Alright, thanks Mike. The last speaker today is Nigel Stipa, who is a medical student coming from Long Island. And he will be talking to us about OCT and the optic nerve. Okay, can you hear me? So again, I'm going to be talking about the role of optic nerve OCT in the evaluation of central retinal vein occlusion. But my talk is going to be a little different from the other two talks as I'm going to be talking about the usefulness of the optic nerve OCT in light of an interesting case. So let's get started. Sorry about that. Alright, so the patient is a 64 year old Caucasian female with a history of type 2 diabetes and malignant right breast melanoma, complaining of blurry vision for about one week and left sided headaches for a month that ranged from 2 to 9 out of 10 in severity and was worse in the evening. It seemed to have an insidious onset as she noticed that she had some blurring of her vision and she covered her right eye and kind of noticed that she had very, very, very little vision in the left eye. And she reports no other symptoms, no systemic signs, no fever, no jaw claudication, no myalgias and no other ocular symptoms, no foreign body sensation, no pain of the eye, just the headaches on the left side and the blurring of vision. Now given her recent history of malignant melanoma, it's important to note her timeline. Eleven months prior to presentation she had surgical resection for a right breast melanoma and was found to have positive sentinel lymph nodes and consequently interferon therapy was initiated. Three months prior to her presentation the interferon therapy was discontinued, secondary to severe weight loss and alopecia and at that time a PET scan was negative for metastatic disease. Just to give a little more history she has no significant ocular history. She allergic to codeine, she takes metformin and a multivitamin. Her father had type 2 diabetes and diet 68 due to an MI, mother had breast cancer and diet at 86 and there's no significant ocular family history. And of note in the social history she has been smoking one pack per day for the past 35 years. So on exam her visual acuity in her right eye was 2020 and hand motion on the left. There was also an APD present on the left eye. The pressure in both eyes bilaterally was normal. Her color vision was undetectable OS and the visual field was unattainable. Her right eye was normal. Both eyes had full motility and the slit limp exam was within normal limits on both sides except for the posterior exam. So the dilated funnest exam on the left showed significant discodema, some scattered hemorrhages throughout the posterior pole while the right eye was normal and I left out the stage because as a teaching point quickly I like to go through the frisson scale which grades discodema. So I've listed a couple characteristics for each stage but I bolded kind of the important points to quickly determine the stage of discodema. So stage one is characterized by obscuration of the nasal border of the disc and you can see that in this picture that nasal border is obscured while you maintain the superior temporal and inferior border of the disc. Stage two is similar in that you have an obscuration of all the borders. Stage three you have an obscuration of one or more segments of a major blood vessel as it's leaving the disc and that's kind of important to identifying the stage. You can see the vessels on the disc but as you know it right here that there's an obscuration of one of the major vessels as it leaves. Stage four is characterized by total obscuration of the discs, of the vessels on the disc margin and near total obscuration on the disc surface. And then five is simply just total obscuration of vessels on the disc surface. So now that we've gone through the scaling, let's look at the fondest photos of our patient and so how would you classify that? So it's stage five because all the vessels are obscured and as you can see the discodema put together with the hemorrhages scattered all over the posterior pole that this patient is presenting with a CRBO. Now given the patient's age and the fact that she has diabetes, it's not surprising that she may present with a CRBO. Other factors that can contribute include hypertension or a hyperquaggable state, hyperlipidemia, inflammatory conditions or a tumor. So her age is significant but her diabetes, maletus was actually pretty well controlled. So in light of that and her OCT, this is the OCT of the optic nerve head of her right eye and these two images below is the OCT of the optic nerve head of her left eye and you can see the significant discodema in both images but what else do you notice in the lower two images? Of note, if you look at the RPE in the normal right eye you can see how it's kind of deflected downward in the normal position, in a V shape that's pointed away from the vitreous here. Whereas in the left eye the RPE is kind of deflected towards the vitreous at least on this side and you can kind of see it here in this other image and Patrick Sibony, the chairman at our home institution and neuro-ophthalmologist has recognized this kind of pattern in patients that have intracranial hypertension and so he hypothesized that the intracranial hypertension can be manifest as a deflection of the sclera that can be assumed to also be seen as a deflection of the RPE so he hypothesized that you have this translaminar pressure gradient in combination with causing a deformation of the sclera and that's a deformation of the RPE and so Dr. Sibony utilized geometric morphometrics and SDOCT to compare the peripapillary retinal pigment epithelium Brooks membrane shape in eyes with papillodema, eyes with anterior ischemic optic neuropathy and normal eyes. Here again you see a normal eye, the normal position of the RPE Brooks membrane and so he looked at 30 normals, 20 eyes with AION and 25 with papillodema and intracranial hypertension. So as I said he utilized a technique called geometric morphometrics. It's an analytical technique to quantify and statistically analyze the shape of biological forms. So he used 20 equidistant semi-landmarks and digitized them onto the OCT images of the RPE and Brooks membrane spanning 200 microns on each side of the neural canal opening and data analysis was performed using standard geometric morphometric techniques including a generalized least squares across just superimposition, which in layman terms kind of superimposes the multiple images. A principal component analysis which can determine how close or how different the shape is and thin plate spleen is kind of a smoothing program. And so he found a statistically significant difference between eyes with intracranial hypertension and papillodema and eyes with AION and the normal eyes. So the peripapillary retinal pigment epithelium of normals and eyes with AION displayed that characteristic V shape directed away from the vitreous whereas the peripapillary RPE of eyes with papillodema have an inverted U shape inward toward the vitreous which is what our patient displayed. And of significance is that there was no significant difference between normals and AION and this is critical. So what that means is that the discadema alone is not enough to explain the change in shape of the RPE. And then in select cases of papillodema the pre- and post-treatment OCTs demonstrated a change from that inverted U shape associated with intracranial hypertension to the characteristic V shape associated with a normal pressure. So A shows the points, the semi- landmarks that were superimposed on the OCT from the three groups. So the blue represents the points from the patients with papillodema. The black represents the points of the normal eyes and the red represents the points of the eyes with AION. And so you can always start to see that there's this one shape for the blue which is the eyes of papillodema and the other normal shape for the normal eyes and the eyes of AION. And then B just takes the means for each group and then C draws a line through each point so you can kind of see the two different RPE shapes. The blue one associated with papillodema and intracranial hypertension, the red and black are the normal and the AION associated with no intracranial hypertension and hence the normal shape. And then here's one of the patients with papillodema. We have a pretreatment and a post-treatment OCT. And so you can see the deflection of the RPE and the eye and both eyes with intracranial hypertension papillodema. And then two days later it's not quite back to normal but you can see two days after an LP with the normalization of the pressure you can see a flattening of the RPE that's getting closer and closer to that normal V shape that we saw. So he went one step further and he looked at the shape of the peripapilly RPE in eyes with presumed optic nerve shape meningiomas versus normal eyes using a very, very similar technique. Now they're denoted presumed based on clinical data and MRI data. So he looked at 30 normals and 10 patients. So there were 11 eyes with presumed optic nerve shape meningioma because one of the patients actually had bilateral involvement interestingly. And he performed a similar shape analysis using the SDOCT and the geometric morphometric techniques. And he also looked at other variables including tumor size, proximity to the globe, age, and the thickness of the retinal nerve fiber layer. And he found very similar results that there was indeed a statistically significant difference in the shape of the RPE between nearly all eyes with presumed optic nerve shape meningioma and normals. Now the shape was statistically different but in this case the shape ranged from that inverted U to kind of a flattening of the regular V shape of the RPE. And that makes sense because there was, you know, the tumor sizes were different and the proximity to the globe was different. And they found that the greatest deformation associated with meningioma was abutting the globe but they also saw deformation among patients with the tumors remote from the globe. However, patient 11 displayed no apparent deformation but this kind of makes sense because that patient had the smallest tumor and that tumor was the furthest from the globe. So they found a correlation of 0.75 regarding the size and proximity of the tumor to the globe. So they concluded that similarly to the eyes of papillodema causing that deformation of the RPE that a tumor of the optic nerve sheath can kind of cause a local increase in pressure and cause a pressure gradient, a transformer pressure gradient that can cause deformation of the sclera and thus a deformation of the RPE. So if we go back to our patient, MRI of the brain and the orbits revealed a six millimeter lesion in the right frontal lobe and extensive tumor involving the left optic nerve sheath that was hyper intense on T1. The top differential is a brain met in addition to meningioma of the optic nerve sheath. However, meningiomas of the optic nerve sheath typically are iso intense on T1. So the fact that it was hyper intense on T1 is concerning. And in addition, this CSF cytology was normal. So here we go. So on T1, you can see the hyper intensity of this optic nerve sheath tumor kind of going along the length of it. And you don't really see it as well on the T2 or the STIR. But you can also see it here on the T1 with contrast. So optic nerve biopsy and fenestration was performed. And very interestingly, the surgical pathology revealed malignant melanoma with immunohistochemical standing MA-RT1 and HM45, which was consistent with the patient's previous diagnosis of malignant melanoma of her right breast. And this patient was going to get cyberknife due to the single met in the frontal lobe. However, a follow-up MRI revealed multiple met since she subsequently received whole brain radiation. Then six months later, after her whole brain radiation she was no light perception OS, although the hemorrhages and the venous stasis had resolved. So just a couple final thoughts. So this is her OCT before, which I showed you earlier, and then after the optic nerve fenestration. So this correlates with Dr. Sibony's theories about the deflection of the RPE as a representation of a trans-laminar pressure. And it's either caused by intracranial hypertension and papillodema, or as seen in the optic nerve shape in angiomas or in this patient, the metastatic melanoma to the optic nerve that you can actually see, see the deflection regardless of whether it's a local pressure or intracranial pressure. And then with the release of that pressure through optic nerve fenestration, you see a return to the normal V-shape that's directed away from the vitreous. And so this case exemplifies the utility of recognizing the peripapillary RPE deformation in the detection of infiltrating optic nerve sheath tumors presenting with CRBO and or discodema, and especially in a patient with a history of malignant disease. And that's the thing, they haven't really looked at that yet. And as I kind of talked about, when they studied with the presumed optic nerve sheath in angiomas, there was a gradient depending on the size of the tumor and where the tumor was in reference to the globe. Because the one tumor was missed. So there really isn't, I think, perhaps more studies need to be done to kind of find a threshold. But especially in a patient with a CRBO with stage five discodema in addition to any kind of risks including a history of cancer, I think, warrants, they have not, that's very interesting. That's a very interesting thought. Yeah, I know you looked at the anterior skin of optic neuropathy, and that showed that has this significant discodema as well, but no pressure. And so the AION had the regular RPE look. But I'm not sure, I don't think he's looked at optic neuritis specifically. Okay, I'll let him know. They all had discodema. Yeah, that was one of the criteria. I think they only included, at least in that study, they included the patients with discodema. I don't know if they saw ones without it or not, I'm not sure. I was involved in that study, per se. That sounds amazing. Thank you. Oh, okay, nice to meet you.


