 Good morning and welcome you all to this session of the course. In the last class, we were discussing the work required or work done to the fluid and the pressure rise. Let us again continue little bit the earlier discussion. We were trying to express the compression process thermodynamically in T s plane by showing two pressure lines constant pressure line one is the total pressure at the inlet to the compressor another is the total pressure three at the outlet to the compressor note it is three at the outlet to the compressor which includes the diffuser two that means if you see this figure you see that this is the inlet to the compressor that is the impeller and this is the out the final pressure rise if we just show this p three t and p one t i want to find out the total pressure rise in the compressor. So now in this case if the entire process is isentropic then we can show the process in the T s diagram as i already told that this is one and this is the t one t this is the t one t and this is the t three t this is the t three dash t rather this is t three dash t three t dash t three t dash this is the actually process we just state three let this be three dash this is an ideal process and the actual process as i told which incurs the internal irreversibility due to fluid friction and internal heat transfer due to temperature gradient and we land up to the actual point three which hills right this way to increase the efficiency this was well known now the work per unit mass as we found or energy per unit mass from the steady flow energy equation is c p this is t three t this is this is t three t is c p t three t minus t one t and at the same time we found from the momentum momentum theorem which is known as euler's equation that e by m equals two psi the power input factor into sigma the slip factor into the u two the peripheral speed at the outlet square at the outlet of the impeller square okay so this is the energy now now you see if we want to relate the pressure rise in this process then the pressure rise can be written so pressure rise can be related through the isentropic process by the isentropic process relation is like this p three t that means this pressure this pressure and this pressure same that same pressure line divided by p one t is t three t dash that means it is through the isentropic process that is the end of the isentropic process t one t to the power gamma by gamma minus one now if we have to relate this t three dash two t three t we have to take care of the isentropic efficiency of the compressor as I told you earlier the isentropic efficiency is defined as the ideal work done in absence of any friction or internal irreversibility in the process to the actual work done to the fluid or actual work input with in consideration of the friction in this case the actual work input is more than that in the ideal case so therefore if we write that the ideal work done from the steady flow energy equation will be this this is found from the isentropic case and similarly by application of the steady flow energy equation it is like this this is the actual work input and since air is an ideal gas with constant c p c p cancels out this become this eta c then we can write the t three from the heat this we can write t three t dash divided by t one t is equal to what eta c into this eta c into t three t minus t one t this is divided by t one t plus one am I correct because this divided by t one t is this by t one t eta c into t three t minus t one t divided by t one t plus one so this is divided so now if it is now if we this I will use if we now please wait this if now we use this expression here then we can write that p three t by p one t equals to what t three dash by t three is this that means one plus eta c into t three t minus t one t divided by t one t to the power gamma by t one t gamma minus one again I can substitute this temperature difference t three t minus t one t the difference in this stagnation temperature at the end of the compression that means end of the compressor after the compression in the diffuser two and the inlet stagnation of total temperature this difference in terms of the work per unit mass we can write one plus eta c into this will come sigma psi sigma power input factor u two square so this is e by m now we are replacing this thing divided by c p t one t sigma not visible oh yes I am sorry I am sorry that it is not visible now it is visible so this we can now write to the power gamma by gamma minus one so here you see that the pressure ratio which is an important parameter for the compressor is expressed in terms of the peripheral speed of the impeller at its tip now here what happens is that sigma is usually not a variable one it lies between as I told earlier some value point round point nine eta c is the compressor isentropic efficiency this value is almost fixed to something like point eight five now for a given inlet total temperature therefore we see this pressure ratio is proportional to the impeller speed in this fashion so this is a very important relation of the pressure ratio to impeller speed now I will come to a very important thing of the centrifugal compressor not centrifugal centrifugal or axial compressor now as I told earlier since the compressor handles fluid which are compressible in nature they are gas they are not liquid they are bulk model of elasticity is little less so therefore depending upon the flow velocity the density changes and if the change of density is appreciable flow is compressible and in compressible flow first consideration is that the change in density with pressure there are other considerations depending upon the flow regime which takes place in compressible flow which I will discuss afterwards when I will be telling you about the compressible flow that