 Welcome to today's lecture, this is continuation of application and selection of accumulators. Now various means are adopted to drive the fluid from accumulators to the main system. Therefore, type of accumulators according to how they are driven to the main system these are as follows weight loaded accumulators this has unique advantage that it can maintain the constant pressure spring loaded accumulators that obviously the force reduces when the compressive spring expands. So, therefore, there will be change in pressure variation of pressure gas charge accumulators which are commonly used. In fact, weight loaded accumulators may be the best in that point, but for high pressure you have to use huge amount of load and the construction of such an accumulator is difficult. And it is found that spring loaded although this can be used, but gas loaded it based because of the reason in some cases you can regulate the gas pressure from the outside although it is not normally done. Gas charge accumulators are again mainly three types the most common you will find the bladder type what it is if we study this figure then we will find that outside this is the main casing of the accumulator. So, this you can consider this is a steel pressure vessel and inside that there will be a bladder which is usually charged by gases nitrogen is very common. However, one can use the ordinary air also. Now, if we look into the other details then what we find that this is a closure cap this is just to protect the main cap which is you can say valve cap or the total valve system. If you remove the closure cap then we will have a valve cap and if you remove that one then there is a valve it is basically non written valve. And we can insert the gas and then this is you can say this is the valve body this is fittings of the valve on the steel vessel. Then there is a rating plate which is by tightening which we can make it leak proof with gasket of course, gasket is there here is also a gasket and then. So, this is for charging the gas inside. Now, if we look into the bottom side then there we will find pressure fluid valve. So, there is another valve which the oil is allowed to the main system and then this is a vane screw it is if there is some bleeding is necessary bleeding is necessary then it is done through this. Then this is a slotted round nut to fix this one and there are many other small components to make this fittings leak proof to from the accumulator. And this symbol of this accumulator whether it is bladder or other type is usually given by a single symbol like this. Now, next one is the diaphragm type in case of earlier one the bladder is filled with gases with pressure. So, when the oil is required from this accumulator then bladder expands gradually which is having the oil was having the same pressure as the pressure inside the bladder. In this case instead of that bladder we have a diaphragm this diaphragm is fitted to this body. Now, the gas pressure is gas is put or inserted in the upper portion and lower portion is filled with oil. Now, this diaphragm is commonly will be harder than this bladder. So, this is usually for small volume displacement but higher pressure. Now, this is again some this closure button and this there is a plug screw etcetera. So, what will happen when this oil excess oil is being pumped in to this accumulator then this will contract a little bit and this volume will also contract. And then when again this oil is required by the main system this will expand and this oil will be pushed in to the main system. Definitely pressure will vary that means here inside the gradually the pressure of this oil will reduce pressure of this gas as well as this pressure of this oil will reduce when it is being injected to the systems. But it is obviously the lowest pressure here will be equal to or higher than the pressure required by the system. And the third one is the piston type. In this case we can imagine a cylinder finished inside bore is finished to accommodate a piston. This piston is having no rod then oil is being injected from this side and the gas is being gas is charged from the other side. So, this works in the same fashion but here also this work for very high pressure. But the displacement of the oil may not be very high or can be made high if we make this piston longer. But we have to keep in mind this gas when it is expanding then gradually the pressure is decreasing. So, it is not may not be very worthy to make it very large one. But this as well can be made very small and it can be fitted wherever required in the system. Next if you recapitulate our knowledge that the accumulator is used usually there will be a pump of low pressure sorry low flow q 1 low flow and the excess volume if it is required for the short period it is supplied by the accumulator. So, if you look into this figure the q 1 is the pump flow maximum pump flow rate wherever system may require the flow up to q 2 for a time period t 1 then t 1 to t 2 is the volume required is v 3 and then t 2 t 3 is volume required is v 2 and then t 3 to t 4 this volume requirement is 0 this is the cycle. Now in that case pump when this pump is running then for this period oil is being injected from the accumulator to the system in this point if this is a fixed displacement pump then this oil excess oil is going to the accumulator and here again from accumulator to system and in this case full volume is going into the accumulator. And after the accumulator is completely filled in the oil in case of fixed displacement pump system oil goes to tank via the pressure relief valve. Now here one relation we must remember that v 1 plus v 2 must be less than equal to v 3 plus v 4 that is otherwise if the excess oil is required by the systems we cannot supply it accumulators movement flow and pressure pulsation or ripple. So, this