Many of you will have seen my recent Paris marathon video. If you haven't, then you can click up there and watch it now and then don't forget to come back here. And I managed to break my PB in the Paris marathon, getting 255. My previous PB was set at Goodwood in 2020, in which I got 258 something. And I thought today what we'd do, I know it's not many people's cup of tea, but if you like your stats, I thought we'd go over the differences in the training block between my Goodwood marathon training block and my Paris marathon training block to see what the difference was. Where did I gain those extra three minutes? So let's jump right into the spreadsheet. And you can see I've got two sets of data here, one from Goodwood and one from Paris. And I've broken it down into a 13 week training block. Now that's just a kind of estimation. The Paris marathon training block was around about 13 weeks. But for the Goodwood marathon, I had been training quite a lot before then for other races as well. So I came into the Goodwood training block with quite a lot of mileage already behind me, regular 100 kilometer training weeks. Whereas with Paris, I came in after a long break, a big hiatus of big mileage. So from back the summer onwards, I reduced my mileage. And then certainly from November and December, I was doing very little mileage. So when I came into the training block in January, I was pretty much fresh starting a new block. So let's start with distance. And you can see in the spreadsheet that for Goodwood, my distance overall was 1,548 kilometers over the period of 13 weeks training. And that averaged out at around about 119 kilometers per week. Whereas for the Paris marathon training block, I did significantly less mileage, 1,409 kilometers in total. And that worked out at around about 108 kilometers per week. So a good 10 kilometers per week less for the Paris marathon training block. In terms of time spent running, again, I did more time on my feet for the Goodwood training block 13 weeks. And the total was about 150 hours of running, which worked out around about 11 and a half hours per week of running. Paris marathon, on the other hand, around about 140, nearer to 139 hours of training. That was about 10 and three quarter hours of training per week for Paris. So at the moment, you can see already we've done fewer miles and less time on feet for Paris. Average pace, well, you can see here for the Goodwood marathon training block, I averaged five minutes 47 per kilometer. But for the Paris marathon training block, I averaged 556 kilometers closer to six minutes per kilometer. So a slower overall average pace for the Paris marathon training block. And now we come on to heart rate. And this I think is quite significant. Average heart rate for my Goodwood marathon training block was 130 beats per minute. Now relatively low, you might say. However, if you look at the Paris marathon training block, my average heart rate for the Paris marathon training block one 23 beats per minute. And we could argue that that is because generally over the course of the training block, I was running slower for the Paris marathon training block around about six minutes per kilometer, as opposed to near 545 per kilometer for the Goodwood training block, not a significantly massive difference, but possibly enough to suggest your heart rate might be lower on average overall. But this is where I think the kicker is. This is where the difference was made for Paris. Let's look at the time I spent in zones four and five. So if you remember, if you know about heart rate zones, zones four and five are full on effort. So zone four, threshold efforts, you're working very hard. Zone five is anaerobic. You are all out here in zone five. So time spent in zones four and five for the Goodwood training block in 2020. So nine hours was spent in zones four and five. So out of the 150 hours I ran, I spent nine of those hours in zones four and five, an average of 41 minutes. Let's move across to the Paris marathon training block. And you'll see I spent a significantly larger amount of time in zones four and five, nearly four hours more, almost 13 hours. So of the 10 and three quarter hours I spent running each week, I spent an average of one hour in zones four or five. Let's go back quickly to Goodwood. And of the 11 and a half hours I spent running each week on average, I only spent around 41 minutes in zones four and five. Significantly less time doing hard efforts, significantly less time running fast, significantly less time doing interval sessions. And I know that on the ground, I know I did three sessions per week, two to three sessions per week for the Paris marathon training block where I was doing fast running. So I did every Monday, I went to the track and I did a track session. Every Wednesday, I did an interval session on Zwift, on the treadmill. And then regularly on a Saturday, I was running park run on Saturday morning, which is a 5k fast all-out effort. So I was definitely doing at least two and often three fast sessions a week for Paris. And just to show you the gains made, how significant this is, I don't know because it was from my watch and it is an estimate, but it's worth looking at. VO2 max estimate on my Garmin watch for the Goodwood marathon basically stayed at around about 53, 54 VO2 max. Whereas there were significant gains when I did Paris. I started at around 55 VO2 max. And over the course of the 13 week training block, we managed to get it up to 57. Not a huge increase in VO2 max, but perhaps significantly different to help me gain that extra three minutes on the marathon time that I got in Paris. So two hours, 58 minutes for Goodwood, two hours, 55 minutes for Paris. So if you watch the channel regularly, you'll know I really am a big advocate of 80-20 running. But the problem with 80-20 running sometimes is that you do forget to do the 20%. It's all very well running the 80% really slow, easy, comfortable efforts. But then when it comes to doing the 20%, it's hard to get yourself out of that really easy running to doing the really hard stuff, the zone four and five stuff where you are hurting for 45 minutes at a time, where you run all out, where you give everything you've possibly got and collapse on the floor at the end of the training session. Those are the tough ones to do. But I think looking at these two training blocks, it's fairly obvious to see that the main gain has been made from doing more of those tough interval sessions, more of that running in zone four and five to increase my speed, to increase my VO2 max to give myself more oxygen to draw from so I can run faster for longer. So I hope you enjoyed that. If you haven't subscribed to the channel, please do so. I really appreciate your support. Really helps out the channel a lot. If you haven't seen my Goodwood video where I broke three hours for the first time, then you can click that link right there. And we'll see you next time on the start line. Bye-bye.


