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(#44) Designing Real World Rotating Machinery · Mechanical Engineering Made Simple

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  Welcome back design junkies to mechanical engineering Made
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  simple. Today we are buckling up for a
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  high velocity journey right into the heart of rotating machinery
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  design. For for too long, the classroom
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  really focused on this simple, clean world of two-dimensional
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  flow analysis. Right, the perfect.
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  World, the perfect world. But the reality inside an axial
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  compressor or a turbocharger or these massive hydraulic
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  turbines, it's fierce, complex, 3 dimensional storm.
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  Absolutely. So our mission for this deep
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  dive is to move past those, you know, comfortable, simplified
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  models, and really get what engineers have to master to
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  design machines that don't just work, but operate at peak
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  efficiency. And that's our core a mission
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  today. To unpack the compromises, we
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  need to understand precisely where those early theoretical
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  models, the ones assuming perfect frictionless flow, where
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  they breakdown. Because engineers aren't just
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  balancing efficiency, they're balancing it against brutal real
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  world constraints, the expensive manufacturing, the aerodynamic
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  limit of the Mach number, and the frankly terrifying reality
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  of cavitation. We're going from paper theory to
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  steel reality. OK, so we've got a deep dive
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  laid out that builds this up sequentially.
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  We'll start by establishing why 2D models fail and how engineers
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  try to fix that with tools like radial equilibrium and free
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  vortex flow. Then we'll move into more
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  complex modeling with the actuator disk concept and the
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  power and pitfalls of CFT. Computational fluid dynamics.
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  Yeah, we'll look at high speed compressor inlets, the
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  advantages of inward flow radial turbines, and finish with the
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  ultimate fluid challenge, water and the physics of the
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  cavitation limit. So let's start where most
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  textbooks do the ideal axial turbo machine.
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  We pretend flow velocities are only axial and tangential.
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  We just ignore any radial or span wise movement.
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  When is that fundamental 2D assumption actually justifiable?
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  You know that simplification only really holds up if you're
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  looking at a machine with a high hub to tip ratio.
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  OK. What do you mean by that?
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  If that ratio, the size of the inner hub relative to the outer
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  casing, is greater than about 4/5, then the flow path is
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  narrow enough that you can, well, you can essentially get
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  away with treating the flow as 2 dimensional.
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  But the moment you drop below that 4/5 ratio, the complexity
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  just explodes. Yeah.
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  What's the physical driver that forces the flow into 3
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  dimensions? It's a battle of forces right
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  across the span of the blade. As the fluid moves through the
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  rotor, you get these strong centrifugal forces that start
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  pushing the fluid outwards towards the casing.
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  And what's fighting that push? The only thing resisting it is
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  the radial pressure gradient. So in a machine with a low hub
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  to tip ratio, that balance is temporarily lost inside the
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  blade row. The centrifugal force just
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  momentarily overwhelms the pressure forces and you get
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  these appreciable radial velocities.
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  And what's the engineering concept of that uncontrolled
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  radial movement? What does it break?
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  Oh, it seriously messes up the system.
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  It redistributes the mass flow, which means your outlet velocity
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  and your flow angle distribution are just wrong across the
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  radius. So the next set of blades gets
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  hit with completely messed up airflow.
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  Exactly. And that's catastrophic for the
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  next blade row because it hits the blades at the wrong angle.
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  It just shreds efficiency. O To tackle this, engineers
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  developped the radial equilibrium method.
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  It sounds owerful, but you mentioned it relies on a couple
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  of major assumptions to make the math easier.
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  What are those shortcuts? The first assumption is that any
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  radial flow that happens is completely finished within the
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  blade row. The second, which gives the
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  method its name, is that the flow outside the blade row is in
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  radial equilibrium. Meaning the pressure forces and
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  centrifugal forces are perfectly balanced again.
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  Precisely, perfectly balanced once the flow is clear of the
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  blades. Now, within that framework, a
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  design approach emerges. Free vortex flow.
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  This is the theoretical ideal, right?
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  Where you aim for equal work at every radius.
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  What's the mathematical definition of that?
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  It's defined by the property that the product of the radius
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  and the tangential velocity so are multiplied by CQ must remain
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  a constant. A constant.
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  Yeah, sometimes you'll hear the term vortex free, which is maybe
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  more accurate because it really means the axial component of
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  verticity is 0. And the big theoretical benefit,
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  assuming ideal flow, is that this means your axial velocity,
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  your CX, is also so constant with radius perfect balanced
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  work. So what's the practical penalty
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  for chasing that perfection? Money and manufacturing
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  difficulty to get that characteristic.
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  The rotor blades need a massive complex twist from the root to
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  the tip. And that twist means you can't
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  just cast the blade. You need these specialized multi
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  axis milling machines. It adds huge expense.
