Hello everybody. So we're going to continue our discussion of Python under the hood today, and we're going to focus on data itself variables and types and Last time we introduced a new way of thinking about Python programs, which was situating them in the context of the greater computer itself Now we said every computer has basically followed this architecture For the since the 40s and 50s Which is that you have your input and your output devices and then in the middle you have a brain Which is the central processing unit that does all the computations and it you have memory where the data resides that these computations are done upon right so the Python itself you need to think of it as a machine a program that's sitting there running and It sends instructions to the CPU to do things like add and subtract and do Boolean comparison and assign variables And then you have memory which is where those values the data values live over extended periods of time and You know the fact that Python is like a Program and is running inside this computer is really what Alan Turing is famous for he came up with a computer and A definition of what it means to be a computer and what made his definition so special is it's a computer that can run Any sort of program right as long as that program is in a specific format and has certain properties And that's what's so magical about computers themselves. It makes them better than calculators They can run any sort of program as long as that program fits certain properties Okay, but anyway, we also introduced a new way of looking at Python programs in terms of what variables are And how they relate to memory And what we said was when you create have a variable assignment like this Remember variable assignments and assignment statements in Python evaluate right to left So we do the right-hand side of the equal sign first So Python creates a value called 42 Somewhere in memory in the physical memory. It turns on those ones and zeros that encode the number 42 as an integer that Python understands and Then it assigns the variable the answer to that and what the answer really is Is it's a named bookmark and that bookmark points to the address in memory where this value lives Okay, and then we also did a tracing exercise where we're trying to make sure that we really kind understand when Variable values are created and destroyed So today we're going to explore Variables and data and memory a little bit more and we're going to switch over to pie charm to do that Okay, so we're I'm going to walk you through these steps So let's switch over to pie charm now and get started So I already have pie charm open here. I mean make it a little bit bigger so you all can see it, okay? And the first thing I'm going to do actually before I even go to pie charm. I'm going to go to my desktop and Here I have my handy-dandy CSE 231 folder which everyone else should have whoops and Inside of it.  Okay, so I've got a new folder here. I'll call it lab zero, okay? You can call yours lab whatever you want Okay, let's go back to pie charm now and I am going to open up that folder. I just created Okay, so mine is in my desktop CSE 231 and You may have noticed when I first got here lab zero one wasn't showing if you know that you made the folder And you know you're in the right spot click this little refresh button up at the top It'll make sure that it appears. Okay, so I'm going to open up the lab zero one folder Pie charm asks me do I want to do it in this window or a new window? Either one is fine. I'm going to do this window All right, so I got my blank pie charm project here nothing in it Let me go ahead and create a new Python file. So I right-click on the folder new Python file and Let's just call it lab zero one dot pie Okay, so here we are. I'm in a blank Python folder Let's do some fun stuff here, right? So if I go back to my Slides you can grab this code At least this code here on the left hand side and paste it in there if you want, okay, or you can type it So I'm actually going to go to some To my notes here, I'm going to grab This code from slide number five. I'm just going to paste it into pie charm Let me get back to my pie charm screen Okay, so I grabbed the code from slide five and pasted it into pie charm and you can do that too Now our focus here is going to be Examining this type function Type is a built-in function of Python and it returns a value specifically it returns a string and all I'm doing is I'm printing the type of these various pieces of data these are values that are going to be created in memory and I Asked Python. What is the type of each of these values and it prints them out? So you've probably seen this function before and you've probably seen the outputs of it before 42 is class integer 3.14159 that's a float True is a bool. It's a Boolean and Alice here is a string. Okay, so when we print out the type it says class in Int okay integer float boolean string, but there's also this class thing Okay, we'll get back again to what that means in just a second Okay, so now next slide Let's look at another function, which is the id function. So I'm going to manipulate this a little bit Okay, so I just copied and pasted my code and instead of type. I'm going to use the id function here Okay, it's also a find and replace feature. I could have used Alright, so let's run this code Alright, so ID ID is another built-in function. And what do I get down here? Well, I get some numbers when I print these things out Now what are these numbers? These numbers if you're running basic Python that you downloaded from Python.org These numbers are the address in memory of these values that were created Okay, so remember whenever you run Whenever you create data it gets put into memory Well, this id function gives you the address in memory of data that was created Pretty cool. Huh? Let's run it again Okay, and I want you to notice something notice something on my screen and then also notice something on your screen as you run it Note the value here of Alice Okay, I'll mine your numbers are going to be different and that's to be expected. Okay, that's fine But I want you to note your value for Alice write it down somewhere Okay, mine is actually I'll put mine in a comment right here Okay, let's run this code again Now if you remember you can right-click anywhere in your script and click run I like to use the little keyboard shortcut for Windows as control shift F10 Hmm, something's different, right? Now this ID The location in memory is 44887520 Okay, that's different than it was before That's because every invocation of Python that you do every time you start up the Python interpreter and run the script And then it shuts down It is grabbing new places in memory new locations in memory These values are volatile. They are not consistent But maybe let's just take a look at this guy. What's the ID of 42? Okay, for me, it's this for you. It'll be something different. Whatever it is Copy it Note it Let's rerun Hmm This value stays the same. Well, that's a little weird Okay, well, that's because there's an optimization that Python does Python knows that the numbers I believe it's negative 15 through 250 something like that are all Reused those numbers appear a lot so as soon as Python runs like as soon as Python dot exe starts before it even gets into your script It puts these values these special values in a place in memory and just reuses them over and over and over and over Instead of creating and destroying them over and over as well same thing for true true will be in the same location Okay, so that's kind of neat what I want you to take away though We've got the type function that will tell you what kind of data you're dealing with and you've got the ID function Which will tell you where in memory it resides now usually however We don't think of memory addresses as integers usually they are referred to using Hexadecimal right, so let's hex is another function that is built into Python So what I'm gonna do is wrap this value in a hex Ooh, okay, so what are we doing here? We've got the ID function. These are nested function calls okay, and Recall so the parentheses operator in this context is a function call parentheses operators, you know, they're grouping you do the inside first and then work your way out just like you do in Algebra So it evaluates this Which gives you an integer, okay? So it's going to give you an integer like this and then it's going to call hex on this integer and that's going to give you something else it's going to give us a whole bunch of stuff that looks like this and Then we print it Okay, so when we don't have to store the return value Right, we could do something like The ID gets ID 42 or 43 and then we could do Hex value gets hex The ID and then we can finally print hex value We could do that But we don't need to and actually it's kind of wasteful to do that because Generally, this is a general rule of thumb something to remember You only need a variable to put a value in a variable if you reference it from more than one place Okay, so I'm referencing the ID only in one place. It's kind of wasteful. I don't need it I can just replace the value of the ID With it's computed value Same thing for hex value. I don't need this variable Right. I only need the value that comes back from this function All right, so it's a little optimization to keep in mind, right? So that's what I'm doing here a nested function call Let me wrap the rest of these in the hex function Because again, this is the way that Memory addresses are conventionally referred to they are conventionally Reference using hexadecimal format and you should have learned what hexadecimal format is. It's base 16, right? So here's what mine look like, right? This is just my integer values converted into this hexadecimal format Now I believe I must be running 32-bit Python if you see a value that is much bigger than this If you have a much longer string, that's okay. That means you're running 64-bit Python Don't worry about it. The difference isn't terribly important right now, okay? But this is how we normally view memory addresses All right, so cool cool We're just reinforcing the idea here that let me get this out of the way and let me Get back to my presentation screen We're just reinforcing the idea here that Variables values exist in memory and you can get the memory address if you want to okay, so Lot of code. Let's take a look at a different actual visualizer of this thing So what I want you to do is open up a web browser and go to this site here python tutor dot com okay, and Let me get my web browser up Bring it over here How we looking on the screen not too bad all right? So this is python tutor dot com it was written by Philip Guo when he was at Stanford. It's very smart guy Very cool thing. I Encour this is a really great tool and especially if you're a visual thinker I encourage you to use this website Especially if you're stuck on something and values aren't coming out the way you want and you just need a break from looking at code And it would be helpful to look at something visual check this place out so python tutor dot com I'm going to click on start visualizing your code now and That'll take me to this screen now before you do anything I want you to go to the live programming mode. So click this button down here live programming mode Right, you're gonna see something that looks similar, but it'll say here at the top. This mode is experimental All right. Now what I'm gonna do is I'm gonna put some information in here At sorry before I do that Look down scroll down a little bit Down here. There's a couple of drop-down boxes Change this one in the middle that says render all objects on the heap make sure yours says that Make sure it says render all objects on the heap. The default is something else Okay, render all