Welcome to The Commentaries, a podcast series from Tan in which you'll learn how to read and understand history's greatest Catholic works from today's greatest Catholic scholars. In every series of The Commentaries, your expert host will be your personal guide to not just read the book, but to live the book, shining the light of its eternal truths into our modern darkness. Visit tancommentaries.com to get your copy of the book and to subscribe for access to all the great reading plans, new episodes, bonus content and exclusive deals for listeners of The Commentaries. Hello, and welcome back. I'm Father Robert Nixon, a Benedictine monk and director of the Institute for Benedictine Studies at the Abbey of the Most Holy Trinity in New Norcia in Western Australia. And this is The Commentaries series on The Imitation of Christ by the great Thomas A. Kempis, a true masterpiece in Catholic spiritual literature and one of the most widely beloved and best-selling books of all time. Today is day eight of our series of podcasts, and we'll be covering book three, chapters seven through to twelve of the ten edition of this great book. But before we get into the details of this work, let's begin by calling upon God to assist us and to guide our hearts and minds in the path of His truth. We pray in the name of the Father and of the Son and of the Holy Spirit. Amen. Enlighten, Lord, our souls and hearts, and to our minds thy grace impart, lead us by thy gentle hand, teaching us to understand the wisdom of thine only Son, the humble, patient, holy One, help us imitate Christ's ways and live His gospel all our days. Amen. So, as I mentioned, we're continuing with book three, chapters seven to twelve. And book three, by the way, is by far the longest of the four books which together make up the volume of The Imitation of Christ. And we encounter some fascinating spiritual material in these few chapters. I should mention, by the way, as we go through it, that you possibly have noticed that several of the chapters present almost the same material, but in different words and different formats. He does this deliberately because the book is intended to be the kind of thing which you can read each day. So sometimes we'll get the same kind of meditations presented in different form. If you sit down and read the book from cover to cover, you might be struck by a certain amount of apparent repetition. But I think this is actually part of the author's plan. Chapter seven tells us, or is entitled, that grace is to be hid under the guardianship of humility. In this chapter, he talks about the value of not advertising whatever graces or blessings we've received from God in our spiritual life, but rather to treat them as private gifts, never to boast about them, never to make a show of them. Because as he says, the best way we can protect them is by keeping them to ourselves. And I'll read a little bit for you. So this is Christ speaking, giving us this advice. My son, it is more profitable and more safe for the to hide the grace of devotion and not to be elevated with it, not to speak much of it, not to consider it much, but rather to despise thyselves more and to be afraid of it, as given to one unworthy. You must not depend too much on this affection, which may be quickly changed into the contrary. When you have received grace, think that you are miserable and poor, and how so you much were without it. Nor does the progress of a spiritual life consist so much in having the grace of consolation as in bearing the lack of it with humility, resignation and patience. So this is so important.  And the purpose of our faith is ultimate salvation. It's not just to get, you know, nice, warm, pleasant feelings out of prayer and spiritual life. Sure, we'll have these sometimes and that's great, but they're not the ultimate goal. And so many people find that the joy or the devotion they once felt during religious practice seems to go away. And the response then is critical. We don't just turn away from God then, but we stick to it. And this is the time of true purification and testing. And he says that there are those who would rather follow their own judgment than believe others who have more experience.  They that are wise in their own eyes seldom humbly suffer themselves to be ruled by others. It is better to have little knowledge with humility and a weak understanding than greater treasures of learning with self-conceit. It is better for thee to have less than much, which may puff thee up with pride. So sometimes God seems not to give us so much as we might hope for, but then to remember that we're here by God's grace, not by our own merits. And on the other hand, we shouldn't rejoice too much at the things which God seems to have given us, because God himself is our ultimate reward, not any of his gifts. Chapter eight continues then with acknowledging our unworthiness in the sight of God, and this is so important. It springs only not from looking at ourselves and finding ourselves unworthy, but rather from looking at the infinite greatness of God and realizing that in comparison to this infinite greatness, we're very small indeed. Chapter nine reminds us that all things are to be referred to God as our last end. And this term last end or ultimate cause, as it sometimes translated, it means our ultimate purpose. What have we really created for and created for nothing less than God himself? So everything else which we do and care about and pursue needs to be done only in the context of this ultimate goal of God and to keep our eyes fixed on this eternal goal of the glory of heaven, of the love of God, of union with Christ. And these, in fact, although we use different terms for them, are really the same one and the same thing. So Christ speaks to the disciple, saying, my son, I must be thy chief and last end, if thou desire to be truly happy. But this intention of yours shall be purified, which too often is irregularly bent upon thyself and created things. For if in anything you seek yourself, you presently faint away from yourself and grow dry. Refer therefore all things principally to me, for it is I who have given thee all. Consider everything is flowing from the supreme good, and therefore they must all be returned to me as to their origin. Very profound there, and God is the supreme good. If we think about why we love or desire anything in this world, it's because we sense within it some element or some form of goodness. And of course, this can't be denied. But this goodness is only a reflection or a participation in the ultimate goodness of God. And what our hearts truly desire is this ultimate goodness itself. So to redirect our focus upon this, to see the goodness in other things merely as being reminders or reflections of the insurpassable goodness of God. In chapter 10, we are told that it is sweet to serve God, despising this world and how true that is. Now, despising is a word which we probably don't use so often in our contemporary spiritual discourse. It's got a negative context, because when we say despising another person, it almost sounds like worse than hating them. But its original meaning was kind of being detached from, literally to look down upon something, to view it in its proper perspective. And so that's what it means when it talks about despising the world. You know, to keep everything in proper context and proportion. And we're reminded of this. He says, And this is truly inspiring that this dedication to the service of God is the source of our ultimate joy and freedom. Because in dedicating ourselves to serving God, we're making our will his own. We're making his will our will. And by that union of will, we come to participate in his own perfect omnipotence, in his own eternity and so forth, to share the very life of God. In Chapter 11, we're told that the desires of our hearts are to be examined and moderated. And this is a theme which we've seen several times so far. We need to look into our hearts and see what it is which we're desiring at the moment, either in a general sense or in terms of our practical everyday goals which we might be working for. And then we need to ask ourselves, you know, why are we working for these? Is it in the context of the glory of God or our proper duties in relation to God? And this doesn't mean that things like work and family are to be disregarded. No, because these things, if properly ordered, are done for the glory of God. But we need to undertake this self-examination on a regular basis. And we begin this chapter with Christ saying, Son, which of course can be understood as daughter as well, thou hast many things still to learn, which you have not yet learnt well. And then the disciple asks, what are these things, O Lord? And Christ answers, that thou can form all things to my desires, to my will, and that thou be not a lover of thyself, but earnestly zealous that my will be done. Desires often inflame thee and violently hurry thee on, but consider whether it is for my honour or for your own interest that you are so moved. If you have no other view but me, you will be well contented with whatever I shall ordain, but if there lurks in the anything of self-seeking, behold, this is that which hinders thee and troubles thee. This is so important, this contrast between seeking of the self and seeking of God, and a term which we find a lot these days, which wasn't a term back in the time of Thomas the Kempus, was the false self. And that's what he's talking about when he's talking about seeking the self, because ultimately God desires our own good, he desires our happiness. And at an authentic level, we also desire our own good and our own happiness. That is for our true self, the true self which is in the image of God. But then there's also this false self, which is a servant of the world, of the vanities of the world, which works for things which don't really lead to true happiness. So this is the self which we need to be careful of, to be alert of. We're told that all our desires should be regulated by the will of God, moderated by the influence of his grace, and referred to his glory. True mortification of the heart consists in repressing the ardour of our desires, in turning their earnestness against the false self, and directing them all to their proper object, which is God. So this is all about fighting against the evils of the false self, to turn instead to what is true and everlasting. And I think this is a wonderful lesson which we can benefit from every day. Chapter 12 deals with learning patience and the fight against concupiscence. Concupiscence, again, is a word which we don't often hear outside of moral theology. But it's talking about disordered desires, or desires which are purely fleshly or material. And everyone battles against these because we're, you know, we're in a body made of flesh. But learning patience of making the Spirit the true leader, and in the Spirit we're united to the ultimate truth, united to God, and it's in the Spirit that we find true joy and true peace. So this brings us to the end of our session today. And this has been session 8 of our study of the imitation of Christ. Thank you so much for listening and for joining me upon this wonderful journey to deeper growth in the spiritual life. Next time we'll be continuing with Book 3, discussing Book 3 Chapters 13 through 12. Until then, may Almighty God bless you. This has been an episode of The Commentaries, a podcast brought to you by Tan. To follow the show, study more of the greatest Catholic classics, and to support The Commentaries and other great free content from Tan, visit tancommentaries.com to subscribe and use coupon code COM25 to get 25% off your next order, including the imitation of Christ and countless more spiritual works to deepen your interior life and guide you to heaven.


