid is heated from
inlet temperature Tfi here, at this point is Tfi, Tfi, it is Tfo so outlet temperature is Tfo. And
let m be the mass flow rate, mass flow rate of the fluid that is flowing through the tube.
And if we are interested about concentration ratio of this configuration, so it will be something
like this, effective aperture area to the absorber tube area. So, this effective aperture area
is something like W minus this D, D naught, D naught is the outer diameter of the tube
multiplied by L it is the length to the pi D L, so D naught is the diameter of this
tube. So, that way if this L is common in numerator and denominator, this will goes off
then, W minus D naught divided by Pi D naught is the expression for concentration ratio.
So, if we know aperture of the concentrator and then outer diameter of the absorber then we
can straightaway calculate what will be the concentration ratio of that configuration. Now,
let us draw an energy balance or write an energy balance expression on the absorber plate.
So, this energy balance on an elementary slice of the absorber tube at the distance x from the
inlet. So, this gives a relationship of something like this. So, qu is the useful heat gain which
is equal to Ib into rb W minus D naught rho gamma tau alpha is for beam radiation, because
beam radiation is only employed.
So, this part is the direct radiation
which is falling on the absorber tube and this part is for losses. So, this component
is coming from the reflector, so from here, from this reflector solar radiation is
falling here, it will go, this will go. So, first component is contribution from this
reflected radiations, second component is, since it is exposed to the sun, so it will
directly fall on this absorber. And this is the losses. So, Ul it take cares of this conduction
and convection losses from the absorber tube.
So, this Ib is the beam radiation and tilt this rb
is the, that component which has to be multiplied, because all the radiations are not coming, so some
losses will be there. Then this is a reflectivity of the reflector and this is the gamma, which
has to be multiplied because all the radiations are not coming and striking on the absorber. And
these values are already defined and these are the losses. And Tp is the absorber plate temperature
or absorber tube temperature, this is the ambient temperature and is the dx or is the slice.
So, absorber solar flux we can write something like this. So, using this equation,
in equation A then this equation simplifies to something like this. And also heat gain rate, we
know hf multiplied by pi Di Tp minus Tfi dx which is nothing but mCp dt because mass is flowing.
So, m is the mass flow rate, Cp specific heat of the thermic fluid and we know the temperature
difference Tfi and Tfo. From that we can calculate what is the rate of heat transfer is mCp dt.
So, now combining this equation C and D what will have, useful heat gain in that particular
section will be something like this. So, F dash is the collector efficiency factor, which can be
expressed something like this. And if we combine this equation E and F, then we will have this
kind of equation. And we need to integrate this using the initial conditions, at x is equal to
0, Tf is equal to Tfi, which is already shown.
So, once you do it then we will get temperature
distribution of something like this. So, fluid temperature is obtained by putting
Tf is equal to Tfi and x is equal to x naught, so this should be Tfo. So, if x is equal to L,
the Tf will be Tfo. So, if we substitute this, then we can have this kind of configuration.
So, now we can calculate what is the useful heat gain rate. So, this useful heat gain rate can
be calculated and it is found to be something like this. And also we can define collector
heat removal factor, which is expressed by this expression. So, once you know this, then
we can calculate what will be the instantaneous efficiency of the collector. So,
this instantaneous efficiency is expressed something like qu by Ib
into rb plus Id into rd W into L.
So, this is the diffuse radiation component which
is coming from the ground. Sometimes this may be neglected. If we neglect
this term, then this equation for instantaneous collector efficiency simplifies
to this equation. So, if we know qu and Ib into rb multiplied by W into L, then straight
away we can calculate what will be the instantaneous collector efficiency. So, rb
already we know for beam radiation, what is the rb that is the cos theta by cos of theta z.
So, there is a long expression for all the angles. So, this can be calculated and Ib is known and
see here, no diffused components are present. Only beam radiations are included. So, this analysis
will be very much important to characterize a parabolic trough. So, we must know the
procedure, how this can be characterized.
So, now next phase is how to calculate the heat
transfer coefficient. So, once we know those values, instantaneous efficiency value, Fr value,
F dash values and then useful heat gain, then we need to know the heat transfer coefficient.
How this heat actions is taking place from the collector to the absorber, then absorber
tube to the glass tubes and then fluid? So, all the things we need to calculate.
So, this overall heat transfer coefficient and heat transfer correlations need to be understand.
So, this is the ql heat losses, we can express ql in terms of Ul as well and also we can use
this expression for calculation of heat loss. And then heat transfer coefficient between
the absorber tube and the cover can be estimated by using this expression. This Ra is
the modified Reynolds number, which is defined something like this. Once you know this, then
finally what we can calculate, the heat transfer coefficient from the plate to the cover.
And then next phase is to calculate heat transfer coefficient on the outside surface
of the cover. So, the correlations proposed by Hilpert s are normally used. So, it is expressed
Nusselt number is equal to C1 multiplied by Reynolds number to the power of n. So, there are
different conditions, for Reynolds number value between 40 to 4000, this C1 to be
used as 0.615 and n will be 0.466.