depending upon the flow regime specially when the flow velocity is very high some typical features which is typical which are typical to compressible flow take place if the flow velocity is very high and close to the acoustic velocity or the velocity of sound relative to the fluid at that state then a different physical pictures are observed so therefore in a compressible flow one of the very important criteria to specify the flow is the ratio of the flow velocity to that of the sound velocity relative to that flow at the state of the fluid and that dimensionless number is known as mac number so therefore I write you a mac number consideration and this is for all machines or all device that handles compressible flow or the flow of compressible fluids mac number that is m a which is defined as the ratio of the flow velocity divided by the velocity of sound or acoustic velocity this is the velocity of sound or acoustic velocity a is the velocity of sound or acoustic velocity velocity of sound or acoustic velocity relative to the fluid flow at that state of the fluid so it very much depends upon the state of the fluid state means for example density and temperature of the fluid so this is a very important criteria and when the flow velocity equals to the sound velocity then mac number equals to one and we call the flow as sonic flow this flow is called as sonic flow when the flow velocity is less than a mac number is less than one the flow is known as subsonic flow subsonic flow this is this will be discussed after just a introduction I am giving you so that you can understand things when this is greater than a that is mac number greater than one the known as sup the broad classification supersonic flow and there is a regime in the subsonic flow when v is less than roughly 0.3 a or mac number is less than 0.3 then the flow may be treated as incompressible flow incompressible flow understand incompressible flow that means the density does not change with the pressure or the change in density with the pressure is negligible relative change in density is negligible so these are the regimes of flow now what happens if the flow is supersonic at any stage depending upon its velocity then some features are observed which causes extra losses of energy and incompressible which causes extra losses of static pressure which is undesirable so therefore for compressor design one has to be very careful that mac number of flow should not exceed necessarily or usually at any point of flow in the compressor over the sonic level so that other complicated features of compressible flow will come into so this is known as mac number considerations so therefore at each and every section of the compressor the mac number has to be considered and here the mac number if you see the definition that in the definition the velocity of flow it is the velocity relative to the moving solid surface so when there is a flow velocity past the solid surface it is the velocity relative to the solid surface and in a turbo machines the solid surface are also moving solid surface as also the velocity so therefore the relative velocity of the fluid has to be considered in defining the Mach number which has to follow this criteria of being less than one to make the flow subsonic to avoid excess losses. So one of the important section is the inlet to the impeller actually the Mach number velocity of flow will be high at the outlet of the impeller where it gains kinetic energy from the impeller where the energy is being imparted to the fluid. So to restrict that Mach number which is maximum at the outlet tip we have to check the Mach number at the inlet of the impeller too. So therefore the inlet design has to be made in such a way that Mach number is relatively low. Now you see an inlet section of the impeller that is the inlet part this is known as inducing section of a centrifugal compressor you see this is the eye this is the root of the eye and this is the tip of the eye. So this is the tip diameter of the eye and this is the root diameter of the eye and this is the passage of the flow normal flow that means it is the cross sectional area of the flow velocity the flow turns like this try to understand very well like this. So therefore the design of the tip should be such that the Mach number should be low now how do you define Mach number just I told you in at this moment that Mach number at entry to the fluid here if you define it has to be defined based on the relative velocity that means V r 1 divided by a. Now a depends upon the fluid state here but the V r 1 depends upon how the fluid is being allowed to enter to the impeller eye. Now as you remember the impeller is like this the impeller design again I show you the impeller blade is like this at the eye the design is like this. So this is a velocity triangle you see that this is the relative velocity which angle matches at the angle of impeller blade at the inlet. Now these two are specific or typical velocity diagram this diagram is for a very large impeller diameter where the peripheral speed is more u 1 and because of the large diameter the frontal area becomes large for which the flow velocity or the absolute velocity is less which gives rise to a higher relative velocities and we have to be very careful here the Mach number will be more. But at the same time the mass flow it can accommodate more mass flow but if you now reduce the velocity this is the typical diagram of a small eye tip diameter there what we will get we get a u 1 like this relatively lower than this but the flow velocity is high so that V r 1 may be reduced. But it is very difficult to conclude which one is greater or lower that depends upon the relative values of u 1 and the value of v 1. However this v r 1 is of our prime important such that v r 1 by a that is