We have been talking about axial flow compressors, they are fundamental theory, to some extent we have covered the ground on various aspects of three dimensional flow through the axial flow compressors. In today's class, we will initiate some discussion on how these axial flow compressors are indeed designed. We need to understand that axial flow compressors are essentially uniquely designed. They are not the kind of products that you can buy of the shelf or they are not the kind of products you can easily create with the help of you know very simple handbooks, design handbooks. There are no you know design handbooks for designing axial flow compressors and turbines. So, these are aerodynamic machines as we have called them and these aerodynamic machines are typically uniquely designed and created. So, every axial flow compressor in every aircraft engine is uniquely designed. There is almost no possibility that one particular compressor from one engine can be used all over again in another engine. The possibility is extremely remote and normally it is not done, which means that every time a new aircraft engine is created a new gas turbine engine is created. The axial flow compressor inside that would need to be designed a fresh in fact right from scratch. Now, this requires a lot of effort. In fact, it takes more time to design that part of the engine than indeed any other part of the engine. It takes more time to design a multi stage axial flow compressor than any other component including combustion chamber turbine and other components. So, it is a costly business, it is a time consuming business. It also requires a team of people, lot of people to work towards creating this new axial flow compressor unit and it requires a lot of effort. It is costly because it requires effort in terms of design, it requires effort in terms of computational analysis and then it requires a lot of effort in terms of actual rig testing before it can be considered as a good enough piece of axial flow compressor for actual engine. So, lot of design analysis and testing is required before you can say that a certain design is final and can go on an inside an engine. There is a lot of matching to be done afterwards when it has to go inside the engine, but that is a separate issue altogether. So, the whole business of creating an axial flow compressor is a long drawn out affair. It takes sometimes years for a team of highly qualified engineers with PhDs and masters to create a multi stage compressor. So, some of these things need to be understood that they do come out of some of the theories that we have done and we will try to encapsulate some of the things that we have done in the last few classes into a first cut, a very simple methodology with which one can possibly create an axial flow compressor design. However, that is only the beginning, that is only the start of a long drawn out of work which would require a lot of people to work in it and a lot of time and effort to be spent in it. So, that you have an axial flow compressor that is competitive, that has a good performance, good efficiency and matches with the other components of the engine. That is indeed very important, you have to match the compressor with other components of the engine. Now, some of these things we may be talking about in some of the other lectures in this lecture series, but today we will be talking about a method or a methodology by which you can initiate or create a first cut compressor design. So, over a period of two lectures, I will try to bring to you what fundamental theories can be used to create an axial flow compressor. So, we start with axial flow compressor design. Now, when we talk about design, you need to understand that design is something which you undertake essentially to create a product for a particular performance. Now, this performance is something which you have to decide a priori. An engineering product is created to perform in case of aerodynamic machines like compressors and turbine. The performance schedule has to be very accurately pre decided and design is accurately made to meet that particular performance requirement. If the performance requirement is not accurately pre created before the design is undertaken, the design process would be long drawn out before you can finalize the design. So, it is necessary to create a performance schedule on which the design is to be created. Now, this performance schedule essentially is another issue which we will be talking about a little in today's lecture also that you need to create what in aircraft engine terminology is known as design point. An aircraft engine is designed to perform or give its performance at its best at its design point. Now, this design point has to be decided a priori. It is something, lot of thinking, lot of parameters and lot of matching between aircraft and engine and various components of the engine have to be thought about before you can fix the so called design point. We shall see later on that before the design is finalized indeed, you would need to think about how this particular component or the whole engine would behave under so called off design operating conditions. Because a typical aero engine operates under many off design operating conditions and if you do not take care of them to a large extent during the design process, some of the off design operating conditions may be very poorly performed, something which an aircraft engineer would not like to risk anymore today. So, those are the issues that would come up before the design is indeed taken up. Let us look at what constitutes design. When we talk about design, there are two aspects that come into the design. One is creating the blade shapes, another is creating the compressor flow track shape. We will take up the flow track shape first and come to the blade shape design a little later. Now, we are talking about a multi stage compressor, which by now you know actually is composed of a number of stages. So, the flow comes to the initial stages gets compressed and as a result you actually require less and less flow area for the flow to be processed and sent backwards inside the engine. Now, this fundamental aerodynamic requirement born out of continuity equation requires that your flow track gets narrower and narrower as it goes through the compressors. So, it enters the flow into the compressor and as it gets compressed it requires less and less area and as a result of which you require much less area over here than at the entry. And now, these two ends ought to be decided first.  That comes out of the initial engine analysis, the cycle analysis and the engine configuration that has been decided upon and that engine configuration decision provides the initial compression ratio. This compression ratio decides prime of AC, what is the pressure ratio across this and hence what could possibly be the density ratio across this. That means, pressure ratio and temperature ratio across the compressor are known and hence density ratio can be found and that density ratio essentially gives us prime of AC, what should be the area ratio across this. Of course, assuming or considering that mass flow is conserved, whatever mass of flow is coming in here same mass would be going out of the compressor. Now, what happens is this flow track is then decided by the step by step change in density. Density changes with the pressure and now step by step change in density actually provides the flow areas required at various stations. So, that the annulus area required at any station is found out from the local density which you can find out from the local pressure and temperature values. Now, to get the local temperature and pressure values you need to know what is the step by step pressure ratio that is going through the multi stage configuration. Now, to do that the overall compressor that has come out of the overall engine design now needs to be decomposed or split into so many stages. Now, that is one of the things that needs to be done and once that is done you can create the flow track. We will have a quick look at how to split a overall compressor into number of stages very shortly. We will quickly take a look at if we have the number of stages decided a priori then how do you create the flow track and what kind of choices do you have. Now, this first flow track that we are looking at is a flow track in which the tip diameter of the compressor is held constant and the hub diameter is allowed to change. As we can see here the hub diameter has changed quite drastically in the initial part of the flow track. Now, this is typically done for high pressure ratio compressors in the initial stages of a multi stage. So, all multi stage compressors have high pressure ratio initial stages and the pressure ratios are much lower in the later stages. So, the flow track there is normally you know rather shallow or almost parallel to each other whereas, the flow track requirement in the initial stages requires a sharp change in area. Now, this sharp change area has to be smooth and this smooth flow track creation is one of the first things that a multi stage compressor designer would need to create after creating the split in the stages. Now, the first choice as we see is where you keep the tip diameter constant and the hub diameter is made to change to affect the change of area of the flow. Now, this gives us a situation where the u tip is maintained very high through the entire multi stage configuration. The tip diameter being constant the value of the tip blade velocity u tip is held constant and this allows the value of the work done by the various stages to be held more or less constant through the entire multi stage configuration. Now, this is something which people have done over the years because this is one of the things that allows you to give height u tip value and increasing u mean. Now, as the u mean is increasing the mean work done through the stages is also amenable to increase. So, you can increase the mean work done through the stages as you go towards the later stages and as we know in the early stages with modest amount of work input you get a very high pressure ratio in the later stages even with high work input your pressure ratio or pressure rise is going to be rather small. So, you would like to put a good amount of work through all the stages and increasing u mean is a attractive proposition. This particular change of flow track allows rapid change of density through the stages by changing the hub diameter and the tip diameter corresponds to let us say a high tip diameter that is allowed by the engine designer. Compressor designer would have to design his engine within the overall space allotted to him by the engine designer and hence the maximum size that is allowed by the engine is used for this particular compressor design in which the tip diameter is held constant. In the next choice is exactly opposite where the hub diameter is being held constant and as a result of which the u mean now you can see is continuously decreasing through the stages. So, stages would have lesser and lesser work input as it goes towards the rear stages. So, you have high work input in the first stage and then corresponding lesser and lesser work input through the rear stages. Now, this is sometimes done quite deliberately because if you are trying to put in a lot of work through the stages as we know the density changes very fast and the flow track area requirement would also go down very fast which would mean that the size of the blades that you would need to put in the rear stages would go down very fast. Now, very small size blades are not favored by the designers because they are amenable to aerodynamic flow distortions and loss of efficiency during actual operation. So, very small size blades are often not a favored design choice of the compressor designers. To avoid that situation this is one of the choice where if you keep the hub diameter constant effectively the compressor overall or mean diameter is being brought down as a result of which the density change is much slower and as a result the size of the blades is does not go down so fast and hence a reasonable blade span or blade length is arrived at by design which is comfortable for the compressor designer and is not amenable to lot of loss of efficiency under various operating conditions. So, this is the other choice which the compressor designer often uses and it is often used in the middle stages as I mentioned to avoid the blades going very small. The