Björn Gwiasda
email: gwiasda@mv.uni-kl.de

Ma Hias Mohr

Martin Böhle

S Y Mpo

O Tatin

Investigations of Inducers Operating with High Rotational Speed

Keywords:

Suction performance, pressure rise and efficiency for four different inducers are examined with CFD simulations and experiments performed with 18 000 rpm and 24 000 rpm. e studies originate from a research project which includes the design of a new test bench in order to judge the design of the different inducers. is test bench allows to perform experiments with a rotational speed of up to 40 000 rpm and high pressure ranges with water as working fluid. Experimental results are used to evaluate the accuracy of the simulations and to gain a be er understanding of the design parameter. e influence of increasing the rotating speed from 18 000 rpm to 24 000 rpm on the performance is also shown.

INTRODUCTION

e inducer is a component of hydraulic fluidmachinery that is typically applied in turbopumps of liquid fuel rocket engines that operate at high rotational speeds. It belongs to the group of axial flow impellers and can be characterized by high solidities and very small blade angles. A lot of information on the hydraulic design and the characteristics of this type of impeller can be found in textbooks well known in the field of turbomachinery, e.g. [ , , ]. Although many design guidelines for inducers exist, especially a reliable prediction of the suction performance of inducers still remains an unresolved issue. erefore the design process of inducers has to rely on numerical and experimental methods that ensure the compliance of the new design with the requirements. e prediction of the non cavitating hydraulic performance is described in [ ] for example. While it is widely accepted that CFD can be used to estimate and evaluate the performance characteristics of fluidmachinery under non-cavitating conditions, the prediction of the suction performance is a task fraught with uncertainty because of the modeling involved when simulating the cavitating flow. Hence the comparison of the numerical results with experimental data is still a mandatory job. As liquid rocket engine turbopumps are operated with cryogenic fluids a typical approach to significantly reduce the cost and effort needed when handling these fluids is to use water as the working fluid for the experimental investigation [ ]. How the results of such tests can be transferred to the real application has recently been adressed by the authors of [ ] and [ ]. e authors have developed an elaborate testbench that uses heated water to validate a method to consider thermal effects on the cavitation phenomena occuring in inducers for turbopumps. Descriptions of two other sophisticated testbenchs that are used to investigate rotordynamic phenomena in turbopumps a ributed to inducers and their interaction with the surrounding pump components can be found in [ ] and [ ]. All of the aforementioned test configurations have in common that they operate at lower rotational speeds than can be found in the real application. As a part of a research project granted by the German Aerospace Center (DLR) a new water testbench that allow tests with high rotational speeds has been developed at the Technical University of Kaiserslautern (TU Kaiserslautern). In the course of this project four inducers with differences in hub shape and blade angle distribution have been designed. One requiremente of the project is to test the inducers as close as possible to the design speed of 24 000 rpm . To avoid premature damages of the prototype as well as the test bench equipment a first series of measurements at 18 000 rpm are conducted. A detailed comparison between the results of simulations and experiments for the four inducers is performed. In particular the influence of the design details on the obtained performance characteristics is discussed. Also the influence of rotational speed on performance is addressed.

. METHODS

In this section an overview of the methods used in the remainder of the current paper is given. First the parameters that are used to calculate and visualize the hydraulic and suction characteristics are introduced. In section . details about the design are given. Performance and suction characteristics for a rotational speed of n = 18 000 rpm are obtained numerically and experimentally for all of the designed inducer variants. Details of the numerical and experimental setups are presented in section and respectively. Section includes a detailed comparison of these results and an interpretation of the influence of the blade design on performance and suction behavior. Furthermore the same set of data is presented for inducer variant A (see table ) at the rotational speed n = 24 000 rpm and the influence of the change in speed is discussed.

