Hello and welcome to lecture number 22 of this lecture series on turbo machinery aerodynamics. The last few lectures we have been talking about axial flow turbines. We started off with an interaction to axial flow turbines and then subsequently we spent about lecture on discussion basically towards the two dimensional flow in axial flow turbines and to do with cascade analysis of axial turbines. We also had some discussion on the performance of axial flow turbines and in today's lecture we going to basically talk about the performance characteristics of axial flow turbines. In the last class we had discussed about the performance parameters which are used in analysis and understanding of axial flow turbines and we will use some of those parameters in today's lecture to look at how the performance of an axial flow turbine can be characterized. And we will also spend some time to look at the different types of blade shapes and the flow characteristics through a turbine blade passages and we will also towards the end of the lecture have some preliminary discussion on matching of the turbine exit flow with downstream component let us say nozzle. And so these are some of the topics that we shall be discussing in today's class. So, we will begin with discussion on axial flow turbine performance characteristics. If you recall some few lectures earlier on when we are talking about axial flow compressors we had spent quite some time in understanding the performance characteristics of axial flow compressors and we will also in today's lecture follow a very similar approach towards understanding of the performance characteristics of axial turbines. But as what we going to see very soon the performance characteristics of compressors axial compressors and turbines are entirely different even though the parameters based on which they are assessed are very much the same basically pressure ratio the mass flow rate non dimensionalized and efficiency. And so though the parameters are the same the way these two components behave are quite different and that is very much to do with the fundamental nature of flow in axial flow compressors and turbines. In the sense that in compressor the flow has to undergo an adverse pressure gradient scenario where as in a turbine the pressure gradient is always favorable and that primarily leads to lot of difference in the performance characteristics. When we are discussing about axial flow compressors and the performance characteristics of compressors we had carried out a kind of an analysis to look at and understand what are the non dimensional parameters which could be used for gauging the performance of axial flow compressors. So, from the dimensional analysis we had identified a few distinct non dimensional groups which can which basically have a significant effect on the performance of axial flow compressors. So, the very same performance parameters are going to be used for judging the performance of turbines as well. And so in the case of axial flow compressor what we had seen was the exit pressure of the compressor and the efficiency are functions of variety of parameters like mass flow rate and the inlet conditions like the inlet stagnation pressure, inlet stagnation temperature, the rotational speed, the ratio of the specific heats, the universal gas constant, the viscosity in design and the diameter and so on. So, this we reduced by dimensional analysis and we arrived at this expression which relates the pressure ratio in the compressor and efficiency to these different non dimensional parameters. The first one that you see here is a function of mass flow rate and a set of other parameters. The second one is a function of the rotational speed and there are of course, a few other parameters. So, for compressors we have seen that for a given design we can assume that this gamma and nu does not change or does not affect the performance significantly. Similarly, the diameter and the gas constant are fixed. If that is the case the set of parameters would now simplify and reduce to the pressure ratio and efficiency being functions of m dot mass flow rate multiplied by the inlet stagnation temperature divided by inlet stagnation pressure and the rotational speed divided by square root of T 0 1. So, this is what we had derived for an axial compressor and what we will see is that the exact same logic can also be applied for a turbine and so we will use similar parameters for plotting the performance characteristics of axial turbines. So, in the case of turbines what we will see is that the exit state the pressure ratio rather of the turbine and the efficiency are again functions of similar parameters mass flow rate times stagnation temperature divided by the stagnation pressure and the speeds n by root of T 0 1. So, we will use these parameters for characterizing the performance of axial flow turbines as well. So, in the case of turbines just like we had done for the compressor we will first take a look at the pressure ratio versus mass flow rate and subsequently as a function of varying non dimensional speed and subsequently we will also look at the variation of efficiency. Now, the interesting thing to observe in the case of turbine that we will very soon see is that unlike in a compressor where we had the performance characteristic which was rather elaborate set of characteristic lines and you also had a surge line and choking line and operating line and so on. In the case of turbines the performance characteristics are much more simpler in the sense that there is only one primarily one limiting line as you could call. In the case of turbines we have the performance which is limited by choking at one end and there is nothing like a turbine surge or instabilities and so on and that is one distinct difference between a turbine performance as compared to a compressor performance. So, if you look at a performance characteristics of a typical axial flow turbine. So, here we have the pressure ratio and mass flow rate as a function of the varying speed. So, as speeds change the performance characteristics also tend to change, but what you see here is that as you keep changing the speed non dimensional speed all these characteristics would kind of bunch and merge towards the single line and that is the choking mass flow. So, there is a certain limiting mass flow that kind of affects the performance of an axial turbine and that is limited by choking. So, this is very much unlike the case of axial compressor where we had seen a distinct variation in performance with non dimensional speed and there was also a limiting line on the left hand side of the compressor characteristic which was to do with the onset of instabilities and that was referred to as a surge line. So, do not really see this kind of a limiting parameter in the case of axial turbine. So, from the performance map of a turbine which is basically the pressure ratio versus mass flow rate for different non dimensional speeds as speeds change you can see that towards a certain mass flow all of them kind of merge and you have a limiting mass flow that is the choking mass flow. So, compressibility in the case of turbine limits the performance and that is one of the limiting performance parameters in the case of turbine. So, we will also look at some of the other limiting parameters like the stresses and temperature which also limit the performance of axial turbines. So, the other parameter that we would be interested in the case of turbine is the efficiency of a turbine and how the efficiency of a turbine is affected by variation of let us say the pressure ratio and what is the effect of pressure ratio on the efficiency of an axial turbine. Now, in the case of efficiency we have plotted efficiency again as a function of the speed as speed changes what really happens to efficiency. So, if you look at the efficiency characteristics here. So, here we have the turbine efficiency as a function of the speeds and on the x axis we have the pressure ratio. You can immediately see that the pressure ratio in the case of turbines can be substantially higher than that of a compressor per stage which we have also discussed in the last lecture that a single stage of a turbine can actually drive multiple stages of compressor because the pressure drop that a single stage of a turbine can handle is much larger than the pressure rise that can be achieved through a single stage of an axial compressor. Now, if you look at the efficiency characteristics you can also see that the efficiency is quite flat and in the sense that the variation of efficiency is very is rather insignificant over a wide range of pressure ratios as well as mass flow rate. So, efficiency as speeds change efficiency characteristics are relatively flatter as compared to a compressor which we had seen is likely to have very sharp change in efficiencies unlike the case of turbines. And it is also known that typically the turbines are operate at much higher efficiency than compressors and turbine efficiencies are usually slightly on the higher side as compared to compressor which is operating under the same pressure ratio range. Now, so there are few aspects that one would one can derive from these performance characteristics of a turbine and one of the important aspects that I just mentioned is the fact that efficiency variation of efficiency is rather the amount of change of efficiency that you see in the case of turbine is very insignificant for a wider range of mass flow rates and pressure ratios. So, efficiency plot basically shows us that the efficiency tends to remain constant over a wide range of rotational speeds and pressure ratios. The main reason for this being the fact that in the case of turbines the flow basically has to operate in a favorable pressure gradient unlike the case of compressors where the lot of limitations which the flow would encounter because it is operating in an adverse pressure gradient and that is one of the reasons why turbines generally tend to have better efficiency and at the same time the pressure ratio that one can achieve is much higher in a turbine as compared to that in a compressor. Now, the other aspect that we also noticed from the mass flow characteristics is that the choking point or choking line in the case of turbine limits the performance of a turbine and that sort of becomes the limiting line in the case of axial turbines and whereas in a compressor you also had a surge line on one side which was limiting the performance of axial flow compressors. And what we also see is that the mass flow characteristics would kind of merge into a single line or a single curve as we keep increasing the rotational speed and we have seen that at higher mass flows all these are individual characteristic lines merge and form a single line which will eventually become the choking limit or choking line for the axial turbine. Now, there are few more aspects that we need to understand here that is where an axial turbine is operating very close to the design point that is at low incidence levels the performance characteristics as one would notice would kind of merge and reduce to a single curve. What is also seen is that as the number of stages increase there is a noticeable change or tendency for these characteristics to become ellipsoidal and this was kind of formulated in way back in 1940s by Strodola who formulated what is known as the ellipse law and which was for a long