next choice which is kind of a very obvious mean choice in which the mean diameter of the flow track is held constant which of course means that the u mean or the mean blade velocity of the rotors of various stages is held constant throughout all the stages. So, the mean work done or the average work done of all the stages work done per unit mass flow of all the stages is actually held constant. Now, this is as I mentioned a very simple and obvious choice of most designers and gives rise to a compressor in which both the tip diameter and the hub diameter would have to be changed simultaneously. Now, it is entirely possible that here what I have shown is the hub and tip diameter are changing almost in a similar manner that means the curvature of the tip and the curvature of the hub that is shown here are exactly mirror image of each other. On the other hand it is entirely possible that the modern designers would make a little diversion here and make a choice in which the curvature of the hub and the curvature created at the tip for the flow track are not exactly a mirror image they are different. And as a result it is possible that the mean diameter or the mean u mean the mean blade velocity would vary slightly through the stages and this is done deliberately by the modern designers to exert a little control over the change of density that occur through the stages which as I mentioned allows them to control the size of the blades. The combination is of course the choice of the modern designers where in the initial stages you have the hub diameter going down very fast and in the later stages you have the tip diameter going down and as a result of which the later stages the blade sizes are not very small. If this had continued to go up like this the size of the last stage blades would have been extremely small because they would be operating at very high u mean and as a result of which they would require a very small blade size and the flow track annulus area would be very small and that would something which the compressor designer would not like to favor because two small blades in terms of blade length is something as I mentioned quite often creates aerodynamic efficiency penalties. So, this combination is to avoid the fact that the blade size towards the end is not very small it is little more than very small ones and as a result you have a control by creating this combination you control the size of the blades. Now, in a multi stage environment this combination also allows that this front part in which the hub is changing may be one spool of the compressor and the second part could be the second spool of the compressor and the intervening duct would have this kind of shape. We shall see later on that is quite often the done thing that this combination is indeed used to for a multi spool multi stage actual flow compressor design. So, many of these variants of these four shapes that we have seen are quite often used in actual multi stage compressor design many of which are indeed multi spool. So, these compressor stages then actually are arrived at from the mass flow and the continuity applied to the local flow through the stages. The split of the stages we will be talking about a little later today allows you to calculate the annulus areas at various stations and then create the flow track. Now, you see when you just calculate the flow areas and put them together one after another the flow track need not really be smooth it is entirely possible that you arrive at a flow track just putting all the areas one after another of various stages after the rotor after the stator and after the rotor and stator and so on and so forth you might get a flow track which is not smooth it may be zigzag. Now, that is a flow track that is not acceptable flow track has to be smooth it has to have a smooth aerodynamic flow from the first stage to the last stage of the actual flow compressor. So, not only you have to create the work distribution of the stages you also have to recreate the work distribution in a manner that the density variation that you get actually finally gives you flow track that is smooth until you get a very smooth flow track your design is not complete. So, a multi stage compressor designer finally has to create a smooth flow track in creating very smooth flow track the fluid flow equations would have to be used and the compressor work distribution the pressure ratio distribution the sizes of the compressors would have to be moderated in a manner that finally you have a smooth flow track in which all the blades are very nicely fitted in a manner that they actually give very high efficiency performance. The other business which quite often is done is as I was mentioning just a little while ago that in multi stage compressor you also have multi spool you have the high pressure spool and then you have the low pressure spool in front of it in between these two spools quite often you have what is known as a inter spool duct. Now, this inter spool duct during which there is no compression flow is going from high low pressure spool to high pressure spool and then this passage has to be done smoothly it also needs to be done in a manner such that the entry to the high pressure spool is not only smooth, but it provides a uniform flow into the high pressure spool for stage that means as far as possible the uniformity of the flow needs to be restored which may not be true when it is coming out of the low pressure last stage. The flow may be you know having a world component or a rating component the pressure distribution along the length of the blade may not be you know uniform as there are many such non uniformities with which the flow comes out of the low pressure spool. The intervening duct now the inter spool duct has a job as far as possible to restore uniformity of the flow before feeding it into the high pressure spool and this is something which the flow track designer has to achieve by designing the flow track. So, the flow track design has a number of responsibilities actually to discharge in creating a multi stage actual flow compressor flow track design. Many of these modern flow track designs would indeed not only require design of the various stages quite often as I mentioned you may have to redesign and re redesign those stages to create a smooth flow track to fit into a smooth flow track. So, it is a iterative design process of various stages till that process is over you do not get into individual blade design. So, individual blade design of rotors staters come only after this multi stage configuration has been finalized and completed. Now, to do that many of the modern designers also use computational flow dynamics because rig testing is often very costly and that can happen only after all the stages are designed and fabricated and put on the rig which is a very costly affair and time consuming affair much before all that you can have a computational flow dynamics to aid the process of flow track design to aid the process of compressor design. So, quite often many of the modern designs are indeed aided by computational flow dynamics or CFD towards creating the final flow track shape. Now, some of these things are initially created with the help of some very simple considerations. So, what we are looking at is a simple conical annulus track. So, the track is annulus if you remember. However, the cross section of the track can be considered to begin with a conical one. Now, we have seen this cone can be a curvilinear cone of various kinds that we have just seen. If we just consider it as a simple conical flow track a very simple mathematical expression can be used to capture this conical linear conical flow track. Now, what happens is simple fluid mechanics or aerodynamics would tell you that you would like to restrict this angle of this flow track or angle of this cone to certain values which could be definitely less than may be 10 degrees at any point of time or any point on the space in that compressor flow track. Normally, it may be of the order of 6 to 8 degrees modern designers are trying to go to higher values. If we go to the earlier flow tracks that we had a look at, if you look at this flow track you would see that in the initial stages this curvature would seem to be giving you a flow track angle of a much higher order. However, if you come very close and take a very close look at the change of angle of the flow track from one point to another between two very nearby elements you will probably find that the change of angle between let us say this point and this point is indeed actually very small. So, a bit by bit in a curvilinear manner a lot of change of angle has been affected in this particular design, but a very small angular change is theoretically possible through the flow track if one considers fundamental aerodynamics. So, this is a very simple you know theory which people often check out to ensure that at no point of time you are violating the fundamental aerodynamic principles and the checks and the limitations that need to be kept in mind while you are designing this modern axial flow compressors. If we look at this very modern axial flow compressor design you would see what I was talking about in the initial stages you have a flow track that is very rapidly changing through the stages you have a rotor stator, rotor stator, rotor stator. So, it is a three stage low pressure compressor spool which allows the flow to flow into the high pressure spool which comes later on which is a six stage high pressure compressor and as we can see the flow track here has rapidly changed because of large amount of work that has been pumped into the flow and rapid change in density and then the flow is compressed and it is again ducted into the high pressure spool as I was mentioning quite often the high pressure spool is at a lower average radius than the average radius or diameter of the high pressure spool. So, the u mean in the high pressure spool is much lower than the u mean of the low pressure spool and of course, the u tip of the low pressure spool to begin with is very high the u tip here is continuously going down as we can see. Now, high pressure spool here is where both the tip and the half diameters are changing almost linearly towards the end of the high pressure spool whereas, here they are changing in a curvilinear manner and the change at the hub end is much faster and the change at the tip end is much shallower, but it is changing at both the casing and at the hub and by the time it hits the third stage of the low pressure compressor the flow needs to be now ducted inwards into the high pressure spool and hence the tip actually starts coming down and the hub also starts coming down. So, the flow track here has taken a downward turn because the flow now has to be sent downward into the high pressure spool and of course, this is a low bypass engine. So, small amount of air would go bypass into the bypass duct. So, this is a modern axial flow compressor flow track design which as you can see has used the concepts that we were talking about a little earlier, but use them in a very clever manner to create a modern two spool multi stage compressor configuration. Now, we come to the fact that to create a compressor you need to fix the design point. Now, design point fixation is often done on the basis of a number of parameters. We will look at the compressor characteristic map which you have done before. In the characteristic map if you remember a functional relationship was established between the performance parameters which is the pressure ratio, the efficiency and the temperature change that occurs through the compressor which is a measure of the work done normalized by the entry temperature. Now, these performance parameters are connected to the functionally connected to the various flow parameters which is the mass flow parameter which we have said earlier is a normalized mass flow parameter, the Reynolds number of the flow and the normalized speed of the rotors that are being utilized inside the compressors. So, these parameters on the right hand side are not really non dimensional parameters. So, we call them normalized parameters because actual non dimensional parameters are not very useful in the sense they carry some parameters which are dimensionally to be fixed by design and at this stage of design they are not yet fixed. So, we consider the parameters which are not non dimensional, but normalized and are useful for characterization of compressors. So, this is the