Turbopumps

Introduction

A turbopump is one of the most complicated parts on a rocket engine. Often the bottleneck for space startups developing their own propulsion systems, turbomachinery is a difficult field to master, but one that offers great reward. A turbopump uses high pressure gases to spin a turbine which powers a pump. These pumps can be multistage (contain several impellers), have multiple configurations (axial, radial, mixed), and can pump all kinds of fluids (from RP-1 to LOX). Turbopumps are used mainly because they greatly reduce the weight of an orbital class rocket. In fact, there's a certain threshold where a rocket can no longer be pressure-fed (like Halcyon) to carry its payload to orbit, because the tanks would require too much hardware and be too heavy. Turbopumps are designed using existing empirical data (often found in Cordier Diagrams) and equations that highlight a relationship between turbopumps of similar application (affinity and similarity laws). These will be described in more detail later. 

Source: Oleg Baturin (YouTube)

History

Turbopumps first entered the aerospace industry when German engineers needed a way to power their long range missiles during WW2. Hermann Oberth first introduced the idea and later Wernher von Braun asked a fire-fighting company, KSB ( Klein, Schanzlin & Becker), to design the first one. Designed to be used with the V-2 Rocket's hydrogen peroxide fueled engine, it used steam to move the turbine and pump alcohol and gaseous oxygen into its combustion chamber. The first turbopumped rocket engine flew on the V-2 Rocket on October 3rd, 1942. if you'd like to dive more into turbopumps in general, this video is an awesome documentary on the V-2 and its pumps.  

This image shows the redstone missile turbopump, but in principle both the V-2 and Redstone missiles were the same thing.

Source: Heroic Relics

Pump Classification

A turbopump can look very different depending on its application. To start with the basics, rocket pumps are a type of dynamic pump and can have axial, mixed, or centrifugal/radial flow configurations. These pumps can also have different impeller types (shrouded, semi-open, and open), and can also have different shaft configurations. Below are diagrams outlining these details and it should be noted that this REP project will focus only on a specific application of turbopumps, in this case, one that uses RP-1 and LOX and has a rotational speed around 20,000 RPM. This will simplify the topic's discussion and design later on. 

Each configuration is determined by the speed at which you run your pump and in turn the density of your fluid and the required head you want your pump to achieve. Head can be thought of as energy added to a fluid or the energy carried by a column of water of a certain height (measured in meters or feet). For the most part, rocket turbopumps tend to be centrifugal/radial flow pumps due to their high rotational speed (20,000 to 90,000 rpm) and their working fluid (RP-1, LOX, LH2, and LCH4).  Rocket turbopumps that use LOX/RP-1 frequently use centrifugal configurations with semi-open and/or closed impeller types. Despite their difficulty to make, closed impellers are more preferable mainly because they prevent cavitation more easily and provide more support to the blades. Finally, turbopumps that use fluids with similar densities can be run at similar speeds, allowing them to operate on a single shaft. For this project, I'll be looking at a single shaft configuration where the turbine and propellant pumps all share one shaft. This will option reduces complexity and is quite common in industry (NASA'S Fastrac engine, Merlin 1D, etc). 

Source (left to right): Nourbakhsh et al. (first two images), Empowering Pumps

Source: NASA SP-8107 and Suarez et al.

Pump Design Using Affinity and Similarity Laws

The design of a single shaft, LOX/RP-1, centrifugal turbopump is incredibly difficult and relies on the ability to run complex simulations and gather a huge amount of data. Tools like CFturbo and AxStream greatly simplify this process (tutorials for AxStream can be found here), but these software options can be expensive. Fortunately, there's a few design equations that we can exploit to avoid a lot of this process. For reference, pumps are defined by the following variables:

​​volumetric flow rate (Q)	​Net Positive Suction Head (NPSH)
​total head or manometric head (H or sometimes gH)	​Head Coefficient (Ψ)
​​shaft power (P)	​Flow Coefficient (δ)
​useful power (Pq)	​Power Coefficient (π)
​overall efficiency (ƞ)	​Specific Speed and Specific Diameter (N' and D' respectively)

Similarity Laws allow us to use data from other turbopumps and effectively scale a turbopump up or down for a new application. However, there are a few conditions to similarity. Impeller angles must be the same (velocity triangles must be the same, those will be covered soon), all dimensions must be scaled by some constant, both pumps must be from the same family or class (flow configuration and impeller type), and working fluids must have similar properties (namely density, whether they're cryogenic, etc). If pumps A and B have similarity, then the following relations hold:

Where W is relative velocity, U peripheral velocity and V is absolute velocity from the pump's velocity triangle. A velocity triangle is simply a way of modeling the flow through an impeller. Peripheral velocity is perpendicular to the radius of the impeller, relative velocity is tangent to the impeller streamlines, and absolute velocity is the vector sum of the previous two. With these three velocities, you can determine the blade angle for your impeller.

