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Controlling condensation with sawteeth and electricity · Mechanical Engineering Made Simple

0:00
Welcome back, design jokies to mechanical engineering made
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simple. Today we are jumping right into
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a Honestly, it's a microscopic battlefield.
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Oh, absolutely. It's a chaotic kind of violent
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environment right on the surface of a metal tube.
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Right Liquid is basically the enemy here, and engineers are
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fighting it using, you know, everything from microscopic saw
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teeth to literally 2000 volts of raw electricity.
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Yeah, it's the absolute definition of thermodynamic
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Muddy Waters. I mean we usually think of a
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phase change like vapor turning into liquid as this clean binary
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event. Yeah, gas to liquid.
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Boom. Done.
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Right, but what actually happens when vapor meets cold metal is
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incredibly complex. And that is exactly why today we
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are taking you on a deep dive into the fascinating, invisible,
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and honestly, often entirely ignored physics of condensation.
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We really are getting into the weeds on this one.
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For sure, we're drawing straight from this massive engineering
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text. Chapter 10 Condensation by MA
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Kidzerski, JC T Chato, and TJ Robbins.
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It's an exhaustive source. Very.
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And our mission today is specifically for you.
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We want to look past the dense textbook jargon and really help
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you grasp the actual physical intuition behind the math of
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turning vapor into liquid. Because you know, before we can
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build massive multi $1,000,000 power plant condensers or
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optimize an industrial HVAC system, we really have to
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understand what happens to a single drop of water on a flat
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piece of metal. Right, the microphenomena
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completely dictate the entire macro world.
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Exactly. So let's start with the 2 main
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ways condensation actually happens, right?
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We've got film condensation and drop wise condensation, right?
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For you listening, think about your car drop wise.
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Condensation is like rain perfectly beating up and rolling
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off a freshly waxed hood. Yeah, that perfect bead.
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Right. The drops form, they roll away,
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and they leave the surface completely exposed for the very
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next drop to form. But then film condensation is
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like a sheet of dirty water sticking to an unwaxed
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windshield. It just coats the entire thing.
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It's a mess. Total, and the crazy part is
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drop wise, condensation is up to 100 times more efficient for
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heat transfer. Which is massive.
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But almost all industrial engineering relies on film
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condensation. So I got to ask, why don't we
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use the method that's 100 times better?
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Well. The problem really boils down to
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sustainability. In harsh environments, dropwise
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condensation requires the liquid to have a basically a lack of
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affinity for the surface it has to want to beat up.
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Like the wax on the car? Exactly.
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To achieve that in a massive industrial condenser you would
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have to constantly coat the metal with special promoters or
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polymers or noble metals. And in a real world high
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temperature, high pressure environment, those chemical
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coatings degrade incredibly fast.
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Oh. So it just wears off, yeah.
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It is simply not economically or physically viable to maintain
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that perfect waxed car finish for decades.
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So film content sensation basically becomes the default
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reality that engineers simply have to deal with.
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We play the hand we're dealt, basically, and the engineer who
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wrote the rule book on that hand was Nusselt way back in 1916.
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Oh yeah, Nusselt's pioneering analysis of a vertical flat
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plate laid the foundation for, well, pretty much everything we
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do in this field, right? But his biggest take away was
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actually a pretty sobering one for heat transfer design.
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He proved that the liquid film itself acts as an insulator.
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Wait. The water is insulating the
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metal. Yep.
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Water does not conduct heat nearly as well as copper or
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steel, so as that continuous sheet of water flows down the
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plate, it gets thicker, and the thicker that film gets, the more
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it literally blocks the heat from escaping the vapor and
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getting into the cold metal. Wow.
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And there's this really elegant energy equation in the text that
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models exactly what is happening inside that insulating film.
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Right. So for a steady state laminar
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film, applying Nusselt's assumptions, the energy equation
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reduces to this Det divided by D, y = t subset minus T sub West
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all divided by delta. OK, let's unpack this.
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Looking at those variables, what is the actual physical story
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playing out on the metal there? Intuitively, it represents a
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thermal bottleneck. The temperature gradient, that's
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the DT divided by DY is the rate at which heat moves through the
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liquid. OK.
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And this movement is driven by the temperature difference
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between the hot saturation temperature of the vapor, which
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is T subset, and the cooler wall temperature of the metal, which
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is T sub W. So hot vapor, cold wall.