kind of compressor characteristics that you have done before and we will take a quick look at this characteristic map. Now, this line that you see is the characteristics of the compressor at it so called design speed. Design speed is given by n by root over t 0 1 and this n is the n design. Now, this has to be decided as quickly as possible what should be the design speed of the compressor and then you quickly arrive at this non dimensional design speed. Then the characteristics of this compressor needs to be decided upon. The first cut characteristic that you get may not be the final characteristics because that you would get only after the compressor design has been completed. So, you have a provisional characteristic map that may come out of the engine overall design and that gives some idea about what kind of characteristic map the overall compressor should have so that you can initiate the design process. At the end of the compressor design you would create a more detailed characteristic map out of various theory and CFD that is available and that would be used as the design map till the compressor is tested on the rig. Once the compressor is tested on the rig you get the actual design characteristic map of the compressor that has been created. So, this design map is a provisional one to begin with. Now, you need to fix the design point. Now, you can see here there is a problem. The problem is a typical actual flow compressor as we have done before has a peak pressure ratio somewhere over here and immediately following the peak pressure ratio that means if you somehow throttle the mass flow or the mass flow comes down a little the compressor would have a tendency to go to stall and it could become uncontrollable stall into surge. Now, that is not an area where your compressor should be working. On the other hand if the compressor works at a higher mass flow on the right hand side of this characteristic map it would be working at a lower pressure ratio. Now, as far as the engine is concerned higher the pressure ratio more is the engine efficiency. The basic thermodynamic efficiency of the engine is directly related to the compression ratio. So, higher the pressure ratio, operative pressure ratio higher is the operative efficiency of the engine and this is true for all kinds of heat engines. So, you would like to peg your design point at a higher pressure ratio with the provision that the compressor would work under higher mass flows where you would get lower pressure ratios. If such a working operating point is accepted for a particular engine operation or the engine aircraft operation that is fine and you can make the compressor work under such a condition. Let us say such a condition is 0.5 where you are working at a higher mass flow of the engine through the engine, but it is working at a lower pressure ratio. Typically 0.5 could be representative of the aircraft cruise operating condition when the aircraft is cruising at very high altitude. The compressor is often working at a higher throttle open higher open throttle at which the non-dimensional mass flow is little on the higher side and the necessary pressure ratio is on the higher side because at high altitude you can manage with low thrust creation, but your design needs to be done for high pressure ratios. Now, if you peg the design point over here at a higher pressure ratio so that it can produce a little higher pressure ratio if required which may be required during takeoff or climb you cannot work at low pressure ratios during takeoff and climb. Under those situations you have a little problem over here at hand. If the pressure ratio is pushed to higher values you can do so only by throttling the mass flow to lower values and if you throttle the mass flow to roll values this compressor is liable to go into stall. Now, this difference between the maximum pressure 0.2 and the design 0.3 is popularly or is generally known as stall margin which you have done before in our lectures. This stall margin by design needs to be comfortable to the operation of the engine. The modern designers would like to make it as high as possible if the design pressure ratio can be pushed as high as possible so that by design you create a stall margin. So, creating a stall margin where the stall is on where the design is design point operation is indeed decided by the designer. This stall margin creation is the designers job it is does not happen it is not to be decided by the operator it is not to be left later on to be decided by operational schedule it is built into the design of the compressor it has to be designed in. So, stall margin is something that has to be designed in and that makes the choice of design point a little more difficult. You know that you have to create so much of stall margin which is indeed safety margin of operation of the compressor and indeed that of the whole engine because if the compressor stalls the whole engine is stalled. This is a problem this is a problem which the compressor designer has to deal with right in the beginning throughout the compressor design that at no point of operation of the compressor at the engine the compressor should stall because if it stalls the engine is gone. And this stall margin has to be created as we shall see later on that this stall margin has to be created for each stage design of the compressor because you would actually create a similar compressor characteristic for each stage if you have 10 stage compressor we just saw a 9 stage compressor 3 low spool and 6 high pressure compressor each of those 9 stages has a characteristic map like this and each of those stages would have to have a comfortable stall margin of its own all 9 stages together the entire low pressure spool together the entire high pressure spool together would have a stall margin of its own. So, you can have overall stall margin of the entire compressor you can have a stall margin of only the low pressure spool you can have stall margin of only the high pressure spool you can have stall margin of each of those 9 stages and they have to be designed in they are not going to happen you are not going to leave it just to happen they have to be designed in and that is the designers one of the tricky and rather challenging jobs of the compressor designer. So, finding the design point is one of the tricky design decisions that need to be taken early on in the design sometimes you may have the latitude to change the design point a little, but not much when you are putting all the compresses together slight change in the design point may have to be adopted to get the final design, but not much. So, choice of the design point is a tricky business then we come to the fixing of the initial design point parameters what needs to be done is as I was just mentioning that the entire multi stage compressor needs to be split up in individual stages to begin with it needs to be split up may be in two spools or three spools in many modern actual flow compressors are actually three spools.  Now, these numbers are decided by the state of art of the design of these compressors you see the state of art is decided by the design methodology that has been developed where we are today we have talked about subsonic transonic compressors most aero engines today do not use supersonic compressors. So, that state of art of the compressor design has to be used to get these numbers when you are initiating the compressor design process during the research which you have to do to create this design you may try to push this design numbers to somewhat higher values in terms of pressure ratio or efficiency. However, that is going to be normally marginal. So, I have tried to give some numbers here that gives you some idea which means in the initial stages you can actually get pressure ratios of the order of 1.4 to 1.8 by putting in substantial amount of work the temperature rise that is shown here is of course, the measure of the work to be done delta T into C p is the per unit mass flow work done and the efficiency I have shown here is of the order of 0.6 to 0.7 you may like to push it to a little higher may be difficult if the initial stages are transonic most of the modern aero engine first stages are transonic. Once you have transonic as we have seen in the earlier lectures you have shocks and the shock losses bring down the efficiency a little and as a result of which the efficiency of the initial stages are often a cut or two below the efficiencies that are possible with the subsonic stages. In the middle stages the modern actual flow compressors have indeed put the efficiencies to very high values if they are subsonic you can indeed get efficiencies of the order of 92 percent if they are subsonic you may have to go below 90 89 percent or 90 percent at the most or 88 percent. Now, in the middle stages your efficiencies are normally a little on the higher side compared to the initial stages and one of the reasons is in the initial stages the flow often admits flow through the intake which has invariably certain amount of non-uniformity or certain amount of unexpected non-uniformity this is catered to by the design and if you do that you pay a very small penalty in the design efficiency. So, that under non-uniform inlet flow operating conditions the efficiency of the initial stages do not drop very much. So, to cater to such off design vagaries of actual flow compressor operation the efficiency of the design point is sacrificed a little. This is a pre-meditated sacrifice it is done deliberately by the compressor designers and it is a well sacrificed you know choice because under various off design operations you still get good efficiencies of the order of 84 85 percent this is a good compromise. However, in the middle stages you do not have those problems the initial stages actually act almost like a filter. So, the non-uniformities go away and the flow delivered to the middle stages are often very uniform and hence in the middle stages you can aspire and prepare to design compressors of very high efficiencies of the order of 91 92 percent. In the last stages what happens is the blades as you have seen become very small when the blades are very small the three dimensional flow that we have discussed earlier in this lecture series engulfs the entire blade and when that happens many of the two dimensional aerofoil theories that we have discussed do not really operate that way and hence the efficiency of the compressor suffers a little. So, the aerodynamic efficiency of the compressor the aerodynamic losses actually go up and hence it shows up in the efficiency and hence the last stage efficiencies are not as good as the middle stage efficiencies. So, they are a cut or two below the middle stage efficiencies as we can see the pressure ratios keep going down through the stages in the initial stages very high middle stages it is lower down and then in the last stages it is very low no matter how much work you try to pump in the flow is already at a very high pressure very high temperature and indeed very high density. So, from the fundamental thermodynamics on aerothermodynamics you know that working at very high pressure and temperature you can only affect very small change in density. So, that is what happens in the last stages. So, the work done in the last stages is deliberately kept on the lower side because you are not going to get much profit out of pumping in lot of work and hence the work done is somewhat on the compromise side even to get that you have to actually put in a lot of work. So, the last stages are normally the high pressure spool the high pressure stages which normally as we know run at high speeds. So, this initial parameter fixing essentially requires you to fix from continuity the mass flow that goes to the compressors a factor of change of mass flow may be taken between HPC and HPT if you are catering to cooling of turbine. So, some amount of mass flow may be taken out and of course, fuel is pumped into the turbine. So, different between turbine mass flow and compressor mass flow as to be a factor into the design and then from work balance you decide what the compressor mass flow should be between the turbine work and the compressor work and this is to be done separately for LPC and LPT and then of course, you get the split between the fan and the HPC and as a result of which you get the bypass ratio and then you get the rotating speeds of the fan the LP and the HP spools. These of course, mean that the compressor or fan speed has to be of the same