Fixed Bed Regenerator Analysis
Welcome to this lecture, in this lecture we’re going to talk about the fixed bed type regenerator analysis and in the last class we have talked about the different type of regenerators and in that one we have talked about the bulk type or the fixed bed regenerator and we also talked about the rotary type regenerator. In this lecture we are going to talk about the analysis of the fixed bit tighter generator and in that context we just want to look into the actual system had this kind of regional wrestling news and it will be easier for us to analyse it if we look into the action or the operation of this particular type of exchanges so far that we have taken an example of a crowd cheering application particularly it is called the Pulse tube refrigerator Valley find clean world mtq is periodicallyand on the other side we have another cord and exchange of this is according to exchange it and this is periodically this is periodically pressurized and depressurized with the gaseous helium now if we look into this operation even find that there is a small ball and this valve we call it as a rotary valve so this rotary file periodically sends high pressure gas into the system or after one cycle it will connect it to the suction side of the compressor in one cycle it corrects it with the discharge site on the high pressure side in one cycle in the alternative cycle it will connect it to the section of the discharge inside section of the low pressure side of the compressor so alternatively it connects it to the high-pressure and low-pressure and between the past you on the antique you and this compressor we have one regenerators this is the regenerated disease of fixed-base type and we find that diesel generator is basically what it is doing is it is trying to connect using will the high pressure gas is coming from this sent to this side this will allow the gas to pass through this if it is in this configuration for the gas will be high pressure gas will be coming from the site and it will pass through this tree generator and then it will come to this all sleep so now 152 what’s happening this high pressure gas is coming to this side and this is at say the hot th temperature and on the other side when it is knowing the steady-state operations we will find that this is the cold side and this is also at the course I’m still here we had the refrigeration require refrigeration kci in the in this cycle so what’s happening the high-pressure gas is coming and flowing through the regenerator so this gas is at high temperature and by the time it is coming over here it is passing to 2601 passing through this regenerated matrix it will be heated up this metrics will be heated up and the gas in turn will cool down to TC and at the end of this cycle what we will find thatso the gas is that you say you’re slightly listen to see and this guy is going back to the suction side of the compressor where this originated when it is passing through the region writer it will become the heat it has left earlier in the area cycle to this originated be so now you can understand that in one cycle the hot gas is coming generally this gas is helium gas is helium and the specialised gaseous William will be passing in the one cycle through this configuration and in the other cycle when it is getting discharged today so no pressure helium and our expanded helium will flow through this erratic and you know in this configuration it will pass through this one and go to this one so this is how it works in both the PSI helium is the gas which is passing through this originalno pressure helium expanded helium pump to see it will move to 58 in the ideal condition so this is what is the configuration of a fixed but originator of the principle of working in the Pulse to refrigerator operation this is the basic pasta configuration with this basic knowledge of the refrigerator if we move to the next term in its analysis part we understand that in one cycle gaseous helium or the heart which stream is snowing now from one direction to the other direction and in the other side of the Coldstream is flowing from the sale to the lizard from x equals 2 l to XY cornstarch the same as it can understand that this extreme and cold springs are automatically flowing through this direction and the direction is riversdale is coming counter-current in nature that means in one cycle air flowing from the heart strain is flowing from the straight decide to decide in the next cycle Coldstream is flowing from design to decide so the configuration is basically of counter-current in a chat if you look in detail about this element barium between x sin x DX basically it is one dimensional model and this is x equals to zero we have a sheet of 12th in between we have taken some bonding between x and x + 8 we find that into this and it is it is moving with velocity 2x and it isit is given by v and there is no traction so now if we look again into this part we find that we have some amount of heat transferred from the fluid to the solid part so if it is heart rate we find that the heart rate is giving key to the solid particles and this is the amount of heat transfer which is the a transfer coefficient c is the temperature of the fridge stream tsn 1050 on the solid particles are the metrics temperature and we have considered that for the length l we have some area associated with it is a and in the length TX we have a y l into DX area associated with this into a pile into DX is the area and this is the temperature difference that’s the amount of heat that will be transferred on the heart rate to the solid particles now what will happen because of this changing of the oven as the heart rate is giving usapartment happen because of this change and I’ll be honoured as the hot word is getting that to this solid particles it’s temperature there any of that is a change in the entirety of the gas and entering as the gas is flowing through it is giving hit her to the solid particles and what we guess which is dead inside I’m in some part will be in other energy will be stored in this in this fraction that is we find that this is the amount of energy that will be stored within this one didn't the gaseous follow what is the gas that find x in the city of that 1:30 is the gaseous epicthe role of the gas and fee of the cash so that is the fight of volume x the actual total volume of that system so we’ll come to that part 2 how to evaluate the parts and so now we can understand that we’re in this element we will have this much amount of gas associated with it and that’s how the energy will be stored within the volume and with this I mean I mean knowledge this is the energy balance inside the element of disguise light and energy balance I would be able to$20 into DX then the spot is also moving out so it is 18 to 3 – 2 years and then we have a bye yell into DX and that’s exactly what is it is