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Exactly. But the crucial part is that
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this driving force is divided by delta, and delta represents the
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film thickness. Oh, so it's an inverse
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relationship. As delta, the film thickness
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gets bigger, the entire temperature gradient drops, the
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heat transfer just crashes. It proves mathematically that
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the film is the real enemy of efficiency.
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Which means your whole goal as an engineer is to keep delta as
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close to 0 as physically possible.
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But if gravity alone isn't pulling that liquid down the
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vertical plate fast enough, what do we actually do?
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Well, we cheat. We cheat, I love.
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It we start physically shaping the metal to force the liquid
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off the surface way faster than gravity could ever do it alone.
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OK, so we're talking about putting fins on the outside of
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the tubes, but not, you know, massive cooling fins like you'd
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see on an old motorcycle engine. We're talking low fins, less
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than 1.5mm tall. Basically microscopic
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architecture. And you know, most people assume
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fins are just there to increase the surface area because more
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metal equals more space for heat to transfer.
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Right, right. That's what I would think.
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But with condensation, these low fins serve a completely
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different primary purpose. They use surface tension to
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physically RIP the liquid off the fin tips that thins out that
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insulating layer right where the heat transfer is highest.
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Wait, surface tension? Like the exact same force that
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lets a water strider bug walk across a pond.
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The exact same force. How does shaping a piece of
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copper manipulate surface tension to physically move
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liquid? It all comes down to the Laplace
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equation. It describes the pressure
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differences across a curved liquid vapor interface, and the
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math here is just brilliant. Let's hear it.
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P sub L -, P sub G equals Sigma times the sum of 1 / r sub one
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and 1 / r sub 2. OK, so Sigma is the surface
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tension of the fluid and those R variables are the ones really
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doing the heavy listing here, right?
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Yeah, they are the radii of curvature of this liquid
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surface. The smaller the radius, meaning
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the tighter and sharper the curve is, the larger that whole
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right side of the equation becomes.
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And that creates a massive pressure difference between the
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liquid which is P sub L, and the surrounding vapor P sub G.
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You know, it's kind of like squeezing a long water balloon.
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Oh, that's a good way to look at it.
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Like. If you grab one end and squeeze
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it incredibly tight, creating that high curvature, the water
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doesn't just sit there, it is violently forced away from your
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hand right toward the wider, lower pressure end of the.
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Balloon. That's exactly what's happening.
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By machining the fin tips to be incredibly sharp, engineers
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force a tight radius of curvature in the condensate film
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right at the tip. This induces A localized high
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pressure in the liquid, which literally sucks the condensate
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down into the wider troughs between the fins where the
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pressure is lower. Yeah, it constantly drains the
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tip, leaving a microscopically thin film, a tiny delta like we
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talked about, which causes the heat transfer to just skyrocket
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right at the fin tip. That's wild, and the sources
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actually have some real world examples of this.
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They compared 2 commercial tubes, the turbo chill tube
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which uses 2024 trapezoidal fins per meter, and then the turbo
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CDI tube which uses 1575 sawtooth fins per meter.
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Right, and the sawtooth fins are literal sharp notched teeth.
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The text says that sharp curvature of the sawtooth shade
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literally double S the heat transfer performance compared to
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the trapezoidal one just by making the metal sharper.
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It's amazing. But what's fascinating here is
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that as an engineer, you need a way to know if this surface
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tension trick is actually going to work for a specific fin size,
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or if gravity is just going to overpower it anyway, right?
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And to calculate that tug of war, we use the bond number.
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The bond number right? So bond number or BD equals the
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difference between rho sub L and rho sub G times G * E to the
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power of 2, all divided by Sigma times Theta sub M.
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Exactly, and the key take away for you as a designer is the
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result here. If the bond number is less than
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one, surface tension dominates gravity.
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Looking at the math, you achieve a bond number of less than one
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by having a small fin height, that's the E term, and a large
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fin angle, the Theta sub main term.
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So small, sharp fins give you strong pressure gradients that
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totally defeat gravity. OK, here's where it gets really
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interesting. We've sculpted the metal into
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microscopic saw teeth to, you know, manipulate surface
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tension. But what if we just abandoned
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the metal sculpting entirely? What if we blast the tube with
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an electric field instead? Ah, Electro hydrodynamic
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enhancement ahd yes. The text outlines using a high
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voltage, low current electric field to literally blast the
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condensate film off the surface of the tube.