the ratio Mach number should be low and we try to design the impeller tip in such a way that the Mach number lies between 0.7 to 0.9 usually 0.8 so that we avoid losses. What happens I tell you in little brief which will be discussed in more detail when I will teach you the compressible flow what happens if the flow is supersonic that means in a compressible flow if the flow velocity is more than the local acoustic velocity then what happens if under certain boundary conditions or in the disturbance of the flow. Flow has to adjust and accordingly decelerate then the supersonic flow suffers a sudden deceleration through a sudden discontinuity and that discontinuity is known as shock so therefore a shock takes place a supersonic flow cannot adjust itself to have a gradual and smooth transition in the form of deceleration from supersonic to subsonic it cannot happen and incompressible flow when the flow is supersonic due to the circumstances or the boundary conditions imposed on the flow flow has to decelerate and this is adjusted by a sudden deceleration or a sudden discontinuity in the flow and this discontinuity is a really mathematical discontinuity which takes place within almost infinite small region whose length is in the terms of molecular diameter and that shock discontinuity in the flow is known as shock in general and that shock what matters to the practical case due to that shock there is a abrupt loss in the total energy this is a total irreversible process so what matters is that because you can ask me sir when the deceleration takes place when the fluid comes to subsonic stage what happens that pressure increases yes static pressure may increase but if you consider the total mechanical energy there is a huge loss in the total mechanical energy some of the pressure part that is pressure energy you can call loosely and the kinetic energy there is a loss so therefore in design of any compressible flow machines or compressible flow device one has to be very careful first of all it is better to avoid the supersonic state of flow and or supersonic state of flow is unavoidable one has to be very careful so that supersonic flow should be decelerated in a way that shock doesn't here again I am telling you which I will explain after what it is not that always shock will take place it depends upon certain boundary condition imposed on it so that shock has to take place but it may occur that flow may be made in such conditions with design back pressures and many other things that I will discuss afterwards where shock may be avoided but in practice it may not be done because the supersonic flow when it comes for example when an aircraft moves with a supersonic velocity as you know that when an aircraft moves with a supersonic velocity that is velocity more than the sound velocity at the state of the fluid there at high altitude then what happens relative to the aircraft the fluid moves with supersonic velocity so far upstream the fluid approaches the supersonic velocity when it approaches the nose of the aircraft then what happens the fluid has to decelerate fluid has to decelerate when it tries to strike the nose and that deceleration is causing the shock and a oblique shock occurs at the nose of the aircraft so these are the things probably you know today these are popular thing so therefore I must say that this Mach number consideration is very important consideration and therefore the impeller eye design has to be made so that Mach number at inlet that is based on the relative velocity at the inlet should be low now next is this diffuser now I come to the next part that is the second component diffuser now what is diffuser that is same as that of your centrifugal pump diffuser now we know that impeller and diffuser are the two important part this is impeller impeller this is now what happens energy is added to the impeller so when air comes out of the impeller what happens the air acquires energy by the momentum transfer transfer of angular momentum by the rotating action of the blade which we have done how to find out the increase in sorry how to find out the work input to this now what happens when it comes out of the impeller tip the energy is stored in the form of both kinetic energy velocity of the fluid and the static pressure the impeller passages are made divergent so that the pressure will increase in the direction of the flow but we want finally from the outlet of the compressor that means if you see this diagram it will be better that at the outlet of the compressor from here the delivery we want a we want air at relatively much low velocity but at high pressure why this is because the practical use of this compressors are with the engines or with the plants gas turbine plants turbo jet turbo pop turbo fan engines where this air is used in a combustion chamber to burn the fuel and when the fuel is burned a high temperature is generated or a high temperature the air is heated to a high temperature by the energy generated because of the burning so to make the burning more efficiently what is required is that a high pressure air at high temperature and high pressure air but at very small velocity as low as possible sometime it is unavoidable the different reasons that you will know afterwards if you read the jet engines or the gas turbines in more detail but as far as it should be avoidable because a high velocity in the combustion chamber for burning fuel causes several problems like combustion instabilities combustion cannot be made so efficient so to make the combustion more efficient it is required that a relatively low velocity but high pressure air okay so for that we want that the total energy of the air at the outlet should be mostly in the form of static pressure or you can tell the stagnation or total temperature at the