. Performance Parameters

To ensure comparability of the data when matching the numerically calculated quantities against the ones obtained by the test runs the following formulas for Head H, efficiency η and net positive suction head N PSH are applied:

H = p 2 -p 1 ρ g + c 2 2 -c 2 1 2 g ( ) η = Q ρ H g M ω ( ) N PSH = p 1 -p v ρ g + c 2 1 2 g ( )
Indices and denote the positions of the evaluation planes in case of the numerical simulation which are located at the same axial coordinates as the pressure taps in the experimental setup. e velocities are calculated as function of the corresponding cross sectional area as follows:

c 1 = Q A 1 , c 2 = Q A 2 ( )
With u t = π D t n being the blade tip speed and

c LE = Q π 4 (D 2 s -D 2 L E, h
) the following representations of head, flow and cavitation coefficient are obtained:

Ψ = 2 H g u 2 t ( ) ϕ = c LE u t ( ) σ c = 2 g N PSH u 2 t ( )
Furthermore the dimensionless form of suction specific speed Ω ss according to [ ] is employed:

Ω ss = ω √ Q (g N PSH) 3/4 ( ) L L+N D LE,h D TE,h D t Figure .
Main dimensions of the inducers

. Inducer Designs

An institute-owned design procedure is used to design the four inducers under consideration. e design parameters and additional requirements that had to be satisfied are summarized in table . All inducers are designed to operate at a rotational speed of n d = 24 000 rpm and a flow coefficient of ϕ d = 0.1. e head coefficient ψ d has intentionally been treated as a free parameter to gain a be er understanding of the influence of the geometrical variations on the head and efficiency characteristics. now are equal for all the inducers under investigation, the parameters listed in table give an overview of the differences in their geometrical details. e designed inducers are named A , M , M and M . As can be seen from table the inducer variants differ in their axial length L. A more significant difference can be observed in terms of the hub shape of the inducers. e hub diameter of variant A is constant, that is D h, LE = D h,TE , whereas the hub diameter increases from 20 mm to 36 mm for the remaining variants starting with le er M. e hub shape for inducer M , M and M , to increase the hub diameter, is the same. Furthermore the variants A and M basically feature the same blade design without any change in blade angle with respect to the axial direction. In contrast the remaining variants M and M can be characterized by a variable blade angle distribution. While the change in blade angle is equal on the tip section for both designs the trailing edge blade angle at the hub for the inducer M is smaller than the exit blade angle of variant M . e four inducers have been manufactured in the university-owned workshop by CNC milling and turning. ere are two possible modes of operation marked with red and blue. e red line shows the flow in the case of closed loop operation and blue in the case of operation with open loop. In the la er case there is flow through the tank. For the closed loop configuration the shut off valves at the tank are closed. To regulate the inlet pressure during operation with closed loop a small connection between tank and the suction pipe with a small tube is used to imprint the pressure inside the tank on the intake section. Especially to measure the suction performance at low inlet pressure the closed loop operation (red line) is recommended in literature [ ]. A dissolved oxygen sensor is implemented to ensure comparable conditions for each measurement. To observe vibrations an acceleration sensor is implemented at the intake pipe near the inducer. 40 bara is the maximum possible pressure at the inducer outlet. Inside the tank the pressure can be adjusted from 0.1 bara to 6 bara. To compensate the pressure losses in pipes and components a booster pump is installed. is allows for operation at high overload, that means high volume flows. In the suction pipe of the inducer the temperature is measured. e torque meter is placed between the drive motor and the inducer sha . As mentioned before the working fluid is water. To get visual access the inducer casing is made out of acrylic glass. A steady view of the rotating impeller is realized with by using a stroboscope which is synchronized with the actual rotating frequency. e pictures and videos at each measured point are taken with a HD networkcam so that a real time look at the inducer is possible during the measurement. Table lists the sensors with the corresponding measurement ranges utilized at the test bench. An inlet pressure of p tot,1 = 4 bara is realized during performance measurements to avoid the influence of cavitation effects.

