The hydraulic performances of a 3bladed inducer, designed at Alta, Pisa, Italy, are investigated both experimentally and numerically. The 3D numerical model developed in ANSYS CFX to simulate the flow through the inducer and different lengths of its inlet/outlet ducts is illustrated. The influence of the inlet/outlet boundary conditions, of the turbulence models, and of the location of inlet/outlet different pressure taps on the evaluation of the hydraulic performance of the inducer is analyzed. As expected, the predicted hydraulic performance of the inducer is significantly affected by the lengths of the inlet/outlet duct portions included in the computations, as well as by the turbulent flow model and the locations of the inlet/outlet pressure taps. It is slightly affected by the computational boundary conditions and better agreement with the test data obtained when adopting the
Propellant feed turbopumps are essential components of all primary propulsion concepts powered by liquid propellant rocket engines. Due to the severe limitations imposed to Space Transportation Systems, liquid propellant feed turbopumps must meet extremely demanding pumping, suction, and reliability requirements [
Ongoing improvements of computational fluid dynamics (CFD) are rapidly promoting its role and use as an effective tool for research and development of hydraulic machinery with respect to complex and expensive experimentation [
Computations have been carried out by means of the commercial ANSYS CFX 14.5 software package installed at Jiangsu University, Zhenjiang City, China, in the Blade HighPerformance Computing Clusters System, whose main operational parameters are listed in Table
The parameters of Blade HighPerformance Computing Clusters System.
CPU  2x Intel Xeon X5650 CPU with 6 physical cores for each, 2.40 GHz, 12 M Threelevel buffer 
Memory  24 G DDR3 RDIMM, 18 slots, the maximum memory 384 G 
Hard risk  2x 146 G 10K SAS 6 G 2.5, HotSwap hard disk 
Blade server  Dawning Blade Full View Manager System 
Operating system  SUSE Linux Enterprise Server 11 for 64bit 
Geometrical and operational parameters of the DAPROT3 inducer.
Design flow coefficient  [—] 

0.065 

Number of blades  [—] 

3  
Tip radius  mm 

81.0  
Inlet tip blade angle  deg 

82.10  
Inlet hub radius (fully developed blade)  mm 

44.5  
Outlet hub radius  mm 

65.6  
Axial length (fully developed blade)  mm 

63.5  
Rotational speed  rpm 

1500  
Inlet hub radius  mm 

35.0  
Axial length  mm 

90.0  
Mean blade height  mm 

25.95  
Diffusion factor  [—] 

0.47  
Ratio between the incidence and blade angles ( 
[—] 

0.33  
Tip solidity  [—] 

1.68  
Incidence tip angle @ design  deg 

2.58  
Outlet tip blade angle  deg 

70.56 
The computational model includes the threebladed inducer, whose main dimensions and characteristics are reported in Table
Details of mesh elements.
Computational domains  Mesh elements  