outlet which is the index of the work given to the fluid should come in the form of only the static temperature or the static pressure not in the form of kinetic energy kinetic energy will be there as required for to maintain the flow so therefore what happens the excess that means the kinetic energy which is there which is undesirable is then converted to pressure energy or to convert it to higher static pressure in the diffuser the similar thing which is done in the case of centrifugal pump so this diffuser is like this there are first of all there is a vaneless space first of all there are no vanes so it is a vaneless space where the diffusion takes place partly and after that there are number of vanes which makes the final diffuser now why the number of vanes are made to divide the air stream in several channels to make an effective control of the flow and at the same time we can get the diffusion that means a rise in static pressure at the cost of the kinetic energy in a short length as short as possible so because of this the vanes number of vanes are there to direct the flow in different channels now I will come to the vaneless space afterwards let us first discuss this vanes so this vanes create the passage so each and every passage this is the width of the passage has a divergent width the width diverges which depends upon the shape of the vanes so vanes are so depending upon the curvature the widths are made so that the cross sectional area normal to the flow increases because of which the velocity decreases and pressure increases the depth which is perpendicular to this plane of the figure the depth of the diffuser is usually constant in the direction of the flow this means that means it has a constant depth this is the perpendicular to the plane of the figure now before going to explain this I will tell another criteria what should be the curvature of the vanes so that the diffusion process that is the deceleration of the fluid is efficient without losses so that is more important in a diffuser so therefore we must tell something about boundary layer separation boundary layer separation now let me tell you something about boundary layer separation now let me tell you something about boundary layer separation now you see that when a fluid flows come to the basic principle of fluid mechanics which probably you have learned in fluid mechanics again it is a recapitulation of the earlier things that when a fluid flows from one point to another point or in an average from one section to other section what is the gradient which makes the flow possible it is the energy gradient that means fluid flow from a higher energy to a lower energy so therefore when the fluid flows from a point or a section to another point or section downstream where the pressure increases then the fluid flows against an adverse pressure gradient why because fluid element faces a higher pressure at the downstream that means the direction in which it is flowing but still the fluid flows because of the energy gradient energy at upstream is always higher than that at the downstream but what happens you see that when the fluid flows past a body let us consider this recapitulation let us consider the fluid now to understand this let us consider an external flow a fluid is flowing past a curved surface for example now let a fluid enters with uniform velocity let us recapitulate what is boundary layer flow now you know that when the fluid flows past a solid surface at the solid surface the relative velocity of the fluid with respect to the solid surface or the velocity of the fluid relative to the solid is zero this is purely because of the interaction between the solid and the fluid this is pure interaction between the solid and the fluid I am not going into details of it this can be broadly conceived as a consequence of the addition between the fluid and the solid and their interfacial process by which the fluid is not allowed to slip over the solid that means its velocity relative to solid is zero that means if the surface is at rest the fluid velocity will be zero and what happens the fluid just above it in the near vicinity of the solid is being retarded to a very low velocity because this happens to the momentum transport in the cross direction because of this momentum transport from fluid to fluid because of the molecular transport it is at the molecular level the fluid velocity from zero if we consider the solid at rest ultimately attains the free stream velocity ultimately attains the free stream velocity it attains actually asymptotically at any section but if we consider some 99 percent of the free stream velocity as the free stream velocity itself then we can call this as the boundary layer thickness at that section and this grows like that means there is a boundary layer within which the fluid velocity changes from zero to almost the free stream velocity so this retardation of the fluid from its free stream velocity it takes place within the boundary layer because of the momentum transport the fluid is retarded within a layer very close to the solid surface this is known as boundary layer or the shear layer which is a function of x now this x at a distance x i denote the free stream velocity as u infinity x which may not be the same as the u infinity at the entrance this is because of what if the surface imposes a pressure gradient that means surface due to its curvature may impose a pressure gradient in the potential zone that is the zone above the boundary layer where the flow velocity in the transverse direction for example y is uniform and this is known as boundary layer region so therefore this boundary layer is impressed with a pressure gradient which is imposed by the curvature of the surface that is del p del x now when the pressure at the downstream let