Scientific description highlighting the results of the annual stage and the degree of achievement of the objectives

Abstract

This paper represents the deliverable of Phase I of the project "Research and Development of an Innovative Centrifugal Pump Design for Space Applications", funded through the National Plan for Research, Development and Innovation 2022–2027, PNCDI IV, 5.8 – European and international cooperation program, 5.8.3 – Bilateral/multilateral subprogram, complex bilateral projects with the Republic of Moldova, competition identifier: PN-IV-PCB-RO-MD-2024-0188.

The study presents the modeling and numerical analysis of a two-stage centrifugal pump, using SolidWorks for geometry generation and ANSYS CFX for performance evaluation. The rotor–stator geometry was built parametrically, including blade definition using Loft features and the configuration of the fluid domain required for simulation.

The results validate the numerical model and establish the comparison basis for the optimized geometry to be analyzed.

Introduction

Centrifugal pumps represent essential equipment in fluid engineering, being widely used in various industries such as water supply, chemical, energy, or petrochemical industries. Their operation is based on the conversion of mechanical energy supplied by the rotor into an increase in pressure and velocity of the fluid. The efficiency and hydraulic performance of pumps depend on the geometric parameters of the rotor, casing, and blades, as well as on operating conditions.

In recent decades, the development of digital design and simulation technologies has radically changed the way industrial equipment is conceived and analyzed. The evolution of computer-aided design (CAD) and computational fluid dynamics (CFD) analyses has enabled a much more detailed understanding of the behavior of these hydraulic machines, largely eliminating the need for costly experimental testing.

SolidWorks and ANSYS CFX are today two of the most widely used tools in this field. The former provides a robust three-dimensional modelling environment capable of accurately describing the complex geometry of a centrifugal pump, while the latter allows detailed analysis of internal flows, pressure distribution, and hydraulic losses. Recent studies in the literature show that integrating the two platforms significantly contributes to optimizing hydraulic performance, reducing energy consumption, and improving the durability of the mechanical assembly.

The first studies dedicated to the application of CFD methods in the analysis of centrifugal pumps appeared in the 1990s, but their truly significant development occurred after 2005, with the increase in computational power and the refinement of turbulence models. El-Emam, M. A. and collaborators (2022) provided one of the first comprehensive reviews on the development stage of numerical simulations for centrifugal pumps, highlighting the extremely complex nature of three-dimensional flows within them.

They showed that turbulence, recirculation effects, and the interaction between blades and the casing volute generate nonlinear velocity and pressure distributions that cannot be described by classical analytical methods. This type of analysis opened the way toward full integration of design and optimization stages using digital tools.

CAD modelling represents the essential starting point. SolidWorks, widely used in both academic and industrial environments, offers the capability to accurately model each component of the pump — from the rotor to the volute and the suction and discharge pipes.

In recent works, emphasis has been placed on obtaining a geometric representation that faithfully reflects the fluid flow and can be transferred without errors to the CFD analysis environment. The study by Cenci, G. and collaborators (2006) describes the process of designing an impeller in SolidWorks and the subsequent analysis in ANSYS CFX, aiming to optimize the blade angle to increase overall efficiency.

The authors showed that small modifications in the blade exit angle can lead to considerable variations in static pressure and pump flow rate, demonstrating the high sensitivity of the system to geometric parameters.

The CAD modelling process is not limited to the construction of the solid volume. In order to perform a correct CFD analysis, the researcher must generate the so-called fluid domain, meaning the volume actually occupied by the liquid during pump operation.

This involves defining internal surfaces, cleaning the geometry of unnecessary details, and preparing a model that can be efficiently discretized. Any imperfection at this stage can lead to major numerical errors in CFD simulation.

SolidWorks offers the advantage of an intuitive interface and the possibility of exporting in standard formats (STEP, IGES) compatible with ANSYS Workbench, facilitating a clean transfer of the model between the two platforms.

An essential aspect highlighted in the literature is the influence of the turbulence model on simulation accuracy. The k–ε and k–ω SST models are the most commonly used, each having specific advantages and limitations.

The k–ε model, for example, is stable and fast, but tends to underestimate velocity gradients near walls. In contrast, the k–ω SST model provides a more accurate prediction of flow in the boundary layer, but is more sensitive to boundary conditions.

The choice of the appropriate model depends on the purpose of the study and the level of detail required. In general, for standard centrifugal pumps, the k–ω SST combination has become preferred due to the balance between accuracy and numerical stability.