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  Plus that design creates really large fluid deflections near the
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  inner wall which is detrimental to performance.
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  It's that classic trade off. Theoretical perfection often
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  means manufacturing impossibility.
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  That's a great example. And Speaking of reality,
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  experiments later show that the radial equilibrium assumption
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  was well, it's flawed. Especially in those low hub to
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  tip ratio machines, equilibrium is not established inside the
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  blade row. Precisely.
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  You can still measure radial velocities downstream.
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  That fundamental disconnect led to the actuator disk concept.
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  This is a brilliant theoretical step forward.
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  How does it? Work.
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  We stopped treating the blade row as a thick physical thing,
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  and instead we conceptually shrink its axial width down to a
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  flat plane, a discontinuity the disk.
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  And this model let's engineers use a key relationship, the mean
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  value rule. What does that tell us about the
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  flow at that conceptual disk? So the mean value rule says that
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  the axial velocity right at the disk, let's call it CX0, is
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  equal to the average of the axial velocities far upstream
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  and far downstream. OK, the average.
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  Why is that so critical? It's critical because it lets us
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  model how those velocity perturbations that start at the
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  blade row then decay exponentially as you move away
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  from the disk. It captures the non equilibrium
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  position that the old model completely missed.
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  Actuator disk theory provided great insight, but as machines
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  got faster, more complex, engineers had to embrace pure
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  computational power. CFD.
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  Before modern CFD, what were the early workhorse methods?
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  The streamline curvature method is the oldest and it's still
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  widely used. But we also saw finite different
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  solutions and for high speed transonic flows where you have
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  shock waves, time marching methods became essential.
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  O What's the role of modern CFD now?
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  Is it just about modeling the flow more accurately?
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  It's far more strategic than that.
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  Modern CFD allows designers to actually exploit the
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  threedimensional nature of the flow.
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  Instead of just tolerating the 3D complexity.
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  We can use it. Use it how?
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  We can design blade shaping to actively suppress or mitigate
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  things like corner stall and compressors, or the strong
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  secondary flows that just eat up efficiency and turbines.
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  That sounds like a magic bullet, but you often hear experienced
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  designers warning against over relying on the computer.
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  What's the human insight that has to come before any CFD
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  analysis? The insight is this.
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  CFD is a refinement tool. It is not a foundational design
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  tool if your preliminary 1 dimensional design is
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  fundamentally flawed. If your velocity triangles are
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  wrong, no amount of CFD is going to save the machine.
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  Garbage in, garbage out. Exactly.
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  You must begin with sound physical understanding or you
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  just get pretty pictures of a bad design.
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  Let's pivot to specific machines then, starting with compressors.
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  Centrifugal compressors powered early jets, but were eventually
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  replaced by axial types for large aircraft.
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  Why was that? Mainly due to the axial
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  machines, smaller frontal area and higher efficiency, but
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  centrifugals are still the undisputed champions for
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  applications that need very low air mass flow rates.
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  Like a turbocharger on a car engine.
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  Exactly like that. They're robust, compact, and
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  give you a lot of pressure rise in one go.
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  So whether it's an air compressor or a liquid pump, the
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  inlet I the entrance to the impeller is critical.
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  What are the 2 main physical limits designers are always
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  fighting against right there? Both limits come from high
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  relative inlet velocity. In a compressor, that high
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  velocity leads to high Mach number losses, which crushes
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  your efficiency in and pump. In a pump, that same high
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  velocity causes the local pressure to drop, which can
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  trigger cavitation. So for an in compressor
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  application, there's an ideal geometry for that inducer tip to
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  get maximum flow. What angle are designers aiming
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  for? The analysis shows that the
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  optimum relative flow angle at the inducer tip, which we called
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  betas one, typically lies in the range of 56 to 60°.
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  That's the sweet spot, the. Handle the high Mach number
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  problem in compressors. Engineers introduce what's
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  called positive pre whirl. They use guide vanes to spin the
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  flow in the same direction as the impeller.
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  What's the big trade off that comes with that?
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  Pre wall is fantastic because it significantly reduces the
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  relative inlet Mach number. Fewer shock waves, fewer losses,
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  however. There's always a, however.
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  There is if you look at the fundamental work equation.
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  The specific work done on the gas is inherently reduced by
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  that pre wall. So to get the same pressure.
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  Ratio. The only way out is to increase
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  the blade tip speed. You have to spin the hardware
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  faster so you save the aerodynamics, but you pay for it
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  with increased structural stress and mechanical challenges.
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  OK, now let's reverse the process and look at radial
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  turbine, specifically the 90° inward flow radial or IFR
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  turbine. These are common in things like
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  turbochargers and small gas turbines.