also we have already studied a system without an accumulator even having the pulse like this and if you put an accumulator then this pulse is reduced it is may not be possible to eliminate the pulsation completely. Now again for if you look into the applications then this also used for the transfer transfer means say for example this is a test vessel this is being tested by water. So, what we can do inside bladder we can put the water and this also we can filled into water side that is usually oil hydraulic oil and then by a reciprocating pump or actuator you can say it is of equal rod both the side. What we can do we can generate a pulsating load here which is transferred through this accumulator to this vessel and then this vessel is tested for fatigue load. Now if you look into the gas pre-charge pressure in general purpose applications pre-charge pressure is usually equal to pre-charge pressure is P 0 is equal to is usually 0.9 into P 1 also the volume of the vessel if we can estimate what is the maximum requirement from the accumulator then the accumulator inside volume is usually point sorry the gas charge we do 0.9 percent of the total volume and that means 0.9 that percent or sorry 90 percent will be the volume required we make it and if the volume of the accumulator is 100 percent in that way. And the limit values are P 0 is minimum is 0.25 that is 25 percent of the maximum pressure whereas P 0 maximum is equal to greater than equal to 0.9 of minimum system pressure. Now method and application it is important to establish if the gas during operation is subjected to isothermal or adiabatic condition. So that we have to look into this isothermal process as you know that if the process is occurring very quickly then we can go for isothermal or otherwise it will be the adiabatic or isentropic conditions and then we have to calculate accordingly. Now as well the operating temperature is important type of liquid is also important maximum required flow rate that we have to look into the location where we should put that accumulator this type of depending on the type of liquid we can select what should be the bladder material usually the outside body is still. If it is not corroded with the still this main oil if this main oil is cannot be used with the still then we can think of other material but inside gas and oil or whatever is flowing the main medium of the system looking into that we select these materials. Then compression and expansion of gas inside accumulator takes place according to the boils priority law with regards to the status change in the perfect gas. This means we considering the isentropic change the pressure volume relation is expressed as P0 V0 equal to P1 V1 is equal to P2 V2 that V0 V1 and V2 these are the volumes of the bladder. Now N is the this power N power is equal to 1 in case of isothermal in case of adiabatic usually it is 1.4 or something like that in between that we can select according to the time taken we can select this will I am coming to that later. Now here this I have already explained but still V1 is the nitrogen volume at pressure we have assumed this gas is nitrogen. So, P1 is the pressure minimum system pressure V2 is the nitrogen volume at pressure P2 is the maximum pressure system pressure V0 is the volume at pressure or stored liquid P0 is the pressure at pressure P1 is the minimum operating pressure P2 the maximum operating pressure etcetera. And this is polytropic exponent N is the polytropic exponent. Now if we look into this normal this very ideal then PV diagram is usually as follows for a gas and you can we can see this is the maximum pressure it is like that over the range and P was in the working pressure and P0 is the minimum gas charge pressure and this is the volume stored volume being used for for the system. This is the used volume for the system that means when the pressure P2 then volume minimum volume and then V1 is the minimum pressure that is the maximum volume and this is the charged volume. Now obviously if this is 1 N is equal to 1 this is a straight line, but this is ideally it would follow this curve whatever may be this this value we can have the curve is of this nature. The curve of volume variation as a function of pressure is dependent on exponent N that is I have explained which for nitrogen is content between the limit limiting values of N is equal to 1 in case of compression or expansion or nitrogen takes or so slowly that a complete interchange of heat is allowed between the gas gas and environment that is at constant temperature. So, this is for the slow process. Now, this condition is we call it isothermal sorry this perhaps I told that very quick process is isothermal it is not that we have to this interchange time is required and N maximum is equal to 1.4 when operation is so quick that no interchange of heat can take place the condition is adiabatic. So, if there is a very quick change then this condition is adiabatic and, but when it is a relatively slow process then we can call it is isothermal. However, these are theoretical and not practical condition then it is possible to state with reasonable accuracy that when an accumulator is used as a volume compensator leakage compensator or as a lubrication compensator and the pressure compensator the condition is isothermal. Whereas, if in the remaining application such as energy accumulator pulsating damper emergency power source dynamic pressure compensator water hammer absorber shock absorber hydraulic spring etcetera it is possible to state that the reasonable accuracy with reasonable accuracy that the condition is adiabatic that that means there is the very quick process is going on. Now, should a more accurate calculation be needed it is possible to use intermediate values of N that is exponent as a function of T that is of expansion or compression