objects on the heap Okay This one. All right. So now we're in some code I am going to if you switch over to slide number nine There's some code in there and I'm gonna grab it and paste it in here Okay All right, so this is code that you can find it on slide nine you can type it in go grab it paste it into this editor So what is my code doing? I am printing a string I'm saying print the address of value 42 at hex ID 42, right? So 42 the data value 42 lives at some integer memory address convert that to hex and now print it okay Now I Assign, let's let's run this in real time. Okay down at the bottom You have some controls here. Click where it says first Okay, you see a little arrow here. It's kind of like our tracing exercise It's getting ready to execute this first line of code and you can think of this as the instruction memory It's getting ready to execute it and after it executes. It's going to show you the value of all variables in memory Okay, so let's go next So What do we see? We've got the printed output, but you'll notice there's nothing in memory Right. No variables were created The implication is that this 42 was kind of created It was used and Python forgot about it. Right. It's gone. Nobody. I didn't assign a variable value to it, right? All right, so we've just executed this line line one. That's green. We're getting ready to execute line two So let's do that click next down here All right, so what has happened? I got this thing on the left called the frame Okay, the frame think of the frame as an address book The global frame is the address book for the variables that are in the main part of your program I've created a variable X and it is pointing To the value 42 in memory Okay All right, cool No output has been produced yet But this is what happened draw this link in your brain when you do a variable assignment X gets 42 we're connecting The variable X to the place in memory where the thing lives How do we know that check out this next line of code line three address I'm going to print out the address referred to by X print ID X and convert it to hexadecimal. So I'm getting the ID of the variable X. What do you expect to see? Well, X is pointing to the location the address of the value 42 in memory Right and what is the value of X? Okay, so when you do this Print the value of X and you just give a variable value, right? Here I'm printing a variable if you do addition X plus Y division X 5 by Y if you put a variable in a string What you are really doing? This is so important for you to understand What you are really doing is taking this variable Going to its address in memory and Seeing what the value there in memory is Okay, the value of X is 42 Because that's the digits. That's the bits. That's what's in memory at this address Okay, so so so important that you understand this Right X right here says go to the address in memory pointed to by X and Get the value that's there. Okay X itself is not a value It holds a memory address Right, let's do another example so go to slide 10 in the slides and You'll see this code, right here I'm not going to step through it's the exact same code except I'm dealing with a float 3.14159 right Actually if I go back and I run it I should get a slightly different address to Can walk forward and backward kind of cool Okay, so again, I've created a variable called I've created a value 3.14159 I assign pi to 3.14159 so Python once it creates a data value It's kind of smart enough to reuse it if it's already in memory if it knows it's in memory somewhere Hex ID of pi pi is pointing to this thing, but you'll note as well Python knows this thing as a float That's very important Python knows that the thing living here is a float if you go back to the old code with the integers Can I just undo here? I think nope can't undo and pi tutor at least only limited amounts if you go back and you put the code from a couple minutes ago This will say int right when we were dealing with 42 All right now Really important really important maybe the most important thing of today, okay? Go grab the code from slide number 11 and paste it in here Okay Go ahead and pause while you're doing that and once you've done it once you've done it go back to the beginning Restart click the first button. Okay? All right, so you should have the code from slide number 11 and you should have started over again Okay So let me step over here. We're gonna walk through this line by line Just printing out the address of the value 42. Okay, no problem. I Assign the variable x to point to that address All right, cool So I've got the value 42 and I've got the variable x pointing to it Now this statement line number seven What happens? What do you think happens? I've got y gets x What's gonna happen? What's gonna happen over here? in this block Well, what's gonna happen is I create a new variable in my global frame my address book and I'd say point to The same place x points to why I'm gonna create y and point to This x look up right here Variable value by itself returns a memory address okay X point why I want you to point to x Okay, so now x and y are pointing to the same address in memory there. There is only 142 in memory Okay, and you can see that go ahead and run these prints if we print The address of x and we print the address of y they are the same one data value in memory Two variables pointing to the same location Okay, very interesting very important a lot of ramifications to that Okay So and we'll see some of those ramifications at a later date, but very important What's gonna happen now if I do x gets three point one four one five nine What do you think's gonna happen? What's gonna happen over here? What happens to x in what happens to y? Let's see boom We have a new float that was created in memory and x now points to it but Why still points to 42 okay? Look at their memory addresses. They're different x is pointing somewhere new y points to the old place Okay, super important. Okay, very interesting Now you may have heard the terms mutable and immutable data types Integers floats strings. These are all immutable Immutable is a 10 cent word that means you can't change it Can't change it Mutable data types are things like lists and dictionaries Mutable meaning you can change the value. We're talking about values not data, right? so When we did x gets three point one four one five nine x was pointing to 42 But 42 is an immutable data type. You cannot change it You cannot change the value at that address location. So python says oh This guy he is immutable. I can't just replace him here Integers are immutable. I can't replace this value what I have to do is python talking is create a new value and Then point x to it. That's what happens If we did we're working with lists here. This would be a different ballgame Okay lists are immutable, but this is the essence of immutability in python You cannot change the value. You can reassign variables all you want. That's fine But you cannot change values. Okay values live in memory Variables point to values in memory. You have to now make that distinction Okay, you have to draw that line before variables and values Wishy washy same, but they're not the same draw that distinction. Okay Big concept let it digest in your brain All right, I'm gonna switch back to My slides here for a minute if I can There we go All right, so recap here data are Bits that represent something like the number 42 or 3.14159 These are data or values. Okay. Think of values data are the same thing data and values When you create data in python it puts these bits in Computer memory somewhere. Where in memory? Where did these things go? That's an interesting question Python does it for you. You don't have to worry about it But the way it works is remember our notional machine We had this thing called heap memory Python's got this big pile of memory just sitting on a plate next to it and whenever it needs to create a value It says hey, give me a bit it grabs something off the plate and Scribbles in it says 42. You're here But that little something it grabbed that little box has an address and that's how it knows right so the heap Python says I need a new value and it says heap I need some place to put it and the heap says here's a place in memory You can put it and that's the address the variables then is Python saying all right x. I'm going to name this address x so I can look at it later, okay Super important that you have that View of variables data values and memory moving forward Okay, I want to look at one more thing kind of one more trick in Python and That is sys dot get size of so I'm going to go over here to Pie charm again. I'm going to be back in pie charm I'm going to go ahead and delete the stuff I have before and I'm going to use first of all I'm going to add this statement called import sys to the top So you may have seen this for maybe not Probably have Import and then this is what is known in Python as a module Modules are related groups of functions that you might find useful. You probably use the math module before What I can do is I've created a variable and a value here I've created a value more precisely and assigned a variable to point to it and sys dot Get size of this is a function. I Probably need to do something like print that Okay, and what this gives me back is the number of bytes That are required to represent This number three point one four one five six. Okay, I'm not sure why that's six But anyway, three point one four one five six I Got to change it. It's driving me. It's going to drive me bonkers, right? There we go. Thank goodness So this is the number of bytes remember eight bits in a bite that it takes to represent this number in memory That's a lot right takes 16 bytes 16 times 8 right bits to represent this number Let's try let's do something else. Let's do 42 right 42 takes 14 bytes Let's do a Million a million takes 16 bytes. Let's do. Oh can't do that Let's do this that gonna work. Oh, I still got an L in there. Don't worry. Just mash a bunch of numbers 26 bytes so the bigger my integers get The more bytes it takes to Represent them right just typing in some integers here and you can kind of see this growing You may see different numbers and that's okay. That's okay How about a string all right, let's do print sys dot get size of the string Alice Alice takes 30 bytes to represent Wow, right Alice five characters this Number I don't even know how to describe it only took 26 bytes Alice took 30 Whoa, well computers are really good at representing numbers the way that it Python stores Strings very complicated right very complicated Let's make the string bigger Alice in Wonderland 44 bytes, okay decent amount So I want to show you one more kind of interesting thing Let's try sys dot get size of let's do a different float. Let's do 34.4 They're both 16 All right, let's do another one. I just duplicated this line So if you hit control D or command D, it'll duplicate the line your cursor zone could be very useful It's type of much bigger float like this Still 16 interesting Let's do a really small float Yours might be 32. That's okay All these are the same right Turns out the way that the data that Python represents floating points is consistent and it doesn't matter You know floating point their name derives from the fact of Where this decimal point is represented inside the computer? Okay, just a fun fact You would learn if you're taking CSE 242 computer organization. You'll learn how floats are represented inside a machine It's kind of interesting, but you know just realize that yeah floats are fixed size in data land But integers and strings in Python they can grow All right, so Let's switch to Where I'll leave off with all of this is that just be aware that the different data types You know 42 whether it's an integer whether it's a Boolean whether it's a