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  Right, and their key advantage over an axial turbine becomes
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  really clear when you break down the specific work equation.
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  We find that the largest contribution to specific work
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  comes from the centrifugal action term, which is that is
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  1/2 multiplied by the difference between the square of the inlet
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  tip speed and the square of the exit tip speed.
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  And that term is of course 0 in an axial machine because the
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  inlet and outlet radii are the same.
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  Exactly. This term is what gives the IFR
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  turbine its punch. In some examples, that one term
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  can account for almost 38% of the total specific work.
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  It's the core mechanism for high work extraction.
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  Now for the performance surprise.
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  For decades, designers assumed the nominal design meant aiming
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  for a 0 incidence angle at the rotor inlet.
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  They thought the relative flow should be perfectly radial when
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  it hit the blade. What did research reveal?
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  Reality threw the textbook out the window.
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  Research showed that the condition for optimal efficiency
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  occurs at a significant non 0 incidence angle, often between
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  20 and 40° for radial veins. Wait, hold on.
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  So for decades, designers were aiming for the mathematically
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  simplest entry point, but they were actually leaving huge
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  efficiency gains on the table. That's the surprise.
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  That high non 0 incidence angle is physically necessary.
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  It correctly locates the inlet stagnation point on the vein
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  leading edge, and it lets the fluid smoothly negotiate the
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  complex rotational effects into the passage.
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  And the theoretically simple 0 incidence flow.
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  It ends up causing flow separation and massive losses.
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  It's a perfect example of 3D effects just completely
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  overriding 2D intuition. Let's shift away from gas mass
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  and look at water flow hydraulic turbines like Francis or Kaplan
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  turbines. These things can achieve
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  efficiencies up to 95%. They're engineering marvels, but
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  the defining challenge for any water based machine is
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  cavitation. This is the spontaneous
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  formation of vapor bubbles when the local static pressure drops
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  below the water's vapor pressure.
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  And we know cavitations just devastating.
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  It causes severe vibration and can literally erode solid steel
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  blades. How do engineers quantify and
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  predict that limit? They use the Tama coefficient
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  designated by the Greek letter Sigma.
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  This is the crucial design metric.
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  It directly correlates the net positive section head or NPSH
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  with the available effective head HE.
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  Let's quickly define NPSH in simple terms.
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  What is that? NPSH is simply the available
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  pressure margin you have above the point where the water
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  physically starts to boil into those destructive bubbles.
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  If your turbines operating Sigma is less than the critical value
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  Sigma, cavitation is inevitable. So given that limit, what's the
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  key strategy to avoid it, especially in say, a huge DAM
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  installation? The only way to guarantee safety
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  is through physical placement. The turbine has to be located
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  low enough relative to the tail race water level.
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  Or keep the. Pressure up to keep the pressure
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  up exactly. And crucially, the greater the
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  head HHE that the system is exploiting, the lower that
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  turbine must be submerged to suppress bubble formation.
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  And finally, let's talk about the violence of this.
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  The vapor bubbles collapse. How violent is that really?
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  The collapses it. It's almost unimaginable.
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  It's so rapid and localized that it generates shock waves
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  reaching 4000 atmospheres. 4000 times the pressure of the air
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  around us. That's right, the process is
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  called sun illuminescence and it's so violent it produces
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  brief flashes of visible light. They've actually seen light in
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  the tail raise of high energy installations like the Boulder
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  Dam at night. Wow.
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  That's why steel and concrete just disintegrate over time.
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  That kind of violence is staggering.
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  We've certainly traveled a huge distance today from the flaws of
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  2D modeling to these brutal physical constraints.
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  We really have. We saw the need to move past
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  simple 2D models with the axial equilibrium method and how the
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  actuator disk concept better captures that non equilibrium
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  zone. We identified the huge work
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  advantage of the IFR turbine from its centrifugal term and
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  the surprise that optimal efficiency needs a highly non
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  radial flow angle. And finally we looked at the non
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  negotiable limit of the TAMA coefficient and cavitation.
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  Thank you for joining us on this deep dive into the philosophy,
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  physics, and hard constraints of rotating machinery design.
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  And here's the final thought for you to carry forward.
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  We talked about CFD and its power to model these complex 3D
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  flows, but remember that while CFD can design highly optimized
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  blades, predicting the subtle complex viscous losses like
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  turbulence generation remains one of the most difficult areas
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  in all of engineering physics. So when you're faced with two
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  competing CFD models for a new blade, both showing near perfect
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  efficiency, but one models turbulent slightly differently
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  than the other, why is the human judgement of an experienced
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  engineer the one who can mentally map the fluid physics
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  onto that data? Why is that always going to be
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  the most critical factor in achieving true peak performance
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  in a physical machine? Something to consider until next
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  time.