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(#103) Turbomachinery Design From 2D to 3D · Mechanical Engineering Made Simple

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  Welcome back design junkies. If you enjoy the podcast, let us
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  know if the like a follow or a comment A&D get ready for
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  mechanical engineering made simple.
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  OK, let's get into it. Today we are diving deep into
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  the really complex world of axial turbo machinery.
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  We're. Talking about the core
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  principles here, what makes turbines, compressors and fans
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  actually work? And our sources for this deep
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  dive really take us on a journey.
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  We start with these, you know, perfect idealized 2 dimensional
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  theories. And then they throw us right
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  into the deep end, straight into the messy realities of
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  three-dimensional flow, instability, all of it.
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  That's the real story here, isn't it?
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  This core conflict You start with these clean simple
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  assumptions to get a basic design.
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  You have to. It's the only way to begin.
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  But those assumptions, they they have a very short shelf life.
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  They breakdown almost instantly in a high performance engine and
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  then designers are forced to grapple with these really tough
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  problems. Flow separation stall.
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  Huge pressure changes from the root of the blade to the tip.
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  Right, The perfect model gets you started, but managing all
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  those imperfections, that's what makes the engine actually
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  perform. So to set the stage, we're
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  talking about a standard setup, right?
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  A state which is. It's the guide.
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  Vanes or nozzles, yes. Yeah.
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  Followed by a rotor. The moving blades.
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  And the key metric we're tracking is specific work.
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  Which is really just the drop in total energy, the stagnation
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  enthalpy across that stage. And that energy transfer
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  immediately creates a divide in a turbine.
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  The flow is accelerating, it's being pushed along.
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  Which makes it inherently more stable, less prone to losses.
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  But a compressor is the exact opposite.
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  You're fighting the flow, decelerating it.
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  It's a diffusion process. It's an aerodynamic nightmare,
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  really. That's why compressors are so
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  vulnerable to stall and massive pressure loss.
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  And that one difference dictates, well, pretty much
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  every design choice from there on out.
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  OK, so let's start in that idealized world, the
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  two-dimensional flow model. The foundational approach really
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  you have to start somewhere simple.
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  So the idea is to look at the pitch line, the mean radius.
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  And just assume the flow conditions there are the same
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  everywhere else. Exactly.
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  You just assume it represents the whole flow, which is, you
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  know, only remotely reasonable if the plates are short compared
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  to the machine's radius. So we're already ignoring a lot
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  of reality near the hub and the casing.
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  But how do we even judge performance in this simple
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  model? We need metrics.
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  We do, and we lean on 2 main types of efficiency.
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  First is total to total efficiency.
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  OK, think about the core of a jet engine.
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  This metric is critical there because the kinetic energy
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  leaving one stage isn't lost, it's fed directly into the next
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  stage and recovered as pressure. So the energy is conserved and
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  passed down the line. What's the second type?
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  That's total to static efficiency.
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  You use this when that exit kinetic energy is just gone,
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  dumped to the atmosphere. Like the last stage of a power
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  turbine or an exhaust fan. Precisely and by definition,
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  it's always a lower efficiency value because you have to count
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  that dumped energy as a loss. What I find fascinating is that
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  even for modern preliminary design, the sources point back
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  to these almost ancient tools like Soderbergh's correlation.
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  It feels like it should be in a museum, doesn't it?
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  Developed from steam turbine tests decades ago.
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  But still relevant. It is, and that says so much
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  about that early empirical work. Soderbergh's method.
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  It just it calculates loss based on how much you turn the flow
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  and the geometry. It capture the basic physics of
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  friction and turning so well that it still gives you a
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  fantastic first estimate. A quick way to get maybe 80% of
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  the way there before you fire up the supercomputers.
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  Exactly that. OK.
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  Another fundamental concept we have to cover is the reaction
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  ratio. R Right.
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  This is all about where the work is happening in the stage
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  reaction is the ratio of the static pressure change in the
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  rotor compared to the static pressure change across the
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  entire stage. So it tells you how the work is
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  split between the moving blades and the fixed ones.
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  Perfectly put. Let's look at a couple of key
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  design points for a turbine. What happens when R = 0?
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  That's a zero reaction stage. It means the static pressure is
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  the same at the rotor inlet and outlet.
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  All the pressure drop happens in the stator in the nozzle.
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  And the rotor is just changing the fluids direction.
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  Surely extracting work from the velocity change.
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  Now, the sources were very clear that this is not an impulse
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  stage. That was a bit confusing.
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  It's a subtle but really important distinction.
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  An impulse stage is a design goal.
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  The aim is 0 pressure change, but in the real world because of
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  friction you always get a tiny increase in enthalpy across the
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  rotor. Ah, so for a true impulse
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  design, the reaction ratio R is actually a small negative
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  number. That's it.