time according to diagram N figure figure 5 say for example, if time taken more than 10 minutes this is again I I think with respect to the nitrogen and hydraulic oil then if more than 10 minutes then we can call this is isothermal and we can take this value is 1. And if this time is 0 to 10 minutes then depending on the time required for that process we can select that N obviously that may this curve may be different for different gases we are using in the system. But if it is very quick process only then we call it adiabatic and we take this value is 1.4 this means if usually in the classroom type problem or examination problem we mean it is adiabatic then you have to take 1.4 otherwise sometimes it is given this curve will be given to you and this time will be mentioned and from there you can select what will be the power of N. In all calculation pressures are expressed as absolute bar and temperature as Kelvin degree that we have to remember. Now this is for the selection while we are selecting a and accumulator. So, this curve is usually supplied by the accumulator manufacturer say for example if we consider that V volume 1 by volume 2 is 2.20 litre 2.20 litre then we can have this curve and then this is the actual volume of the accumulator that means if we measure the vessel volume it is 10 litre capacity. But actually available is 2.20 we are working within this range obviously it may be slightly more may be available from this system. And then for different this is the for different pressure curve and this is 1, 2, 3. So, this is 50 and pressure is P 1 to P 3 that means we are working may be from 70 to this is 140 say let us assume this is 1.20 litre capacity is 150 say 140 70 to 140 we are working that means within this pressure range and within this flow range these are the applicable area. Our calculation all estimation will be within this region and here average volume of pressure of fluid in litre. So, we can estimate how much volume will be available for working we will just consider a pressure range and from there we will get it and here this is also available volume on same scale and both the side it is given. So, in that way we can use this graph now this is again this is for bladder type accumulator and this is for diaphragm type accumulator. This lines are from diaphragm type accumulator and these lines are for bladder type accumulator. And here it is on the curves are on N is equal to 1.4 and there are some other say tolerances are given. So, if you would like to select what should be the say suppose our using volume is a 2.2 litre we can maybe we are tempted to go for a 4 litre accumulator, but in that case we may not have that good pressure range that you can study this graph separately to understand this. Now these are a few systems are shown. So, application of accumulator and accumulator storage that means how the volume is being stored in accumulator for different process that is given over a chart here. Let us consider a system this system is like this that there is three we can consider two linear pistons and one rotary pump is there and this is being run by the same system. So, we put the accumulator over here. So, it is like that this non-return line is there because from the accumulator oil should never come to the pump side that is why it is there. And then oil from here can directly go to the system it is we do not need any other valve there because whenever the excess oil is there first this will be filled then when it is completely filled then this oil go through this relief valve. Now what we find these operations this is cylinder A this is cylinder B and this is pump C and both are having a flow control valve. This means that maybe this system is required we need motion of this forward and backward or return motion both are with control speed that is why control flow control valves are there and this is by operated by a this is completely closed center 4 by 3 directional valve. And in this case what we find this is this is also 4 by 3, but it is not closed center it is only partially open center partially open center means in normal conditions neutral conditions oil goes back to tank. And in neutral position the pump is closed center that means this pump is always ready with pressure if it is in all are in neutral. Now what we do cylinder A we are extending means this is going out then definitely valve we will put accordingly that means with this side will come here to operate this one. Then volume required is 1.96 litre this you see we have used this flow control valve and this is the requirement and it is required is in one second. So, one second means this process is 1.4 polynomial adiabatic process almost. So, we will consider that and then say this is this guideline is given to how to select this accumulator looking for the volume into this that chart. Then supply from pump is 1.46 that is Q 1 if you remember that this is 1.46 litre only at that conditions supply from accumulator is 0.5. So, volume left in accumulator is 0.50 litre and then supply into the accumulator is 0 and then at that conditions that means to have 1.96 1.46 from the pump and 0.5 from the accumulator at that condition and we find this is the curve. Next we come to the cylinder A it is retaining then we need 1.19 litre for the same type 1.0 because why we need less while because there is a rod is there. So, for the same period definitely while requirement would be less in that case 1.46 is the from the pump. So, volume left in accumulator is it was this much, but this is definitely higher than this one. So, excess while is going to the accumulator. Next we are extending B requirements 2.70 and within 0.5 time again in this adiabatic and 0.73 litre supply from the pump and 1.97 litre from the accumulator. This might be due to the pressure requirement this is it is taken like