Once boundary conditions are established and the mesh is generated, the simulation can provide a complete picture of velocity and pressure fields. Thus, researchers can observe recirculation zones behind blades, low-pressure regions susceptible to cavitation, or flow variations in the casing volute.

The study by Derakhshan et al. (2013) mentions that the impeller is the component with the greatest influence on the overall performance of the pump, and its optimization through CFD can lead to efficiency increases of up to 10%. This finding confirms the importance of numerical analysis as a geometric optimization tool.

Another relevant example is the study by Bellary, S. A. I., and Samad, A. (2014), who conducted a parametric study on impeller geometry, varying the blade exit angle and the trailing edge shape.

Their results showed that small adjustments of these parameters can lead to significant improvements in hydraulic efficiency. In addition, it was observed that the volute shape plays a crucial role in converting kinetic energy into pressure energy, and mismatches between the volute cross-sections and the flow direction can generate additional losses.

The integration between CAD and CFD represents, beyond the technical aspect, a paradigm shift in the engineering design process. If in the past CAD models were viewed only as geometric representations, today they become “intelligent” models, directly connected to performance analyses.

When a designer modifies a rotor dimension in SolidWorks, the effect can be observed almost instantly in the CFD simulation, due to the bidirectional interface between the two applications. This integrated approach allows rapid development of multiple design versions and the selection of the optimal one based on multiple criteria, such as efficiency, cost, and dynamic stability.

A concrete example of applying this methodology is provided by the research team led by Faisal, A. R. (2021), who combined CFD analysis with structural analysis using the finite element method (FEM) for a standard centrifugal pump.

They used SolidWorks for 3D modelling, ANSYS CFX for hydrodynamic simulation, and ANSYS Mechanical for evaluating structural stresses on the blades. Their study demonstrates the benefit of integrating geometric modelling, fluid analysis, and mechanical analysis, resulting in a complete understanding of system behavior.

This hybrid approach is increasingly encountered in the literature and reflects the current trend of treating the centrifugal pump not only as a hydraulic system, but as a complex fluid–structure assembly.

The evolution of software, the increase in computational capacity, and the growing accessibility of these technologies open wide possibilities for researchers and engineers. Currently, a complete pump model can be built and virtually tested in just a few hours, a process that previously required weeks of design and physical testing. Moreover, CFD simulations provide information impossible to obtain through direct measurements — for example, pressure distribution on each blade surface or local fluid velocity in the corners of the volute.

The literature analysis also suggests several future research directions. One of these is the use of artificial intelligence and genetic algorithms for automatic optimization of impeller geometry. Parametrically generated CAD models can be automatically modified according to defined objectives (for example, maximizing efficiency or minimizing losses), and CFD simulations can evaluate the performance of each variant. This iterative loop, supported by high-speed computing, promises to revolutionize pump design. Additionally, combining CFD with vibration and noise analysis opens new perspectives on acoustic comfort and equipment durability.

The present report aims to document the CAD modeling process of a centrifugal pump using SolidWorks and the CFD analysis of the initial geometry in ANSYS CFX, in order to determine hydraulic performance such as flow rate, head, and efficiency.

Thus, the report will detail both the stages of CAD model construction, as well as the preparation and execution of CFD simulations, interpretation of results, and discussion of the hydraulic performance of the initial geometry.

CAD modeling of the centrifugal pump

Centrifugal pumps operate based on the principle of transforming the mechanical energy of the impeller into kinetic energy and pressure of the fluid. The fluid enters the impeller axially and is accelerated radially by the motion of the blades, exiting into the casing with increased velocity. The kinetic energy of the fluid is then converted into pressure through the casing and diffuser, according to the Bernoulli equation:

P+1/2 ρv^2+ρgh="constant" (1)

The hydraulic efficiency of the pump is given by the relation:

η_h=ρgQH/P_mec (2)

A standard centrifugal pump includes the following elements:

• impeller – the rotating component that imparts velocity to the fluid. Types of impellers include: open, semi-open, and closed;
• casing – collects the fluid from the impeller and directs the flow toward the outlet. The volute shape helps convert velocity into pressure;
• blades – their profile and angle determine flow rate and head characteristics;
• shaft – transmits torque from the motor to the impeller, supported by bearings;
• seals and gaskets – prevent fluid leakage and the ingress of impurities.

The main parameters defining the performance of a centrifugal pump are: Volumetric flow rate (Q) – the amount of fluid pumped per unit time; Head (H) – the total energy difference between inlet and outlet, expressed in meters; Efficiency (η) – the ratio between useful energy transferred to the fluid and mechanical energy absorbed by the impeller; NPSH (Net Positive Suction Head) – an indicator of cavitation risk.