. Comparison of inducers

e influence of the different inducer designs on head coefficient and efficiency may be seen in figure and . Where experimental results at n = 18 000 rpm are compared for all inducers. Comparing the axial version A and version M without changing the blade angle distribution at the trailing edge a subsidence in efficiency and head coefficient level can be observed.

e slope for A is also fla er than for M looking at the head coefficient. Taking the design Point at ϕ = 0.1 as a reference the point of best efficiency is in overload for A . For M the point of best efficiency shi s to partial load. Changing the blade angle distribution at the trailing edge an increase in head coefficient and efficiency can be observed by comparing M and M to M . Also the point of best efficiency is closer to the design point for inducer M and M . Comparing M and M la er has a slightly higher level in head coefficient and efficiency. Looking at the suction performance in figure we can see that the point a first drop in head coefficient occurs is almost the same for all inducers σ c ≈ 0.1. e first drop of head coefficient is not this distinctive for M and M compared to M and A . e drop is most pronounced for inducer M which differs from A only by its hub shape. Clearly the data summarized in table shows that there's an substantial offset between the suction performance predicted by CFD and the one obtained by experiment. Furthermore the trend of the experimental results is not represented by the simulation data. . Influence of rotating speed

In figure , and a comparison of the results of CFD and experiments at 24 000 rpm for inducer A is shown. e overall progression of head coefficient and efficiency is similar to the ones seen at 18 000 rpm. In part load a reduction in slope of the head characteristic curve is predicted by CFD which cannot be observed in the experimental results. Comparing suction performance results of CFD simulations and experiments, it is obvious that in case of the experiment the head drop occurs at higher values of σ c . Consequently the point of 10% drop in head coefficient, already included in table , is predicted at a lower value of cavitation number in case of the CFD simulation. For all of the inducers under consideration good agreement between CFD simulation and experiment could be observed near this point. At off-design conditions, especially in part load, the discrepancy between simulation and experiment is ge ing larger. To evaluate the different inducer designs the data from experiment is used. e inducer with constant hub diameter, named A , shows a lower efficiency compared to inducers with increasing hub diameter and adjusted blade angle distribution at the trailing edge. e head coefficient curve is fla er for the inducer A so the operating range is larger than for the inducers with increasing hub diameter.

Only increasing the exit hub diameter of this inducer, as is done for inducer M , leads to a reduction in head coefficient and efficiency. Hence the blade angle distribution at the trailing edge has to be adapted to improve head coefficient and efficiency for inducers with increasing hub diameter. Two possible modifications of blade angle are realized for inducers M and M . As a result of this modification not only the performance can be improved but also the best point of efficiency can be moved closer to the design point for the inducers M and M . In case of the suction performance substantial deviation between the numerical and experimental data are found independently of the inducer design under investigation. erefore the simulation results can only be regarded as a first guess of cavitation behavior. To perform a quantitative analysis of cavitating inducers calibration of the applied cavitation model is necessary. is can only be done by using experimental data.

Looking at different rotating speeds there seems to be no visible influence on the head coefficient. ere is a small but not negligible influence of rotating speed on suction performance.

is influence for σ c where 10% drop of head coefficient occurs can be seen in table . For experiments σ c decrease with higher rotational speed. However it has to be taken into account that the reduced speed is still a high rotational speed. Further investigations must show how far the speed can be reduced until an apparent influence can be recognized.

Indices

  Figure shows a drawing that illustrates the parameters used to describe the main dimensions of the inducers. Although the operating conditions have been derived from a real turbopump application there is only an academic interest in the investigations. Based on the operating conditions the design of the inlet eye has been predetermined by the specification of the hub diameter D 1h at the leading edge and the diameter of the cylindrical shroud D s according to table . e tip clearance amounts to 0.3 mm, which leads to a tip clearance area that is smaller than 3% of the flow area as recommended in [ ]. With the inlet geometry and the flow coefficient predefined the theoretically obtainable suction specific speed according to Brumfields equation (see e.g. [ ]) is also predetermined. For the given inflow conditions one can estimate Ω SS,d ≈ 12 or expressed in terms of cavitation number σ c,d ≈ 0.03. e blade angle along

  the results in [ ]. e value used for the sweep back angle at the tip diameter is ∆Θ t = 75°. Furthermore the sharpening of the leading edge suction surface is accomplished by se ing the ratio of wedge angle to blade angle α w /β b, LE ≈ 1/3. By the application of the aforementioned details the resulting blade angle, wedge angle and incidence angle at the leading edge tip lie quite well in the range of the historical data summarized in [ ]. While the parameters discussed until Table .