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I mean it sounds like complete science fiction, but the physics
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are highly effective. You have to keep in mind it only
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works on fluids that have very low electrical conductivity.
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If you tried this with regular water, it would immediately
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short out, but it works beautifully with refrigerants.
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The numbers in the research are just staggering.
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Beloga achieved a massive 2000% enhancement on a plate.
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It's unreal. 2000% The electricity rips the liquid off
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the surface so violently that it creates this pseudo drop wise
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condensation. It artificially tears that
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continuous film into discrete drops.
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But wait, hold on, If blasting tubes with 2000 volts gives us a
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2000% efficiency boost, why isn't the air conditioning unit
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sitting outside my bedroom window electrified right now?
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It's a fair question, but it really comes down to
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manufacturing practicality and cost.
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I mean, you can't just plug the tube into a wall.
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It requires really complex electrodes.
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OK, yeah, you have to wrap a highly calibrated screen around
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the outside of the tube, spaced at an exact distance to generate
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the electric field without artsing.
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Or, you know, if you're enhancing the inside of the
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tube, you have to run a straight rod electrode perfectly
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suspended down the center. That sounds like a nightmare for
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an. It adds massive complexity, plus
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it really only works best at low Reynolds numbers, meaning slower
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fluid flows. So it is an amazing tool for
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specific high end industrial applications, but it's
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definitely not a universal solution for consumer hardware.
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That makes sense, yeah, but carving the outside of the tube
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or even electrifying it is completely pointless if the
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inside of the tube is choked. Yeah, because vapor convinces
10:51
inside horizontal pipes too, right?
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And the environment in there is completely chaotic.
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Oh, absolutely. Depending on the mass flux,
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which is the speed of the flow, and the quality, which is the
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ratio of vapor to liquid, the flow inside the pipe takes on
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completely different personalities.
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We call them flow regimes. It's kind of like weather
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patterns inside a pipe. That's exactly what it's like.
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You start with stratified flow, where it's essentially a lazy
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river. Gravity cools all the liquid at
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the bottom and the vapor lazily floats on top.
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Then you speed up the mass flux and you get WAVY flow where the
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vapor acts like wind whipping up actual waves on the liquid pool.
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Go even faster and you get annular flow.
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The vapor is moving so fast through the core of the tube
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that it shears the liquid into a perfect uniform ring against the
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entire inner wall of the pipe. Yep.
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And finally, mist flow, where the vapor just completely
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obliterates the liquid into a dense fog of droplets.
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And looking at all these complex flow regime maps in the text
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from, you know, Manthane or Tetel, Duckler or Solomon.
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Do we really need to know the weather pattern inside the pipe
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though? Like why can't I just calculate
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the heat transfer at the beginning and the end of the
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heat exchanger and call it? Well, this raises an important
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question, and it's actually a super common trap in early
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design phases. You cannot just use one
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overarching equation. Why not?
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Because the fundamental physics of the heat transfer totally
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change depending on the flow regime.
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Think about the stratified flow, your lazy river.
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The liquid is pooling at the bottom.
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The heat transfer there is driven purely by conduction
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through the thin film falling down the sides of the pipe
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pulled by gravity. But in annular flow you have a
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high speed ring of liquid being dragged by violent vapor shear
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forces. That is forced convection.
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Conduction driven by gravity requires entirely different
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math. And forced convection driven by
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vapor shear. Oh wow.
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If you use a gravity based nussle equation to predict an
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annular flow, your entire thermal design will just fail.
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So you absolutely must know the weather inside the pipe to pick
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the right math. You have to.
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And the Tiddle Duckler map uses a really important parameter to
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predict when that transition from lazy river to annular ring
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actually happens, the modified fraud number.
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Right F sub TD equals the square root of rho sub G divided by the
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difference between rho sub L and rho sub G times GX divided by
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rho sub g * sqrt d * g times the cosine of alpha sub T.
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Whoa, OK, that is a massive alphabet soup.
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Yeah. If I'm staring at that on a
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whiteboard, what is the actual story it's trying to tell me?
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Well, look past the individual symbols for a second and look at
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the physical structure of the math.
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It is essentially a ratio of two competing forces, vapor inertia
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versus gravity. The GX term represents the vapor
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speed, it's forward inertia. The G term represents gravity
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pulling the liquid down to the bottom of the pipe.
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So when vapor speed increases, the top half of the ratio gets
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bigger. Inertia wins.
