Why Use an Inducer?

Suppose you want to build a turbopump to increase the pressure of your working fluid. However, you find that the fluid that you are working with keeps vaporizing in the impellers you design, causing all sorts of performance issues. What can you do in this case? One solution is to design an inducer for your turbopump.

Axial inducers are used in turbopumps upstream of the impeller to avoid cavitation, reduce the inlet pressure requirement, and/or allow for operation at higher turbopump rotational speeds for a given inlet pressure [1]. For a turbopump to function properly, the inlet pressure of the pump must be high enough to avoid cavitation. Cavitation is a phenomenon where vapor bubbles which form in the flowing fluid collapse suddenly – potentially causing surface damage of the impeller, performance degradation, as well as catastrophic failure.

The cavitation phenomenon can be visualized in the below image. The inlet flow (flowing from the left side of the image) hits a blunt body in the fluid channel. This causes the pressure to locally drop and vapor bubbles to form. As the fluid continues to flow (towards the right side of the image), the vapor bubbles collapse once the fluid pressure has sufficiently increased.

Now that we understand the problem, how can we make sure these cavitation effects won’t happen in our pump? To predict when cavitation will occur, two parameters are commonly used. The available net positive suction head (NPSHa) describes how much greater the local inlet static pressure is relative to the local inlet vapor pressure. Essentially, NPSHa indicates whether the conditions for cavitation to occur are met. The required net positive suction head (NPSHr) describes the inlet head corresponding to a certain drop in performance capability. A typical NPSHr parameter is the standard 3% NPSH (NPSH3) which describes the inlet pressure corresponding to a 3% drop in head rise capability of the pump at a particular flow rate. Generally, NPSHr is measuring whether there is enough cavitation present to cause a noticeable decrease in the pump’s performance. If the NPSHr is much greater than NPSHa, then significant performance decreases due to cavitation may occur. That is to say, when the available net positive suction head is insufficient, bad things can happen, ranging from performance degradation to outright damage and failure.

In certain applications, the inlet conditions of the pump are such that the cavitation conditions cannot be avoided. These applications include rocket turbopumps, aircraft fuel pumps, and boiler feed pumps [2]. This makes them excellent applications for implementing an inducer! An example of an inducer used in a rocket turbopump application is shown below [3]. Some characteristics of this inducer to notice include a swept-back leading-edge, high blade solidity, relatively long flow channel, and low number of blades. The pump inducer increases the static pressure upstream of the impeller. The result of this can be thought of as either the reduction of NPSHr for the overall machine or an increase in NSPHa at the inlet of the impeller, both of which result in the minimization of the degrading effects of cavitation.

Inducer Design Considerations

Relatively long blade channels

Now that we know we want an inducer, what are some characteristics they can be expected to have? We’ll start by noting that inducers are an axial flow element with a relatively low number of blades (typically 3 or 4) [4]. Using a low number of blades results in longer blades with increased axial length to perform work on the fluid. A benefit of longer blades is that they provide enough time and space within the flow channel for the collapse of any vapor bubbles prior to the rotor inlet, but the tradeoff is a lower efficiency. Let’s look at why this is the case.

Energy is imparted from the inducer blades onto the fluid very gradually. One of the downsides of this geometry is that within the flow channels, the flow may experience significant viscous effects and secondary flows. Due to the low blade numbers, there is more space in the flow channel for secondary flows to form. The introduction of vapor bubbles in the flow also adds to the turbulence and viscous losses. These cause the flow energy to more easily dissipate, leading to lower efficiency values across the inducer [1].

Because of the increased chord length of the blades, inducers have a high blade solidity (typically between 1.5 – 2.5), which is the ratio of the chord length to the cascade pitch. A benefit of higher solidity is that it improves the suction performance and can also help counteract oscillations from cavitation [4]. Note in the below image how even with the low number of blades, inducers will have a high solidity compared to impellers.

