I’ve had jobs of some flavor almost continuously since I was fourteen years old. From delivering newspapers to cutting grass to flipping burgers to showing movies to mixing giant vats of coleslaw to instructing an aerodynamics laboratory course to hand counting vehicular traffic to researching the derivation of combustion stability equations, before I finally settled into something resembling a career (and while I was winding my way through the maze of secondary and higher education), I did all kinds stuff. But when I did get my first job after graduate school it was doing test data reduction and performance calculations for the Space Shuttle Main Engine (SSME).

In past articles we’ve discussed rocket engine performance. We’ve talked about the “Big Three” operational points and performance measures that characterize an engine: thrust, mixture ratio, and specific impulse. Okay, but how do we know what these values are for any given engine? I mean, we can do calculations with analytical equations, formulas, algorithms, or models that tell us what these parameters ought to be for a given rocket engine design; but when I’ve got an actual rocket engine sitting in front of me — a big, shiny, complex hunk of metal standing ten feet high and weighing thousands of pounds — how do I know how it actually functions and performs?

Well, duh, you test it. Of course! But making smoke and fire (and steam) does not, by itself, give you any data. The most that you could say from just watching an engine test is that it’s really, really noisy and that it makes a really, really big exhaust plume. So, more than just observe, you have to take measurements during the test. That’s how you get data. As I’ve said many times, there are only two reasons to conduct rocket engine tests: (1) to impress your friends, and (2) to collect data. In order to get data on the “Big Three,” you need to measure thrust and you need to measure propellant flowrates. For this article, we’re going to focus on propellant flowrates. I will talk about thrust measurement in the next article.

Propellant flows are measured on a rocket engine test stand with “propellant flowmeters.” Makes sense, right? But calling something a “meter for flow” doesn’t tell you how it works. That’s like saying, “How do I make popcorn?” Answer: “With a popcorn maker.” No kidding. Thank you for playing and you’ve conveyed no useful or interesting information.

There are a number of different ways to measure fluid volumetric flow. The units that we use for the very large flowrates feeding an engine are turbine flowmeters. Have you ever blown into a small fan that’s turned off or perhaps a pinwheel? If you blow hard enough, you can make the fan or pinwheel spin. That is, quite simply, how a turbine flowmeter works: it’s a fan, i.e., turbine, stuck in a tube that spins as fluid flows through it. The faster the fluid flows, the faster the turbine spins. The thing that we measure is the speed of the turbine spinning. The turbine has a number of blades (just like that small fan that you blow into). We pick a spot on the tube in which the turbine sits and count how many blades pass by. If we count, say, ten blade passes in a second, then there is more flow than if we’d only counted eight blade passes in a second.

So, how do we count blade passes? Well, there’s a little window in the side of the propellant duct and we sit a young college co-op in front of the window with a little hand clicker and scream “GO!” from the blockhouse… Okay, I’m fibbing. We don’t treat our co-ops nearly that bad. Usually. Besides, there would be no way that the human eye and brain could keep up since we’re talking about hundreds of blade passes per second. Instead, we measure it electronically. Each blade contains a magnet in the tip. The sensor on the outside of the tube is activated by the magnet. Each magnet pass generates an electronic pulse or blip — what we call a “pip” — and we keep a continuous count of these accumulated pips. The pip count is then recorded with each time step in the data collection process. Then, after the test, we can translate this ever-increasing pip count into a pip-rate based upon these recorded times. Mathematically speaking, the pip-rate at any given point is the slope of the pip-count plotted against time.

In order to translate a pip-rate into a volumetric flowrate, such as gallons per minute (gpm), the flowmeter needs to be calibrated. We need to know how much flow is required to generate a blade passage, i.e., a pip. If, for example, we knew that the passage of one gallon was enough to move the turbine exactly one blade pass of rotation, then a measured 100 pips-per-second would equal 100 gallons-per-second, or 6,000 gpm. Thus, calibration of a flowmeter consists of flowing a known volume of fluid through the meter and counting the pips read:

The truth is that it’s a bit more complicated in that the calibration varies with the speed of the turbine due to kinetic and mechanical issues of the rotating hardware and due to fluid dynamic effects of the fluid interacting with the turbine blades. However, these are secondary effects as compared to the simple notion of figuring how much a pip is worth in terms of volume.

Luckily enough (or, really, strategically enough), the engine test stands are themselves set up to function as a calibration facility for the flowmeters. This is because the propellant tanks have a known geometry and are equipped with fluid level sensors.

As shown in the figure above, if we know at a particular time the height of the fluid in the tank and then, at a later time, we know a lower height of the fluid, then, using tank geometry, we know the volume of fluid that exited the tank and ran through the flowmeter. In practice, we actually perform this calibration during an engine test. That way we can be assured that the flowmeter rotor is spinning at a speed representative of where we’ll need measurements.