string. Don't worry about typing this Just be aware that these things occupy different amounts of memory. That's the important thing to take away here All right, so one last thing one last but holy cow a very important thing I'm gonna go back to my Python tutor in live mode and Let's grab a string. Okay, so if you go to slide number 15 slide number 15 grab that code and paste it in here Okay, so I've got some code here that is going to it just creates a string That looks like this. I've got Alice with some white space around her She's got some blanks tab characters some new lines and you can see when I print it It's got some gunk in there. Let me expand this a little bit okay But nonetheless, you know, I can get the memory address of that this variable points to I can convert it to hex I See here I'm printing out the type and I'm seeing here that the type of name The type of data value that name variable points at is a class string Okay, well, let's manipulate this string a little bit. Okay, let's let's do the following Let's do x gets name dot strip, right? We talked about Don't like that and let's print x Okay, I don't like that it keeps resizing on me, but that's okay Remember in ours go if you don't recognize the strip method or strip function go back to the last week's module and check out the the string functions, but what name dot strip does is it removes leading and Trailing white space But strings are immutable remember it was one of our immutable data types. So The string here name or Alice is not getting changed itself instead Name dot strip returns a copy of Alice with all this white space removed okay Same if we were to do like Why gets name dot? Let's do why gets name dot upper and then print why So here why gets x dot upper we took x which points to this string and told it to go uppercase that's what upper does and That result is assigned to why and we print it Okay, so I've got three different copies of kind of my original string But they've been modified in a different way because string is immutable but All right, let's let's Take a deep breath because this part is really really really important. Okay Let's take a deep breath shake it off get up walk around for a minute grab a glass of water take a take five Okay, because this is gonna be really important. What's coming up next? Hey my deep breath Name dot strip Okay, what is that?  Right, by the way, you don't have to use this dot on just You don't have to use this dot on a variable you can use it on a Literal on the value itself you can do Alice Dot lower Right take the string Alice and dot lower it give me the result of this computation You get little Alice back, right? What in the heck is this dot thing, right? What is it? Okay So what it is is that This thing that is put into memory, right those bytes that we just looked at You know the 14 bytes for the integer and so on It's more than just the data and the value There are also Operations that you can perform on that data right, okay Recall when you type type Right, you type a variable or type of value you get something that says class and Then string or inter float class Okay, what does this mean? What this is really telling you is that Alice this string here is more than just a value All programming languages have a concept of data types Data types are consisting of two things the data. Okay, so the characters Alice that's the data and Operations the things you can do to or with that data Okay so This thing here, right it says class string What does this mean? Classes are a Python language feature that provide the means of bundling together data Value and the operations the things you can do that value together Defining a class creates a new data type in Python. Okay Data types are data and operations classes Are how Python creates data types classes actually a keyword? We'll see it next time So the Python stir class this guy Holds the data that make up the letters and several operations Which are technically called methods for manipulating the data a Method is the same thing as a Python function Except that it is defined on a particular class okay, if you go to the string the definition of a Python string right there are many many many string class methods What that little dot is is The way of accessing the operations okay, so before we've been thinking of variables We've been thinking of classes. We've been thinking of values We've been thinking of these things that we create a memory as the values But they are more than that they are more they are also operations and That is what those little dot blah blah blah things are sis dot get size of string dot split list dot append those are Operations and in Python those are called methods. Okay methods are a lot like functions But they belong to something they belong to a particular data type Wow, okay, that's kind of crazy right so when you create data What you are making are multiple instances of a class With different data, but the same functions Or same methods is what it should really say same operations. Okay, so Suppose you've got x gets Alice y gets Bob z gets Chuck Okay, you will see these are all instances of a string string String string class string class string class different instances But they have different values. Okay, however You can do dot upper On x you can do dot upper on y you can do dot upper on z and it will all do the same thing to the data Okay, so the in your classes in your data types for Python Each time you create a value you are creating an instance of a data type and Those instances have different values, but you can do the same things to Different instances of the same type So all of these guys know what upper means they all know what lower means they all know what strip means they all know What split means? cool Different classes can do different things Right, so if you have an integer class I've got two integers 42 and negative one if you do 42 minus 1 No problem the integer data type knows specific now remember we're Data typing classes are kind of interchangeable terms. They are at least in Python So if I say data type you think class if I think class you think data type They're the same thing just turns out that data type is a more General concept class is the Python specific word for it. Okay Different classes can do different things so integers for example know how to subtract from one another but strings Do not know how to subtract from one another and if you do this go type it in pie charm You will see something that says type error type as in data type type error unsupported operand types for The different sign the subtraction string and string. This is Python's very non-intuitive way of saying Strings don't know how to subtract from one another. Sorry. You can't do it Okay, because I went into the data type for string and I said hey subtract yourself from this other guy and Python said Nope, don't know how to do that. Okay So data types again Different data types have different operations they can do All right, so instances of classes go back to our visualization here instances of classes are Generically referred to as objects. Okay objects in memory Everything in Python is an object every variable you have ever created every Value you have ever computed is stored in memory as an object. Okay, so say it with me everything Everything in Python is an object The number 5 and number 42 the float 3.1416 the Boolean true the string Alice They are all objects in memory These objects are instances of different classes. They are instances of different data types But collectively when they're living in memory, we say they are objects in memory Heady stuff heady stuff. Okay So let me Wrap up on this slide This is probably the most important lecture of the whole semester So if you have to watch it five times until you get it, please do ask me questions. Okay Data types appear in every programming language They are comprised of the data they store and the operations that can be performed on the data Okay, this is a step up in our understanding of what Python does and how it works Creating a class in Python defines a new data type class string class bool class int and Python has many built-in classes and you've been using them already, but maybe not fully appreciating What's going on with them? Okay when you declare or use a variable Python creates an object in computer memory That is an instance of a class This class instance holds particular values it holds particular data, but All the different instances of the same class know the same operations upper split Strip all strings can do it The location of the object in memory is given by its memory address okay Lot of big time concepts study study study know the difference Everything that's underlined on the screen. It's vocabulary know what they are okay Use the Python tutor on maybe some of your old programs to really Concretize what these different things mean, okay? It's important that you have a good visual model of them So so far in your career You have used pythons built-in classes things that Python ships with int string float list program Next week next time we are going to learn how to make our own data types using our Using pythons class feature Okay Talk to you next time again study all this stuff and hit me up with the questions you have good luck


Saint Lucia's ecosystem is one known to be very diverse. The island boasts a number of animals which are endemic to their location, including various species of reptiles. Hence, the prevalence of snakes in and around certain locales come as no surprise. On Thursday, September 21, health practitioners on the West Coast participated in a training session meant to bring awareness to snake species in Saint Lucia. Snake Health No Supervisor Yasmin Gabriel says the training is in line with plans to make the Ancelary Wellness Center, a hub for snake bite education. Ancelary Wellness Center is going to be renamed the Center of Excellence for Snake Bite Education. We do not treat snake bites in our wellness centers, but we believe that the most crucial measure in reducing fatalities from snake bites is education. So today, we are starting our education of the staff. Friday's session covered topics ranging from how to identify the snakes which are venomous and how to protect oneself. At present, Saint Lucia's snake population consists of four species, one of which is venomous. Assistant Chief Forestry Officer Pius Haynes says being able to differentiate is very important. Our training was more focused on more or less our snake identification, you know, how can we distinguish, for example, between the Saint Lucia boa and the Saint Lucia feralas, because persons have had a lot of issues identifying one from each other. Also, you know, what are some of the ecological requirements, where would you most likely encounter a feralas and a boa, and what constitutes the diet and so on. Hostages from the Ancelery, Vana and Canaries Wellness Centers were all in attendance. Health Center attendant Daniel Francis recounts her experience treating a snake bite victim. I'm an employer brought along his staff who was, I guess they were in the woods area, agriculture, and he got bitten by a snake and then we had to quickly call on the head nurse. We quickly went to him, attended to him, tried to, you know, bandage up the wound for him, but then we know we had to refer him right away. So we referred them right away to the Wen King Hospital. And while Region 7 is being viewed as a well-known snake habitat, the Forestry Division is reporting an increase in snake sightings around the island. The Assistant Chief Forestry Officer assures the public that the life-saving anti-venom, though only available at the OKEU Hospital, is always readily on hand. For the Communication Unit of the Ministry of Health, Wellness, and Elderly Affairs, I'm Sands Justin.