Leading-edge geometry

Let’s figure out how large our machine should be – we can start at the inlet. The inlet tip diameter is determined from the desired flow coefficient (typically between 0.07 – 0.14) [2], which relates the absolute fluid velocity at the inlet to the circumferential velocity of the rotating blade tip (see equation below). The desired minimum hub inlet diameter will typically be limited based on mechanical constraints (e.g. shaft size), and the flow coefficient will aid in determining the inlet tip diameter (using the calculated tip speed and specified shaft rotation rate). We now know the required size of our pump inlet! Typical resultant inlet diameter ratios (the ratio of the inlet tip diameter to the inlet hub diameter) are between 2 – 5 [4].

Let’s also try to reduce entry losses near the inlet of the inducer. To do this, a small radius of curvature (or small wedge angle) is used at the blade leading edge. Ultimately, the lower limit on the leading-edge radius will be due to the structural stresses of the blade. To deal with the structural stresses generated by the centrifugal and pressure forces, the blade must be sufficiently thick. The thickness of the blade tapers from a maximum thickness at the hub to a minimum thickness at the tip. Fillets are also present at the hub section to reduce stress concentrations.

Inducer Design in Action

To demonstrate the inducer design process, we’ll perform a preliminary design in AxSTREAM using the specifications of the turbopump from the RL10A-3-3A Rocket Engine [5]. The rocket engine uses a 2-stage fuel turbopump, with the first stage consisting of an inlet duct, inducer, centrifugal impeller, vaneless diffuser, and conical exit volute. The model of this first stage is shown below.

Operating Parameters

Operating parameters of this first stage predicted by AxSTREAM are given in the table below. The two values of NPSHr provided are for the inducer and impeller only. That is, if the inducer or impeller were operating on its own at the design flow rate, the individual NPSHr would result in a 3% drop in head rise capability across that single-component stage. The NPSHr value of the entire machine will typically be based on the NPSHr of the first stage since the inlet pressure is higher for the following stages and thus the possibility of cavitation is reduced. The first thing to notice about the operating parameters of the RL10A is that the NPSHr of the inducer is lower than the impeller, so it is designed to handle lower operating pressures. (This is good – otherwise why design and use an inducer?!) Additionally, notice that the NPSHa of the inducer is very close to the NPSHr of the impeller. This shows that if the inducer was not present to raise the inlet pressure prior to the impeller, there would most likely be significant performance degradation in the impeller.

Geometric Parameters

The inducer modeled in AxSTREAM had the resulting geometric parameters shown in the table below. The inducer geometry was generated in AxSTREAM’s preliminary design solver based on both operating boundary conditions supplied in literature, as well as certain geometric constraints to ensure that the design has realistic geometry and performance. Note that the entry tip flow coefficient is within the desired range indicated previously [2]. The geometry also has a high solidity and a high inlet diameter ratio.  Finally, the leading-edge wedge angle is small and decreases along the height of the blade. These are all geometric features we identified earlier as typical in axial inducers.

We have taken a brief introduction into the types of parameters that should be considered when designing turbopump inducers. Using design tools such as AxSTREAM, these parameters can be controlled and manipulated during the turbopump design process. Cavitation is a design challenge that needs to be addressed by engineers, and the implementation of an inducer provides a potential solution.

References:

• [1] L. d’Agostino, L. Torre, A. Pasini, D. Baccarela, A. Cervone and A. Milani, “A Reduced Order Model for Preliminary Design and Performance Prediction of Tapered Inducers: Comparison with Numerical Simulations,” AIAA, Hartford, CT, 2008.
• [2] D. Japikse, W. D. Marsher and R. B. Furst, Centrifugal Pump Design and Performance, Concepts NREC, 1997.
• [3] A. Cervone, L. Torre, A. Pasini and L. d’Agostino, “Cavitation and Flow Instabilities in a 3-Bladed Axial Inducer Designed by Means of a Reduced Order Analytical Model,” in International Symposium on Cavitation, 2009.
• [4] J. Jakobsen and R. B. Keller Jr., Liquid Rocket Engine Turbopump Inducers, NASA SP-8052, 1971.
• [5] M. Binder, T. Tomsik and J. P. Veres, RL10A-3-3A Rocket Engine Modeling Project, NASA, 1997.