An observant reader would note here that if we know the volume consumed over time just from the level sensors in the tank, then we don’t need a flowmeter in the middle. All you need is volume divided by time, right? The problem is one of fidelity. Because the level sensors are discrete points on the pole submerged in the tank, the measures of volume used for calibration are relatively big chunks, as in enough propellant to run the engine tens of seconds. In order to get a decent calibration across several discrete level sensors, we typically need to run between 100 and 150 seconds of steady, mainstage engine conditions. The use of a calibrated flowmeter allows you to see variations in flowrate at much smaller time increments and this allows us to collect and observe more data with regarding to engine characterization at different conditions. You can almost think of the flowmeter as a useful interpolation tool between large chunks of time and consumed propellant.

You will note that so far we’ve just talked about volumetric flowrates and yet, when we talk about engine performance we refer to mass flowrates. The difference between the volume and the mass of something is its density. For our very pure propellants, fluid density is simply a function of fluid temperature and static pressure. So, we take temperature and pressure measurements immediately downstream of the flowmeter and, using either an interpolated look-up table or empirical curves, we can get density. So, you put it all together and you end up with something along the lines of the following:

That is how you measure and calculate the mass flowrate of the propellants flowing through the feedlines and going into the engine using a turbine flowmeter. The item from the “Big Three” to which this can be applied directly is the engine inlet mixture ratio, which is defined as the oxidizer mass flowrate divided by the fuel mass flowrate.

However, depending on the engine and vehicle design, not all of the propellants that go into an engine go overboard. Often, warmed propellants are returned from the engine to the stage to act as pressurizing gases for the stage propellant tanks. On the Space Shuttle, both gaseous oxygen and gaseous hydrogen were flowed back to the stage for this purpose. The rocket equation that essentially defines the parameter we know as specific impulse is only concerned with propellants that leave the vehicle so for specific impulse calculations you need to use inlet mass flow minus pressurization flow.

As compared to the engine inlet mass flowrates, which for large rocket engines can amount to hundreds of pounds-mass per second, the pressurization flowrates are typically less than one or two pound per second. Flows this small are more effectively measured using flowmeters different from the turbine flowmeters I’ve described above. For our engine testing we use Venturi meters for these small flows. Venturi meters use a variable flow area coupled with pressure measurements to feed Bernoulli Equation relationships between pressure and fluid velocity. Once you know the fluid velocity, fluid density, and fluid flow area at any point, you can then calculate mass flowrate (for now, at least, I’ll not go any further with Venturi meter calculations).

This, then, wraps up the story with regards to propellant mass flow measurements and calculations on the engine test stands. In the next article, we’ll go into the measurement of and calculation of thrust. All of this discussion reminds me so much of my first days/weeks/months on the job working with SSME test data. At first, it was just a bunch of bewildering numbers and data reduction tools and rules and calibration factors and work procedures. I had no idea what was going on. But gradually, as I dug into the data and talked to people and dissected the computer codes and tools we used, I began to piece it all together as to what these measurements and calculations actually meant. Seemingly every day brought a new epiphany in understanding. Boy oh boy, that was fun!

I’m wondering, is NASA (and their subcontractors) still using the arbitrary impirial (not calling it english, because great britain has converted already) measurement units of pounds, long tons, ounces, gallons, cubic inches, feet etc?

No wonder every calculation involves a maze of byzantine and error prone lookup operations…

It would bode these posts well, to stick to the proper formal units (as the US has formally signed into law in 1893). All scientific papers and publications use the metric system, which makes unit conversion a straight forward process, and one can even verify if the calculations were done with the proper SI units (kg, m, s, A, K, mol, cd).

For the casual citizen of the US, the awkward units can be appended, but the majority of the earths population would surely appreciate the use of easy understandable and convertible units.

Thx

@Anonymous Coward: In actuality, all measurement systems are arbitrary to some extent. There is no perfect system. For example, if the SI system was perfect, then why is the acceleration of gravity not exactly 10.0 rather than 9.82 m/s^2? That would make calculations even easier.

And what makes the use of 10 the single best conversion between units? Ten happens to also be completely arbitrary. It’s based on the number of fingers that humans have, right? What if humans had eight fingers rather than ten? Would then the perfect measurement system be base-8 rather than base-10? Something else to consider: The current definition of a meter is that it is the distance that light travels in a vacuum over 1/299,792,458 of a second. Now that is a weird, non-intuitive number if ever I saw one.

My point is not to be snarky or defensive because there are indeed lots of things to find pleasing about SI units. Rather, my point is that so long as you know what you’re working with, and so long as you are consistent, you’ll be fine. The biggest issues that we ever have along these lines are when we need to flip back and forth for entirely arbitrary reasons to satisfy someone’s personal sense of what is better rather than sticking to that which we know works.