some typical downstream section pressure is d and some typical upstream section pressure is u when pressure of the downstream is less than p u by mathematical term we tell that del p del x is less than 0 because this is in the increasing direction of x in the direction of flow that means the fluid is flowing with a negative pressure gradient there what happens if you consider a fluid element since this pressure is low and this pressure is high upstream pressure so fluid experiences a net pressure force in the direction of flow that is why this is known in fluid mechanical term as favourable pressure gradient favourable pressure gradient but when due to this curvature the pressure gradient becomes other way that means the downstream pressure at any typical downstream location is greater than p u then by mathematics del p del x is greater than 0 so a negative pressure gradient means favourable pressure gradient and this is known as adverse pressure gradient in this case pd is more than p u so therefore the fluid is facing a force net pressure force in the direction opposite to its flow that means it opposes the flow though this creates an adverse effect so that is known as adverse pressure gradient so when this type of adverse pressure gradient takes place in case of diffusion which we are discussing now where the pressure is increased this is the static pressure so downstream pressure is higher than the upstream pressure this case prevails so fluid faces an adverse pressure gradient but still the fluid flows because the energy gradient pushes it energy gradient makes it possible to flow but what happens for the fluid particles very close to the wall the kinetic energy is totally consumed the kinetic energy is destroyed because kinetic energy is ultimately coming to zero fluid is retarded because of this momentum transport okay and this is being manifested by the property fluid viscosity so therefore for the liquid fluid particles close to the surface kinetic energy falls appreciably so that they cannot surmount the adverse pressure here that means the total energy becomes insufficient at the upstream to flow that means the energy gradient is reverse okay that means the fluid with low kinetic energy near the solid cannot surmount the adverse pressure here and then what happens at some point it happens where the only the gradient of energy opposites becomes reverse and the fluid flows in the opposite this is known as flow reversal if you draw the here the velocity after the flow reversal after the flow reversal here the flow reversal if you draw the velocity profile you will see the velocity profile is like this you understand so this part the fluid flows in the opposite direction this is known as boundary layer separation and this creates a large number of eddies recirculatory flows and form by virtue of which the a total mechanical energy of the fluid is being curtailed is being reduced and what happens energy totally conserved so because of this creation of local recirculatory flow in the form of eddies which takes place because of the flow reversal the boundary layer is detached and all boundary layer assumptions fall there so what happens from the practical point of view that part of the mechanical energy that means the static pressure is being converted into intermolecular energy which from the viewpoint of mechanical energy is a loss and that is why people tell this is the separation loss now when we give a diverging passage therefore now if you consider a diverging passage the same thing now with this was with the external surface now you consider a diverging passage now one thing if the pressure is favourable then the fluid particle does not have any flow reversal the always flow so therefore this flow reversal or boundary layer separation takes place whenever the pressure gradient is at first this is clear because in favourable pressure gradient even if the kinetic energy becomes low the pressure force itself this is the favourable pressure gradient this is that this case that there is always a pressure force in the pressure force will help it to push in the direction of the flow so it will never happen with the favourable pressure gradient this is a very important thing to remember now when the fluid flows in a diverging channel for example the streamline may be like this so here what happens the fluid flows that any typical section pd and pu so pd is greater than pu so here del p del x is if this is x del p del x is greater than 0 that means this is an adverse pressure gradient here the separation will take place whereas this is the decelerating flow decelerating means decelerating that means its flow velocity is reduced and the pressure is increased in an accelerating flow if you consider the flow through a converging duct that is the nozzle in case of this is the nozzle flow this is the streamline so therefore this is the streamline from a far distance this is parallel so in a nozzle flow this is accelerating accelerating flow accelerating flow that is nozzle where in subsonic flow that I will again discuss afterwards a converging passage acts as a nozzle or accelerating flow and a diverging passage acts as the decelerating flow so that I am not telling now this will be discussed afterwards in detail that in a converging passage when the flow is accelerated which we usually known as nozzle del p del x is less than 0 that means a downstream pressure is always less than upstream pressure so therefore always there is a force in the direction of the flow to push it so therefore a diverging passage anywhere where you have the diffusion process that the pressure is increased in the direction of flow you have to be very careful of the boundary layer separation now this separation is very sensitive with the angle of divergence if the angle