Case 1  Case 2  Case 3  Case 4  Case 5  Case 6  
Inlet  624134  7234222  
Outlet  296934  469918  
Inducer  820816  1340548  1548792  1762226  1762586  3675103 
All domains  1741884  2261616  2469860  2683294  2683654  11379243 
(a) A 3D view of the inducer; (b) the extended inlet duct; (c) the outlet duct.
ANSYS CFX uses a finite volume formulation to solve the RANS momentum, continuity and turbulence equations for incompressible, turbulent flow in the inducer. Since it was originally proposed by Launder and Spalding [
Since the computational cost is known to depend also on the inlet/outlet boundary conditions, it is important to investigate the impact [
set
set
respectively.
The Cavitating Pump Rotordynamic Test Facility (CPRTF, ALTA S.p.A., Pisa, Italy; Figure
The Cavitating Pump Rotordynamic Test Facility and the experimental setup.
Type The DAPROT3 inducer used in the experimental tests has been designed by means of the well validated reducedorder model developed by Alta for the inducer design and performance prediction of axial inducers [
The characterization of the pumping performance of the DAPROT3 has been assessed throughout a series of tests conducted in water at room temperature (20°C) and at inlet static pressure well above the cavitation inception conditions. The pumping performance has been evaluated in terms of static head coefficient
Test section setup for the characterization of the noncavitating performance of the inducer.
Simulations have been typically considered to have reached convergence when the residuals of the mass continuity equation fell below
Convergence curves for monitors (mesh case 1 to 5).
Five different computational meshes have been taken into consideration and their resolutions have been optimized based on a sensitivity analysis on the hydraulic performance of the DAPROT3 inducer. Finally, these meshes have been used to assess gridindependence of the simulations.
The effects of the number of grid elements and of the boundary conditions on the prediction of the inducer performance operating at a flow coefficient of
Grid independence check (mesh case 1 to 5).
Simulations of the fully wetted flow through the DAPROT3 inducer operating at 90% of its design flow (
Position 1: one diameter upstream of the blade leading edge for the inlet station and one diameter downstream of the blade trailing edge for the outlet station, corresponding to the locations where the inlet and outlet pressure transducers have been installed in the experimental tests on the inducer with 0.8 mm blade tip clearance.
Position 2: 20 duct diameters upstream/downstream of the blade leading/trailing edges.
Position 3: two diameters upstream of the blade leading edge for the inlet station and 2.5 diameters downstream of the blade trailing edge for the outlet station, corresponding to the locations where the inlet/outlet pressure transducers have been installed in the experimental tests on the inducer with 2 mm blade tip clearance.
Position 4: six diameters upstream of the blade leading edge for the inlet station and one diameter downstream of the blade trailing edge, corresponding to the locations where the inlet/outlet pressure transducers have been installed in the experimental tests in order to eliminate prerotation effects.
Comparison of different pressuring measuring positions at the flow coefficient of
Distributions of pressure monitors
Comparison of four different pressure monitors
Comparison of grid elements and four different pressure monitors
As expected, the results shown in Figure
Four turbulence models (namely,
Comparison of different boundary conditions and different turbulence models.
Comparison of turbulence models and boundary conditions at the flow coefficient of
Comparison of deviations of the pressure rise coefficient at the flow coefficient of
Comparison of the hydraulic performances of the inducer
The static pressure pumping performance of the DAPROT3 inducer, operating at 0.8 mm blade tip clearance, has also been evaluated using the
According to the above analysis of the predicted inducer performance is still lower than the experimental one. Computations have therefore been extend to longer portions of the suction and discharge ducts with different lengths in order to better simulation the inlet/outlet flow and its influence on the inducer performance. In the shortest configuration the computational domain comprises inlet/outlet duct portions both 10 diameters and 15 diameters upstream and downstream of the inducer. In addition, a finer grid (mesh 6; see Table
As expected, good agreement with the experimental performances is obtained in Figure
Comparison of different lengths of the inlet and outlet pipes.
Comparison of pump performances of the inducer based on three different lengths of inlet and outlet
Comparison of pump performances of the inducer based on the pressure taps located at position 4 based on experimental and CFD methods
Next, the reference position for the evaluation of the inlet pressure has been located six diameters upstream of the leading edges of the inducer blades (position 4 in Figure
The results of experimental and numerical pump performances of the inducer have been mainly analyzed. Moreover, the influences of four different turbulence models, 2 different boundary conditions as well as four different positions of inlet and outlet pressure taps were specially investigated in present simulations in comparison with the experiment. In addition, the different inner flow structures in the inducer in design and offdesign flow rates are obtained.
From the present numerical analysis of the fully wetted flow in the DAPROT3 inducer and its comparison with the pertinent experimental results, the following conclusions have been drawn:
The more refined mesh proved to be better capable of modeling the internal flow through the inducer. The influence of the boundary conditions on the prediction of the static pressure rise turned out to be small, while the lengths of inlet and outlet ducts did show to significantly affect the inducer performance prediction.
Comparison with the experimental results indicated that the
The large deviation between these ФΨ curves was found at the flow rate coefficient lower than
In summary, the simulated hydraulic performances of the test inducer agree well with the relevant experimental results over a wide range of operating conditions, indicating that the proposed numerical model and methods adequately capture the internal flow in the DAPROT3 inducer. Moreover, the different pressure tap positions used for measuring the inlet and outlet static pressure were first discussed both by numerical and experimental ways in this study. The model represents therefore an effective tool to understand, analyze, predict, and control the mechanisms of the complex phenomena taking place in the flow through inducers operating over a wide range of conditions above and below the design point.
Tip blade clearance, m
Diffusion factor
Axial length, m
Number of blades
Inducer rotational speed, rad/s
Static pressure, Pa
Volumetric flow rate, m^{3}/h
Flow coefficient,
Static head coefficient,
Tip clearance
Blade angle from axial direction
Liquid density
Azimuthal blade spacing
Blade solidity =
Reynolds number,
Inducer hub radius, m
Inducer tip radius, m
Mean blade height, m
Mean blade height, m
Blade angle evaluated with respect to the normal to the axial direction.
Design conditions
Tip radius
Leading edge
Trailing edge
Vapor pressure
Upstream station
Downstream station.
The authors declare that they have no competing interests.
This study is supported by National Natural Science of China (nos. 51609107 and BK20160539), Jiangsu University Senior Personnel Scientific Research Foundation (no. 15JDG073). The present DAPROT3 experimental work has been carried out in Alta under ESA’s support (no. 4000102585/10/NL/Sfe).