this. So, 0 is accumulated in the accumulator. In case of C the motor is running 0.50 volume requirement within 3 seconds. So, supply from pump 4.38 litre supply from this is from 0 and then this is of course volume left in accumulator it is unknown because 4.38 litre is being pumped. So, 3.88 litre we will try to go into the accumulator and then cycle B again return of V 1.06. And this is the chart you can follow this chart and then what is theirs. So, total volume requirement will be there and time etcetera all and it is found that 2.20 litre is the working volume keeping that is the working volume and 10 litre that what we have seen 10 litre accumulator size is suitable. And from this graph again this graph is generated and then when the oil is going from the accumulator and when oil is being stored in the accumulator this is shown in this graph. So, this means that when we are going to design a system with accumulator we have to make a such pressure and volume history of the total cycle of operations and then from there we can select a an accumulator of suitable size and to make the system more efficient. Suppose if we use a bigger accumulator here this will be no use and performance may not be that efficient and if we use a smaller one definitely the purpose will not be served. Now, this is another application is shown here in that this is unloading valve we have earlier learnt what is unloading. Unloading means while the system is loading means is not working in that case we have to unload this pump first of all it can go through the relief valve, but going through this relief valve means there is huge pressure loss. Now, we can go for an open central valve, but open central valve is the problem is that the oil does not remain ready with working pressure. So, another option is that we can use 4 by 2 valve that is on off type valve the changing the directions and on off there is no intermediate positions. If we use this valve as well there is a flow control valve depending on the requirements then what we can do we can put an accumulator here and this is the our unloading valve unloading valve how it works say it is working at say let us consider the pressure is 0.2 very low pressure in that case oil is flowing through this tank and also how it is flowing through the tank oil is coming over here it is coming over here, but this cannot move this one because the pressure requirement pressure is low pressure or ideal it is not working in that case the oil is going through this place and there is a differential pistons that means this side is very small pressure and this side we can assume there is no pressure. So, this will move in that way this oil is going to the tank completely now suppose here we have a requirement with a pressure in that case what will happen this will move this is having a setting pressure of course by adjusting this one then piston this side will have a pressure the same pressure or may not be same pressure little lower pressure will be this way and then this will be in a controlled position because earlier there was a pressure whatever may be the low pressure, but still it was there in that case we have a differential pressure with a controlled load. So, this flow will reduce and this flow will be there and when this is completely filled or when this is completely filled or may be the excess flow is there then this requirement here then this will be accumulated in the accumulator. So, this is some unloading system applications without this accumulator only thing this operation operation will be definitely that will be done, but this will not be that smooth what is available with this accumulator. Now, another application is that we have pump with 4 by 3 tangent center DC valve this is a tangent center means in normal conditions the oil is going to the tank. So, this operation it is written here in a chart say a b c are the three position of this valve what we have in this system we have one tangent valve a no sorry this has two position a is that cross connection b is the straight connection and this is an intermediate positions and for this one this is simply on off type switch. Now, what is written here a is closed b is closed c is closed that means this is in that condition pump flow to the tank now then a is closed b is also closed, but c is connected in that case accumulator to system oil is going to accumulated to the system right from here to it is going to the system then a is closed b is open and c is closed that means we are having this connections then pump and accumulator the pump is applying oil to the system as well as to the accumulator of course depending on the requirements of the main system then a is on b is off and c is off then only this accumulator is being charged because this oil from the main system is going to the tank and this is oil is being charged to this accumulator. So, this is another the application of accumulator with a hydraulic system is shown here how it can be arranged. Now, next to that application of accumulator storage with simple pump now in that case this is a very simple system, but we are having again on off type valve 4 by 3 on off type valve this means that either this position or this position it will be there. So, let us consider the normal position which is shown in that case oil is going to the accumulator as well as to the system depending on the pressure and flow requirement accumulator will be charged or from the accumulator oil will flow to the system. Now next when this is being charged like this, this is coming to this positions then oil will go to this side and oil from here it will come back to the system again in that condition also the accumulator may be charged according to the requirements here. Now, another system this is for pulsation reduction in that case we have used 4 by 3 closed center valve and