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It's like a hurricane force, wind building up inside the
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pipe. Yes, until it is strong enough
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to physically pick the water up off the floor and plaster
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against the walls, whipping it around the whole tube into that
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perfect ring of annular flow. So it's a mathematical tipping
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point. If vapor inertia beats gravity,
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you're an annular flow. Exactly.
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So just like we added fins to the outside of the tube,
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engineers must have figured out how to rough up the inside to
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force the flow into these highly efficient forced convection
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regimes, right? No, they did, and the most
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common method today is the microfin tube.
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What exactly is an internal microfin?
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Are they like the saw teeth on the outside?
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They are drastically smaller. We are talking about 30 to 80
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tiny trapezoidal fins, just 0.1 to 0.25mm high.
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Oh, that is tiny. Yeah, and they spiral down the
14:36
inside of the tube, kind of like like the rifling in a gun.
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Barrel less than 1/4 of a millimeter.
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How does something that microscopically small do
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anything to a roaring flow of refrigerant?
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They act like microscopic speed bumps.
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They add just enough roughness to mix the flow right at the
14:51
boundary wall, physically disrupting that insulating sub
14:54
layer of liquid. And more importantly, even at
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that tiny scale, they still provide about 50% more surface
15:01
area than a smooth tube. That's brilliant.
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But you know, microfins are modern, high tech manufacturing.
15:08
The text brings up a historical artifact that I absolutely
15:11
loved, Twisted Tapes. Oh yeah.
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Back in the 19th century, marine steam boilers on ships used
15:18
literal twisted ribbons of metal.
15:21
They call them retarders and they just shove them down inside
15:23
the pipes to physically spin the flow.
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And that 19th century trick is actually still incredibly
15:28
relevant today. Twisted tapes force the fluid
15:31
into a swirl flow, and the math used to model this, the swirl
15:35
parameter, is surprisingly elegant.
15:37
Yeah, Southwest equals RE sub d / sqrt y, right?
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RE sub D is the Reynolds number based on the tube diameter.
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It essentially represents the flows forward momentum and Y is
15:49
the twist ratio of the tape. Basically, how tightly the
15:51
ribbon is twisted. It perfectly models the physical
15:54
intuition. Spinning the fluid increases the
15:56
path length it has to travel through the pipe, but more
15:59
importantly, it utilizes centrifugal force.
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The spinning motion physically throws the heavier, cooler
16:06
liquid out against the heated wall, constantly mixing the
16:09
fluid. That is a brilliant way to
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correlate the complex physics of swirl flow into a single highly
16:16
usable variable. It really is.
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OK, So what does this all mean? We've perfected the
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microphysics. We've analyzed a single drop on
16:23
a plate, the sharp tip of a single fin, the weather inside a
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single pipelet. Zoom out.
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What happens when you stack 10,000 of these perfectly
16:31
engineered tubes inside a massive power plant X shell
16:34
condenser? I'm guessing it isn't just
16:36
10,000 times better. Right.
16:38
If we connect this to the bigger picture, you are exactly right.
16:40
It introduces macro chaos. Macro chaos.
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A single tube performs beautifully in a vacuum.
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A bundle of 10,000 tubes the size of a city bus creates A
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cascading series of nightmares for a plant engineer.
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I mean, a 2% drop in efficiency here means millions of dollars
16:56
wasted on excess coal or nuclear fuel.
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And the two biggest threats to that efficiency are condensate
17:02
inundation and non condensable gases.
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Condensate inundation. That sounds biblical.
17:08
Well, it is a flood. Remember how hard we work to
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thin the liquid film off our single tube?
17:14
Yeah, blow fins. Well, in a massive bundle,
17:17
gravity pulls that liquid off the top tubes and it rains down
17:22
directly onto the tubes below them.
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Oh no. So the tubes at the bottom of
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the bundle are just getting drowned in an insulating
17:27
waterfall of liquid from the thousands of tubes stacked above
17:31
them. Exactly.
17:33
The thermal performance of the lower tubes completely plummets
17:36
because their delta, their film thickness, is artificially
17:39
massive. OK.
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And then you said the second nightmare was non condensable
17:42
gases, stray air that inevitably leaks into the vacuum system,
17:46
right? You know, I think of it like an
17:48
air bubble trapped in your home plumbing.
17:50
You turn on the faucet and it violently sputters because that
17:53
pocket of air is completely blocking the flow of water.
