Joint Operation of the Turbine and Pump of a Liquid Rocket Engine

The turbopump unit (TPU) is often referred to as the heart of the liquid rocket engine design. By the late 1950s, developers realized that pressurized fuel supply systems were only efficient for combustion chamber pressures up to 40 bar. As a result, design bureaus began working to increase engine thrust, specific impulse, operating time, and improve the engine’s weight and size characteristics—a challenge that continues to this day.

The key thermal parameters of the liquid rocket engine (LRE) combustion chamber are the temperature and pressure of the combustion products. Higher temperatures increase the velocity of the combustion products and specific impulse, while higher pressures increase mass flow rate, leading to greater thrust. Higher pressure also enables significant reductions in the size and weight of the combustion chamber (Fig. 1).

Nearly 70 years ago, preliminary calculations showed that achieving high combustion chamber pressures required a turbopump system to feed the propellants. For example, to reach 70 bar, the TPU rotor needed to spin at 7,000 RPM; for 100 bar, at least 10,000 RPM was necessary. At the time, these speeds seemed astonishing. Yet, only a few years later, engineers achieved 13,000 RPM, along with mass flow rates of up to 2 tons per second and pump outlet pressures of 600–900 atmospheres.

 

During this time, the two major technical challenges were steam cavitation and bearing design. Cavitation—caused by liquid fuel boiling on the pump blades—led to reduced flow and blade erosion. The issue was addressed with improved pump geometries. The bearing problem was tackled with hydrodynamic bearings, which use a thin fluid film to separate moving surfaces, reduce wear, and distribute loads. Today, rotational speeds up to 1 million RPM have been achieved in miniature motors. For high-flow, full-scale TPUs, speeds typically range from 15,000 to 35,000 RPM.

While early rocket engines operated within just a few percent of nominal values, modern LREs support a much wider range (40% to 110%). Ensuring stable and reliable turbopump operation remains a critical challenge, however. Global statistics indicate that about 70% of LRE failures are due to TPU malfunctions.

Let’s shift our focus from history to the present. Today, turbopump units (TPUs) are an integral part of liquid rocket engine design, and their analysis is a critical aspect of engine development. At the core of TPU design lies a straightforward principle: matching the turbine’s output power to the pump’s required power.

At first glance, this may seem simple. Given the mass flow rate through the pump, the input and output pressures (which define the required pressure rise), the inlet temperature of the fuel component, and the pump’s efficiency, the required pump power can be calculated. This value must match the turbine’s power. For the turbine, the inlet temperature and pressure are typically known, along with its internal efficiency. By adjusting the gas flow rate through the turbine and the pressure drop ratio, the remaining parameters can be determined. This is the approach used in AxSTREAM System Simulation for TPU design.

STEP ONE

We begin by modeling a turbopump unit. Let’s consider one possible design: a single turbine driving two centrifugal pumps. If the oxidizer and fuel pumps must operate at different angular velocities (often due to cavitation risk in one of the components), a reduction gear is introduced. However, this increases the overall mass and may raise reliability concerns. For simplicity, we’ll examine a configuration that does not include a reduction gear.

STEP TWO

After setting the necessary input and output parameters for each component in Simple Design mode, we define the remaining values. For convenience, watcher elements are added—these allow us to monitor specific parameters of interest during the calculation process. Parameters that need to be defined are highlighted in red, calculated values appear in black, and those used to initialize the calculation are shown in blue. We then verify the power balance: the turbine power must equal the combined power required by the pumps. The efficiency of each component is selected based on the prototype.

STEP THREE

Once the TPU design is defined and the joint operating point of the turbine and pump is identified, the system’s behavior can be analyzed using performance maps.

For example, a performance map of the mass flow rate of gaseous hydrogen—used as the working fluid for the turbine—can be utilized. By varying two parameters—the pressure ratio and angular velocity—it is possible to identify the optimal balance between them to achieve maximum internal turbine efficiency.

Working with the performance map is straightforward and largely intuitive. An example is shown below.

The results of the TPU analysis using performance maps are shown in Fig. 7.

This approach made it possible to identify an operating mode in which turbine efficiency increased from 0.78 to 0.905, while the mass flow rate of gaseous hydrogen decreased from 2.75 kg/s to 2.705 kg/s.

This method can be applied to the calculation of a complex liquid rocket engine configuration using cryogenic hydrogen and oxygen as propellants. The TPU operates on gaseous hydrogen, which is heated as it flows through the cooling jacket of the nozzle and combustion chamber. This setup eliminates the need for a gas generator, significantly reducing the overall mass of the propulsion system.

The TPU includes a gearbox before the oxygen pump, while the hydrogen pump is configured as a two-stage system. In the presented diagram, the pumps operate with incompressible liquid, which reduces calculation time with negligible impact on accuracy.

 

Once map parameters are set (Fig. 9), results can be generated (Fig. 10).

 

As a result of the calculations, the operational parameters of the TPU turbine, functioning within the overall diagram of the liquid-propellant rocket engine, were obtained: the flow rate of gaseous hydrogen through the turbine is 2.682 kg/s, the pressure ratio is 1.4, the angular velocity of rotation is 31,500 revolutions per minute, and the internal efficiency of the turbine is 0.75.

Finally, we check the calculation in Simple design mode.

Using CAE tools like AxSTREAM System Simulation significantly simplifies the design and analysis of complex turbopump units in modern liquid rocket engine design. With just a few clicks, engineers can perform detailed calculations, balance turbine and pump operation, and generate complete performance maps—accelerating innovation in propulsion system design.