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  A zero reaction stage is just where we measure the static
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  enthalpy change to be 0, ignoring that little friction
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  effect. Got it.
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  OK. So what's the more common
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  balance design choice? That would be the 50% reaction
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  stage where r = 0.5. This gives you some nice
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  symmetrical velocity diagram and crucially, the ently drop.
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  The work is split evenly between the nozzle and the rotor.
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  And regardless of the reaction, the main goal in a turbine is
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  always the same. Avoid diffusion at all costs.
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  Absolutely you are accelerating the fluid.
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  If you let that velocity decrease even a little, you
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  create an adverse pressure gradient, and that with the high
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  turning angles is just begging for the boundary layer to set.
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  Like catastrophic losses. Massive losses.
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  A turbine is built for speed, for acceleration.
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  Which brings us to the compressor, where we have no
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  choice but to do the opposite. We have to decelerate the flow
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  to build pressure. And that's the whole challenge.
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  This force diffusion is why compressors are so prone to
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  loss, and it's why a jet engine needs way more compressor stages
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  than turbine stages to get the job done.
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  I assume the 50% reaction design is popular here too.
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  It is often it's the top choice for efficiency.
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  Why does r = 0.5 works so well in a compressor?
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  Because you're sharing the pain, you're splitting that difficult
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  adverse pressure gradient evenly between the rotor and the
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  stator. So you don't overload one row
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  and cause it to stall. You're distributing the risk of
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  boundary layer separation. Speaking of risk, we have to
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  talk about the big villains of compressor instability, rotating
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  stall and surge. What's the difference?
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  They're very different beasts. Rotating stall is less
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  catastrophic, but it's still really dangerous.
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  The blades don't stall all at once.
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  It happens in these discrete patches that, well, they rotate
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  around the annulus. So parts of the engine are
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  choking in a wave that travels around the machine.
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  Yes, usually at about half the rotor speed.
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  The big problem there is that it creates these cyclical loads on
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  the blades which can lead to fatigue failure, but the total
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  mass flow through the engine stays steady.
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  And then there's Surge. Surge is the one that keeps
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  engineers up at night. It's not a rotating patch, it's
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  a massive, violent axial oscillation of the entire flow.
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  The whole flow field can break down and even reverse direction
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  for a moment. That sounds destructive.
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  It can be. It can destroy an engine if the
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  control systems don't catch it instantly.
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  So how do you fight these things?
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  I read about an early technique called casing treatment.
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  Right, using groove casings, often with skewed grooves right
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  over the rotor tips. The idea was to delay the onset
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  of stall. By stabilizing the flow near the
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  outer wall. It helps re energize that
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  sluggish boundary layer fluid near the casing.
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  It was most effective against what we call wall stall, but
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  there was catch. An engineering trade off.
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  Always. The grooves themselves create
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  more friction and mixing, so you take a hit on overall stage
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  efficiency. You gain stability, but you lose
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  performance. So what's the cutting edge
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  approach now? Controlling these things before
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  they even start. It's all about active control
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  systems. One method is active feedback
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  control. You place these tiny sensors
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  like hot wires in the flow to detect your very first hint of a
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  disturbance. And it's still incredibly small.
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  Exactly, and then you use individually actuated veins,
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  tiny super fast flaps to generate an opposing disturbance
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  that cancels out the first one. You kill the instability before
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  it's born. And the other strategy, aero
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  mechanical feedback. This one is just beautiful
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  physics. You have a chamber with high
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  pressure air in these little flexible Reed valves.
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  If a disturbance causes the local flow to slow down, the
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  static pressure there rises. That higher pressure pushes on
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  the Reed valve, which opens and injects a jet of high momentum
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  air right into that troubled spot.
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  It uses the problem, the pressurize to trigger its own
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  solution. That's brilliant.
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  And all this talk of instability just brings us back to the
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  limits of that 2D model we started with.
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  It completely fails when the blades get tall.
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  It does because with tall blades you get significant radial
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  velocities. The flow starts moving up and
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  down the blade span, completely redistributing the mass flow.
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  The physics of the tip can be totally different from the
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  physics at the root. So we need a better tool, and
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  that brings us to radial equilibrium theory.
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  A way to handle that span wise variation, but it still has a
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  couple of big simplifying assumptions.
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  First, any radial flow has to finish inside the blade row, and
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  2nd, the flow outside the blades is perfectly smooth and uniform
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  in a circle. And when designers use this,
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  they often choose something called Free Vortex Flow.
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  This is where the name is a bit misleading, right?
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  It is mathematically it's where the product of the radius and
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  the tangential velocity. So r * C sub Q kept constant.
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  But a more accurate name would be vortex free because it
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  results in 0 axial vorticity. It's a very clean, ideal
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  solution. And the design benefit is huge.