Centrifugal pumps can be classified according to several criteria: impeller geometry: radial, semi-axial, axial; number of stages: single-stage or multi-stage; operating conditions: for clean liquids, viscous liquids, or suspensions. Their application fields include: water supply, chemical and petrochemical industry, energy generation, HVAC, and industrial cooling systems.

For this study, a standard two-stage centrifugal pump with closed impellers was selected, used in general industrial applications. The main geometric parameters are presented in the table below.

Table 1 – Geometric parameters for the initial pump

The computer-aided three-dimensional modeling was carried out using the SolidWorks 2024 platform, with the main purpose of generating and rigorously defining the flow domains required for the subsequent stages of numerical simulation in ANSYS CFX. The modeling process included the construction of the functional geometry of the internal pump components, the definition of fluid boundaries, as well as the creation of surfaces and volumes to be discretized for CFD analysis. This preliminary stage is essential, as the accuracy of the flow domains directly influences the quality of the numerical solutions and the reliability of the conclusions obtained during the simulation phase.

Within this first stage, a detailed evaluation of the performance of the classical two-stage centrifugal pump configuration was pursued, considered as the benchmark for the present study. This conventional solution was analyzed from the perspective of its hydraulic characteristics, fluid dynamic behavior, and overall efficiency, in order to establish a solid and objective comparison baseline. The results obtained from the simulation of the traditional pump will subsequently serve as a reference against which the new pump concept developed in this project will be investigated and validated, allowing the highlighting of performance improvements, identification of constructive advantages, and confirmation of the technological benefits that the new geometry may provide.

The CAD modeling process of the two-stage centrifugal pump in SolidWorks was structured in such a way as to allow the clear definition of the three main components – the first-stage impeller, the stator acting as an intermediate guiding element, and the second-stage impeller. At this stage, the final volute was not modelled, as the focus was placed on developing the internal hydraulic block required for analyzing the flow between stages.

The modeling began with the construction of the skeleton of the first-stage impeller, by defining the characteristic diameters and blade thickness, fundamental elements for establishing the hydraulic architecture. Once the geometric layout was defined, the number of blades was configured using the Circular Pattern function, ensuring uniform distribution around the rotation axis and maintaining functional symmetry. The same principle was subsequently applied to the second-stage impeller in order to maintain geometric consistency between the two stages.

Performing the CFD numerical calculation for determining the performance of the initial geometry

The Reynolds-Averaged Navier-Stokes (RANS) formulations together with the corresponding turbulence models are very useful especially for the “rapid screening” of a large number of cases or configurations in Computational Fluid Dynamics (CFD). The steady-state RANS technique is the preferred method in industry for analyzing turbulent flows due to the large number of configurations that can be simulated in a short period of time, identifying trends in flow behavior.

Within the RANS method, two-equation turbulence models are the most widely used. The most popular two-equation model is the standard k–ε model, which is robust, fast, and provides reasonable accuracy for a wide range of turbulent flows. Another two-equation model is the standard k–ω turbulence model, based on Wilcox’s k–ω formulation with two transport equations for k and the specific dissipation rate (ω).

An improved turbulence model is the SST k–ω model:

█(∂k/∂t+u ̅ ∂k/∂x+v ̅ ∂k/∂x+w ̅ ∂k/∂x=@=Γ_k ((∂^2 k)/(∂x^2 )+(∂^2 k)/(∂y^2 )+(∂^2 k)/(∂z^2 ))+G ̃_k-Y_k@∂ω/∂t+u ̅ ∂ω/∂x+v ̅ ∂ω/∂x+w ̅ ∂ω/∂x=@=Γ_ω ((∂^2 ω)/(∂x^2 )+(∂^2 ω)/(∂y^2 )+(∂^2 ω)/(∂z^2 ))+G_ω-Y_ω+D_ω ) (3)

Using the commercial CFX solver (ANSYS, Inc.), the two-equation turbulence model (SST k–ω) was employed to investigate the flow in a classical two-stage centrifugal pump design. The geometry of this case is presented in the figure below.

The target for the final mesh size was approximately 1.8 million cells for all domains, with a number of elements along the blade height of 50. The first near-wall cell size was defined to achieve a y+ value on the order of unity at the first point away from solid walls.

At the inlet, the total pressure was set to p_in = 1 atm, while at the outlet, the mass flow rate was imposed for all sectors, Q̇ = 36.11 kg/s, and a monitoring point was set at the inlet with this variable to verify convergence of the numerical solution.