One of the things that I try to do as part of writing the blog is to bring folks into our world and, for better or worse, our world primarily uses English units. We use inches, feet, pounds-mass, pounds-force, and degrees Rankine. We talk of power in terms of horsepower and we of heat flux terms of Btu per second (British Thermal Unit). Sometimes we talk of gallons, but we usually stick to cubic feet for volume.

FYI, 1 hp = 550 ft-lbf/s, and 1 Btu = 778.17 ft-lbf, so 1 hp = (550/778.17) Btu/s in case you ever need to express heat flux in terms of horsepower. See, easy peasy.

Does whether the flow in question is liquid or gas or some mixture factor into these flowrates? Or has the liquid been entirely converted to gaseous form by this point in the flow path? The calibrated points in the tank would be liquid phase, and then comparing volume to gas phase flow would involve knowing pressure and temperature and ideal gas laws?

@5 Matt,

The cryogens are still liquid before being combusted, so liquid flowrates are being measured throughout. The RS-25 and J-2X engines use liquid hydrogen for cooling parts of the engine–the combustion chamber, nozzle, and preburners. Hydrogen gas does not transfer the heat away fast enough: the engine would melt.

What a workplace! Look at that LH2 pipe going right across a walkway at head height! All those dangling ropes, structs at weird angles — so many trip and bonk hazards. OSHA must love this place! 🙂

@Matt: Excellent question. Yes, it does matter whether we’re measuring liquid or gas. The turbine flowmeters that I described tend to work best with liquid flows. Yes, it is certainly possible to make turbine flowmeters work with gaseous flow, but for us the better answer is usually a Venturi flowmeter, which bases the flow calculation on Bernoulli Equation considerations and a variable-area pipe.

Where we really have problems measuring flow, FYI, is when we have mixed flow, i.e., a mixture of gas and liquid. We do our best to avoid needing to measure such situations since it’s really more of an art form than a science (in my humble opinion).

@Mark: Actually, internal to the engine, most of the fluids are supercritical. Once you raise the pressure high enough, the transition between liquid and gas goes away. It is simply a “fluid” and that’s nice since the process of boiling can be violent and potentially destructive. One of the issues for any engine start sequence is pushing through some transient violent boiling within the cooling passages until the pressure reaches supercritical conditions.

With regards to the test stand as a dangerous workplace: Yes, it is. And I will be the first to admit that I have indeed bonked my head once or twice while out on the stand. However, that’s not my normal workplace. If I’m out there, then I’m a visitor. The guys and gals who work out there take all of the appropriate safety measures possible given that it’s a functional test stand first and foremost. There are signs and warnings and emergency/contingency systems. They take workplace safety very, very seriously and do an outstanding job.

Yes, reading Biggs’s paper, describing what goes on during startup and how difficult it was to keep the RS-25 from melting or exploding in those first few seconds, was pretty fascinating reading.

I didn’t realize the critical point for hydrogen was so low, so thanks for the bonk on the side of the head — err, correction.

I’m sorry if this question appears simplistic, but I am mired in a discussion with someone who believes this:

Rockets cannot work in a vacuum because the vacuum would draw away oxidiser and propellant before it had a chance to ignite.

I have maintained that the flow rate and psi of the fuel and oxidiser is high enough to prevent this, but my opponent refuses to accept this.

Is this correct, and is there any way to explain it more simply?

@Kris: The simplest explanation is that we demonstrate the ability of a rocket to work in a vacuum every time we launch a payload into orbit! If propellants vaporized before they had a chance to ignite, we wouldn’t be able to place satellites into orbit, or send new crews to the International Space Station.

So why don’t the propellants vaporize? You are right in your assumption that the flow rate and pressure are high enough to prevent this, but why? The answer is two-fold;

1. Because the combusted gases still experience some expansion to vacuum conditions through the rest of the nozzle (downstream of the throat), the pressure on the downstream side of the throat is at some value higher than zero. Even the pressure at the nozzle exit cannot be zero, because absolute expansion requires a nozzle area that goes to infinity! All rocket engines are under-expanded in the vacuum of space.

2. The flow at the nozzle throat has reached the sonic velocity of the combusted propellants, or is at choked flow conditions. There is a large pressure drop across that shock. The upstream pressure needed to maintain choked flow is related to the specific heat ratio of the gas and the mass flow of the propellants.

Essentially, the main combustion chamber never sees pressure conditions below the vapor pressure of the propellants (so long as the required propellant pressure and mass flow for choked flow are maintained). That being said, the vacuum of space does an excellent job of purging the engine of propellants after it has been shut off!