time being used by a lot of designers. Basically what ellipsoidal law tells us is that as you keep increasing the number of stages the mass flow characteristic kind of sort of resembles an ellipsoid and so that can be you know theoretically or empirically correlated and so that was sort of used as a thumb rule by designers for a long time just as a starting point for the design. So, what is basically being implied here is that as we let us take a look at the performance characteristics once again. Now, this is pressure ratio versus mass flow characteristic and we have seen that we have already seen the performance characteristic which was limited by choking on one end. So, as you keep increasing the number of stages let us say we increase the number of stages from 1 to 3 and tending towards a multi stage turbine the performance characteristic as you can see changes and eventually becomes or resembles an ellipsoid and that is something that was empirically correlated in Strodola ellipse law and which basically relates the mass flow versus with the pressure ratio through an empirical correlation. And so for a long time that was sort of used as a thumb rule in the design preliminary design of axial turbines. And so these are some of the aspects that one can observe from the performance characteristics mass flow versus the pressure ratio and efficiency versus pressure ratio or mass flow. So, here I mentioned that there are few aspects that limit the performance of turbine and so we can identify three distinct aspects which limit the turbine performance. One of them is compressibility and that we have already seen in the performance characteristic that the mass flow is limited by choking mass flow and so that is an effect of compressibility. Besides compressibility there are two other aspects or parameters that limit the performance. The other parameter is the stress that these blades would need to undergo while operating under extremely high temperature as well as rotational speeds. So, stress is the other limiting parameter and the third parameter of course is the inlet temperature. So, we if you have if you recall during your course on let us say propulsion basic propulsion course that I assume you would have carried out a cycle analysis of jet engines. You must have noticed that an engine performance is very sensitive to the turbine inlet temperature which is the maximum temperature in a Brayton cycle. And so higher the temperature better is the performance of the Brayton cycle and so one would always want to use a higher and higher temperature at the turbine entry. So, that the performance of the engine can be improved and therefore, turbine is it is always desires that we use a higher temperature of the turbine inlet for better performance of the whole engine. But as we know that material limitations would prevent us from using extremely high temperatures in the turbine and so inlet temperature also limits the performance of a turbine in the sense that though aerodynamically it would be possible for us to use higher temperature. It is a mechanical limitation because the materials that are currently available have certain amount of temperature limits that would prevent us from using very high temperatures in the turbine. So, if you look at the performance of a turbine these are limited by these three parameters compressibility stress and the inlet temperature. And compressibility as I mentioned limits the mass flow that can pass through a turbine stress on the other hand limits the rotational speed. And since we know that turbine inlet temperature is also a very significant aspect of performance turbine entry temperature also limits the performance. But if you look at the second and the third parameter which is stress and temperature they are quite related in the sense that temperature also affects the stress because it induces a thermal stress on the blade. And so temperature and stress are in some way limited and so there is in a typical design exercise there is always a sort of compromise that is used to arrive at an optimum balance between the stress that a blade can sort of withstand which also limits the rotational speed. And also the maximum temperature that one could use in a turbine and that is why there are lot of technologies which have come in the reset years to use higher turbine entry temperature. Some of these are to do with using artificial cooling techniques to keep the blade cooler and permit higher temperature that could be used. There are also lot of research going on to identify and develop newer materials which can withstand higher temperature as well as stress. And so a turbine performance which is basically limited by compressibility stress and temperature. So, for a turbine designer it is like we have seen also for a compressor there is certain amount of optimization that would be required to be carried out by the designer to arrive at a set of parameters which would give us the best performance. And at the same time it would also enable the materials that are currently available to be used in the current design scenarios. Now, so it is a known fact that the turbine inlet temperature has a significant effect on the engine output. So, it is known that if you look at just a thumb rule 1 percent increase in the turbine inlet temperature can produce up to 2 to 3 percent increase in the engine output if you are looking at the overall engine. And therefore, it is necessary that we identify methods by which one can increase the turbine entry temperature to the extent possible. And which is why there are elaborate mechanisms which are used for keeping the blade cooler than in fact the turbine entry temperature in most of the modern day engines have temperatures which are actually higher than what the materials can withstand. But it is possible for us to use these higher temperatures because of the fact that we employ cooling technologies to keep the blade cooler or the blade surface protected from very high temperatures. We will of course, be discussing about turbine blade cooling techniques in detail in some of the later lectures. And this is just to highlight the significance of the fact that the temperature turbine entry temperature has significant effect on not just the turbine performance, but also on the engine as a whole. So, now that we have been talking about the turbine performance and its effect or the parameters which affect the turbine performance that is also discussed about the turbine blades in little more detail and what are the different types of blades that are used. We have already discussed that there are two fundamental types of turbines axial turbines. And one of them is called the impulse turbine and the other is called the reaction turbine. So, let us now try to understand the aerodynamic shape of these different types of blades. All these blades as we know are fundamentally airfoil sections. But let us also try to look at the different types of blades which are being used in various types of turbines. And so depending upon the application the very shape of the blades can change significantly and that is what I would like to explain in the next few slides. Now, the blades that are used in turbines can be quite different from those that are used in compressors. Something that you have you must have realized by now the last few lectures that we have been discussing. And there are variety of parameters which affect the performance or the shape of these blades. Some of these parameters are to do with the mach number at which these blades have to operate the stress levels and the host of other parameters. Now, depending upon the application the thickness distribution or the curvature of the blade the trailing edge shape all these are varied and these are strong functions of the application for which the turbine is to be used. And a turbine can also be operated or designed for a variety of mach numbers ranging from subsonic to transonic or even super sonic. So, turbine blade shapes can vary substantially as one changes the mach number. This is something you have also seen for compressors. For low speed compressor the blades shapes that are used are quite different from the blades that are used in let us say a transonic axial compressor. So, in the case of turbine as well these blades can be quite different. And there are various ways in which these blade shapes or profiles are derived or developed. Some of these are basically derived from agencies like NACA series. You must have seen NACA series of blades which were discussed during compressor discussions. So, there are series of blades which NACA had developed way back in the 1940s. And so these blades are these are of course some of the sources of blade profiles. And there could be various other profiles that are used in the case of turbines. So, some of these I have listed here. And the most fundamental form of these blades are derived from the NACA series. You could also have turbine blades from the Agard series or one could use profiles with circular arc or parabolic arc camber like what is done in the case of compressors. And profiles could also be derived either graphically or empirically from a specified pressure distribution or a mach number distribution. And most of the engine industries have their own specific proprietary turbine blade shapes which they have developed over the past many years. And so they have their own specific forms or blade shapes which are proprietary to their product. And they have developed these over the past many many years. And there has also been a recent trend towards developing custom designed or custom tailored airfoils. And which are not really related to any of these profiles that I have mentioned like NACA series or any other series. But to develop and design airfoils which are specific to a particular turbine geometry which meets certain set of design parameters. So, turbine profiles blade profiles can be developed or and designed through a variety of these methods which is also very much applicable for compressors. Compressor blades also can be derived either from some of these conventional blades like the NACA series or it could be circular arc or parabolic arc or custom built airfoils which many of these industries have developed over the many years. So, let us take a look at some of these very typical blades which have been developed and used in the last 40 odd years or so. So, some of the very basic turbine profiles which have been derived from the NACA series are shown here. These are two distinct types of turbine blades which are derivatives of the NACA series where they have a certain thickness distribution as you can see here and a certain camber distribution as well. And so you can see here between these two profiles the thickness distribution as well as the camber distribution is quite different and this is from this is along the chord of the airfoil and this is of course, the thickness distribution of the airfoil. One could have profiles which have been designed for a subsonic inlet and a supersonic outlet and this is as I had discussed in the last lecture very similar to a convergent divergent nozzle which has a subsonic inlet a throat and then a supersonic or a divergent section which leads to a supersonic flow at the exit. So, one might have an inlet flow which is subsonic and that accelerates and reaches a throat and then again there is a divergent section which leads to