The walls (blades, hub, and casing) were defined with slip condition, and a rotational speed of 2950 RPM around the Z axis was imposed. Turbulence at the inlet and outlet was set to a medium intensity equal to 5%.

The boundary conditions for this case are presented in Figure 14.

A three-dimensional CFD analysis was performed on a single passage using water as the working fluid. The results of this numerical investigation will be used in a comparative study between the classical pump configuration and the new design developed within this research project.

Figure 15 presents the streamlines in a blade-to-blade view at 50% of the blade height. It can be observed that no recirculation zones are developed that could influence pump performance.

The analysis of the total pressure variation obtained through CFD simulation in ANSYS CFX confirms the proper operation of the two-stage centrifugal pump, highlighting two distinct pressure increases characteristic of each rotor–diffuser stage. The total pressure increases progressively from inlet to outlet, with significant jumps in the regions corresponding to the stages, followed by short stabilization sections between them. The final pressure value at discharge remains nearly constant, indicating a stable flow regime and efficient conversion of kinetic energy into pressure energy. The results confirm the consistency of the pressure distribution with the operating principles of multistage pumps and support the validity of the numerical model used.

Figure 17 presents the variation of total pressure along the flow direction, from inlet to outlet, in a classical two-stage centrifugal pump analyzed through CFD simulation using ANSYS CFX. The vertical axis represents total pressure, while the horizontal axis represents the streamwise position corresponding to the fluid path through the pump.

The pressure distribution highlights the characteristic behavior of a multistage pump:

1. Inlet region (0 – ~0.4) The pressure remains almost constant, at a relatively low value, representing the hydraulic conditions in the inlet diffuser. No significant pressure increase is observed, indicating stable flow before entering the first-stage impeller.
2. Pressure increases in the first stage (0.4 – ~1.0) In this region, a rapid and substantial increase in total pressure occurs, corresponding to the conversion of kinetic energy into pressure energy within the first-stage impeller and its associated diffuser. This pressure rise is typical for high-efficiency radial stages.
3. Inter-stage / stabilization region (1.0 – ~2.0) After the diffuser of the first stage, the pressure oscillates, with a slight downward trend. This region usually corresponds to the intermediate zone between stages, where losses due to recirculation or local velocity redistribution may occur.
4. Pressure increases in the second stage (2.0 – ~2.8) The graph shows a second major increase in total pressure. This reflects the operation of the second-stage impeller and the reconversion of hydraulic energy.
5. Discharge region (2.8 – 3.1) The total pressure stabilizes around maximum values, indicating the final regime at the pump outlet and confirming the cumulative effect of the two stages.

Conclusions

The conducted study had as its main objective the evaluation of the hydraulic performance of a two-stage centrifugal pump through the integration of CAD modeling in SolidWorks and CFD numerical simulation in ANSYS CFX. The performed analysis confirmed the importance of using modern digital tools in the design and optimization of turbomachinery, demonstrating that the CAD–CFD approach provides a detailed and accurate picture of internal flow behavior, inaccessible through classical experimental methods.

The three-dimensional modeling performed in SolidWorks allowed obtaining a rigorous geometry for the key components — the first-stage impeller, the intermediate stator, and the second-stage impeller — as well as the correct definition of the fluid domain required for simulation. Geometry validation and interference control ensured compatibility with the ANSYS CFX numerical environment, contributing to the generation of a high-quality discretization mesh with approximately 1.8 million cells and parameters suitable for turbulent flows in turbomachinery.

The CFD simulations carried out using the SST k–ω turbulence model highlighted a stable flow regime, without significant recirculation zones, confirming the proper design of the hydraulic channels. The evolution of total pressure along the flow direction indicates two distinct increases corresponding to the efficient operation of each rotor–stator stage.

Overall, the analyzed numerical model demonstrates that the classical two-stage centrifugal pump geometry exhibits robust hydraulic behavior, with velocity and pressure distributions consistent with theoretical principles and literature data. This study establishes a solid basis for comparison with the new design proposed in the project, the results obtained here serving as a benchmark for evaluating efficiency improvements, loss reduction, and flow optimization in future configurations.

By integrating CAD and CFD stages, the report confirms the value of modern digital processes in the development of hydraulic equipment, providing a fast, reliable, and efficient tool for the design, optimization, and validation of centrifugal pumps.