of divergence is more what happens that the rate of pressure increase that is the adverse pressure gradient is more so that the separation occurs early so therefore angle of divergence the angle of divergence is very important in a diffuser duct divergence is very important and that should be less than equal to 10 degree 10 to 11 degree so angle of divergence should not be made more than 10 degree so it is restricted for design of any diverging passage so therefore here also the divergence passage divergence angle should be restricted at each and every point okay now I come to the vaneless space now the divergence angle at the inlet to the diffuser vanes should also match with the direction of the velocity and since the diffuser vanes are static vanes so direction of the velocity means the velocity absolute velocity which comes out of the impeller that direction should match the direction here otherwise what will happen otherwise there will be incident loss loss at the incident however here we cannot say so because the velocity with which the direction of the absolute velocity with which the fluid comes out of the impeller is not same to that at which it will enter because there is a vaneless space so therefore we have to know what the fluid flow nature of the fluid flow or the flow field in this vaneless space now the first question is that sir why I will give a vaneless space why not the diffuser vanes should be given or should be provided right at the outlet of the impeller tip so that the fluid which will come out of the impeller will go to the diffuser but it is not done always a vaneless space is provided this is because of two reasons first one is that the Mach number of flow is reduced before it enters to the diffuser vanes and Mach number has to be reduced means that the velocity of flow has to be reduced so therefore it is required that before the fluid enters or impinges or the glides whatever we tell the diffuser vanes its velocity should be reduced so therefore some space should be given which will act as a diffuser to reduce the velocity and number two reason is that if we do not give that space what happens there will be an excessive circumferential variation of static pressure if you give all the if you provide all the diffuser vanes very close to the impeller tip then there will be an excessive variation of the circumferential stress which is radially propagated upstream in order to the impeller and creates a vibration and impeller blades may fail due to this vibrational fatigue and this vibration is a function of the relative velocity of the fluid and the number of impeller vanes and it is more dangerous if this frequency of this vibration coincides with the natural frequency of the impeller and to avoid this usually the impeller vanes are not multiples of the diffuser vanes this is one of the reasons so therefore because of reduction of Mach number and the velocity and the circumferential variation of static pressure there is a vaneless space now vaneless space is a space which having a increasing in constructional area and in the vaneless space if you want to know the principle of the flow field then we can write like this since there is no energy transfer the vw2 that is the tangential component of velocity at the tip of the impeller into at the angular momentum comes out that is constant that means vw2 decreases with increase in r is inversely proportional to r so therefore with the increase in r the vw2 decrease there is a decrease in vw2 with the increase in r okay now another thing is that if you consider the flow velocity vf this also decreases this is because with the radius for a constant depth that means depth is constant in the perpendicular to the plane of the figure the flow area flow area with the sorry with the increase in r the flow area increases so I write simply the increase in r because with the increase in r flow area increases that means f increases with the increase in r so because of that this takes place that means both the tangential velocity component and the flow velocity okay both decreases as a whole the absolute velocity decreases so a diffusion takes place so therefore the Mach number is reduced but at the same time this vaneless space has to be designed in such a way that should be in conjunction with the inlet angle of the diffuser vane so that finally the absolute velocity direction should match the diffuser vane this is okay this is almost all about the design of the diffusers now I will come to another thing which I forgot to tell you earlier in this connection regarding this inlet Mach number here okay please wait I just will show you here yes here I just forgot to tell you that this inlet thing which I have shown you this well sometimes what happens to reduce the Mach number at the inlet it is not required here I told the reduction of Mach number at the inlet I go back to the earlier discussion that if this is the vane at the impeller tip this is the impeller vane so we know that this is the typical diagram this is the typical diagram at the inlet this also I just forgot to tell you must know that this is u this is vr1 this is v1 this already we discussed the impeller vane here vr1 is the relative velocity that is v1 it is u1 minus u1 now here what happens to reduce this Mach number we already discussed earlier that a now a is gamma rt1 how this is because that this acoustic velocity which will be again told you afterwards incompressible flow classes that for a ideal gas the acoustic speed or sound velocity can be expressed as root over gamma that is gamma is the ratio of specific heat are the characteristic gas constant and the temperature t1 so therefore this is the expression of Mach number now the vr is sometimes reduced by what do you know by giving a deflector and the thing is