order as the turbine speed. So, that something which again has to come out of matching between the turbine and the compressor and the power balance between the compressor and turbine fixes the compressor work that has to be done. Of course, there are the efficiencies of the turbine efficiency of the compressor and the mechanical efficiency of the shaft that comes into the picture in deciding how much work the compressor should do. Having obtained this you can now decide the amount of work to be done for the rotor of the individual rotor individual stages. There are certain parameters that normally we talk about the axial velocity is often normalized into a what is known as flow coefficient phi and this is normally kept less than 1. These are figures that people have used over many many years. So, axial velocity by u is normally less than 1. The work done that is being performed again is normalized by u square. In some books it is may be written as 2 u square and this gives us psi which is the work done coefficient and this work done coefficient is normally of the order of 0.5 or lesser in conventional compressors. In modern compressors this is being pushed to higher values of the order of 0.7 or 0.8. So, the actual work done on the compressor on individual stages is decided by first deciding on the work done factor of the individual stages. The radial gap that you can keep for the individual stages depending on which stage you are considering. As we know the radial gap in the last stages have to be you know a little more than actually of the same order as the initial stages in terms of it is called it is higher. So, some of those things would have to be decided as we go along and then of course, the fan loss that occurs in big fans. All that put together gives you some idea as a first cut idea about what should be the work done or work supplied to the compressor compared to the amount of theoretical work that the compressor needs to do from the fundamental two dimensional plate theory. Having decided this you have to decide quickly the work done factor as we see the work done factor goes down with the number of the stages. The first stages the work done factor is very high. In the later stages the flow is three dimensional and the work done factor is often somewhat on the lower lower values. So, that has to be also decided these are pre decided by the designer from earlier experiences or earlier data that is available with the particular design group. And then of course, you need to fix the initial parameters that means the work to be done by the individual stages. A conventional method is if you having a sub sonic stage you can try to pump in certain amount of work. If it is transonic stage you can pump in certain amount of work. So, the different between the work you can pump in for a transonic stage and then of the transonic subsonic stages are slightly different. Once you decide that how much work you can possibly do stage by stage then you can get the number of stages. So, z here is a first cut value of the number of stages of a multi stage axial flow compressor that allows you to arrange the stages and then try to design the flow track. Now, you can go back and try to design your flow track. So, that you get a smooth flow track to begin with of course, you may have to come back here if these stages are redesigned or re redesigned due to many other reasons then the flow track would have to be re smoothened back into a final smooth shape. So, these initial parameters are fixed by deciding on the work done the efficiencies of the individual stages and to make sure that you have correct distribution the pressure ratio of all the stages put together must of course, give you the overall pressure ratio given by the engine designer. The density variation and the annulus area variation gives you the flow track which we talked about earlier and this of course, comes from fundamental aerothermodynamics and this annulus areas variation has to be kept smooth. This sometimes the axial velocity for the design may have to be used as a moderating parameter to give you the smooth flow track. So, axial velocity is something which the designer may use he may held it back and use it for design later on to moderate and get a smooth flow track. So, this is how you get a first cut axial flow compressor configuration and it is distribution and it is first cut smooth flow track over a multi stage configuration. In the next class we will get into blade design. We will look at using the blade fixing the design point fixing that we have done in this class we will get into individual blade design methodology. This is what we will be doing in the next class where you will be attempting to tell you how to design rotors and stators of individual stages of a multi stage axial flow compressor.


*** *** *** *** *** *** *** Jain Wanjiru and she is a teacher and a mentor and she will be telling us more about herself and her mentorship program. Welcome. Thank you so much. So how are you feeling today? I'm feeling good. Thank you so much for making time to be with us. Thank you. I should be appreciating. Karibo. I had been praying for such a moment and I got it here finally. Yes. So kindly introduce yourself and tell us what you do professionally. Okay. My name is Jain Wanjiru Moga. I'm a teacher with TSA. A wife. A mother to two boys. Great.  Which grade do you teach? Or rather which level do you teach? Class 6, 7, 8. Class 6, 7, 8. So talk to us about the mentorship program that you have with relation to being a teacher. Okay. Let me take your park words a bit. When I was posted to Kajole, I went to Imara first and then I was transferred to Kajole North for Malimataupeni. And it's a non-formal settlement area. And when I reached there, I realized that children are vulnerable to a lot of vices like trafficking and militia gangs, prostitution and other vices. And so as a teacher in that passion that I had in guidance and counseling which I did at Moutken University, I felt I was in the right place and with the right people. And so immediately with the help of my hand teacher, we started a program by the name Life Skills. And with the help from Life Skills Promoters and UNICEF, they came in and we started that program on mentoring kids taking them through the important life skills programs. And I thank God for the steps so far. So you're saying children from Class 6, 7, 8, they're exposed to all these vices at such tender aids. Have you experienced such cases? A lot, a lot, a lot. In fact, I want to thank the hand teacher, Mrs. Deri. I want to believe maybe she's watching or she'll get to watch this. Together with her, we realized that it was happening in our school actually, it's still happening. Drugs, children are getting access to drugs. Like I said before, the environment itself, we have people selling drugs to kids. And so we have a lot to do in talking to these kids and telling them the digits of these drugs. And of course, the vices, like I said before, it's not about drugs, they are the things that delimitia guns which are there. So you find that is a challenge. These kids, when we raise them in the evening because it's a day school, there's a conflict of interest because as teachers, especially as mentors, we are with them, talking to them about morals, values, taking them through the Life Skills programs. But then when they get out there, they are exposed to such kind of militia groups and other things. And that's how children control, definitely. Yeah, but thank God it's working. Since we introduced this program, we have seen a tremendous change in behaviors by the way. We have kids who have left school, clasit, and we are following them up. We don't leave them when they do the KCP. We follow them up even to high school where they went to and they come back to us, thanking us because we realized that before previously, they didn't have mentors or shoulders to lay down or people to share with. But when we started their program, they came in and we were working together and we thank God for so far. So when was the program Life Skills started? 2015, yeah, 2015. What was your main goal when starting that program? To give hope to these kids, to encourage them and motivate them. We told them it doesn't matter the environment. It's about attitude and the individual, not about the environment they are in. So basically the peer pressure was too much, negative peer pressure. So we told them it's about you as an individual. It's not about the environment, it's not about the group. Fine, your cousins do it, your neighbors do it, but it doesn't have to be you. It's your life. So when we started that, they started seeing sense and it was not easy initially. It has not been easy. Like I said, conflict of interest because of the community around. But I thank God we talk even to parents and the community around and they assume the need of also encouraging these kids just to be morally upright. So is this a program for maybe class 6 to 8 students or it's just from the young ones? No, initially we thought we concentrate with the 6, 7, 8, but we realized even the children 9 years have been recruited into these militia gangs. It was a serious problem. Actually we had a case of a 80-year-old boy being recruited in Gaza. Gaza is a non-militia gang in Kayole. So we thought now we should not rely on class 6, 7, 8 kids only. So we decided to go down level to class 2 even to talk to them. Because the topics are different. The way I approach it in class 2 is not that we are going to approach it in class 6, 7, 8. So is it given as a lesson or it's done maybe you just combine all of them together? I want to learn the government because they have slotted that lesson on Thursday where we have life skills program but that one is not enough. So as a patron of the life skills together with the hand teacher we have a lesson for life skills which I want to encourage the teacher to put into consideration because most of them actually take it to teach their subjects to boost their academic performance but I want that the government for the CBC now that we are not so much into academics like what the president said yesterday let them concentrate on mentoring these kids because I believe they lack the life skills. Most of them don't even know about them they assertiveness all those basic life skills there are about 16 of them even if you're not going to touch on them we touch on the basics like negative peer pressure the assertiveness the decision making and all that so I believe as teachers and parents if we take children through the life skills the basic ones we'll have a better generation in future. So let's talk more about the program. What are some of the challenges you have encountered since 2015? Resistance resistance from the community like I told you recently not from the students the students are good actually they are good since I started the program but the problem is like I said the negative peer pressure from outside sometimes I am not with them during the holiday or at times I am not with them they are at home so you find that they are discouraged and like I told you we had a show just the other day and then from there they were threats what kind of threats? the teacher who is trying to mentor the children they are lacking customers to sell drugs to because I am telling children to keep off drugs actually we had a case that we reported to police station it's a threat to me and to the hen teacher because she has been very supportive of the program so I should not be talking to these kids I should not be mentoring them I should not be telling them about Gaza I should not be telling them about drugs I should concentrate the teaching according to them it's a case with the OCS Kayole it's there but he told me to keep on keeping on encouraging these kids and by then I am not going to stop because it's me mentoring is me besides teaching and you don't feel like kind of a threat when you are walking around no I wouldn't cause one I have a lot of support from the deputy president and I want to believe even if he is not listening he will have to get landies through the wife though I have never met her but through her office and officers they are becoming too square supporting me a lot because we realize that one of the things that these children are being world into the militia gangs and drug trafficking businesses is because of poverty because I go to sit one on one with them and they told me teacher we don't get food so sometimes you are forced to do this to