17:56
That is a perfect visualization, and in a massive condenser these
17:59
air pockets don't just cause a sputter, they create massive
18:02
thermal dead zones. Tinker made a really famous
18:05
observation about this in 1933. In an X shell condenser, the
18:09
incoming vapor is channeled into different bays because the
18:13
pressure must drop evenly across all the bays, but the tubes are
18:17
warming up at different rates. The bays at the cold end of the
18:20
condenser literally run out of steam.
18:23
Run out of steam? What do you mean?
18:24
The vapor all condenses before it even reaches the bottom of
18:27
the cold end Bay. So what fills that empty space
18:30
at the bottom? Non condensable gases.
18:32
Exactly. Massive dead zones filled with
18:35
trapped air form at the bottom of the heat exchanger, rendering
18:38
hundreds of expensive, perfectly engineered tubes completely
18:42
useless. But you just vent the air out,
18:44
right? Like put a vacuum pump on the
18:46
bottom of the shell. Well, proper venting is the
18:48
solution, but it creates a massive operational paradox.
18:52
I was saying if you vent too little, the air pockets grow,
18:55
choking your multimillion dollar plant and tanking your thermal
18:59
efficiency. But if you vent too much, you're
19:01
sucking valuable high pressure steam right out of the condenser
19:05
and venting it into the atmosphere, right?
19:07
You are literally throwing away the very energy you're trying to
19:10
capture. It's a terrifying balancing act.
19:13
It's crazy. It requires meticulous design.
19:16
Engineers have to like orifice vent manifolds meticulously,
19:21
cascading vapor from hot bass to cold bass, all just to manage
19:25
invisible pockets of stray air. It's intense.
19:28
It is wild how much invisible physics goes into a process we
19:31
take for granted every time we see dew forming on a glass of
19:35
ice water. We've gone from nestled
19:37
analyzing a single vertical plate in 1916 to sculpting
19:41
sawtooth fins at the oroscopic level to cheat surface tension
19:45
to electrifying refrigerants to violently blast the film away.
19:48
We really covered some ground today.
19:50
We mapped out chaotic hurricane like weather regimes inside a
19:53
single pipe and finally wrangled the massive cascading
19:56
aerodynamics of a 10,002 power plant condenser.
20:00
It is a phenomenal journey through the scales of
20:02
engineering. But you know, there is one final
20:04
really mind bending fact hidden at the very end of the source
20:07
material that I want to leave you with.
20:08
Oh, let's hear it. We spent all this time talking
20:10
about tubes. What about plate heat
20:12
exchangers? These are compact braised sheets
20:16
of corrugated metal stacked tightly together.
20:19
Oh yeah, they are becoming huge in the modern HVAC industry
20:23
because they are so compact and efficient.
20:24
Right. Well, Kaszewski actually tested
20:26
a plate heat exchanger acting as a condenser.
20:29
It was installed vertically as intended by the manufacturer,
20:33
but then he simply took the entire unit and tilted it
20:37
horizontally on its side. Wait.
20:39
He just knocked the whole unit over 90°.
20:41
He silted at 90° and by doing absolutely nothing else, the
20:45
heat transfer performance was boosted by up to 30%. 30% just
20:50
from laying the plate on its side.
20:52
But why? Because of everything we've
20:53
talked about today, by laying it horizontally, he radically
20:57
shortened the vertical length that the liquid film had to
21:00
travel. Oh, I see.
21:01
Instead of flowing all the way down a long vertical plate,
21:04
accumulating thickness and insulating the metal, the liquid
21:07
only had to flow down the short width of the plate.
21:09
It prevented the film from ever getting thick.
21:11
Exactly. A thinner film means a smaller
21:13
delta, which means a massive spike in heat transfer.
21:17
That is incredible and it really makes me wonder, could the
21:20
industrial condensers of the future abandoned massive
21:23
stationary tubes altogether? Like could we use AI to
21:27
dynamically tilt and rotate massive flat plate heat
21:30
exchangers based on real time fluid flow constantly shifting
21:34
their orientation to artificially cheat gravity and
21:36
keep that condensate film perfectly thin?
21:38
It's definitely an engineering challenge waiting for a
21:40
solution. The physics are entirely there.
21:42
We'll design junkies. That is a problem for you to
21:44
solve. Thank you for joining us on this
21:46
deep dive into Chapter 10. Stay curious, keep questioning
21:50
the math, and we will see you next time.