a supersonic flow at the exit. One may have blades blade shapes which are very different from what I just showed for example, a typical let us say a steam turbine blade which is used the one which is shown here is for the tip section of a typical steam turbine blade. And you may also have a blades which have a supersonic inlet and a supersonic outlet like what is shown here. And so as you can see between these 4 or 5 different examples that I just showed the turbine blades can be entirely different from depending upon the kind of application for which it has been developed and designed for. So, turbine blade shapes can be extend quite extremely different blade for example, if you look at the blade which was used for a subsonic inlet to supersonic outlet kind of geometry compare that with a very traditional NACA type of airfoils which generally tends towards the subsonic kind of application. One would see that the blade shapes can be quite different and so how does one arrive at this kind of a blade shape. So, that is something that will basically depend upon the application as I mentioned and that boils down to the kind of work output that the turbine is supposed to generate. And if you look at that work output from an airfoil sense or from the airfoil point of view it basically boils down to the pressure distribution on the airfoil surface or the loading of the blade itself. And so the blade shape basically dictates the loading of the blade or the amount of pressure distribution on the suction surface and the pressure surface. So, the variation of the pressure static pressure on the suction and pressure surface basically gives us the loading that this particular blade profile or the airfoil section has been designed for. So, let us take a look at a typical turbine blade and try to look at understand the pressure distribution around such a typical turbine blade. So, here we have a very standard so called standard turbine profile and we have an inlet velocity absolute velocity of C 1 which is entering at an angle of alpha 1 and it exits at a velocity of C 2 angle alpha 2. So, here as you have seen in the first lecture on the axial turbines there is a pressure surface and the suction surface like any typical airfoil. And so if you look at how the flow behaves as it moves on both these surfaces the suction surface and the pressure surface. So, I have plotted the pressure distribution on what is seen here the static pressure distribution between the inlet and outlet of the turbine blade. So, if you look at the suction surface pressure distribution that is shown here what is seen is that there is a drastic drop in this static pressure up to a certain level and then the static pressure again begins to increase. So, if you look at the flow that as it passes over the suction surface of a turbine blade this basically means that the flow accelerates and the acceleration is quite steep as defined by the slope of this pressure curve. So, this steep curve here or steep drop in the static pressure indicates that there is a rapid acceleration of flow along the suction surface. And that progresses and continues quite for a certain distance along the length of the blade and after a certain distance the static pressure again usually begins to grow of course, this depends very much upon the blade geometry, but in a typical turbine blade one may also have a recovery of static pressure after it reaches its minimum, which means that there could be a certain gain in static pressure towards the exit or towards the trailing edge of the blade. And this is a typical pressure distribution on the pressure surface you can see there is a mild well initially it can kind of remains constant well the slope is much shallower as compared to that of the suction surface and but there is still a steady drop in the suction well static pressure on the pressure surface as well. If you compare the pressure static pressure as at the inlet that is what you see here by let us say denoted by p 1 and compare that with the average static pressure at the exit. Basically, this tells us the amount of this acceleration that has taken place in the blade passage and so the area between these two curves that is the suction surface and the pressure surface gives us the loading that this particular blade has been designed for. And what is shown here as p naught is basically referring to the stagnation pressure, which occurs at the stagnation point of the blade which could be a point somewhere here. And so the maximum pressure that you see here in this particular blade geometry is basically the stagnation pressure which is true for any air foil and exit pressure that is denoted by p 2 is substantially different from what you see at the inlet. And that is the difference between these two is basically given by the dynamic head across this particular blade. So, this is a pressure distribution which is of a typical turbine blade and if you look at the pressure distribution of all those blade geometries I had shown in the few slides earlier. The pressure distributions can be quite different, but the general trend is quite is going to be quite similar to what you see here I have just seen now. And in general you can see that there is an acceleration of flow right from the inlet to the exit of the turbine except for the suction surface where in some cases you might have a local flow deceleration which in some cases might lead to a pockets of flow separation under certain off design conditions something I had mentioned in the last class as well. And unlike in the case of compressors the flow in the case of compressor is going to undergo a steady increase in static pressure and which is basically the adverse pressure gradient which is quite different exactly opposite to that you have seen in the case of a typical axial flow turbine. Now, this also means that there is a significant defect of the way the blades are placed as well. So, that if you have to get a decelerating flow or an accelerating flow that will very much depend upon the stagger of the blades and also the number of blades. So, if you have more number of blades or if you try to put more number of blades in on the annulus this means that there are more number of blades which can take up the loads and so the loading per blade would reduce. And therefore, the stress associated with the blade loading also comes down at the same time more number of blades mean means that you would need the overall weight of the disc and the blades would increase. And therefore, the associated cost and complexity increases at the same time if you look at a configuration which is lesser number of blades this means that each blade has to now take up a load which is more than what it was for the previous case, but at the same time you save on the weight of these blades and complexity and so on. So, is there a certain kind of an optimum number of blades that can be used for a given configuration. So, spacing between these blades because it is a very crucial parameter there is a certain again an empirical correlation which was developed way back in 40s. And of course, this has been modified and there are modern versions of this criteria which is currently available and used by the industry. And so, how does one arrive at an optimum number of blades for a given turbine configuration. So, there is a criteria which was developed in 1945 by Zwefel which relates the blade loading or the blade force to some of the aerodynamic parameters. So, this is again an empirical correlation which is also related to the blade geometric parameters. So, Zwefel's criteria originally was defined as the blade force divided by half rho v e 2 square into the blade chord. So, this can be related to the geometric parameters of the blade.  So, here you can see that this s by c is basically the spacing to chord ratio. And generally accepted optimum Zwefel parameter is taken as around 0.8. So, if you fix Zwefel parameter as 0.8 then one can actually calculate the optimum spacing ratio from assuming Zwefel criteria of around 0.8 and also the blade parameters like the angles alpha 1 alpha 2 and so on. So, this kind of gives us some empirical some idea about how much the blade spacing should be given these parameters like the blade angles alpha 1 alpha 2 and so on. This was of course, developed about 60 years ago or even more than that and there have been several modifications to this and there are modified versions of the Zwefel criteria which are available and used by industry for developing or arriving at certain amount of optimum spacing to chord ratios. And so, what is also noticeable here is the fact that though this parameter was of course, developed way back in the 40s only slightly modified versions of these are available and even though it was developed way back in the 40s it is still being considered as a sort of an empirical thumb rule parameter which can be used at a design point at a starting point of a turbine design level. Now, what I will do now is to summarize the differences between turbine blades and compressor blades and of course, subsequently discuss about turbine and exit nozzle matching. So, before I move on to matching between turbine exit and the nozzle let me just quickly summarize some differences between a turbine blade passage as compared to that of a compressor. One of the obvious differences is the fact that the pressure drop in a turbine is much larger than the pressure rise in a single stage of a compressor. The flow turning in a compressor is usually restricted to around 20 to 35 degrees whereas, in a turbine it can be as high as 160 degrees as you have already seen the flow turning is substantially different from that of a compressor. In a turbine a designer tends to sort of delay the formation of shocks so that the losses across the shocks are minimized whereas, in a typical transonic compressor shocks sort of form one of the modes of deceleration themselves. So, there is no way designer can actually delay the occurrence of shock there because that is one of the modes of deceleration in a transonic compressor and that is one of the reasons why transonic compressors generally have much lower efficiencies than corresponding turbines because of the fact that in a turbine it is still possible for the designer to delay the occurrence of shock till the later part of the blades and towards the trailing edge and so the losses the shocks actually occur in the lower Mach number region and so the losses associated with the flow across the shock is lower than that in the case of a typical transonic compressor wherein deceleration itself is carried out through the occurrence of these shocks. So, these are some fundamental differences between a turbine blade and a compressor blade and I think that that is something that you need to understand very carefully which is of course from the fundamental aerodynamic aerothermodynamics of the flow through a compressor and a turbine that dictates these fundamental differences in the blade shapes themselves. So, let us now take up a slightly different aspect of the turbine flow and we will now try to understand the effect of the turbine exit flow on some of the downstream components let us say the nozzle. So, how is the exit flow of a turbine matched with that of the exit component like a nozzle. So, the operation of a turbine as you already understood that turbine is linked to a variety of other components like the