Today, we are going to talk about combustion chambers. Combustion chambers as you know is the place in a gas turbine engine, where fuel is burned and energy is supplied from external sources into the engine. That is the place where energy is put inside the engine for the engine to do work and finally produce thrust for flying of aircraft. So, when we talk about combustion chamber, we are effectively talking about what may be called the stomach of the engine. It is indeed right in the middle of the engine, buried deep inside the engine and that is where the energy input is carried out. Now, the way it is carried out is that fuel is supplied into the combustion chamber. Now, this fuel is a chemical entity and the burning of the fuel releases the chemical energy into heat energy and then this heat energy is harnessed by various components of the aircraft engine to finally produce thrust. So, the process of release of this chemical energy into heat energy and how it is finally supplied to the rest of the components of the gas turbine engine is what we will discuss in this chapter. In today's lecture, we will take a look at the fundamental combustion mechanism. There is a lot of physics, there is a lot of engineering and there is indeed a lot of fundamental understanding of fluid mechanics that needs to be put together to make a combustion chamber work. The working of combustion chamber is also subject to a number of theories, some of those theories we will do. Much of the theories including the chemical kinetics or reaction kinetics is beyond the purview of this lecture series because that is a very specialized field, the chemical reaction and we will not get into those issues regarding the combustion mechanism. But we will look at the physics and the engineering of combustion in some detail over the next couple of lectures. So, in today's lecture, we will take a look at the fundamental combustion mechanism and how the combustion chambers in aircraft engines look and how do they indeed perform. So, let us take a look at the fundamental combustion mechanism of combustion chamber of aircraft engines. The combustion mechanism when we are talking about, we are as I mentioned, we are indeed talking about the basic physics and the basic engineering that goes into making of a combustion chamber. Now, typically a combustion chamber has been designed more than 50 years back and for one reason or the other that particular design or that kind of design has been used for many many years. So, the fundamental engineering that goes into making of a combustion chamber has been settled for almost 50 years now. The basic physics was also understood quite long back, however, minor modifications and minor improvements have been going all along and as a result of which each combustion chamber of every particular engine is unique. There is nothing like a generalized combustion chamber design or combustion chamber geometry that you can fit into any engine. For every engine a combustion chamber would need to be designed uniquely for that particular engine and because of this it is necessary to keep an eye on the fundamental issues of the physics and the engineering of the combustion mechanism. Let us take a look at this fundamental combustion mechanism in today's lecture. As I was mentioning the heat addition that is done normally in a combustion chamber is fundamentally conceived as a part of the working Brayton cycle. Now we know an aircraft engine is fundamentally conceived based on the Brayton cycle, the thermodynamic Brayton cycle and combustion has to be in conformity with that Brayton cycle conception. In this process the energy is put into the system by burning of the fuel in a flowing gas. We have seen that the Brayton cycle works in an open cycle. It has a continuous flowing gas initially flowing air and then it becomes flowing gas and the combustion has to be done in this flowing situation. Now that is a different kind of problem and that is what we will be looking into in today's lecture. Now the aircraft gas turbine engine has the problem that the air flow through the engine is at an average speed of close to 100 meters per second. Now that is a pretty high speed actually speaking which requires that the combustion intensity is very high. That means in a very small time if you have 100 meters per second average speed the resident time in any of the elements of aircraft engine is a matter of fraction of a second. So in a fraction of a second you have to release the heat that is available from burning of the fuel. So you do have very small amount of time and very small amount of space to complete the process of combustion and this is one of the challenges of designing the combustion chamber that in a very small space and of course in a very small time you have to complete the process of combustion. Space in an aircraft engine is in premium. You are quite often allotted a very small amount of space for doing your combustion job and this puts a lot of pressure on the engine designer to create a unique combustion chamber in which the combustion can be more or less complete. So this is a kind of challenge that combustion designer often needs to face with every engine design. In aircraft power plant size as I mentioned the size is limited and you have to create your combustion within that limited size. That size limitation puts a restriction on the volume that is available for combustion purpose and the time that is allotted because the air is flowing at a very fast pace and the resident's time of the air inside the combustion chamber is a very small fraction of a second. So within that small fraction of a second a very large amount of heat would need to be released inside the combustion chamber and that was the mechanism which we will look at in today's lecture. Let us continue with this fundamental understanding. The combustion intensity which I mentioned varies from one kind of engine to another. Let us take a quick look at what are the numbers that we are talking about. If you look at boiler furnaces that are typically used in steam engines, the kind of heat release we are talking about is 4 into 10 to the power 5 to 10 to the power 6 kilo joules per meter cube per hour and that is roughly 1 into 10 to the power 2 to 10 to the power 3 kilowatts per meter cube. Now if you compare that value to the piston engine which is an IC engine also where you burn various kinds of fuel to get your work done. Now piston engine is enclosed combustion chamber you do not have flowing fluid and you have a captured volume of air in which a fuel is burned and inside that captive combustion chamber which is the piston head the amount of combustion intensity is 25 to 125 into 20 to the power 5 to 20 to the power 6 kilo joules per meter cube per hour. Now if you compare that to the jet engine that is used in aircraft that is of the order of 75 to 150 into 10 to the power 5 to 10 to the power 6 kilo joules per meter cube per hour that means it is fundamental heat release rate is of a higher order than any piston engine and if you go to rockets the requirement is of the order of 260 into 10 to the power 5 to 10 to the power 6 kilo joules per meter cube per hour. So rocket engines do have the highest heat release rate that needs to be created inside the rocket combustion chamber. So jet engine comes second in the list of high heat release rates that are needed in combustion chamber. Now with this kind of requirement of heat release rate it is necessary that you have a very good understanding of the combustion mechanism. Let us understand how these things happen. The condition at the burner inlet is determined by the outlet operating conditions of the compressor. Now the outlet operating condition of the compressor varies with the varying flight regime. Now depending on whether the aircraft is taking off or it is climbing or whether it is cruising or it is doing maneuvers. Depending on all that the compressor operating condition and its delivery to the combustion chamber would vary in terms of pressure, in terms of temperature, in terms of density and also quite often in terms of the velocity with which they are delivered.  On the other hand the outlet condition of the combustion chamber is necessarily governed by the turbine design operating conditions and is generally required to be uniform and stable. Now as we have discussed before, the first turbine that faces the combustion chamber is the HP turbine. Now HP turbine is what faces the high temperature and high pressure gas coming from the combustion chamber. Now HP turbine is necessarily a high speed turbine which supplies a lot of power in a small size to the compressors. So it is necessary that HP turbine gets a very stable and uniform supply of high energy gas from the combustion chamber. This is necessary to be done or achieved and assured by design. Now to do that combustion chamber needs to be created in a manner that within a restricted space and restricted volume it does provide and supply stable hot gas to the turbine irrespective of whether or not it is getting a stable supply from the compressor. So combustion chamber in some sense apart from doing the combustion also needs to stabilize the flow a little before it delivers it to the turbine. So combustion chamber in some sense is some kind of a stabilizer also in addition to doing the heat addition to the working fluid. Now this stable source of hot gas is necessary to be delivered under all operating conditions specially when the aircraft and the engine is accelerating or decelerating and this requires that the combustion is always held and it is never allowed to be extinguished or what is known as blown out under all kinds of operating conditions. And we shall see that there are certain parameters which are to be held very strictly within those certain specified limits and those parameters are what we are going to discuss in a few minutes from now. So these variability that we are talking about and the stability that we are talking about can be quantified and this quantified parameters are what we are going to talk about in today's lecture and carry on in the next lecture also. Let us take a look at some of the jobs that a combustion chamber is supposed to do. We can indeed list them to raise the temperature of air to the highest level conforming to cycle design. Now this is as per the turbine inlet condition as specified in the cycle design. The turbine inlet condition is indeed decided by the ability of the turbine to withstand high temperature which is decided by the material science, the state of art of the material science and the metallurgy and the cooling technology often employed in turbine design. So all of them together decide what should be the compressor delivery temperature and the cycle design will tell us what the compressor delivery pressure would be which is roughly what combustion chamber receives from the compressor. So combustion chamber is supposed to deliver more or less the same pressure with minimum loss of pressure. Now this is intended to achieve maximum work extraction per unit mass of air flowing through the turbine. Now we mentioned that combustion chamber works in a gas turbine engine in a flowing fluid. So it is necessary that it produces this work working capability or renders this working capability to the turbine in flowing fluid situation. Now as I mentioned this must be done with minimum loss of pressure because lot of care has been taken to build up a lot of pressure in the compressor and one should not lose much of it in the combustion chamber. So combustion chamber design the engineering of the combustion chamber design must ensure that there is minimum loss of pressure and that is where the engineering comes in. The hot gases must be delivered at uniform pressure and temperature within the material limitations of the turbine. So material limitation of the turbine the cooling technology the turbine is one aspect. The other aspect is that it should have a uniform profile temperature and pressure profile as it is going