Source: Nourbakhsh et al.

Furthermore, two pumps in similarity also share the same head, flow, and power coefficients as well as the same efficiency. These coefficients are defined by the following:

R is impeller outlet radius

These equations are what allow us to define the Rataeu equations or Affinity Laws. These equations tend to be more simple and allow for an easier comparison between pumps. 

n is rotational speed for each pump

One final note about these equations is that, since many industrial pumps have head coefficients ranging from 0.45 to 0.55, this value can be approximated to 0.5, yielding the equation: 

This is a good strategy for getting initial estimates of your impeller geometry, since pump head and rotational speed are driven by your engine requirements and material constraints. Finally, specific speed can be given by the following equation:

Where rotational speed is in rpm, volumetric flow rate in in m^3/s, and Head is in meters. 

What's powerful about these equations is that a lot of documentation exists in regard to LOX/RP -1 turbopumps, therefore making the task of designing a rocket turbopump much more simple. One such example of documentation is the data regarding NASA's Fastrac rocket engine. Developed to be a low cost rocket engine capable of 60,000lbf of thrust, the LOX/RP-1 turbopump that powered it operated around 20,000 rpm and had a specific speed of 1327 rpm. All of the dimensions regarding the number of blades, blade angles and volute size can be found on the NASA technical reports server. 

It should also be noted that the Cordier Diagram, a plot of specific speed and specific diameter, is also a useful tool in approximating initial pump performance. By using your rocket engine requirements, you can determine the required head and volumetric flow rate. After that, the only thing you need is rotational speed. This number is frequently limited by the materials you're working with. From here, you can find varying specific diameters and in turn impeller diameters that give an efficiency value between 40 and 80% (turbopumps typically don't get more efficient than 80%). 

Source: Xu and Zha

It should also be mentioned that turbopumps run the high risk of cavitation during operation. This occurs when the pressure just before an impeller's inlet becomes lower than the working fluid's vapor pressure. This can cause the fluid to rapidly vaporize and collapse on itself and is often described as sounding like tiny bullets or rocks hitting a metal surface. This can cause signification damage to the pump (little divets on pump's surface):

Source: Belzona

To avoid this, the pressure inside the impeller should never be below the working fluid's vapor pressure or more formally, the NPSH required should never rise above the NPSH available. NPSH can be found using the following equation and swapping out the pressures in your pump for the vapor pressure and actual pressure:

P1 is inlet pressure and V1 is fluid inlet velocity. Px is either vapor pressure or inlet pressure

Manufacturing

Turbopump impeller materials are selected based off their cost, ease of manufacturing, rigidity, low thermal expansion/contraction, and resistance to sparking. Fuel impellers are frequently made out of aluminum 7075 or titanium because they're lightweight and don't deform or break apart under extreme rotational speeds. Stainless steel, if weight isn't a concern and at low rpms, is also a viable option. For oxygen impellers, Inconel 625 is more suitable, as titanium and aluminum have too high of a risk for sparking. While this project primarily covers the development of pumps for gas generator turbopumps, materials for turbine manufacturing and ducting will also be discussed here. Gas generators can reach extreme temperatures but, by running your gas generator fuel rich, temperatures can be as low as 900F. Despite this, ducting can require complicated shapes and exotic materials. For example, the F-1 turbopump gas generator and turbine ducting can be seen below, with tiny nozzles aimed at the turbine blades and an elbow shaped manifold for the gas inlet:

Source: Heroic Relics

Hastelloy - X, Rene - 41, Mondalloy, Nimonic 90, Inconel 718, and Haynes 282 are all common materials used for turbine blades, housing, and ducting. In particular, Inconel 718 and Haynes 282 (or Hastelloy - X) are more common and more available, with both materials available on McMaster - Carr. There's also a few vendors, like Turbocam, that have the capability to machine or print in these materials using 5-axis CNC machines or DMLS or similar printing methods.