combustion chamber or the compressor and it is actually mechanically directly coupled to the compressor it is also connected to some of the thermo or aerodynamically connected to some downstream components like the nozzle. So, all these upstream and downstream components have a significant effect on the turbine performance and so in a typical design exercise the compressor and turbine performance characteristics would form a very important aspect of engine integration and matching of the performance of the whole engine as well. So, we have seen that in the case of turbine performance very much unlike that of compressors. Turbines do not really exhibit very significant variation in the non-dimensional mass flow with speed which is quite unlike the case of compressors which exhibit a drastic change in the performance characteristics with speed and so the turbine operation. So, if you look at the turbine performance characteristics one might wonder that turbine because the performance does not really change much with the speed it would be rather easy to control the performance of the turbine and match it with the compressor. But what is significant here is the fact that the turbine performance is actually limited by the nozzle which is downstream of the turbine because there is a certain amount of mass flow which the nozzle can handle and even if the turbine is able to operate at different mass flow rate the nozzle downstream would sort of dictate the amount of maximum mass flow that the turbine can actually handle. What we will very soon see is that most of the modern engines for a majority of their operation would be operating with both the turbine as well as the nozzle under choked condition. So, the nozzle exit area has a very significant effect on the turbine performance and its operation and so whether the nozzle is operating under choked or un choked condition would have a significant influence on this matching exercise. And so though if you look at turbine and nozzle from a fundamental thermodynamics point of view and not without actually worrying about what constitutes these components both these components are thermodynamically identical in the sense that both of these components are expanders that is flow expands through a turbine the flow expands through a nozzle as well of course, their functions are entirely different. But if you plot a turbine process and nozzle process on a temperature versus entropy diagram both these are identical they are both expanding processes flow expands through turbines it also expands through a nozzle. And so the matching of turbine with that of a nozzle is very much identical to that of matching between a gas generator turbine with that of a power turbine. If you recall in some of the forms of engines like turboprop engine a separate turbine is used for driving let us say the propeller. And there is a turbine which actually drives a separate turbine which drives the compressor. So, there is also a matching exercise between this kind of a turbine with the power turbine. And the matching between or the matching process between a turbine which is connected to the compressor with that of a power turbine or a nozzle they are quite identical because thermodynamically all these components are very much the same. So, if you look at the nozzle once the nozzle is choked that means the nozzle non dimensional flow has reached its maximum then it is basically independent of the pressure ratio. And therefore, in some sense the flight speed because the nozzle pressure ratio is a function of the pressure build up which has taken place across a variety of components like the intake the compressor the loss of pressure in the combustion chamber and the pressure drop in the turbine. So, all these if you multiply all these pressure ratios that basically dictates the nozzle pressure ratio which means that the once the nozzle is choked it basically becomes independent of this pressure ratio and therefore, the flight speed as well. This means that once the nozzle is choked it sort of fixes the turbine operating point because choked nozzle would mean that the nozzle is operating under a condition where the it has reached its maximum mass flow rate and it is not possible to enhance the mass flow rate any further the nozzle cannot handle any higher mass flow rate. And therefore, the turbine also has to operate under a condition which matches with this nozzle the choked nozzle operating condition. So, a choked nozzle would fix the operating point of a turbine and therefore, when the nozzle is choked or operating under a choked condition with the maximum mass flow rate the equilibrium running line or the operating line would basically be determined or fixed by the turbine operating point and it kind of becomes independent of the flight speed itself. So, I will try to demonstrate this aspect through the performance characteristics of a turbine as well as that of a nozzle. So, here we have the matching characteristics of a turbine as well as that of a nozzle. So, I have denoted station 1 for the turbine inlet station 2 for turbine exit and station 3 for the nozzle entry. So, we have mass flow versus pressure ratio for the turbine and on the right hand side here we have mass flow versus the pressure ratio for the nozzle. Let us take up the nozzle first because this is of course, something you would have learnt in your gas dynamics course as well that the nozzle performance as you change the pressure ratio the mass flow rate increases and then it reaches a peak which is the chocking mass flow after which the mass flow remains the same irrespective of the pressure ratio. So, once the nozzle is choked the mass flow it becomes independent of the pressure ratio and does not change in spite of changing the pressure ratio to any value. So, here if we have a nozzle which is operating under choked condition and if you look at the corresponding turbine characteristics. So, here we have the turbine characteristic here the mass flow versus the pressure ratio. So, this you see here is the mass flow rate of the turbine as a function of its pressure ratio. So, if the nozzle is operating under choked condition which is denoted by let us say this letter a that fixes the mass flow rate of the nozzle and since that fixes the mass flow rate of the nozzle that would also fix the amount of mass flow rate that the turbine can handle. But, you can see here that the mass flow this mass flow rate is higher than the chocking mass flow of the turbine chocking mass flow of the turbine as denoted here as m dot root t naught by p naught is lower than the chocking mass flow of the nozzle. So, the turbine cannot really operate under this condition without operating at a lower pressure ratio which means that the turbine is now operating or is forced to operate at a condition which has a pressure ratio lower than the chocking pressure ratio for which the turbine can is capable of operating. Similarly, if you look at other conditions here in which under which the nozzle is actually un choked. So, here the turbine is actually able to operate at a much higher mass flow rate as well. So, this sort of demonstrate the fact that the nozzle chocking condition would force the turbine to operate under condition which matches with that of the nozzle itself. So, even though the turbine in this example is actually capable of operating at a higher mass flow rate it is forced to operate at a lower pressure ratio because of the fact that the downstream component is choked under that operating condition. And most of the modern day engines as I mentioned would be operating under a choked condition for majority of its operation when it is operating under a high thrust condition that is high mass flow condition like during takeoff or cruise except under very low thrust operating conditions like during landing or taxiing when the engine is not operating under its full mass flow condition these components like the nozzle or the turbine tends to remain un choked under these conditions. But unless it is operating under these conditions most of the time engines would be operating under choked condition. So, only when the aircraft is let us say preparing to land or it is taxiing the nozzle may be un choked and it is also necessary that one would have to ensure the matching even at low speeds. And it is under these operating conditions that when you try to match an un choked nozzle with that of a turbine and eventually with that of a compressor that there could be problems with reference to the compressor operation because under these conditions the operating line might move very close to the surge line which is something that is the designer or the engine integrating team would have to take care. Because if the operation is very close to that of surge there is a risk that the compressor might enter into surge and of obviously that could affect the entire engine operation itself. So, at very low speeds when the operating line tends to become very close to surge and that is where the nozzle and therefore, the turbine tends to remain un choked that lot of care needs to be put in between matching of not just the turbine and the nozzle but also with components upstream like that of the compressor. So, this is just a quick overview of the matching operation there is also an extensive matching that is done between the compressor and the turbine and that is incomplete without taking this nozzle into account because even though a compressor and a turbine might well be matching in their operating range. It is the nozzle which would sort of dictate the or fix the turbine operating point and then the whole matching exercise between the compressor and turbine might require another round of iteration to ensure that all these 3 components operate under a matched condition even at low speeds where the nozzle might be un choked. So, let me now very quickly recap this today's lecture. We had discussion on 3 distinct aspects of turbine operation one was to do with the performance characteristics. We discussed about the different performance characteristics in terms of mass flow and pressure ratio efficiency and pressure ratio and we have seen that the turbine operate performance characteristics is quite different from that of compressor and the turbine performance is usually insensitive rather relatively insensitive to varying speeds as compared to that of compressors which can be quite sensitive to operating speeds. We also discussed about the different blade shapes which are used in turbines and the nature of flow as it passes through some of these different blade shapes and lastly we discussed about matching between the turbine and one of the downstream components like the nozzle. You might have additional components like a power turbine or after burner we have discussed about the nozzle because that is sort of limiting the performance of the turbine itself. So, these were some of the topics that we had discussed in today's lecture and so it is about time that we have a session on solving some numerical problems from axial flow turbine. So, we will devote our next lecture towards a tutorial on axial flow turbines where we will be solving some problems from axial flow turbines and I will also have some exercise problems for you which you can solve based on our discussion in the last few lectures as well as the tutorial session itself. So, we will have a tutorial during the next lecture.


