Sub-microsecond Schlieren photography

(Edit: My entry on the Gallery of Fluid Motion using this technique is online!)

For the ones not introduced to the art of Schlieren photography, I can assure you it was incredibly eye-opening and fascinating to me when I learned that we can see thin air with just a few lenses (or even just one mirror as Josh The Engineer demonstrated here on a hobby setup).

For the initiated in the technique, its uses are obvious in the art and engineering of bleeding-edge aerodynamic technology. Supersonic flows are the favorites here, because the presence of shock waves that make for beautiful crisp images and help us understand and describe many kinds of fluid dynamics phenomena.

FreeJet_CD_NPR_4.4-036.png
Schlieren image of a 2mm supersonic microjet taken at Florida State University FCAAP laboratory. Illumination time is 500 nanoseconds, taken with a Nikon D90 DSLR to demonstrate the potential for hobby applications. Note the crispiness of the image – the flow was effectively frozen.

What I’m going to describe in this article is a very simple circuit published by Christian Willert here but that most likely is paywalled and might have too much formalism for someone who is just looking for some answers. Since the circuit and the electrical engineering is pretty basic, I felt I (with my hobby-level electronics knowledge) could give it a go and I think you also should. I am also publishing my EasyEDA project if you want to make your boards (Yes, EasyEDA).

But first, let’s address the elephant in the room: Why should you care? Well, if you ever tinkered with a Schlieren/shadowgraph apparatus – for scientific, engineering or artistic purposes -you might be interested in taking sharper pictures. Obtaining sharper pictures of moving stuff works exactly like in regular photography. They can be achieved by reducing the aperture of the lens, by reducing the exposure time or by using a flash. The latter is when a pulsed light source really shines (pun intended!). The great part here is that the first two options involve reducing the amount of light – whereas the last option doesn’t (necessarily).

The not-so-great part is that camera sensors are “integrators”. This means they measure the amount of photons that happened to be absorbed given an amount of time. Therefore, what really matters is the total amount of photons you sent to the camera. Of course, if you sent an insanely large amount of photons in a very short instant, you would risk burning the camera sensor – but if you’re using an LED (as we are going to here), your LED will be long gone before that happens.

So the secret for high speed photography is to have insanely large amounts of light dispensed at once. That would guarantee everything will be as sharp as your optics allow. Since we don’t live in the world of mathematical idealizations, we cannot deliver anything “instantly”, and therefore we have to live with some finite amount of time. Brief enough is relative and depends on what you want to observe. For example, if you’re taking a selfie in a party, probably tens of milliseconds is brief enough to get sharp images. For taking a picture of a tennis player doing a high speed serve, you’re probably fine with tens or hundreds of microseconds. The technical challenges begin to appear when you’re taking pictures of really fast stuff (like supersonic planes) or at larger magnifications. The picture of the jet above is challenging in both ways: its magnification level is 0.7x (meaning the physical object is as projected in the sensor at 0.7x scale) and its speed is roughly 500 meters per second. In other words, the movement of the object (the Schlieren object) is happening at roughly 63.6 million px/second, which requires a really fast shutter to have any hopes to “freeze the flow”. If you’re fond to making simple multiplications in your calculator, the equation is very simple:

D=\frac{M*v}{s_{px}}

Where D is the object displacement in px/second, v is its velocity in physical units (i.e. m/s), M is the magnification achieved in the setup and s_{px} is the physical pixel size of your camera (i.e. s_{px}=5.5 \mu m for a Nikon D90).

I know, I know. These are very specialized applications. But who knows which kinds of high speed photography is happening right now in someone’s garage, right? The point is – getting a light source that is fast enough is very challenging. Some options, such as laser-pulsed plasma light sources, can get really expensive even if you make them yourself. But LEDs are a very well-established, reliable technology that has an incredibly fast rise time. And they can get very bright, too (well… kinda).

So what Willert and his coauthors did was very simple: Let’s overdrive a bright LED with 20 times its design current and hope they don’t explode. Spoiler alert: Some LEDs didn’t survive this intellectual journey. But they mapped the safe operational regions for overdriven LEDs of many different manufacturers. To name a few: Luminus Phlatlight CBT-120Luminus Phlatlight CBT-140Phillips LXHL-PM02, among others. These are raw LEDs, no driver included, rated for ~3.6-4V, and are incredibly expensive for an LED. The price ranges from $100 to $150, and they are usually employed in automotive applications. The powerful flash is, however, blinding. And if they do burn out, it can be harmful for the hobbyist’s pockets.

Circuit.png
LED driver power section.