getting scolded so it is aiming to CP and this is guilty by Delta that is equals to the time with you this time this is the energy that has been stalled in this element so that’s x DX and that’s exactly the energy balance for the fluid strictthis is for the energy balance I mean I should have just stayed in the previous signed that that was the energy balance we have you written know if we could do the solid part we find that the solid is receiving some amount of heat from the heart rate and that’s given by this amount so this is basically ancient 2T – tse by yelling 2DX that’s what we have learnt that the straits time is giving this amount of fake to the solid when solid is receiving some amount of weight what happens to the solid temperature it’s temperature is going to rise so if we say that whenwhat happens to the Salem police said that the salad is having a temperature as we know that guilty will it will be the temperature rise and look into the energy associated with that is Delta spirit as I told you and x in celsius so if the mass of this element is a mess and cs is a mass associated with it then we have DX you know the elementary length associated with it then we can write it in a week with this this time and this time and we can find the energy balance equation for the solid and that case we will have if we write both the equations we find the governing equations for the sweet distribute returning them and together we find something like this so this is particularly the amount of heat that has we have talked about the hot plate in the cold cycle I mean when the Coldstream is flowing through the regenerated so this is the amount of heat either receptor-binding given by the hot plate or the receptor by the corporate soap and this is the amount of the stored energy in it and this is the change in the enthalpy so that’s what is for the great now if you look into the for the solid part we have this is the equation written for the solid part and saw this two equations are the governing equations and when we write any differential equation particularly involving the time and space we have to use some kind of boundary conditions or the initial conditions to solve the situation service of the boundary conditions as the awakened in the other accufrate entry condition as I have written it as part of the government'sarticles that you know exactly and it is like turning up at temperature t h we have said that that intersect y h the other end is acting so the other conditions for the cold and flu strength when it is going in the other direction so this is act now it should be now I’m in a situation bxl or I mean if we considered for this direction also in if we change it to a 6-2 decision because well so for this Valentine LBC we have a temperature it is in trading yet to see the initial of the steady-state condition is basically what we mean is that what is the temperature of this bike how it is behaving the temperature of these metrics basically we wanted to calculate so here we have forany distance x is equals to that is same as what it was there in the previous cycle and the same location so I mean if the grass was flowing and the say say it was entering a ph by the end of this sitel so it will leave the bed at a particular temperature so banking’s what is the initial condition for the other fluid like when the corn field strength is moving to this one so that finds that the bed is at that particular temperature at different locations so that is what is the initial steady-state condition for the course with similarly when the cold fluid is flowing in this direction at the end of the cycle it will lead the regenerator date or the Matrix at a particular temperature teachers so that temperature profile that fluid the horse float when it has to come in the next cycle it will find that the bed finally applied those boundary conditions and if we try to solve this one I will suggest up on the ribs are the screws do if someone is interested about this one they can look into the academic ranking every generating heat exchanger book on timing for the detailed analysis of this but if we look at this solution of the ideal regenerator we find that that I’m in at the beginning of April at the end of this month or the cold fluid or the matrix is aiming to be the temperature and the distance I’m in relation to here we have the temperature of the day reduce the temperature on on this site we have the dimension less distance the longitudinal distancetemperature of the gas called gastric to the regenerative and by the time the end of the cycle it will be coming to this temperature and this is the Matrix temperature of this is be there at the end of the cycle this would be the temperature of the Matrix so far on the other way or the other and we find that the Coldstream initially at rest in a flowing from the sound at the beginning of the cycle it is like this and as time passes by the end of the cycle it will be coming to this condition where is the metrics will be in this area so this is what is happening in the original writer and this is a possible balanced conditions and ideal regenerative action that we don’t have any actual production losses and etc we have not considered but if someone is something that the equation and with the boundary condition applied as we have said no one can solve and get this kind of the army temperature profiles in the fluid as well as in the Matrix of the electric oven in the region 8 going into that details of calculating the temperature profile of the Matrix temperature profile in this election but then we’ll be interested not interested to design of simulate a particular type of fajitas originate for applications or any other applications that our job is basically 242 simulator under the particular application as to try to design a generator so we will look into the analysis said the suggestion given by the researcherslet us look into the design part sephora counterflow original test which is very common in in case of academic applications define the 10-q and it is given as the one by CBC me again now we have already learnt about this seeming that is the monster x x the appropriate term in appropriate specific cake and I won’t be back to we have the hot plate and the pulse rate of this is one bite hhhh and this is a set it to the heat transfer coefficient of the hot side and this is a fitted with the oven at associated with the hot side and in general if it is a fixed but most of the time this a h and ac are of the same area and here they say now is the heat transfer coefficient associated with the cold floor so this isn't this result 2000 - 1 so this is how we define the n2 for this counter current regenerator. So with this basic definition we will continue in the next lecture about the design or the simulation of regenerators. Thank you for your attention.
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