into the turbine. Because when it hits the turbine the turbine has a root as we have discussed in the turbine chapter it has a tip and the blade is often twisted and when the air hot gas hits this turbine blade first the stator and then the rotor it should have uniform temperature profile from hub to the root to the tip of the turbine going through the stator and then on to the rotor this uniform it is very important because the turbines are designed for uniform temperature profiles turbines are normally not designed for non uniform temperature and pressure profiles. So the combustion chamber has a job to do here that is to create uniform flow with uniform temperature and pressure and velocity delivered to the turbine in an annulus form you remember the turbine is an annulus construction and so combustion chamber must deliver it to the turbine in an annulus form. So this uniformity needs to be achieved in that annulus. The hot gas generation that must be created now this must be done as I mentioned during engine acceleration and deceleration and during acceleration and deceleration the flame which is created inside the combustion chamber should never be allowed to be extinguished or any kind of pulsations should not be set up or amplified by the combustion chamber. Now these are distinct possibilities these can happen during the combustion chamber operation and combustion chamber designer must ensure that none of these things happen during the operation of the engine because as I mentioned these are realistic possibilities flame can get extinguished pulsations can occur and some of the disturbances that are occurring can get amplified and if those things happen it would be absolute catastrophe. The whole engine would burst like a little bomb and this is something which is must be avoided under all considerations and under all operating conditions. The combustion chamber designer needs to ensure that none of these catastrophic things ever happen during the operation of the engine. The other requirements which the engine designer the combustion chamber designer needs to conform to is that the ignition should be rapid reliable and sustainable in a typical aircraft engine once the ignition is done it is sustained through the entire operation of the engine and ignition is not done every now and then as it is done in piston engine. So it is not as per the cycle ignition once done it continues indefinitely till the engine is shut down it should occupy minimum space something we have talked about earlier and we shall see the mechanism how it is done. And the last of the combustion requirements is that it should be able to burn a range of fuels. We will have a look at a few of the fuels that are normally used they all fall more or less within the same category of what is known as aviation kerosene and but there are variations within that and we should be able to create combustion chamber which can burn any of those fuels conform into the requirement of the particular engine and of course particular kind of aircraft. Now with this let us take a look at some of the combustion chambers that we may like to get ourselves familiar with now the first type of combustion chamber that came into being in a typical gas turbine engine is typically referred to as a can type combustion chamber in which the entire flow coming from the compressor is split up into number of cans and these cans are arranged around in an annulus fashion around the shaft of the engine. So quite often you would have 5, 7, 9 or fairly large number of cans arranged around the shaft of the engine and the entire amount of annulus air coming from the compressor is split into so many cans. Now let us see what happens inside each of these cans which each of which is a combustion chamber by itself. The flow is coming from the compressor high pressure air and then inside the when it hits the can you can see only 20 percent of the air is going inside over here and almost 80 percent goes outside through the bypass. So a combustion chamber indeed has a bypass system. Now this 20 percent of air that goes in it goes through what is often known as a swirler and this is where you can see the swirler it creates a swirl and then it goes through this entry port over here and then enters the combustion chamber. Inside the combustion chamber this is what we call primary zone and that is the primary zone in the lower picture which is a cut out of a real combustion chamber and this is the primary zone where the fuel is actually burnt and the fuel air mixture of gas is primarily created. Now once the fuel is burnt and the primary gas is created excess of 20 percent of air is allowed to be brought inside the combustion chamber from the bypass system. So the can has a bypass system and from that bypass 20 percent comes in here then 40 percent comes in through various other means and 20 percent more comes in through in the last stages which is the dilution zone or often referred to as secondary and finally tertiary zone in which more air comes in. So the hot air that is created here or the hot gas is subsequently cooled to certain temperature which is conformity with the turbine material. So this dilution or cooling is often in conformity with the requirement of the turbine. So the amount of cooling that needs to be done is dependent on the turbine material and the turbine design because in the primary zone the temperature that is often achieved is in excess of 2500 degree centigrade. Now that is the kind of temperature which is not allowed to be delivered to the turbine. So subsequently with this excess air which is brought into the combustion can the inner can so to say so you can say you have a inner can and you have outer can and the bypass carries nearly 80 percent of the air in the outer can and then it comes inside and cools the air to something like 1000 to 1100 degree centigrade and delivers it to the turbine. So this is how it is done you can see that there are two concentric cans over here and you have number of these holes these are the holes through which this air comes in the primary, the secondary and the in the dilution zone in the tertiary zone. So these are the air vents through which bypass air is coming in which is cold air really to cool the hot gas to conform to the turbine requirements. You can see some serrations over here these serrations are indeed openings these are for actually bringing in cool air tangentially into the inner can essentially to provide cooling to the inner can it creates a film a cold film inside the inner can this is done here also. So in every sector of the inner can certain amount of cold air is brought in tangentially into the can inner surface and creates a cold film around the entire annulus and then the inner can is protected by this cold film from the very hot gas created by the combustion. So the can which is also made of high temperature material also is provided certain amount of cold air protection for its life. So that it can perform without getting B shaped or without getting distorted during its entire life. So the combustion also involves a little bit of cooling of the inner can to protect and extend its life. So we have a number of things going on over here air is coming in it is split in two parts minor part actually comes in and participates in the combustion process. The major part bypasses the combustion process and comes in later on for cooling purpose. We will take a look at what happens in the combustion process in the subsequent slides. But let us take a look at the other kind of combustion chambers that are used in the modern gas turbine engines. Now this is what is known as a canular type combustion chamber in which the flow is essentially again split up in number of cans which are inner cans this is a real picture of a can, but the bypass air which I mentioned earlier in the can type is now a common bypass for all the cans. So we have a common bypass for all the cans and the inner cans are individual cans and the one of the reasons many of the modern engines use this particular mechanism of having inner cans to actually perform the combustion process is because the primary zone in which the combustion is carried out gives a protected combustion space to the combustion mechanism. Now this is very important when you are doing combustion it requires certain amount of protection from the vagaries of other aerodynamic and gas dynamic disturbances. And as I mentioned this protection is very important for stable combustion and this protection is provided by creating a can an individual can within which the combustion is done in an isolated manner. And in big engines even today it is considered a good idea to have a number of cans as I mentioned may be 9, 11, 12, 13 cans within which the combustion is held in a protected manner whereas the bypass air is a overall annulus bypass and that can go into any of the cans in the secondary enter series zone for cooling the hot gas, but the primary zone is given a protected zone for protected combustion purposes. We will look into the combustion mechanism in a few minutes, but these can types were created to begin with is to create this protected combustion zone. So let us take a look at the other kind of modern combustion chamber which is the annulus combustion chamber annular combustion chamber in which the entire annulus of the flow which is supplied from the compressor you see the compressor supplies air to the combustion chamber in an annular fashion that annulus itself is carried on through the combustion chamber and delivers to the turbine in an again in an annular fashion. So from this end the flow is supplied from the compressor in an annular fashion and this is you have the combustion chamber here which is an annular combustion chamber you have the primary zone over here and then you have the secondary zone and then you have the tertiary zone and at the end it supplies an annular fashion to the turbine you can see the turbine nozzles or the stator nozzles over here lined up at the end of the combustion chamber. So the delivery from the compressor and then delivery to the turbine both are annulus and as a result this particular combustion chamber is designed to create a design to retain the annular flow that is coming from the compressor and delivered to the turbine and the combustion chamber is indeed created in an annulus fashion. So this is the kind of annular combustion chamber quite often used in the modern aircraft engines specifically in the military engines or medium to small sized jet engines most of the engines today are annular combustion chamber. So if the engine is small or medium sized and more specifically those used in the military aircraft engines the combustion chamber is most likely to be an annular combustion chamber whereas for very big engines used in transport or passenger aircraft the combustion chamber is likely to be the cannular kind of combustion chamber which is a can a number of cans which are arranged in an annular fashion with a common air bypass surrounding all the cans. So these are the various kinds of combustion chambers that are used in the modern jet aircraft engines. We will take a look at some of the issues related to the combustion and then the combustion mechanism. Let us take a look at how the combustion actually happens. What happens is the flow that is flowing through the combustion chamber somewhere in that flow you have spray of fuel. Now this spray is done by injection process and we will talk about the injector later on but first thing that happens is that liquid fuel is sprayed through the injector into the combustion chamber and this spray comes out in the form of small droplets very small sized droplets. Now these droplets essentially are extremely important what is the size of these droplets so the injector is very finely designed to create very small sized droplets and these are the process is called atomization as the name suggests that these droplets are supposed to be extremely small. The idea is that the third step that is required