Everybody forced here ripping dual case NBA 22 23 impeccable basketball first off the line and hobby number three It is a tier random style break the results are on your screen if you're watching live There's a link in chat and you can always find these results at latent sports cards comm at any time results quick link bottom of the website Search bar is a good way to find results to let's do it everybody. Let's get the both these cases open and we'll go Do the hobby first and the photo should have total of five bar cards in in here We should get one in the hobby case then four in the photo three that are first off line exclusives and then One that is like the guaranteed per case. They keep that one in there All right, here we go There's the hobby bar card I'll open all the bar cards up as we get them just because it's a cool case This regular case. I would just wait till the end to do the bar to start us off. Nick's Julius Randall five out of 30 and See Occam to 75 Raptors Bulls the martyr rose in a 99 and Pelicans Jonas Valentunas auto to 99 extravagance Start us off on the autos Pelicans Valentunas Rockets first rookie hit is elegance rp8 at 25 tie tie Washington, Jr. All those silver to color on the patch Hawks with an auto now is Deandre Hunter extravagance to 35 It's a 21 22 impeccable it's Deandre Hunter redemption Tyrese Halliburton watercolor signatures that will go to the Pacers You want to make sure? Sometimes you never know with guys that I've been on two teams especially in a short amount of time. Oh Steve come on What is this guy doing? Yeah, it is Pacers on the Halliburton Pacers and then Packable stats auto Celtics Larry Bird 50 of 60 on the auto Larry legend nice hit Celtics 50 of 60 there and first bar card of the break the last Is 19 of 20 for the Bulls try out to find silver Zach Levine go The Bulls oh No, Steve don't do that. You know if on got that tomato bad Steve Stanley Stars rookie Rockets Jabari Smith, Jr. To 75 a lot of those old tiny scratchers you see on the protective surface there Adhesive cover all right Jalen Green the 99 Rockets followed by Donovan Mitchell six of 20 go into the Cavaliers And you're bar switch junior rookie to 30 Rockets Lakers elegance Jersey auto to 99 Lonnie Walker the fourth. Is that true Steve or you just you just saying things at this point I think you're just saying things indelible ain't got a big Al 9 of 10 Celtics Thunder on the elegance Ricky Jersey auto who's Mon Jang one of 99 Next up is Jeremy so on to 99 on the stainless stars rookie auto spurs on camera focus There we go nice so on Him and when be together should be pretty fun and Celtics again adjacent Tatum indelible Inc. Auto 9 of 25 Celtics are on fire right now Alda 10 a bird in the first box and now we got a Tatum nice nice nice All right last hobby box is what we got is what we got. Yep. Yeah, sometimes sounds like cool. Yeah, I think most people don't prefer them Stainless stars for the Nets Kevin Durant 75 be safer. I don't know That Mookie at second base it is rookie Agbashi to 49 for the jazz Sohan rookie to 75 spurs True holiday to 99 bucks How many games has Mookie played at second base this year? Well, wherever they got him playing Celtics another hit here to 99 Dino Raja auto Pelicans rookie autograph to 99 EJ Liddell Bucks, here's the nice one elegance RPA Marjambochamp 49 of 99 Marjambochamp as Kyle would say This is fast as you can it's card. We got Sean Kemp Celtics auto watercolor to 99 Sorry, not Celtics, but sonics sonics what I meant to say What sonics do go to the Thunder and we've got stainless stars rookie auto Thunder Chet Holmgren in the back of the hobby case 30 of 49 What do you guys think Chet or Wemby for rookie to your better odds? I'm not saying that dealt for sure one of those still for sure went about better odds Chet or Wemby I think he has the edge because the Thunder already have legit players there So like it won't be all chat even if he is very good But the spurs are but at the spurs like when he's gonna light it up, I think All right photo case now one bar per box Number number eight silver number to eight. I think on all of them and this one has two So this one has the It's gonna be the only one with two It's 49 Jalen Brunson nicks one of one Tyler hero Platinum foil one of one base parallel for miami Nice card. Got Malachi Brandon rookie out of 99 spurs I mean chet could have come back in the playoffs. They were saying they just didn't want to have his first game is be like That yeah, you know like important things where you maybe just trying to get him out there for minutes Carousel Ferdinand Tellable Inc. Got up to 99 for the Cavs Like his whole career. Yeah, but I meant like this year because With the Red Sox he played a few at second base like early early on in his major league career And then after like 2015 he didn't play any a second Yeah, yeah, he was he was in a fielder when he was drafted To 99 a rookie auto dylan terry stainless stars for the bulls and they're like, oh, this guy's legit gold glove right fielder So good Robert Parrish immortal ink auto Celtics to 99 Oh, that's this season. Okay. Okay. So you need a second base 13 stars survival. Oh, that's pretty good That's that's quite a bit actually dylan during the 35 rookie stainless stars auto for the pistons Awesome card pistons and rockets to barry smith junior rookie autos two of 99 Awesome hit rockets. It's a good box Box here one of one hero Duren to barry smith and two bar cards coming up Um, I don't know. What's what we'll go here first Rockets try out to find silver eight of ten jalen green That's the non first off the line bar right there And spurs troy ounce of fine silver rookie jeremy sohan two of eight Pink haired sohan. Yeah, I don't fit personally. I don't think chet will be rusty I think he's he's gonna have like an entire off season He has the like we're in the off season.  Chet the 25 rookie david roddy to 49 for the grizzlies 75 lebron james lakers kd Nets to 99 autos now illustrious ink for the nix kazi russell to 99 Pistons another hit here. It's an adrian danley elegance jersey auto to 99 All the veteran jerseys will be game-worn and impeccable Nuggets paint and wots and rookie autograph silver nine of 25 Thunder again thunder thunder killing it now. You got a second year illustrious ink josh giddy auto to 75 47 of 75 Dang okc Clean it up same with the Celtics adjacent tatum impeccable stats auto to 60 Congrats sees again second tatum And two of seven on the troy ounce of fine silver pistol pit maravich jazz The whirling jazz goes to utah jazz Last one everybody. All right stainless stars lamella ball hornets 96 to 99 Him and miller should be pretty pretty good together She's got to keep lamella on the court. I think upside down sleeves The mellow Yeah, again the thing for chet though is he has sga giddy and a few other pieces there. So I don't know like If he's really good, I'm not sure if he's gonna get the run to put up like the counting numbers and all of that to be a rookie of the year I just think a guy like when be you're even like Like miller like those guys will be in situations where they're going to get the ball a lot Simmons 99 nets Simmons 20 nets And pool to 30 for the Warriors Wizards legends jordan pool. What's up, mike? Mike D in the happy sunday, dude Am I doing the place to be? Wizards auto to 10 illustrious ink denny fd Lasers now a lennie wilkins canvas creations auto to 75 Wizards again rookie auto this time johnny davis to 99 Chianta george, I can see that I can see that one in the lottery. I could realistically see but Jason kid immortal ink mavericks auto to 35 Pacers rookie auto benedict mather into 99 Ice hit pacers And jazz again another bar card here one of seven carl malune troy ounce of fine silver Let's go pretty well, man. Good dual case. There are some teams. They're really well some teams hit multiple hits I'm surprised the team like two tatums is pretty surprising. Honestly without mike Hidden a bunch of the same rookie isn't the craziest thing. We've seen that before an impeccable. Okay All a hit recap here all the autos and relics pacers halibur and watercolour signatures redemption Jason kid mabs johnny davis denny avdia Lennie wilkins for the blazers got Peyton watson adrian danley Kazi russell for the next to barry smith jr a robert parish dylan terry carousel verts The cabs there shon kemp going to the thunder via the sonics marjane bowchamp dino raja ej ladel jeremy sohan alahorfer to 10 Usman jang londi walker the fourth a larry bird Deandre hunter ty ty washington jr elegance rpa and a yonas valentudas All right, you've got giddy to 75 illustrious ink thunder silver bar sohan rookie spurs to eight jalen green eight of 10 for the rockets Durin on the stainless stars rookie auto to 35 for the pistons one of one tyler hero heat the base parallel Holmgren stainless stars rookie auto for the thunder that one's to 49 indelible ink tatum the 25cs silver bar levine bulls That one's out of 20 Carmelone jazz one of seven silver bar Mathur and rookie out of the 99 pacers silver bar is maravich to seven for the jazz as well And another tatum celtics impeccable stats out of this time Thank you very much everybody. Congrats those that hit well moving on to football you


Hi, my name is Nola Khadiani, so I'm a data analyst. So, I was a data first earlier this year, and we've been making sure that we don't stay. It has been very, very exciting, very insightful, very... It has been a awesome experience so far. It's just me having to like learn and re-learn, and unlearn somethings, and applying them to like my school studies. Learning, learning all this stuff, all this, learn, learn, learn and learn again.  So, the tools can all come after when you want to properly learn. It's a 1,000 out of 50 cents. I would recommend this to anybody.


Coach Briebel said earlier this week he considers you a starter now, you consider yourself a starter? Uh, I mean, that's a good question.   Can you make some match with that? Yeah.    Um, and just repetition, again, you know, not only when it's like in practice, but also when it's a game, you know, when it's not just walk through, or you don't know what you're getting, you know, how you adjust to those, you know, those situations.  I know you've got a humble hype armband. What's that all about? Uh, it's humble over hype. It's a nonprofit that I reached out to while I was down there in Texas. It's pretty cool. You probably should have looked up on it. But it's basically like trusting that, you know, God and yourself know over hype is what it is and what's the meaning behind it. It's working good. What stands out about the Jets offense to you? They have two pretty good backs, you know, a young quarterback, you know, he's pretty nice. He can make a lot of throws, CDs over there.  You seen the reviews about that film studies, that natural flow?  I think that's why, you know, I arrived a little faster. And as you continue to watch film, like being in the league, like how does that kind of progress? Whereas you understand things better, you see things better. Right. I feel like, you know, a lot of the offenses throughout the league run in a lot of the same stuff, you know.  Whether it's how they put it or how they place the players, it's pretty much the same throughout. You talked about instincts and arriving at the ball fast. How much do you feel like you're in a pretty good groove right now with how you're playing? I feel like I'm in a pretty good place. You know, it's going to be a long season.  Just, you know, just stay on top, being consistent is my main focus right now. The front seven have talked this week about needing to, if you're the second guy to arrive, start ripping at the ball, trying to get some more turnovers. How much will that be on you guys mind on Sunday? It's going to be on a lot. You know, we haven't had any since the first game, I think.  We didn't have any this past Sunday and Coach had three.  I feel like you've got to pride yourself in kind of being an energy guy, a guy who maybe makes big hits, makes things happen out there. I mean, I feel like that's just, you know, in my play.  Does Coach Crabel remind you guys that David Quadri is causing trouble? That's been a emphasis this week, you know, the Office of Lime and Leadness in the first phone, which is pretty funny, but it's real. So we need to, you know... That up more than a timer. Yeah, yeah, you make sure we know. You guys have been the Green Dot guy at Timer 2 this year. What's that responsibility like and how's it different from just, from when you don't have it?   I mean, of course, when we go against tougher crowds and louder crowds, it's hard to communicate because you can't really hear it, but, you know, that's a big responsibility. So I just make sure, you know, I just take that into account and make sure everybody get the call. Is that normally a bigger problem at home? Yeah, but hopefully, you know, sometimes we're on defense. You know, they could probably hear us more. Well, my team is probably hear us more. At Seahawks, it was, you know, that was a challenge.