And for a value of Reynolds number between
4000 to 40000, C1 to be used as 0.174 and n is equal to 0.618. And for this, so if Reynolds
number is very-very high, which is more than 40000 and less than 400000, then we need
to use this set of data for calculation of heat transfer coefficient on the
outside surface of the cover.
Also we can use some alternate
correlations developed by Churchili and Bernstein. So, this correlation is valid
up to a Reynolds number of 10 to the power of 7 and if this Reynolds number
is in between 20000 to 400000, then we can go for this correlation. So, there
is slight change in this value, so this is the difference, so here it will be 1 by 2 of this
section and but here it is 5 by 8 and then 4 by 5 whole to the power this bracket section.
So, once you know this Reynolds number and Prandtl number is known at that temperature,
and then we can calculate what is heat transfer coefficient. Because Nusselt number is h, L or
d now it will be L, h d by k or sometimes it is d also. So, h L or h d by k. so, once we notice
k, L or d then we can calculate what is h, or heat transfer coefficient.
So, this heat transfer coefficient on the inside surface of the absorber
tube if I am interested to know, then we need to go for this kind of correlation.
Nusselt number is equal to 3.66, for the flow having Reynolds number less than
2000. So, if the flow is turbulent having Reynolds number more than 2000, then
we need to use the correlations developed by Dittus-Boelter, which is something like
this. Nusselt number is equal to 0.023 multiplied by Reynolds number to the power of
0.8 and Prandtl number to the power of 0.4.
So, we can calculate the heat transfer coefficient on the inside surface of the absorber tube
by using these correlations. But while using this correlation, we must pay attention about
this assumption. Just flow is fully developed, that assumption has to be done and it is valid
as L by di is larger than 20. So, under that condition we can use flow is fully developed
and we can have this kind of expression.
And Hong and Bergles developed a correlation
which is expressed something like this. So, apart from Reynolds number and Prandtl number,
one term is there which is X, is X is nothing but tape twist ratio. So, sometimes what happens,
heat transfer in a flow can be augmented by using some kind of twisted tapes. So, if
this kind of tapes are introduced in that flow tube then heat transfer
coefficient enhances.
So, in order to define this twisted tape or
this kind of configuration, we need to define this twist ratio. So, this is nothing but H by
Di, so H is nothing but length over which the tape is twisted through 180 degree, so this
is something like twisting. So, once it is twisted and it is introduced in that flow tube,
then it is investigated that heat transfer is augmented or heat transfer can be enhanced by
applying twisted tape in a flow process.
Also once we done with this
heat transfer coefficient, researchers are interested to know the pressure
drop. How much pressure drop is taking place? So, there are many correlations to investigate this
pressure drop. One of the correlations which is applied here in concentrating collectors
are proposed by Date and Singham which is expressed something like this. f multiplied by
Reynolds number is equal to 38.4 Reynolds number divided by X to the power of 0.05.
So, this value should be in between this range and also this friction factor multiplied by
Reynolds number can be expressed something like this, if this value is more than 100. So, this C
can be calculated by using this expression. So, X is known to us from here and then if we
apply here and we will get C2, once we know C2 and Reynolds number is known to us, then we
can calculate f which is friction factor. So, once we know friction factor, we can calculate
the pressure drop. So, this is 4 f L v square by twice g. So, that way we can
calculate the pressure drop.
So, let us summarize what we have
discussed today. Primarily we have discussed the fundamentals of concentrating
collectors and also the classifications, which are made based on reflecting type utilizing
mirrors, refracting type utilizing Fresnel lenses, imaging technologies, it may be point
focus system or maybe line focus system.
So, if we are talking about point focus system, it is a high concentration ratio and its operating
temperature is very-very high. And in case of line focus system, even though concentration ratio
is compatibly higher, but it cannot achieve as normally done in case of point focus system.
And there is also one basis of classifying its concentration ratio, which is nothing but
the operating temperatures as you can see. So, as the operating temperature increases,
this concentration ratio also increases.
And tracking also one of the classifications,
what kind of tracking normally adopted, maybe single axis tracking, may be double axes is
tracking. So, based on the requirement that can be decided. And also we have learned
the energy balance on an absorber plate of a concentrating collectors. So,
this qu can be expressed something like Ap multiplied by S minus Ul by C multiplied by Tpm
minus Ta, where Ul is the overall loss coefficient and Aa is the aperture area, C
is the concentration ratio.
So, if we know mean absorber plate temperature
or tube temperature, an ambient and solar flux, we can calculate what will be the useful heat
gain. Also we have learned the analysis of parabolic trough collectors and heat transfer
coefficient. How this can be calculated heat transfer coefficient can be calculated and how
this can be applied for calculation of useful heat gain? Because as you know qu is S into Aa minus
ql. So, in order to calculate this ql, we need to learn this heat transfer coefficient.
So, once we know this heat transfer coefficient of different system from where to where the heat
transfer is taking place, so once you know this, we can substitute in this equation then we can
calculate what will be the useful heat gain. So, I hope you have enjoyed this video.
Thank you very much for watching.