like this for the same I again draw this diagram for the same velocity red flow velocity and the same so this is the ideal one this is the ideal one v1 u1 and vr1 so the dotted one is like this this will be my final v1 so what happens there is certain amount of pre whirling is given that means what is that I tell you that is like this a deflector of this type is given which deflects the flow in this way sorry sorry sorry this will be this so this will be my let this dash now the ideal one this is v1 and therefore this is vr1 so for the same u1 dash is u1 so u1 remains same flow velocity remains same v1 dash remains same so that flow velocity is this component but the absolute velocity is having some angle that means this portion is the now this portion is now if you understand well I am happy that is the inlet tangential component that means instead of having a axial entry which is perpendicular to the direction of tangent we give an oblig entry by use of a deflector which gives some amount of whirling or tangential component at inlet but for the same flow velocity that means to accommodate the same mass flow rate we have a reduction that is vr1 is less than vr1 dash so sometime a deflector plate is used but here what we lose we gain in terms of reducing the Mach number so that at the impeller tip we may be little sure that Mach number is not supersonic so that shock losses occur there but we introduce a whirling component this is known giving a pre whirling at the inlet so that the energy per unit mass or the work done per unit mass is now vw2 as you know this is the formula but here now vw1 is not 0 so if it is 0 it is this so therefore for a given vw1 small vw1 is generated so we lose so that means the at the cost of specific work we give this pre whirling that means the work input to the fluid will be less that means what we lose is the efficiency of the compressor that means it requires more energy for a given pressure rise but the Mach number is reduced so this was told and so then this diffuser is you know about the diffuser now I come to the losses in centrifugal compressor losses in centrifugal compressors what are the different losses in centrifugal compressors now losses there are different types of losses in centrifugal compressors so they are like this one is the frictional losses frictional losses okay another is the frictional losses another is the incident losses incidence losses another is the clearance or leakage losses clearance or leakage leakage losses okay now one by one the frictional losses are typically the friction now the fluid flows through the compressor blade passages comes in contact of the solid surface and fluid to fluid layer that is because of viscous it is skin friction is there that is purely frictional loss apart from that there is a separation loss boundary layer separation or there may be losses due to shock now these losses are known totally as frictional losses frictional losses mainly comprises the skin friction and the separation loss separation loss is very important in compressors because throughout the flow is there with adverse pressure gradient means that there is always a deceleration of the flow so separation loss and the skin friction combines the total pressure losses and the total frictional losses so what is this loss first of all this is loss again the loss in mechanical energy which is mostly manifested in terms of the loss in the or the shortfall in the static pressure of the compressor at the outlet so frictional losses is because of the friction the skin friction and the boundary layer separation because of the decelerating incident losses are losses because of the fact that when the flow velocity while flowing through the vein does not follow the vein angles specially at incidence to the vein if the flow velocity the direction of the flow velocity relative to the vein is not following the vein angle at the inlet there are losses and this will happen if the compressor doesn't work at its design condition so therefore of design conditions the incident losses will take place when the flow cannot glide the vein both that is inlet and outlet that is the relative velocity angle differs from that of the vein angles another is the clearance or leakage losses which takes place because of the clearance between the impeller eye shaft and the casing of the compressor or the impeller eye and the casing impeller eye tip and the casing these are typical mechanical things we can reduce that by proper sealing but when the impeller eye tip diameter is very large to accommodate more mass flow rate the sealing becomes a problem so we can reduce that by putting glands providing glands to reduce the leakage between the clearance between the shaft and the casing so these are all clearance and leakage loss but this clearance and leakage loss is comparatively very less as compared to frictional loss and incident loss now if you draw a figure of losses verses mass flow this is mass flow then you will see this type of figure frictional losses is like that is always increases with the mass flow like this frictional losses with mass flow it is like this this is zero when there is no mass flow but incident losses gives a picture like this this is minimum at the design point this is the design the design point and of design point take may be there even at low mass flow and high mass flow these are of design point where in both the directions this increases so if you add these two the total losses take place total losses takes this shape total losses okay so these three are the important losses but this is not as important this is relatively less as compared to the friction losses and the incident losses okay I think today I will end here and we will discuss the compressor characteristics in the next class thank you