Summary of progress

By implementing Phase 1 of the project “Research and Development of an Innovative Centrifugal Pump Design for Space Applications”, the partial deliverable provided in the work plan was achieved. In this regard, the following activities were carried out:

• T1.1 – Design of the innovative pump concept;
• T1.2 – Optimization of the model using neural networks and genetic algorithms (GA);
• T4.1 – Project management;
• T4.2 – Dissemination activities.

Regarding the achievement of indicators, it is noted that during the period 20.10.2025 – 03.11.2025, a team of researchers from the Republic of Moldova carried out a visit to the headquarters of the National Research and Development Institute for Gas Turbines – COMOTI, in Bucharest, Romania.

The team of the Technical University of Moldova consisted of:

• Andrei PETCO, Scientific Researcher Grade II
• Marin GUȚU, Scientific Researcher Grade II
• Andrei GHEORGHIȚĂ, Scientific Researcher Grade III

The main purpose of this visit was to establish the initial geometric parameters of the centrifugal pump and to initiate the design process. During the internship, extensive knowledge transfer activities took place regarding the use of software tools and the methodology for preliminary sizing of pump components, according to the practices of COMOTI specialists.

The software tools used include:

• SolidWorks, for 3D modeling of components,
• ANSYS CFD, for numerical flow analysis and determination of hydraulic performance of pump configurations.

Starting from the initial preliminary sizing, point files (XYZ format) describing the geometry of rotor and stator components were generated. These files were subsequently imported into the 3D modeling software to define the flow channel.

For mesh generation, ANSYS Turbogrid was used, and boundary conditions were defined in ANSYS CFX. At the end of the internship, a numerical simulation of the flow through the initial configuration of the two-stage centrifugal pump was performed, consisting of the first-stage impeller, intermediate stator, and second-stage impeller.

As part of the dissemination activities of this phase, the project website was developed and published, available at the address:

https://comoti.ro/reedited-cercetare-si-dezvoltare-a-unui-design-inovator-de-pompa-centrifugala-pentru-aplicatii-spatiale/

Executive summary of the activities carried out during the implementation period (max. 1 page)

The paper presents the results of Phase I of the project “Research and Development of an Innovative Centrifugal Pump Design for Space Applications”. The study analyzes the hydraulic performance of a two-stage centrifugal pump using an integrated CAD–CFD approach based on three-dimensional modeling in SolidWorks and numerical simulation in ANSYS CFX.

Centrifugal pumps, essential in industrial applications such as water supply, energy, and petrochemicals, operate based on the conversion of mechanical energy of the impeller into pressure and kinetic energy of the fluid. Their performance depends significantly on the geometry of the impeller, blades, and volute, and the development of digital technologies has enabled detailed investigation of internal flows that cannot be captured through analytical methods.

SolidWorks was used for complete modeling of the pump geometry, including the first-stage impeller, intermediate stator, and second-stage impeller. For each component, functional dimensions, hydraulic angles, and blade profiles were defined using specific features such as Loft and Circular Pattern. The resulting model was verified to eliminate intersections or discontinuities, ensuring compatibility with the simulation stage. Subsequently, the geometry was exported in STEP format for generating the flow domains in ANSYS Workbench.

The CFD analysis was performed in CFX using RANS formulations and the SST k–ω turbulence model, selected for its balance between accuracy and stability in predicting turbulent flows in turbomachinery. The fluid domain was discretized in TURBOGRID, generating a mesh of approximately 1.8 million cells, with a sufficient number of elements along blade height and an appropriate y+ value in the near-wall region. Boundary conditions included total pressure at inlet, mass flow rate at outlet, and a rotational speed of 2950 rpm imposed on the impellers, while walls were treated with slip condition.

Simulation results indicated stable flow without significant recirculation zones, demonstrating correct geometric design. Streamlines and meridional pressure distributions confirmed proper operation of both stages. The analysis of total pressure variation along the flow direction revealed two distinct increases, typical of multistage pumps: a first pressure rise in the first-stage impeller, followed by an inter-stage transition zone, then a second increase in the second stage. Pressure stabilization in the discharge region indicates a robust and efficient hydraulic regime.

The study confirms that integrating CAD and CFD stages allows obtaining an accurate picture of the internal behavior of centrifugal pumps, significantly reducing the need for physical testing and providing a rapid geometric optimization tool. The analyzed classical model constitutes a solid reference for evaluating the future design proposed in the project, offering relevant data on pressure distribution, fluid velocity, and hydraulic efficiency. The adopted digital approach demonstrates the potential of modern design methods for increasing efficiency and reducing hydraulic losses in turbomachinery.