  Figure depicts the prototypes made out of a high-strength aluminum alloy .suitable for the test in water.

Figure .

 . Figure . Inducers -from le to right: A , M , M , M

Figure .

 . Figure . Simulation modelTwo different sets of simulations are performed for each inducer. One to evaluate performance and one for suction performance. e following simulation se ings are used for both procedures. A total pressure boundary condition is defined at the inlet. At the outlet a mass flow is set. e length between inlet and inducer is 4D s and 3D s from Inducer to the outlet.e turbulence model used is SST. e advection scheme is set with high resolution and the turbulence numeric with first order. Single phase simulations are performed to obtain the performance characteristics. In the case of the simulation of the suction performance curves liquid and vapor phase are used. For this simulation the cavitation option in mass transfer is enabled. Cavitation is modeled by the built-in rayleigh-plesset model. To allow CFX the use of a wall function to describe the flow with the SST model y + is chosen appropriately. A schematic view of the mesh on the surface of the inducer A as an example is shown in figure

Figure .

 . Figure . Hydraulic plan Figure gives a detailed view of the measurement section. P and P mark the positions where the pressure is measured. According to standard [ ] the static pressure is measured with four holes distributed uniformly at the circumference. Distance L 1 is a function of D s with L1 ≈ 3.5• D s . L 2 is constant due to construction conditions with L 2 ≈ 50 mm.To get visual access the inducer casing is made out of acrylic glass. A steady view of the rotating impeller is realized with by using a stroboscope which is synchronized with the actual rotating frequency. e pictures and videos at each measured point are taken with a HD networkcam so that a real time look at the inducer is possible during the measurement. Table lists the sensors with the corresponding measurement ranges utilized at the test bench. An inlet pressure of p tot,1 = 4 bara is realized during performance measurements to avoid the influence of cavitation effects.

Figure

  Figure gives an overview of all the characteristic curves obtained by experiment and CFD simulation at a rotating speed of 18 000 rpm for every inducer. Each plot shows the comparison of experimental and numerical result in dimensionless form. Experiment and simulation are compared looking at the head coefficient and the efficiency both as a function of the flow coefficient. To describe the suction performance a normalized head coefficient is used and plo ed against cavitation number σ c . e normalized head coefficient is defined as the head coefficient at the actual cavitation number ψ σ c referenced to the head coefficient occurring at the maximum cavitation number ψ σ c, max . Head coefficient and efficiency of the experimental results confirm the CFD simulation very good at the design point of ϕ = 0.1. For minor partial load the head coefficient also show a good accordance for all inducers. It can be seen that at heavy partial load conditions the results of CFD and experiments start to differ. For the axial inducer A this effect is much more distinct. In overload the results of CFD and experiments match very good. Close to the design point efficiency matches quite good. While in overload the simulation tends to overpredict the efficiency, the tendency in part load is vice-versa. Especially in case of inducer A this is strongly pronounced and clearly visible. Furthermore it is evident that only inducers M and M are operating close to their point of best efficiency at design volume flow. Looking at the results for suction performance inducer A , M and M show a very good agreement between CFD and experiment. Between σ c ≈ 0.15 and σ c ≈ 0.05 a first drop of head coefficient can be observed looking at the experimental results for all inducers. Pulsation effects could be observed in this range during experiments. is unsteady effects are not taken into account by the steady simulations and because

Figure . Figure .

 .. Figure .Head coefficient at 18 000 rpm (Experiment)

Figure . A

 . Figure . A Suction performance (σ c ≈ 0.04)

Figure .

 . Figure . M Designpoint (ϕ = 0.1)

Figure . Figure

 . Figure . A -Head coefficient at 24 000 rpm

table

	Table . Design Parameters -common to all variants
	Parameter	Unit Value
	Number of blades	-
	D LE,h	mm
	D s	mm	.
	D t	mm	.
	i/β b, LE	-	.
	β b, LE,h	°	.
	β b, LE,t	°	.
	∆Θ t	°
	the blade leading edge has been designed by application of
	a constant ratio of incidence to blade angle i/β b, LE = 0.425.
	is leads to the blade angles at the hub and shroud diameter
	listed in

. To realize the targeted suction performance a sweep back of the leading edge is performed according to

Table . Sensors

 .