here is evaporation. To aid the process very fast evaporation it is necessary that you have very small droplets and as it is mentioned here they should be very small almost as if they are atoms so that the word atomization comes from that concept that they should be very small droplets so that the evaporation process is very fast and then following that the mixing of this liquid fuel evaporated and then mixing with the air. So the evaporated fuel must mix with the air in a uniform manner and this evaporation process occurs next. Once the evaporation has been completed and air and fuel has been mixed in a certain known proportion the ignition is initiated and once the ignition is initiated that mixture of air and fuel starts actually burning. And then the burning process releases the heat and there is a burning zone which is often referred to as flame zone during which this mixture of air and the droplets of evaporated fuel actually burn and this burning zone is where the heat is released. Now the release of the heat through the process of burning takes place over what is known as also flame zone and then once the heat is released it is necessary that you take care of the combustion products. The process of combustion creates combustion products through the process of various chemical kinetic steps. Those chemical steps we are not discussing in this lecture series but there are large number of chemical steps and at the end you create a number of chemical products. The combustion is fundamentally chemically a process of oxidation and this oxidation process creates a number of chemical products and these are called combustion products. It is necessary that these combustion products mix very uniformly throughout the body of the combustion chamber so that they carry the heat uniformly over the entire space given to the combustion chamber and once this uniform mixing has been achieved and the flow has been diluted by cold air it is time to deliver it to the turbine. So this is the fundamental mechanism by which the combustion chamber works. We can put it together in some kind of a flow chart which will tell us how the combustion process proceeds. You have the liquid fuel that is supplied through the injector and you have the air supply that comes from the compressor and that both of them go into the combustion chamber and the injection of fuel in this moving air is done through what we mentioned a process called atomization. These are very uniquely designed injectors and we will discuss them later on in this lecture series. Once atomization is taking place there are two things that need to be taken care of one is the process of evaporation where these fuel need to evaporate and become gas and then the droplets that are there they in fact are liquid droplets and they quite often collide with each other. So the collusion of these droplets often may result in creating bigger droplets and that is something that needs to be avoided. So one should not allow bigger droplets to be created rather the droplets should break up into even smaller droplets and so that they evaporate very fast. So the process of evaporation needs to be aided one way or the other and then of course you have turbulent or diffusive mixing. We shall have a look at how this is achieved this mixing process of air and fuel is extremely important and we shall see how that is achieved in a few minutes. And then this we have two kinds of reaction one is the gas phase that is the evaporated fuel mixed with the air goes into gas phase chemical reaction where heat is released and the other is where the droplets that are still remaining as small droplets start burning and they burn as droplets. So we have two kinds of burning one is the gas phase burning another is the droplet burning and then they create a total reaction process of the combustion and this is what we call combustion. So we have two kinds of combustion the gas phase combustion and droplet combustion and when they put together the combustion is completed we have the reaction kinetics completed and finally the combustion products are created which also carry the heat of combustion with them and they are to be distributed evenly over the entire combustion. So this is how the entire combustion process proceeds from the beginning of the combustion chamber to the delivery end of the combustion chamber. So we can say that the flame that is created by the combustion process needs to be taken care of there is you have droplets burning and there you have the gas phase burning you have two kinds of combustion process going on and it is necessary that the flame that is created for the combustion process is kept under control all the time. Now this flame that is created moves in the combustion chamber along with the flow of air at a speed that is known as flame speed. Now this flame speed is an important parameter and we will go into it in this lecture. The point is that this flame is to be sustained for continuous combustion and if the flame is to be sustained for continuous combustion it is necessary that you held the flame or hold the flame steady throughout the process of combustion and if you cannot do that remember the flame is likely to be extinguished or is likely to create combustion related instabilities both of which are unwanted phenomenon in gas turbine engine. Now outside the flame zone the combustion gas move towards the combustion exit. Now this movement of a combusted gas towards exit is often aided by the motion of cold air that is coming in and as a result of which that is something that needs to be engineered into the combustion chamber design. The process of evaporation of the droplets and mixing of the fuel and air can occur partly aided by the local turbulent vortices which are artificially created around the spray zone and we shall have a look at this phenomenon in the following slide. At the point of ignition all the droplets may not have been evaporated and mixed and hence some of them may burn as liquid droplets as I mentioned in the last slide that the combustion may proceed with the droplets also. So combustion may proceed either in the form of a gas phase combustion or it may proceed in the form of droplet combustion both of which indeed are combustion processes both of which coexist inside a combustion chamber and both of them must finish the combustion process simultaneously and create the combustion products within the so called flame zone which we mentioned. So within the flame zone we have two kinds of combustion going on but both must finish the combustion by the end of the flame zone and deliver the combustion products to the following space in the combustion chamber so that in a uniform manner the hot gas can be delivered to the turbine. Let us take a look at what happens thereafter the process of burning then creates the chemical reactions and these chemical reaction kinetics are what creates the release of the heat from chemical bonding that the fuel has. So the release of the chemical bonds essentially create the heat release and this is overall as I mentioned is called a process of oxidation where air supplies the oxidizer. So air here is oxidizer and fuel of course is the propellant or the chemical unit that participates in the process of oxidation. The combustion process for the whole amount of the injected fuel may not be completed by the end of the flame zone. Now this is something combustion engine designer combustion designer must be very careful about that process should be as far as possible complete by the end of the flame zone. Now it is possible that a very small percentage may be 1 percent may not be completed by the end of the flame zone and then a certain amount of combustion can continue to happen in the rest of the combustion chamber and then more air is remember a broad inside the combustion chamber to bring down the temperature. So carrying on the combustion is going to be more and more difficult because the it is being cooled down necessarily to aid the delivery to the turbine and however it is quite possible that in rest of the combustion zone certain amount of reaction is still carrying on is still going on and in some places the reaction has indeed been completed and the combustion products have already been created. So in the secondary or tertiary zone or in the dilution zone it is entirely possible that a very small amount of combustion is still going on but most of the combustion 98 percent of the combustion may have already been completed. So this is how the combustion is indeed done inside the combustion chamber. It is necessary that sufficient space is provided for all the steps. We saw number of steps. There was atomization, there was combustion, there is a creation of combustion products, there is a flame zone, you have to give the flame certain amount of space to exist and then the mixing of the combustion products and then finally, delivering it to the turbine. So there are so many things to be done inside the combustion chamber very carefully so that the combustion process is complete in all sense of the word. Now this needs to be done in a very small space. However that space needs to be sufficient for doing all these things in a step by step manner. Since the resident period inside the combustion chamber is indeed very small it is necessary that the physical steps and the kinetics of the reaction are matched in time. This is extremely important because you do have small fraction of a second quite often a very small fraction of a second and within that fraction of a second you need to have a physical matching between the reaction kinetics and the physics of the flow and this is important. At the end you must keep an eye on the temperature. The temperature in the primary zone is very high it is of the order of 2500 degree centigrade quite often. However the air above 2200 degree centigrade quite often has a tendency to dissociate locally. So the primary zone temperature which is often available in the primary zone should not be allowed to go inside the rest of the combustion chamber where air may dissociate. Let us take a look at how the combustion actually is controlled inside the combustion chamber. Now this is a typical side view of a typical combustion chamber whether it is a can type or whether it is a annular type. The air comes from this end and delivers into the combustion can or combustion zone primary zone which could be as we saw only 20-25 percent of the air coming from the compressor and in this zone artificial recirculation is created. Now creation of this artificial recirculation is extremely important and this is created by elements that are known as flame holders. These flame holders are of various shapes and sizes. We will have a look at them later on and these flame holders create artificial recirculation zone because of which the air that is coming from the compressor may have an actual velocity of the order of 100 meters per second. As it comes inside through the swirler which we saw the actual velocity is reduced to nearly 30-40 meters per second and then through the recirculation as we are seeing here the forward movement of the actual velocity is brought down pretty close to something like 4 to 5 meters per second because that is where the flame can be sustained at high velocities of air the flame cannot be sustained. The sustenance of the flame requires that the forward velocity is very small so that the so called flame speed matches with the air velocity with which the combustion the gas and the combustion products move. So, it is absolutely necessary that the engineers create a very good recirculation air flow zone over here so that the air forward velocity is brought to a very low value and recirculation is created to aid the process of evaporation. Injection ensures that you have small droplets and that itself is supposed to aid the process of evaporation and then the recirculation of air further aids the process of evaporation. In that small space a very fast evaporation is required because without very fast evaporation