The driver circuit (which is available here) is very simple: An IRF3805 N-channel power MOSFET just connects the LED to a 24V power supply. Remembering the LED is rated for 4V – so it’s going to get a tiny bit brighter (sarcasm). Jokes apart, the LED (CBT-140) is rated for 28A continuous with very efficient heatsinking, which means we will definitely be overdriven. By how much we can measure with R2. Hooking a scope between Q1 and R2 is not harmful to the scope and allows to measure the current going through the LED (unless the currents exceed ~600A, then the voltage spike when the MOSFET turns off might be on the few tens of volts). We don’t want to operate at these currents anyways, because the LED will end up as in the figure below. There’s a trim pot (R3) that controls the MOSFET gate voltage, make sure pin 2 of U1 is giving a low voltage when tuning.

LEDburn.jpg
A sacrifice for science.

What is really happening is that C1 and C2 (C2 is optional) are being charged by the 24V power supply when the MOSFET is off. Then they discharge at the LED when the MOSFET is activated. No power supply will be able to push 200A continuously through an LED, so if the transistor turns on for too long, the power supply voltage will drop and the power supply will reset. Actually, this is one of the ways to tell if you melted the MOSFET (which happened to me once). The MOSFET needs to turn on in nanoseconds, which will require a decent amount of current (like 4-5 amps) just to charge the gate up. This means we need a driver IC – which in this case I’m using a UCC27424. Make sure to have as little resistance between the driver and the gate to minimize the time constant. The 1.5 Ohms is very close to giving 4A to the MOSFET. Since the gate capacitance is around 8nF, the MOSFET gate rise time is somewhat slow (12 ns).

Speaking about time constants, during the design I realized the time constants of the capacitor that discharges into the LED and the parasitic inductances in the path between the components will dictate the rise time of the circuit, at least for the most part. In my circuit, the time constant was measured to be 100ns, directly with a photodiode. This means we can do >1MHz photography, which is pretty amazing! Unfortunately the cameras that are capable of 1 million frames per second aren’t really accessible to mortals (except when said mortals work in a laboratory that happens to have them!).

Well, the LED driver circuit is still in development – which means I’ll keep this post updated every now and then. But for now, it’s working well enough. The BOM cost is not too intimidating (~$60 at Digikey without the LED. Add the LED and we should be at ~$200), so a hobbyist can really justify this investment if it means an equivalent amount of hours of fun! Furthermore, this circuit implements a microcontroller that monitors and displays the LED and driver’s temperature. It features an auto shut-off, which disables the MOSFET driver if the temperature exceeds an operational threshold. The thermal limits are still to be evaluated, though.

Circuit.png
Circuit board and a (crude) 3D printed case for the LED.

For now, I did my own independent tests,  and the results are very promising.  Below I’m showing a test rig to evaluate the illumination rise and fall times of the LED. The photodiode is a Thorlabs (forgot the model) that has a 1ns rise time if attached to a 50 ohm load. It’s internally biased, which is nice when you want to do a quick test.

TestsLED.png
Test rig for photodiode illumination response measurements

The results from the illumination standpoint are rather promising. Below a series of scope traces show that the LED lights up in a very short time and reaches a pretty much constant on state. The decay time, however, seems to be controlled by a phosphorescence mechanism that is probably because this is a white LED. Nevertheless, the pulses are remarkably brief.

100ns300ns

1000ns
Scope screen for LED illumination (blue curve) as seen by the photodiode. Yellow curve is current as measured by a 10mOhm resistor in the MOSFET source. Curves from 100ns, 300ns and 1000ns input pulse width, respectively.

The good thing about having high speed cameras is that now we’re ready to roll some experiments. By far, my favorite one is shown below. I was able to use the Schlieren setup to observe ultrasonic acoustic waves at 80kHz , produced by a micro-impinging jet (the jet is 2mm in diameter). The jet is supersonic, its velocity is estimated to be 400 m/s. Just to make sure you get what is in the video: The gray rectangle above is the nozzle. The shiny white line at the bottom is the impingement surface. The jet is impinging downwards, at the center of the image. The acoustic waves are the vertically traveling lines of bright and dark pixels. I was literally able to see sound! How cool is that?

 

 

Just as a final note. You might be discouraged to know that I am one of these mortals that happen to have access to a high-speed camera. But bear in mind, these pictures could have been taken with a regular DSLR. The only difference is that the frame sequence wouldn’t look continuous, because the DSLR frame rate is not synchronized with the phenomenon. Apart from that, everything else would be the same. You should give it a try! If you do, please let me know =)

Design Review – Flying like Iron Man from the Hacksmith

1. Introduction

So I’m a subscriber to the Hacksmith youtube channel, which is a guy who tries to bring superhero devices into the real world. It’s been a while he’s working on the development of the “Flying like Iron Man” project, which is a quite difficult and money-hungry project. Although I’m not quite a fan of the methods that are shown in the channel for the engineering of such a complex device, I also bear in mind that the audience would probably find the engineering details quite boring and unrewarding, so the progress updates are more on the testing side than on the design side.