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  Oh, it's very attractive. You get uniform work done at all
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  radii and a constant axial velocity.
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  It makes everything much simpler to calculate and match between
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  stages. But there's a.
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  Cost. A big one.
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  To maintain that free vortex condition, you need a lot of
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  twist in the blade from root to tip.
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  That's expensive to manufacture. It also tends to create really
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  high Mach numbers near the blade tip, which hurts efficiency.
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  So to avoid that cost, sometimes they just don't twist the
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  blades. Exactly, that's the direct
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  problem. You hold the flow angle alpha
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  constant with radius. It's less aerodynamically
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  perfect but much cheaper to make a classic design trade off.
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  And even this more complex theory has its limits.
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  The experiments show that this equilibrium isn't all contained
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  neatly inside the blades. No.
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  A lot of that flow redistribution happens both
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  upstream and downstream, which led to the next step up in
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  theory, actuator disk theory. This one sounds like pure math.
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  You shrink the whole blade Rd. down to a single plane.
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  That's exactly it. You treat it like a
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  discontinuity, an actuator disk. It abrutly changes the swirl,
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  but the axial and radial velocities pass through
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  continuously. It's a way to model the
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  interactions between closely packed stages.
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  And this gives us two key rules. Right, the mean value rule,
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  which says the actual velocity right at the disk is the average
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  of the velocities far upstream and far downstream, and the
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  settling rate rule. What's that one tell?
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  Us that any disturbance decays exponentially as you move away
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  from the disk. This is so important because it
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  proves that the flow fields of closely spaced blade rows
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  strongly influence each other. OK, before we get to modern
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  computing, there's a really unique case study here, the
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  Wells turbine. The Wells turbine is a fantastic
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  piece of engineering. It's an axial turbine used to
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  get energy from oscillating sea waves.
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  And it's trick is that it uses uncammered symmetrical airfoil
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  blades set at a 90° angle. Right, and because of that
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  geometry, as the air rushes in and out of the water column, the
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  turbine keeps spinning in the same direction.
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  It generates positive power from bi directional flow.
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  Which is just. Genius.
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  And the newer versions are even smarter.
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  They use self pitch control blades.
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  They pivot just a little bit near the leading edge, which
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  helps them produce much more torque and efficiency than the
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  original fixed blade designs. So as useful as all these
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  theories are, modern design really depends on CFD
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  computational fluid dynamics. How do these tools fit together?
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  The CFD is absolutely essential. It lets you model all the
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  complex 3D flows we've been talking about.
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  But, and this is a huge charm, but CFD does not replace good
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  preliminary design. So if your basic 1 dimensional
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  math is wrong, CFD won't save you.
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  It won't fix a bad concept if your stage loading is wrong.
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  CFD will just show you a very detailed picture of your bad
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  design failing. It's a refinement tool.
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  A tool to exploit the 3D flow, not just fight it.
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  Precisely. We can now design things like
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  bowed blades and turbines to control secondary losses, or use
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  sweep in compressors to reduce corner separation.
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  These are techniques that were impossible without CFD, and they
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  work with the complex flow. Let's end on the root Causeway
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  of all this complexity, secondary flows.
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  What's happening there? It's an inevitable consequence
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  of turning a rotating flow. Think of it like a gyroscope.
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  When you try to turn the fluids existing vorticity with a blade,
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  it creates the secondary swirling motion and that's.
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  Worse near the. Walls.
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  It's strongest there because of the boundary layer.
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  The swirling leads to localized overturning and underturning of
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  the flow, which wastes energy and, crucially, is what promotes
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  stall right at the blade ends. It's the very reason we have to
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  abandon those simple, elegant 2D models.
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  Which brings us full circle from this perfect uniform flow ideal
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  to the practical reality where every single radius has its own
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  complex story. It shows that engineering is
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  that constant negotiation between the clean concept and
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  the messy physics. That's it perfectly.
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  It's a process you simplify to get the basic size and shape,
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  then you bring in the complex 3D tools to manage all the
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  unavoidable instabilities and losses.
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  Which leads us to a final provocative thought for you to
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  take away. In highly loaded modern
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  compressors, the work done factor, we call it Lambda.
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  It actually decreases as you go through the stages, dropping to
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  maybe around 0.86 later on. So considering all this 3D
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  complexity, what happens to that miscalculated energy when the
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  flow isn't uniform? And how does that uneven energy
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  distribution affect the life and health of the downstream stages?
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  Something to Mull over. We hope this deep dive gave you
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  a fast track to understanding the fluted mechanics of turbo
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  machinery. And if you haven't already, get
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  over to our YouTube channel Mechanical Engineering Made
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  Simple, where we post hands on how to videos, visual
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  breakdowns, and practical engineering walkthroughs.
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  You can actually use a family that solves together, stays
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  together.