and very good mixing you will not have uniform flame created on the flame zone. So, it is necessary that you have uniformity of the gas or the uniformity of the fuel and air at the end of this zone so that uniform flame front is created. Now, flame front of course, is the flame with which the ignited gas moves and this moves as at a speed which we call the flame speed and it moves within a certain distance at the end of that distance the entire combustion process is over and the flame has produced the combustion products which then move away from the combustion zone and a new flame front is already created. So, this zone is where the flame front initiates the combustion process and the end the other side of the flame front or the flame zone is where the combustion process is completed. So, combustion is initiated at one end completed at other end and as you can see that is a very small zone in which the entire flame has to exist and sustain itself to create the process of combustion. Now, once the process of combustion is over and the flame front delivers the combustion products you again need a process of a recirculation and this is what is done by infusing cold air through those air vents. They come in and create again a recirculation zone again here they are coming in tangentially and creating a recirculation zone and they aid the process of mixing of the very hot gas to the cold air. So, that by the secondary end of the secondary air zone the air or the gas has now achieved a much lower temperature. This lowering of temperature continues into the so called tertiary zone where it is necessary to create uniform flow. The uniform flow needs to be created now in the tertiary zone through which the air is now to be delivered to the turbine. So, at the end over here you must have uniform temperature and pressure. So, this is how the combustion is engineered inside the combustion chamber. The speed of propagation of the flame through a mixture of fuel which is normally hydrocarbon fuel and air is rather low and the flame speed will vary with mixture strength, temperature and pressure. For laminar flow the flame speed is around 2 to 4 meters per second. The average air velocity through a typical combustion chamber is around 30 to 50 meters per second that is even after the swirler. So, which means artificially just around the combustion you need to create air flow of the order of 3 to 4 to 5 meters per second otherwise combustion there cannot be sustained flame there cannot be sustained. So, a low average local actual velocity must be provided if the flame is to be stabilized sustained and contained in one place and that is exactly what is done over here. A recirculating zone has been created and this recirculating zone indeed actually creates the very low forward velocity 2 to 5 meters per second actual velocity and a lot of recirculation here. So, that this flame front is sustained at that 3 to 4 meters per second on a continuous basis over the entire period of operation of the engine. If we look at a simple graph it tells us that the flame speed depends on whether you have a laminar flow or turbulent flow. If the flow is turbulent the flame speed can be a little higher. So, the recirculation zone often creates a bit of a turbulent zone and within which the flame speed can be a little on the higher side. Now, the typical air flow speed is of the order of 30 to 40 meters per second and this is where the flame speed is expected to be without which the flame would not be sustained. Now, the fuel air ratio has a limit within which the fuel will burn and this is referred to as stoichiometric combustion or stoichiometric ratio which is simply the chemically correct fuel air ratio and that has a very small zone within which the fuel air would burn in a combustion mechanism. So, as we can see here it may vary from something like 0.05 to 0.075 within which the fuel air ratio needs to be held during the process of combustion. If it is more the fuel will get extinguished because of the richness of the fuel or the combustion will get extinguished and if it is less it will become what is known as a lean combustion and the combustion may get extinguished because of lack of fuel or too much air. So, too much fuel or too much air will result in extinction of the flame. So, you have to hold the flame within that stoichiometric ratio zone and still hold the air in a low velocity area. The stable burning of the hydrocarbon fuel takes place close to either side of the stoichiometric as we have just mentioned. It is necessary to ensure that the mixture strength is held within those values in that sheltered region. The range of stable operation vary with total pressure of the combustion chamber which decreases with increasing altitude till the cruise fright is reached. Remember as you are flying to higher altitude the combustion chamber pressure is going down and you have to hold a stable operation. The change of fuel air ratio from what is operational and what is stoichiometrically correct this ratio is simply known as equivalence ratio. So, how far you are away from the stoichiometric value is decided by the equivalence ratio. So, this equivalence ratio is going to tell us whether you are rich or a lean fuel and whether you are beyond the sustainance fuel air ratio or not. These are the various fuels that are used in modern aircraft engines all of them are hydrocarbons as I just mentioned and the hydrocarbon ratio is of the same order nearly two of all of them all of them are some kind of kerosene or the other. However, there is very small difference between some kind of fuel used in military engine and some kind of fuel used in commercial jet airliners and there is a kind of fuel in which it is supposed to be safe fuel because of various reasons. So, one of the reasons is that it has a high initial boiling point that means it does not catch flame very easily and hence it is called a safe fuel, but some of the fuel that used in military and commercial have slightly lower boiling points and they of course, have certain freezing points and this is the heating value which you have used in your cycle calculation and as you can see the heating values are more or less constant for all the fuels that are used. Density is of the same order as you can see here the density of the commercial fuel is little on the higher side for economy reasons and the stoichiometric values are of the same order of various fuels. So, we have covered a ground over which we have looked at various kinds of combustion chambers. We have looked at the fundamental combustion mechanism by which the combustion is sustained and created inside the combustion chamber. We have seen the basic fluid mechanics that needs to be engineered inside the combustion chamber to have a sustained combustion process. In the next class, we will look at some of the other issues of combustion chamber. We will look at the aerodynamic pressure losses that needs to be contained. We will look at values like combustion efficiency and we will look at the combustion intensity which decides the heat release rate in the combustion chamber. So, these are the parameters that engineers use to decide whether the combustion chamber is good or not so good by design and we will look at these engineering parameters in the next class.


Yeah, I thought my sinker was too elevated. I kind of realized that with the first three batters were fly balls. And obviously, as a sinker ball, I want the ground balls. And then I threw a couple of good change-ups. And then I tried to kind of really get that arm side run on a couple. That's like the one that hit Vladdy was a change-up. And I really tried to like overpronate it and just push it right at him. And then even like Bichette, when I walked him in a 3-2 count, it was supposed to be a change-up that I just really tried. I tried to make it better than it needed to be. But I also kind of got away from what my game plan was. I wanted to really throw a lot of off-speed pitches, because last year was predominantly fastball. And I want to kind of see how the off-speed pitches are working in that first inning. I threw more fastballs than I wanted to. So I talked to Tarino a little bit about mixing more in. And we got in a better zone in the next inning. But again, the hit-by-pitch kind of cutter in that was decently executed, but just kind of a couple inches too far. Barely touched him. And then stolen base double right after it. So it kind of escalated quicker than I wanted to. But in the second inning, I felt like I was able to get more ground balls and kind of execute those off-speed pitches.


Tilburg University accommodates about 13,000 students per year. Among them we have about 12% international students. This year we had almost 1,240 international students from 96 nationalities. A very diverse group and that's I think one of the most unique points of this university. Quality of education and other very important aspects of Tilburg University where we pay a lot of attention to accreditations, to rankings and whether transfer of knowledge what we call it happens in a proper way. With respect to the teaching methodology from day one I knew that I've made the right voice because from the first lecture I've noticed that my teachers had also a professional background besides their teaching careers so they are very practice oriented. They are very available and open and I was very much surprised about that. They are always available to help you and to make you understand which direction you want to go within your studies within your master's thesis and you learn more than academic content going to classes you learn on a personal level. I study in master's in economics and I chose Tilburg University for a variety of reasons. First the program is structured well and it has different available specialization tracks and at the same time you can also compose your own curriculum which is the flexibility is offering the great level of flexibility and second there's an availability that you conduct research, you can write your thesis and I took into consideration before I came to Tilburg University and third it was a financially feasible move for me and this because I receive a generous scholarship. The benefit for me of doing my international master degree here is that I can make friends here right now from all around the world with a great diversity but in the future they are going to be my colleagues so I can create a network with them and work with them in the future. Tilburg University offers tremendous number of international master programs and with lots of specializations more than 50 actually a fully English thought and these programs offer actually a variety of tracks also where students can specialize under a broad label. We offer a lot of programs in the fields of economics, business, management, law, social sciences, humanities, communications and not to forget a very important one that's data science and in that way this specialist university can offer lots of different programs for international students. Tilburg University's motto is understanding society and that means that we focus on broader societal aspects in addition of course for the students it's important to gain analytical and critical skills and that means that they don't always go for the obvious solutions but that they really go for the creative analytical ability to solve problems. From international perspective I think our research output is very important at Tilburg University our research approach I have always said there is difference between the answers if you would ask one plus one the answer can be two but it could be also four minus two so we look at the question in a totally different way and there might be different answers possible that's typical I think for Tilburg University to profile itself. Tilburg is part of the fastest growing region in the Netherlands and one of the most entrepreneurial areas in Europe and this is also the reason why our graduates find a job within three months after graduation.