get food and all that so we reached the office of the deputy president and they brought a feeding program and when they brought the feeding program they felt the need besides feeding them physically also morally and so they introduced a club it's the deputy president wife club known as CHE community health evangelism so when they came she has never been there but she has been sending her officers there so they occasionally come to our school and when they came and they got to see what I do programs she was impressed of course through her officers and she incorporated the CHE club with the life skills so we work hand in hand together and I thank God for the progress so far so the feeding program and the CHE club plus life skills it's working miracles I am hoping that next time I will get a chance and I come with some of the kids who have entered some confessing that teacher if it was not for you and they have told you that they have told me that actually one time when you invite me again and come with them because those are the kids they are peer educators they are the kids who are encouraging others and they are like oh if this did it and she is in the same environment I can also do it because if you see your fellow students doing it then you believe in yourself so you told me some of the challenges that you are having is maybe threats and resistance from the community any other challenge well well well and maybe the children themselves doubting themselves it's like can I remake it from where I come from you know can I remake it you know they doubt themselves but you are trying to put that hope in them telling them we also came from such places and I thank God at least that perception is clearing now accepting the changes and I thank God and we are involving them I want to thank the ADMP he is really supporting me also in the program whereby he involves these kids in environmental conservation you see we are killing two birds at the same time they are learning the importance of conserving environment at a tender age and also engaging them positively because what I tell these kids is not about because most of them are not right most of them are not right so they are discouraged and that is why I am thanking the president for the new system curriculum I am really supporting it as much as it is being opposed by Nat which I am a member but I am opposed to him resisting that cause CBC competence based curriculum it's emphasizing more on the pupils areas of competence as opposed to academics A and B but you can be disciplined very great degrees masters but they are wasted to nothing exactly so I want these kids from primary level to secondary to tertiary by the time it will challenge them whatever you are doing challenge them oh teacher talk to me we were mentored the MP was there for us and you know gone are these when you used to tell them don't do this let it challenge them in future so let's talk about the feeding program is this offered to each and every student or are it just specific students all of them for free a balanced diet some that never used to be there before it was a challenge because most kids never used to afford lunch and so absentezim was a problem affecting the performance because if a child is absent and if he decides to them not having something to eat they actually told me I had a case not even one or two so many cases telling me teacher was absent because I was not able to get food teacher I was far doing these because I could not get food my mother and you know okay sorry to say most of the parents they are not how do I put it they are not hopeful of their kids if they go to school so if we don't ask as mentors in teacher most of them by the way they are not they are not there for their kids they are comfortable with their children and so we have a lot we are acting the roles of parents the role of teachers, the role of counselors and all others so it's actually true what they say that these days parents have left the children to the teachers exactly exactly and the problems we are experiencing now for their children so we find that a child will open up the teacher even a very private issue they will come and share with me have you shared with mommy no why that's interesting so this feeding program what meals are included some meals for break and lunch they take nutritious porridge at 11 very nutritious porridge at 11 and then lunch time they take the normal lunch okay that's interesting then the chair program how did you get in contact with the office of the deputy president can I say it was God's grace through a certain parent in our school and he happened to be my friend and so when he's a pastor a parent tree and so I shared with him one time I repeated these kids it was just a normal talk and I told him many kids would come to me in my class I was organizing how children were going to feed I made sure no kid went hungry but I could not feed the whole school because you were going hungry and no people were different so you were doing it with your finances I was doing it but the little that we get we are even on the streets but the little that I was getting and I thank God I never lagged I never lagged like Mother Teresa said if you cannot afford to feed all feed one blessings will follow you so I saw God blessing me a lot and so I talked to this parent and he was like I know a church I go to and Madam Rachel Ruto goes to that church so one day when I get to and I thought it was just a consolation thing you know I will try wife of the deputy president but luckily it went through so when he came to us together the hen teacher telling us she has worked and the deputy and our school has been chosen among the children the schools are to benefit from the feeding program I just thank God I felt like I had achieved and from there she has been very supportive giving them balance to diet giving them porridge she is the one also funding and supporting this feeding program fully so she is in charge of the feeding program high in her office in charge of the feeding program and the chair fully so what are some of the benefits that you have seen from the club chair wow great transformation in behaviors children willing to change we had kids almost joining Al Shaba because the community we have Muslims almost half have the kids they are Muslims and we had kids who were about to be recruited they confessed to us some even about to join Gaza and some even being used to traffic drugs but they changed and this teacher we are not ready to die young so transformation behavior and also absenteism the cases of absenteism have reduced remediously 100% turn out and I would say so behavior changes especially and being present in school in school they learn a lot because teaching is not about chok and the blackboard turns a lot it entails a lot so I think behaviors and also the community has embraced the changes they are very supportive is not 100% we are there at least 80% and the school is known to be disciplined okay that's good any plans of introducing the programs to neighboring schools oh yes now that the MP is supporting it he is not just an MP for kaiola north primary school so we are planning the plans are at the way so currently it's only kaiola north current is only kaiola north but I do it online and many teachers are embracing it but they encourage them a lot because there was this notion teacher go home you are getting less and other than that I told them teaching is a calling it's in the book of James oh and to those who deserve to be teachers take other profession but don't be a teacher because your judgment will be different remember these are innocent kids they are there for you mess them up make them ups up to you when I see a kid coming back to me right from primary school when she comes to me and tells me some of this thing I didn't know we used to hear of children from Saba the council and other things but you brought them to our area teacher I owe it to you I just shant ears I mean I feel I've achieved that's all so I always encourage teachers please do your best do your best cancel these kids not about teaching and God will bless you because the elimination is just discouraging but focus and God that is where you are getting your blessings so other than the office of the deputy president the area MP headmistress who else is on board some teachers some teachers around some parents because again if you work alone and you don't have support from parents it might be an exercise in futility so I have parents assisting even pastors I have from faith evangelism ministry working with Raymond Nelson he has also been very supportive of the program so I thank God so we are getting to a place soon that's good so if someone wanted you are doing the mentoring online where would someone find you if they wanted to contact you maybe parents maybe teachers well well well so far Facebook is Jane Mogo Facebook Jane Mogo I have my email some of them get to me to email Jane Moreny 8 at jmail.com so have my number 0725 339 527 I've worked with parents online some with issues because besides what I do also we have issues like affecting teens they get depressed and they do the unimagined you know like for example committing suicide recently cases of teens committing suicide are rampant juicy we buried a young boy 22 years old he commits suicide parents they don't understand why probably this kid was and then the parents are like this kid never liked anything he was actually about to graduate this deck unfortunately he went with a lot of secrets with him so I always tell parents get to me and many of them are reaching me if I'm not able to get to you one on one we talk via phone and I get a chance to talk to that boy or to that girl and it works many of them are coming online we are dating teacher you saved my boy and other because I believe there is nothing that I can't handle I want to sit with that boy and girl share with me I had a case in our school the boy almost committed suicide he just stopped coming to school and I got concerned because the moment a kid in my class actually class 7 because I'm a class teacher class 7 and so he stopped coming and he was a bright boy so I got concerned so the mother came to me crying and told me teacher I wish I could share with you but I wanted to come from him and all that so to cut the story short the boy had been sodomized I want to tell you the kind of environment you are living in so he was sodomized and unfortunately because of the poverty it didn't go far and then the guys who were responsible just moved they don't know where they went to so the boy was there so he was there and so the mother was concerned but I thank God I got to sit with the boy one on one and we talked and the boy he can smile now because mine is to put a smile on a child's face at least he's good we shared a lot with him and we are still working together with him and many other cases that's just one out of many so apart from school and I get a lot of support from my Facebook buddies some unknown to me, some unknown but they just trust me so I want us to wind up so I want you to just maybe give your final word to parents who are watching to young people who are watching and maybe teachers we have a judgment of society where we find some children, some youth, some teens engaging in some vices to judge forgetting that we are to blame the teachers, the parents and the society are we there for those kids what do you do as a parent how often do you sit with your child you go out with your girlfriends you go out with your boyfriends you go out with your spouses how often do you go out with your kids sit with them one on one get to share, let them open up to you how often, we are busy looking for money for wealth so let's be there for our kids please to save this generation things are bad, I'm a teacher and I know right from primary to secondary to colleges we have many vices affecting our kids we need to listen to them we need to talk to them occasionally don't get tired just talk to them, you're going to save a chance somewhere let them know there's somebody who understands them let them know that there's somebody who can listen to them so thank you so much for your insightful thoughts it's a good job that you're doing out there thank you thank you so much for making time to come thank you so that was Jane and like she has said we need to take care of our children so that they can be prosperous and we can have a better coming generation so don't you go anywhere more of a circuit coming your way