Hello friends! Welcome back to my channel. It is time for our May Wrap Up. I'm already overheating in this top. I'm not enjoying it! I'm not!  So welcome, it's time for our May Wrap Up. We're going to chat about the books that I read in May. So if you haven't watched my Wrap Ups before, we do reading statistics first, then we go through our disappointments, surprises and hits. I don't talk about every book that I read in the month because I think that's boring. I get so bored! And some books I just want to read. For example, I read two of the forward collection this month, which is like a sci-fi novella collection I'm reading. I've only got one more to read before I finish the series. But for that, for those, like, I don't really want to talk about them. They're 50 page novellas. I don't have a lot to say. I kind of just want to read them for my own enjoyment. So I only really talk about what's notable, like what we really want to talk about. So let's just get straight into it. Let's talk about the reading statistics first, then we'll talk about the books afterwards. So in terms of books read, I read nine books this month. It was not the greatest reading month for me in terms of how many books I read.  I was like, I don't want to read reading. Who is that? I don't want to read. So I just wasn't really in the mood in May to read a lot and I kind of just honoured that and didn't make myself read, which I feel like was the right thing to do.  But hopefully in June I can, you know, get ahead and read quite a bit. So I feel like it was the right thing to do. So I read 2,169 pages. So that's an average pages per day of 70 pages, which is below my preferred amount of 100. I prefer to average out on at least 100 pages per day. But you know, 70 isn't to be sniffed at, but you know, that's 70 with me, you know. I very rarely read 70 pages a day. I probably mostly read zero pages, zero pages, zero pages, 300 pages. Like that's typically how my reading goes. I had an average book length of 241 pages. So I think this is my shortest of the year so far. I read quite a lot of short books. So not only was it nine, nine books, it was nine short books. Well, guess what people? I get excited about small things. I just like didn't want to force myself into reading if I don't want to because I think that's when, you know, it becomes a chore, not something I love to do. You have to honor how you feel.  You have to kind of honor how you feel. I did however have an average rating of 3.72, which is pretty high. So out of the nine, we're getting to this, I had quite a few five stars. But I feel like a lot of five stars and then like quite a lot lower books. And the average time a book had been on my TBR was two months, which is really short. I think I read a lot of books that had like literally just come on my TBR that I was kind of buying for videos that happened this month. And in some ways that's good because you're like getting through them quickly, but also there's some poor books here that have been here for a long time. And I don't seem to be getting to them every month. So I guess a goal for me next month is to try to have a much longer average time on TBR. Okay, then let's whip out the bar charts and the pie charts in terms of rating. Like I said, I had three five stars, one four star, four three stars, and one 2.5 stars. So I would say great that I had three stars. It's a really high proportion, like a third of what I read were five stars. We'll get into that at the end of the video. But um quite a lot of three stars as well. They're kind of like meh. You know, it was like five and three stars was kind of the story of our month. In terms of genre, I read one fantasy, one horror, three mystery, one romance, two sci-fi, and one thriller. So I'm pretty happy with that. It's a really nice mix of genres with mystery being the highest genre because I love mystery. So I get happy when I can read more mysteries. You know what's the most exciting thing about winning? It's when you win. I love that feeling. In terms of format, two audio books, four were mixed media, which means I had the audio book and the physical or e-book, and three were just physical books. So again, mixed media is usually kind of my highest pie chart of that now that I've added that because I do really like if I can to have the audio book with the physical. It is expensive, so I often, well I have Scripps. If they're on Scripps, that's great because that's free. But in terms of getting them on Audible, I try not to do too much. There was a few books this month I think of that I purposely didn't get the audio book for even though I couldn't because it's like that's expensive. That's really expensive. In terms of audience, I read seven adult books, one middle grade, and one YA. So very much adult skewed this month. I feel like that is the way that my reading is tending to go. And I think I need to be more conscious with that with the books that I buy because I'm tending to reach for a lot more adult than I think I have in previous years, which is interesting. I still think of myself as a lover of YA. I love YA. I think last month it was pretty much 50-50. But it's hard because I'm like I want to read older YA. I'm not really interested anymore and I've had a lot of issues this past year with picking up YA and it reading as really young YA and that just not being what I'm looking for. However, it's very difficult to tell that before you buy the book or when the book's coming out and you get excited for it because the book doesn't say like young YA, do you know what I mean? So it's hard to know until you get into the book if it's gonna read as older or younger YA. In terms of how I acquired the books, one was a book of the month, one was a gift, two were from Kindle Unlimited, three were books I bought myself, one was from Audible. So that is how the mix there. In terms of series stats, five books were part way through series, which is a great set. You know, part way through series, I'm getting series finished. One was the first in a series, so I'm happy with that. Five series I made progress in, one new series that I started, and three were stand-alones. And then finally, in terms of author status, one was a debut, three were authors I'd read before, and five authors were new to me. So yeah, I'm pretty happy with all those stats, I think. Interesting, interesting stuff to be cleaned from them. And I feel like even though I didn't read a lot, I'm not upset with my reading this month. Right, time for the disappointment. So my biggest disappointment of the month, and this one's actually tricky, but my biggest disappointment was How We Fall Apart by Katie Zhao. This one's tricky because objectively I can see this is for younger YA audiences. This was my book club pick for April. I always tend to read them in the next month because I like to read them really close to our live show, and our live show is usually like the first weekend of the next month. And here's the thing, I know if I had read this when I was 12, 13, perhaps 14, but pretty much when I was 12 or 13, I would have eaten it up. Essentially, we're at this like prep school, like gossip girlie kind of school in New York, and there's a murder and the kind of friendship group all trying to figure out who's done it, and it's very like backstabby and stuff like that.   I'm getting older. I don't know if I can, if I want all this drama all the time, if I'm being honest. The ending for me of this was particularly disappointing. There were elements of this that I liked, perhaps earlier on. I struggle to remember much about it now. I've like cleared it out my memory. The ending of this, the reveal of the villain of the book, if you will, was ridiculous. Perhaps one of the most annoying endings I've read in a long time. I was like, oh, is this really the root? This is really what we've chosen, huh? This is the root we're going down. This is the root we're going down. So I originally had this author's next book, as well as my anticipated release for this year, but I think I'm going to take it off. I don't think I'm interested in it anymore.  Like I remember being that age and wanting to read books that were kind of like scandalous. I felt like, but like are written for my age but still feel scandalous. Do you get what I mean? That's what you want to read at that age. And I think it's great for that audience, which probably is its intended audience. But for me, it wasn't it. And then my other two disappointments of the month were just mentioned quickly because they're not strictly disappointments. They're both three stars. I just expected more for both of them. So the first one is Dark Waters by Katherine Arden. So this is Katherine Arden's middle grade horror series. This is the third in the series. I've only got one more. It comes out in August and then I finish this series, which I'm so proud of. But we're following these kind of group of friends who keep having these interactions with this ghost. I don't want to spoil much because you don't know much in the first book. But anyway, in this third one, they kind of get stuck on this abandoned island. And we were following, we have this kind of main girl who now the name escapes me. I can't remember her name. I can't remember her name. Get a job, learn a trade, get some education. We've had this main girl who the first two books have focused on. And this last one focused on the kind of boy of the friendship group. And I just didn't feel like that switching focus really worked. Like the main girl is barely in the book, which is there. But like the focus is really not on her. And I just didn't feel like it worked. I just wanted like the kind of vibes we had from the first two. And this just felt like a bit of a departure from that. But we've got one last book to come and I'm going to read it and I'll finish the series and I'll be so proud of myself. But I just need Catherine Arden to come out with some YA or adult. Okay, because that's what I'm waiting for. If you don't know, Catherine Arden wrote the Bear and the Nightingale series which is one of my favourite fantasy series ever. And I'm just like, yeah okay, I've had enough of the middle grade Catherine. I've had enough of the middle grade. I've had enough.  