What is good Marvel squad welcome back to our channel today is Mariah's birthday? She just turned 24, and I'm waking her up with just a little surprise to start off the day I got a whole day planned for her. Let's go see if she's I was just Why are you standing by the door? I I was literally telling Marvel squad that I was just about to see if you were awake Do you hear what I said? No, okay? Well, I have your first surprise for the whole day. Okay, so wake up And by the way happy birthday. This girl is 24 years old. What are you wishing for your 24th birthday? another year full of happiness and three million wait we hit two minute three million subscribers three million subscribers, okay? For Mariah's birthday wish what you guys can do for her is keep showing love on our videos If you're not subscribed to our channel yet make sure to subscribe because honestly, that's like best birthday wish ever All right, ready close your eyes. I walked in the store, and I just I wanted the biggest and bet what? You already see it. All right. There you go Happy birthday, baby. I know it's like half of your size. I thought it fit you the best This is literally the biggest one that they had at the store, so I wanted to get like the best and biggest one You're welcome Squeezing my butt it is your birthday, and I want you to be happy So this is not the only gift that I have for you so trust me. Okay. You like it If you see all of our Christmas stuff is just blown up everywhere Mariah for some reason yesterday decided it would be Amazing to go and tear down all of our Christmas stuff, and I I've never seen this girl more motivated in her life taking out everything She was like get the tree box get all the boxes.  Yeah So Mariah just sent me to the store because we did order a cake and while I'm going there I'm actually gonna take a detour. I ordered something really special for her birthday, and it just came in this morning I got her some custom Jewelry necklace that she's gonna be opening so that is her big surprise, okay? I know Mariah is gonna look so good in it and remember guys this girl has my location like she knows where I am So I'm just crossing my fingers that she doesn't check Let's get this necklace and get this cake and get home before she notices anything is up But so I just got home from picking up the cake what I know I got it babe I'm not gonna drop it. Let me just say you literally match your cake Exactly the only reason why you're getting your cake early is because we're filming a TikTok and you're taking pictures with it Otherwise, you would have gotten it like at dinner.  It's starting to melt. Damn. This thing looks good. Oh my gosh It looks so good. They did a good job. So I'm gonna need your help taking it out Okay, so I can film this we gotta do this quick so we can put it back in place Well you take it out like this look at how good this freaking cake looks and this is after filming the TikTok So you guys actually off my birthday more of Bill's clothes came in that I knew I got him He doesn't shop for his stuff Oh my gosh, this is not about me. This is a video about you baby Yeah, it's like a Christmas that just keeps giving even though we took that all of our Christmas stuff already baby. Where are you at? Oh What are you doing in here? No, come out here. Mariah came up to me a second ago after filming the TikTok. She's like I am ready for gifts Oh I'm gonna give you your one gift now one gift now. Yes, because it's a big gift. You're so cute I love this so much. I don't know why they put it in such a big box No, I really don't know why I did pick this out and I had to order it online And I went there twice and the first time they didn't open because their times were off because of holidays That's why I was there earlier. Did you see my location? No, but I thought you were just going shopping Okay, three two one. Oh My god, that's so cute Thank you. Oh my god I want to put it on you. Oh my god. It's so glistening. I'm telling you this thing was the shiniest thing I saw This is like white gold. It's like a point Something carrot. So this is why I don't have a lot of nice things that you can layer Yeah, and she said that this is a really good one to layer so you can wear this one with like your cross Underneath it more. It's so hard to see because I know the camera gets really whited out Beautiful Oh my gosh, this is adorable I knew I met your dress I hope you like it. I really hope you do. Oh my god guys, it shines like that's beautiful Alright, so Mariah has talked me into just giving her all of her gifts There is one more gift and the reason why I can't give it to you is because it's something that we're going to go do so Many years ago Mariah did this thing for my birthday. And do you remember what it was? No, something we did Yeah, okay, so I booked a helicopter ride I don't know for us one of the days Right, you deserve the world. Okay, by the way, Mariah just reminded me that I'm not supposed to say where we are going Which is why I've leaped out the word But we're gonna be doing a helicopter ride tour around the place that we are going In what to me. Yeah, baby. What is that? I Honestly have no idea. I did not do this and I will not take credit for it because whoever did it will get mad Oh my god And an Anthony shot to you guys and they make you so much. These are so freakin cute I'm really about to text you and show you this I love him. Oh my gosh. I love it. I need to do a video now. That's where he's the best I've never seen him like many birthday cakes. I got a light one at least babe. Come on. You have to blow out make one wish What you wish for I can't tell you what I wish come on. I'm your boyfriend. No, I'll bleep it out. No, please Okay, don't tell me don't tell me because oh, she's digging deep into these already am I allowed to have one? Can I please step in? Yeah, one. All right, we're at Mariah's birthday dinner and we got her favorite thing that she's been looking for forever Which is his bone marrow risk it. Oh, yeah, she never tried it because last time we came here She got sick. Yeah, she had to leave early.  Oh my god. It looks so good. Happy birthday, baby Is it on? It's on. Don't shake it. Don't shake it. I'm not shaking it. That is not shaking Get out of here. You can look at it. This is not shaking at all. Get out of here Actually, it's not a bad picture. No, it's not Stop shaking. I'm not shaking the camera Actually better if it is back Hold on. Let me go on the other side You getting the angles. Yeah Brittany keeps getting in the way though. I just finished dinner guys We're out here taking pictures with the fam. How was your final dinner or your first dinner of? Your final dinner, babe. I'm sorry. How was the first dinner of your 24th birthday amazing? Was it good? What was your favorite part all of it like all the food what what was the favorite the brisket the brisket We just made it back home.  How was your birthday? It was amazing. I had one more gift for you One more gift.  What to me?  Okay, my one birthday wish is to know what I got for Christmas So if you guys didn't know I still haven't gotten her anything for Christmas. It's on back order. Can I please? It's my birthday way. All right, I'm gonna give you a hint.  What is this? Oh, it's not a fidget thing now. They're fidget thing that like see how it works. Oh Love it. Okay. I see So on a scale of one to ten how awesome was your birthday today? Let's say ten. Yeah, I'm just a minute. I woke up. Oh, yeah, look at Mariah's bundle of flowers Thank you, Anna and Anthony and Julia for getting her flowers.  We already got the new year stuff up over there Happy new year. Stay safe. Bye Mariah. Happy birthday and guys happy 2022 2023 is gonna be even better and we're gonna come out with some banger videos So make sure to subscribe if you have not already give this video a thumbs up If you guys like Mariah and me follow us on Instagram right now We're just posting a lot on there. We want you to be part of our, you know family and life What's wrong dad? You waiting?  She flashed my dad. Yeah How do you feel about that? Mom, how do you feel that my girlfriend flashed, dad? All right, we're ending up this video right now. We're obviously all tired. Um dinner was awesome Her birthday was awesome and we will see you guys in the next video next year. Oh, yeah. Peace. Love you guys


How are you feeling today? I'm well. Are you having any pain right now? I want you to stay in the vent part, okay? No pain? Okay. How old are you? 74. Alright. Now what month is it? Two. Month two. Very good. Alright. And there, I want you to make a fist. Make a fist. That's beautiful. Now open it up.  That's terrific. Alright. Now look at my finger here. Can you see it? Now follow my finger over here. All the way over here. Now look all the way over here. Good. All the way at me. That's great. Two fingers over there. Hold up the fingers. One finger. Beautiful. How many up here? Two fingers. How many down here? How many fingers? Five fingers. That's great. How many up here? How many fingers up there? How many do you see up there? Okay. How about over on this side? How many fingers do you see there? Two fingers. Alright. How many fingers do you see up here? Okay. How many over here? All of them. That's right. How many do you see up here? Okay. How many do you see over here? Two. Alright. Very good. I want you to show me your gums like this. There you go. That's beautiful. Alright. Now close your eyes real tight. Tighter, tighter, tighter. That's great. Now raise your eyebrows up. Beautiful. That's great. Let go of it. You hold it. One, two, three, four, five, six, seven, eight, nine, ten. Alright. That's terrific. Now I'm going to put this up and I want you to hold it there. Right there. One, two, three, four, five, six, seven, eight, nine, ten. That's terrific. Alright. You can let that one rest. Right there. Hold it up. One, two, three, four, five. Hold it up for one, two, three, four, five. Terrific. That's your finger to mine. Now touch your nose without it. Now my finger. Now my finger. Okay. And now your nose. I want you to look right at it. And now my finger. That's good. Touch my finger. It's kind of far. I'll put it down here where you can reach it a little bit better. About down here. Okay.  Touch your nose. Almost. Alright. Put that heel right there and slide it down your shin.  Alright. That's superb. Now pick up that leg and run it down your shin. It's pretty weak. Run it down your shin. Perfect. Alright. Are they the same? Which one's sharper? Left is sharper. Alright. How about on the arms here? Which one's sharper? Right? Left? Or are they the same? The right is sharper. Alright. Now we'll do your legs. Which one's sharper? The right? Or the left? Or are they the same? The left is sharper? Okay. Okay. What's going on in that picture? Yeah. Are you able to tell me what that's a picture of? Can you see that right there? See that one? Right in the middle? Can you make out what that is? Okay. How about this one here? What's that one? What's that one right there? And what's that one? Swing. Swing. Swing. Yeah. You're saying swing. Yeah. Okay. I don't know. Good. And this one? Okay. Good. And the next one? Where's that? Where's that? Left. Where's that? Both. Yeah. Where's that? Right. Okay. We'll do your legs. Right, left, or both? Right. Good. Where's that? Left. Good. Where's that? Both. Both. Okay, great.