	Sensor	Symbol	Unit	Range (Error)
	Torque meter	M	Nm	0 ...10 ( . %)
	Revolution counter	n	rpm	0 ...60 000 (-)
	Absolute pressure	P	bara	0 ...10 ( . %)
	Difference pressure	P -P	bar	0 ...20 ( . %)
	Temperature at intake	T	K	223 ...673 (-)
	Flow meter	Q	m 3 h

-1 0 ...120 ( . %) Figure . Measurement section . RESULTS . Comparison of CFD and experiment

  is used to perform the simulation. To catch instabilities with the simulation a full transient D simulation is necessary. e head coefficient for inducer M increases with decreasing cavitation number before the first drop in head coefficient occurs in experiment. is effect can only be observed looking at inducer M . For inducer A , M and M the results of CFD and experiments have nearly the same progression before the first drop in head coefficient occurs. To evaluate the suction performance 10% drop of head coefficient is chosen as the cavitation criterion in accordance to the historical data given in [ ]. Table shows the value of σ c and Ω ss where the head coefficient lost 10% compared to the head coefficient at maximum cavitation number. e drop in head coefficient occurs at nearly the same value for σ c in the experiments and the CFD simulations for inducer A , M and M . As mentioned before the difference between CFD and experiment is higher for inducer M . e first drop in head coefficient is much more pronounced. e estimated Ω ss ≈ 12 during the design procedure is in good accordance to the values obtained by experiments, at least for the inducers A , M and M . In all cases CFD overestimates suction performance.

	Table . σ c at a drop of 10% head coefficient
	Inducer		CFD		EXP
		σ c	Ω ss	σ c	Ω ss	n/rpm
	A	.	.	.	.
	A	.	.	.	.
	M	.	.	.	.
	M	.	.	.	.
	M	.	.	.	.

Pulsation effects could be observed in this range during experiments. is unsteady effects are not taken into account by the steady simulations and because only one passage

  Liquid Rocket Engine Turbopump Inducers, volume NASA SP-of NASA Space Vehicle Design Criteria. NASA, . ] D. A. Ehrlich, J. A. Schwille, R. P. Welle, J. W. Murdock, and B. S. Hardy. A water test facility for liquid rocket engine turbopump cavitation testing. Proceedings of the th International Symposium on Cavitation, . Paper No. . ] E. Rapposelli, A. Cervone, and L. d'Agostino. A new cavitating pump rotordynamic test facility. Proceedings of the th AIAA Joint Propulsion Conference and Exhibit, . Paper No. -. ] F. Bakir, S. Kouidri, R. Noguera, and R. Rey. Experimental analysis of an axial inducer influence of the shape of the blade leading edge on the performances in cavitating regime. Journal of Fluids Engineering, ( ): -, . [ ] D. Japikse. Overview of industrial and rocket turbopump inducer design. e th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, . [ ] J. F. Gülich. Kreiselpumpen. Springer, .

	Symbol Description
	1	Intake
	2	Ou ake
	b	Blade
	d	Design point
	h	Hub
	m	Middle
	s	Shroud
	t	Tip
	tot v	Total Vapor			[ ] DIN EN ISO	:	. Rotodynamic pumps -hydraulic
						performance acceptance tests.
	Acronyms
	CFD Computational fluid dynamics
	EXP	Experiment
	LE	Leading edge
	P		Plane
	TE	Trailing edge
	max		Maximum
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	( ):	--	-,	.

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[

ACKNOWLEDGMENTS e authors would like to thank the Federal Ministry for Economic Affairs and Energy (BMWI) and the German Aerospace Center (DLR) for the support of the present work. e simulations were conducted on the high performance cluster Elwetritsch at TU Kaiserslautern, which is part of the Alliance of High Performance Rheinland-Pfalz (AHRP).

Cavitation number -