this is as I told that if this there is pulsating load to tackle such pulsating load with less reduction of ripple or pulsation we can simply use an accumulator in the line. Now we should look into a typical question answering why is an accumulator the question typical question say this is usually 4 to 5 such questions or 5 to 6 such questions to be answered in 3 hours. We will consider let us consider this is about we have to answer 5 questions and this is one full questions the part A is that why is an accumulator used in a hydraulic power transmission system. Second part is that part B in an air over oil that means this accumulator may be we can think of a piston type gas is air and bottom is oil type of accumulator how can the required size be determined assuming isothermal and adiabatic process. Then the recharge pressure of an accumulator is 90 bar 9 megapascal it has to supply 5 liters of oil between 200 bar that is 20 megapascal and 100 bar is 10 megapascal absolute. Determine the size of the accumulator necessary assuming one is that isothermal and two is isentropic process means in this case we may consider adiabatic or something we can we will consider. Now answer of part A why is an accumulator used in hydraulic power transmission system. Then an accumulator is used in a hydraulic system for the following reasons one as an energy storage device to supply large oil flow short period of time which is beyond the capacity of the pump. But when the demand of flow is less the pump flow being excess can charge the accumulator so that this is not corrected so that the it may again supply oil when needed. Then another if you think in application of that as a cushion for pressure surge which are invariably generated in a hydraulic circuit due to acceleration and decelerations of oil resulting from the fast valve operations load shocks etcetera. That means this is the reduction of pulsation this accumulator is used presence of an accumulator sharply reduces pressure peaks thereby protecting the systems so this is the how briefly you can answer the application of the accumulator. Next comes the part B where that air over oil accumulator and we have to express that how the function. Now in this case this is a simple diagram you can use such color to mention so fast when we are charging this volume this you can say that 90 percent of the total volume of the accumulator that is shown this is a pressure and then this is air and this is oil and P 2 V 2 is the say maximum pressure and this is at that condition the volume of the say bladder or the top side of the diaphragm that is nitrogen gas let us consider and then the oil can be used up to this that means the total oil total oil will be pumped from the accumulator to the system can be calculated V 1 by V 2 and by that time pressure reduces from P 2 to P 1. Now the accumulator volume actual is about 10 percent higher than this which I have explained already so you can mention that thing that is why the figure is like that and when the accumulator is fully charged the pressure rises to P 2 and the volume is squeezed to V 2 and accumulator supplies while the volume expands to V 1 and the pressure falls to P 1. Now we consider the isothermal process that is slow changing and charging and discharging then we will consider that the power N is 1 so P 1 V 1 is equal to P 2 V 2 is equal to P 3 V 3. Now the V 2 is equal to P 1 by P 2 is equal to V 1 and V 3 is equal to P 1 by P 3 is equal to V 1 and then for the isothermal process the maximum volume the amount of oil discharge that means maximum volume of oil we can use is V 3 by V 3 minus V 3 sorry this will be actually V 2 minus V 1 sorry this is we have used P 1 P 2 so this will be V 2 minus V 1 is here will be P 2 is P 2 and this will be P 0 sorry equation is not written correctly and anyway we are dealing with this volume so V 1 is the charge volume in this case and this can be expressed in this way and finally we can find out the relations what will be the relations of this volume. Now in this case the instead of using N as the power for isentropic process we have consider isentropic we have not mentioning this adiabatic process we consider this gamma and then with this we can say that gamma is equal to C P by C V is equal to 1.4 that is the for the adiabatic change we take that 1.4 and then these equations come in this form and finally V 1 is calculated within this form. Now we are coming to this part C where the pressure is now this is you see this part charge pressure was said 90 bar charge was done at 90 bar. So now that 90 bar is the gauge pressure there so we add plus 1 to make it absolute pressure 91 bar whereas the system working in 100 to 200 that we consider as a absolute pressure. Now volume is there again this is a mistake this will be V 2 by V 2 minus V 1 minus V 2 is 5 liters and then using this calculation we can have V 1 is equal to 11 liter that means in this case V 0 will be 11 liter. Now if you consider this this this calculation we have shown for isothermal now we are considering this is not exactly adiabatic but we are some isentropic and we have assumed this value is 4 by 3 that is 1.33. Now in that case you see this according to the time say that means that is probably this time of change is this much of that looking into the graph say it is about taking half a second in that case we consider it is 1.33 and according to that we calculate this what is the volume. So volume comes is 13.24 liters earlier in case of isothermal we found it was 11 liter and in this case we need 13.24 liter and then this is the reference we have followed that one is that some tutorial note in a journal that is in 1992. But as well this is a good book I do not know whether it will be available here but this is on the industrial hydraulic control by P. Ravind that is published in 1984. Thank you.