Anyways, he started a crowdfunding campaign on GoFundMe, which means that this might get serious. Although I can’t contribute due to the fact I’m back in Brazil (and here our money is worth quite a lot less than in those developed countries), I thought it might be interesting to give a review on this project. So sorry, the Hacksmith, but this is all I have to offer… =/

I remembered that I made a while ago a spreadsheet to determine the rotor diameter for a personal one-seater electric helicopter for a senior design project class. As the spreadsheet was ready to go, it wasn’t that much trouble to plug in the numbers for his design. You can download it here, if you want to play with it. It’s not a great spreadsheet, though, and its far from a polished user-friendly status that I normally take my spreadsheets to.

 

2. The helicopter equation

The jetpack, the helicopter, the drone and the rocket are vehicles that have something in common: They need to stay afloat by pushing a fluid downwards. The airplane stays afloat in the same fashion (by pushing air down), but it does so with its wings by moving forwards.

But what’s the difference? Well, it requires quite a lot of energy to push enough of a light fluid (such as air) to generate any decent lift. You can see, for example, that a water jetpack is much smaller and feasible than an air-hovering one. It has to do with the fact that in order to get thrust you need to pump mass (as momentum is P=m*v ), which results in a much larger device if the fluid being pumped has little density (as is the case for air).

The problem becomes even more important when we account for energy. As anything that stores energy (fuel or batteries) has mass and needs to be carried with the hovering device, there is only so much of it that you can bring with you. The amount of mass will depend on how much time you want to stay hovering in the air. For a helicopter or any hobby drone, it’s desired to stay hovering in the air for at least 20-30 minutes, so one can get from point A to B. The more you want to stay in the air, the more energy you’ll need to bring with you. But then you become heavier, and will need to bring even more energy to stay afloat. How can one assess whether this will result on an endless loop?

Well, there comes the helicopter equations to help us, designers. I selected the set of equations shown below, which are useful for solving a battery-powered hovering device. Since it assumes no relationship between the mass of the engine/thruster and its size/power, it’s really only useful within a limited range of powers and fan diameters. But it will be enough to show the point I want to make:

(1)   L=\dot m*v=m_T*g [Lift equation]

(2)   P=(\dot m *v^2)/(2*\eta) [Power needed to displace the fluid]

(3)   m_T=m_{bat}+m_{str}+m_{person} [Total mass of the hovering device]

(4)   E_{st}=m_{bat}*\rho_e [Stored energy in the battery]

(5)   t_{flight}=E_{st}/P [Total flight time to discharge battery]

(6)  \dot m =\rho_{fluid}*v*(\pi*D^2/4)  [Relationship between mass flow and volumetric flow]

Solving the equations above for D leads to this very interesting relationship:

D=\frac{(m_{bat}+m_{str}+m_{person})^{3/2}}{m_{bat}} * \frac{t_f}{\eta*\rho_e}*\sqrt{\frac{g^3}{\pi*\rho_f}}

Although that equation looks scary, some lessons can be extracted from it:

  • The diameter of the fan is directly proportional to the flight time t_f
  • It’s inversely proportional to the battery energy density \rho_e , which means better batteries will have a direct impact on the fan size
  • The diameter of the fan has this complex relationship with the battery mass m_{bat} . But it basically means the following: If you were to reduce the battery mass down to zero, the diameter of the fan would need to be infinity (which is quite unfeasible). If the battery mass is very large, then the relationship is between linear and quadratic (D\propto  m_{bat}^{3/2} ). If, on the other hand, it’s in the middle, then there is a minimum diameter.

The minimum value of D will be possible only when:

m_{bat}=2*(m_{person}+m_{str})

Which is surprisingly simple! This leads to a minimum diameter of:

D_{min}=2.598*\frac{t_f}{\eta*\rho_e}*\sqrt{\frac{g^3*(m_{str}+m_{person})}{\pi*\rho_f}}

Unfortunately, normally that’s a lot of batteries. Therefore, the best choice normally is not the minimum diameter. Also, for the case in analysis, it would lead to a supersonic exit speed, which throws all the equations shown here through the window…

3. So, is it possible to fly like Iron Man?

Yes, it indeed is possible to do so. It’s not some crazy stuff, and the Hacksmith data seems to be accurate and adequate. The spreadsheet I linked in the first section is based on his data. So what does the graph of diameter versus battery mass look like for the Hacksmith’s design?

Point of Operation.png
the Hacksmith’s jetpack point of operation

This curve was generated for a device that uses 6 EDFs. It seems that he will be able to hover just a little bit less than 2 minutes, which also corresponds to the claims in his GoFundMe campaign. So it seems legit, although it wouldn’t be very fit for a transportation device. If he wanted more hover time, it’s just a matter of increasing fan size or transporting more batteries. Or both!

For this calculation I considered a fan energy conversion efficiency of 50%, but the fans linked in his campaign page seem to claim an efficiency of 70% (which seems kinda too much for these devices). So there might be some difference between calculations and reality, but that’s exactly what engineering boils down to anyways!

 

So I hope this helped you to understand the underlying principles with a benchmark case. I hope you guys at the Hacksmith channel actually manage to build it! I’ll definitely stay tuned!