I gave this three stars. So this is a disappointment because my other two Ali Hazards that I've read, the Love Hypothesis and my brain. I can't remember what the first one's called. But I gave it 4.5 stars. So I've given it a 5 and a 4.5. And I was expecting this one to be along those lines. This is another of her Seminist novella series. It's the second one. Can't remember what the first one's called but I liked it. And this one... I just didn't feel the romance. Um, but it's not what I paid for. It's not.  I didn't feel any kind of like connection between the characters. The sex scenes didn't do anything for me. I just didn't feel it. I didn't feel it. In this one it's uh, they're stuck in an elevator together and they kind of had some history like a couple months ago. And it's kind of flashing back between what happened months ago and what happened now.  And I just didn't, I didn't like that. I think I like to be taken on the journey with my romances and like build up, build up, build up. But this one we were kind of like, the build up was in the past, not in the present. So that didn't really work for me, I feel like. But you know, it's still, Ali Hazel's still good. I'm still gonna finish probably this series this month, hopefully with Below Zero. But um, yeah, my least favorite Ali Hazel would that I've read so far. And it had the whole he's so big, she's so small trope again. And I know the last one's gonna have it. And Ali Hazel, I've just had enough, please. Please say the next book doesn't have it. I just like, once I can deal with it. But like every time. Oh Lord. Again.  Nothing new, nothing changed.  Right, so I only have one surprise this month. And the last three books I'm going to speak about in this video all come from one vlog, which is my Mara from Books Like Woe, booktube twin test video, which I will link. So if you don't want to be spoiled for that vlog, go watch that vlog now. Because I'm going to speak about all three of the books from that video. Okay, time to leave, time to leave if you want to, time to leave. Okay, let's get into it. This surprise can be classed as a hit as well. This was five stars, but I didn't really have any other surprises this month, so I wanted to pick one. And it is The Rook by Daniel O'Malley. So this is one of the books Mara chose for me to read. And I've never heard of this book, ever in my life. I've never heard of this book. And so I wish he quickly, and I was like, okay. But it's a very interesting fantasy mystery where the main character wakes up and she has no knowledge of who she is. No knowledge of who she is. And we find out that the person whose body she's in knew she was going to lose her memory and she's left extensive notes for her to tell her how to live her life and kind of pick up as if nothing has happened. And she works at this like secret, intelligence, magical, it says MI5 for wizards on the front. So that's like the vibe that we're going with. And I loved it. It was such, such, such, such a clever fantasy.  It's very difficult for me to describe concisely in a wrap up. So I would really recommend you go watch the vlog if you haven't already because it's just a lot. It goes on so many different pathways. We have so many characters. We have such detail of this magical world and these magical powers that these people have. I just haven't really read anything like it. I haven't really read anything on this level lately. Talented, brilliant, incredible, amazing showstoppings. It took me forever. It took me like two weeks to read, but I didn't mind. Like it was, you know, you really need to take your time with it, but it's just so funny. It's so, you really love both of these kind of main characters that you end up having. You kind of end up having two, even though they're the same person. And it was just so, so interesting. So it was definitely a surprise because I'd never heard of it before. This was Mara's pick that I was most nervous for and it delivered. Okay. And then finally, our two other hits. That is a surprise and a hit. These weren't really surprises necessarily, but they were hit. So we're five stars as well. Another hit was Death of the Nile by Ag Christy. I loved this. So I've only ever given two other five stars to Ag Christy, which are Murder on the Orient Express and the Murder of Roger Accroyd, which they're coming out this year with one of these editions of the Murder of Roger Accroyd. And I'm going to get it straight away. I think it's like November, October, November, they're coming out with this. I think Harper Collins tend to come out with like two a year. This is the third one I've given five stars to. And a lot of people know the story. You've kind of got a cast of characters on the Nile and Murder ensues. Actually, the first part of this book, we're kind of like meeting the cast of characters in their kind of separate locations and they all come together. And this to me, I actually think is the best writing I've read from Ag Christy. It's her latest book I've ever read because the other ones, I'm obviously reading the pro series in order and I broke away from that just for this book. And it's her best writing. I really feel like you can, it was really interesting to go from that to this because you can really see the development. Perhaps the Murder was predictable, but I didn't care because I just loved the mystery and I love these kind of isolated, they're all stuck on a boat together. We don't know who's done it. There could be more murders. I just think it's like the epitome of Agatha Christie. And there's just something about these classic mysteries that she does so well that are so comforting to me and just something that I absolutely love to read. So I loved it and I need to read. I want to read at least my next two in the pro series this year, which are Perala and Taos and Lord Edgware Dies. I would really like to read at least both of them this year if I can. Then my final hit was The Broken Girls by Simone St James. We're following two timelines. The main timeline is present day with a girl whose sister was murdered 20 years ago and she's dealing with that and in the 1950s in a past timeline we have these four roommates at this very strict sporting school essentially. And then on the grounds of the boarding school is being renovated, another body is found. And so it's all like intertwined and wow, like I love it. This is my first Simone St James and it was so good. Her writing was beautiful and haunting. I got so attached to the characters. It's such like a compulsive read.  And I think it just does such a wonderful job of exploring that. There's little paranormal elements sprinkled in which I thought were great. The reveals at the end, there's like one or two reveals. I thought they were pretty predictable but I didn't mind because that is how I would have wanted the story to go. It was just such like it felt like a pleasure to read this book. I actually think part of the reason I haven't read a lot since I made Mara's video and I think it's because I had three five stars and such quick succession and then I've been a bit like overwhelmed. I've had to like chill out for a bit before I dived in something else and just think about these books because they were just so so so wonderful. I just loved it. I can't wait to read more Simone St James. I need to get all of her books. Even her backlist I'm still interested in reading even though I know they're a bit of a different vibe to her present day stuff because I just love this so much. So there we have everyone. That is my May wrap up. Let me know what you thought of any of these books if you have read them before. Let me know how your reading went in May. Let me know how many books you read. Let me know what your favorites were. How many five stars you had. I want all the info. If you want to give me your stats in detail, give me your stats in detail. I love reading that kind of stuff. So let me know that down below in the comments. If you've gotten to the end of the video, comment. Comment the otter emoji. I love otters. I just love otters. Comment the otter emoji down below if you've gotten to the end. Thank you. Thank you so much for watching and I'll see you very soon in another video. Bye.


What's up, beautiful? How you doing today? You look stunning. Oh YouTubers have blessed me with another hair video. It's been a really good month. I'm excited There's honestly not a lot of things in life that make me more excited than when youtubers like do their own hair It's painful yes to watch but also very entertaining So I'm here for it. I love a little entertainment in my life and I'm ready to watch in 20 cars is today Do something to her hair and probably ruin it I've been getting harassed for the last few days in social media by Antonio Garza stands.  Do you think I'm not gonna do that? Do you think I'm actually gonna sit here and not do that for you? Of course I am. All right, let's watch in 20 guards.  No one DJ Khaled and Bramondo another one We're so clever Antonio. I bleach my hair by myself. This is what happened. Bramondo dies. No one Bramondo Antonio Blond hair. Hello Slightly disappointed in the fact that she she did it herself today, but you know what it makes for great content So let's see what exactly happened when Antonio bleached her hair herself and hopefully it's a decent outcome I've been uh waiting to watch this with you guys. So let's freaking press the play button, man Today, I just had a thought and you know what I had a thought that came from my soul and my being and I'm Feeling like this is very important thought. I need to talk about this now. You might not see this The internet might never see this video, but if you're seeing this video, that means I have made a detrimental Risky and almost life-changing decision. I need to have at least once in my life is bleaching my own hair I feel like she does need to experience it herself that way this can never happen again.  I think this might be a good idea just to get it out of her body I saw Joanna Sidiya. She just bleached her hair and I was like, okay If she could do it, I could do it like if she is courageous enough to bleach her own hair And I've been thinking of bleaching my own hair for a while now might as well Freakin send it. Joanna's hair didn't come out good Antonio. It didn't also Antonio You have so much hair seemingly from what I can see here You have pounds and pounds and pounds of hair.  Oh We got quick blue. We got quick blue. We got mixed match developers Great idea. Oh, and we got t18. You can't do any bleaching at home without t18 So quick blue is gonna be one of the strongest Most pungent bleaches you can possibly use it's severe. It's a lot. It's gonna really get into that hair It's gonna really lighten. It's gonna really lighten fast.  This isn't the worst combination of products I've ever seen so we're working with what we got We're seeing what's gonna happen. It might be fine. It might be bad I don't know but that's okay because I'm here and you know what? Yo Antonio has so much hair. It's actually scary for me Extensions are these like tapins Yo, how do you operate life with those nails? How do you do things? I just don't understand It just seems like it'd be really annoying today if you didn't see my thumbnail or title I'm gonna be bleaching my hair. I'm excited at this video sponsored by no one so My bra Mando I miss having dark hair So I really wanted to go back to black hair or like brown hair. I think just like normal brown hair But I was thinking why don't I like blonde hair? What is so deep in me that is making me not love the blonde hair because once I'm more fun I was not having more fun. It's honey. Oh, you look so good as a blonde Honestly, look really good as a brunette, too But I think the blonde kind of makes look a little more like whoo, like Like I don't know. I feel like the blonde looks really iconic on you though really does So this is my Sally's beauty haul.  So there's the I feel like she's actually highly prepared for this. This might actually not be the worst thing ever So, well, I guess I should try to use gloves, but I don't know how because I have 12 inch long acrylic nails Yeah, I'll see how that goes that. Oh, I kind of always wonder why hair So actually I've never wondered that but hairstyles never wear nails because they just get ruined You literally cannot wear acrylics. So actually wait, my mind is so powerful There's a lot of people that wear acrylics to the salon to do hair like a lot of hairstyles and I actually don't ever I've never actually thought about how they wear acrylics with gloves and Tony. Oh, this is groundbreaking stuff How does that work? And like I wish I wasn't but it probably should be I am that looks I'm just gonna not do the back Let's get on your scalp. I don't really know but like it's there So it's like oh my god, right, but like it's not like you know can't be that wrong in my right And I know what you're thinking Brad, she's starting at the roots. Never served the roots, Brad. Oh my god. He said it all the time Today would be a day that you could start the roots because her ends are already lightened She's just trying to lighten the roots except however here She's doing a retouch and she doesn't exactly have retouchable hair She should have got highlights a heavy heavy heavy highlight or a Heavy heavy heavy hair painting the only time we ever do the roots like this is when we're doing a bleach in tone Which is when somebody has hair like me It's already bright bright blonde and it's fully one color and you get that really harsh line of demarcation when your hair grows out Then you're gonna start the roots and you're gonna paint them like that and Tonya your hair is highlighted It is not fully one color even though it kind of looks like that you can tell that it is there's been foils in there There's been lowlights. There's been highlights. There's a lot going on And so if you make the roots all one shade, you're gonna literally have a root That's all really really bright blonde and then the ends are kind of like not as blonde and kind of like Variations of blonde because they're highlighted that in your roots aren't highlighted because your roots are just a single process Lightened it's just not gonna look right and I don't know how this is gonna come together Brad Mondo if you're watching this I do apologize You just sent me some like of your hair stuff, so it's like I'll just use that and my hair will look good Glitterati link below I think it's actually fine if you've run your hair because glitterati will just save your life I think I'm out of a job now because glitterati is just gonna save everybody and I don't need to anymore Is that too much like I think it is What are you doing? My favorite part is that she's like painting the hair very gently like it seems like she's really gives a F*** about this and she's actually genuinely trying to make it look good going right on the root And then painting gently on the end to kind of like smudge it down Root color doesn't really work like that The only time you should use like a painting technique is if you're doing it like from the ends up not from the root down So then you're just gonna have like a bright root and a little bit of brown in the middle and then bright blonde ends This ain't the right technique I don't think people realize how much work it is to color your own hair.  I'm gonna give it to her though this is Really precise she is going in an every little section and it is quite beautiful She honestly looks like she has a really natural talent for coloring hair. Her partings are divine She is doing a great thorough job. However, this is not really the right technique for what she's looking for If she did want to go all over blonder from roots to ends in a salon We probably go in with foil and foil out every darker piece in her hair And then once everything is one solid color from about like an inch from the root down Then we go back in on the root and paint that all so it's even and then you'll get a very very even Platinum blonde color, but again, that's a very difficult thing to do on yourself. Actually, it's probably impossible You're gonna need to like go and seek some help for that. This is like where we're at right now actually like Why did you not do the edges of your hair? You're just leaving the edges out. I don't get it. This is my current Yes, you are married.  So it's like if worse comes to worse I can just fix it all dying your hair from blonde to black Actually is not that easy.  Sometimes it's not but often times and people do this at home And they go to the store and they buy black box dye to go with their blonde hair That's actually not the right thing to do because once you have blonde blonde hair You have no pigment left in your hair You have to replace the red the blue and the yellow in your hair and in order to get a color that looks like it has a Lot of depth and looks natural and looks vibrant say if you throw on like a brown ashy Box dye on your hair first of all, you're gonna get a lot of ammonia in that you don't need it Your hair is already lightened you all you do is tone it back to dark So typically you're gonna want to use in Debbie permit developer for that and then after that you throw on like an ash tone brown You're probably gonna get a lot of green in your hair because you need to fill in the red and the yellow also in order to get a very Beautifully done brown color to replace the body previously had that probably made no sense to half of you and that's okay Wait it actually doesn't look bad okay, so actually kind of like semi confused here because It actually doesn't seem like this is gonna be bad I think she put such a light coating of bleach on her hair that it's not gonna end up lighting that much therefore It's not gonna end up making like a humongous difference. Therefore. I probably won't be that bad I don't know how long she left it on for but seemingly she kind of just like painted the room very lightly with some bleach I think it's just gonna look actually kind of Decent he looks mad stripy man. Hi. This was gonna happen and yeah, and it pretty much came on as bad I was gonna come out. I'm sorry I can press myself as if like it wasn't like the easiest thing to tell her that was gonna happen This is what I was explaining to you guys She's gonna get a light band a dark band and a light band because she painted her roots And then feathered it through the rest of her hair and also she has really dark hair naturally Lifted to orange because you're not using foils if you wanted to lift us that nice pure blonde You're gonna want to use foils man foils are made for incubating giving the hair heat when it's not in the scalp And for keeping your sections clean Um yellow some brownish Yeah, blonde mixed with red. This is going to be so hard to fix Really really hard because now she has all these different variations of like dark and light And it's all just like mixed in there randomly I would literally need to go in and pick out every little piece that she missed with foils and That is a painstakingly Annoying process. I've done it many times and I honestly every time I've done it I never want to do it again, but then I keep doing it because I'm near done You're like, oh, that was totally worth it. That looks What in the fudge you and Joanna missing the sideburns. What is that? She's gonna bleach it again, isn't she? And maybe tonight I will just bleach it again because I'm impulsive and don't care about my whole being. See you then! This may have came out worse than Joanna's hair. And I mean them. Let's be honest here. I can't fix this My hair's dried a little bit now and honestly like I don't hate it. Like it's like it's not good Let's get that out there that like this isn't good and we just have to accept it like it's not good But like yeah, don't tell me she's gonna leave it like this.  There's many ways to fix botched bleach jobs, and What are you thinking about some more? I was gonna try to fix it myself as much as I would love to do it for the content. You know what I'm saying? Do it for the vlog! No, I didn't book appointment tomorrow. Thank God the person has my hair an appointment open because if she didn't I would be stuck with this throughout my vacation this weekend That looks so bad whoever your hairdresser is I am so sorry so sorry I'm not gonna lie guys.  Her hair stylist is talented. They're talented from what I can see I don't know. I can't really see much but talented. It looks really dope You know, I noticed a pattern here. Joanna bleached her hair before she had to go somewhere on a trip And then Antonio bleached her hair before she had to go somewhere on a trip. Antonio You're supposed to mess up your hair and then take a trip to New York to get it fixed. That's how these things are supposed to go Thanks, Antonio for the content. That was amazing. That was actually really good and honestly came out great Your poor hair stylist though. Oh girl. Oh, she had to go in there She had to go out of there and she had to go all around there to probably fix that it ended up looking great You look fabulous. That's all for today guys Make sure you guys follow me on Twitter and Instagram at bramono.myst My hair care brand X mono hair on Instagram check out Brad and Eric my new channel with my brother link below If you guys would like to purchase any of my merch or glitterati, it'll be linked below for you Thank you guys so much for watching.  Peace