Optimization of Medical Injection Pump Nozzle Structure Based on CFD

Medical injection pumps are widely used in clinical settings for drug delivery and treatment. As one of the core components of medical injection pumps, the nozzle directly affects the injection speed, uniformity, and stability of the drug solution during the injection process. With the current development trend of medical technology, an increasing number of drug treatment plans rely on medical injection pumps to precisely control the delivery speed and dosage of drugs. The shape of the nozzle outlet cross-section has the greatest influence on the injection velocity, followed by the contraction angle, while the length of the nozzle outlet cross-section has the least impact. In practical applications, such as medical water jet technology, nozzles with a conical-straight structure are more suitable. When the cone angle is 30°, the jet dynamic pressure is most stable, and energy loss is minimal. However, traditional medical injection pump nozzle structures often suffer from unreasonable flow channel design and non-optimized nozzle shapes, leading to issues such as unstable drug solution flow and large pressure fluctuations. These problems affect the accuracy and stability of drug delivery and may even have adverse effects on patient treatment outcomes. Therefore, optimizing the structure of medical injection pump nozzles can effectively improve the injection precision and stability of drug solutions, enhancing the accuracy and safety of drug therapy.

CFD has been widely applied in nozzle design and optimization as a powerful numerical simulation tool. By simulating the internal flow field of the nozzle, the influence of different structural parameters on the injection performance can be quantitatively analyzed, guiding the structural optimization of the nozzle. Adjusting parameters such as the contraction angle, outlet diameter ratio, and outlet rectification section length can effectively improve the injection performance of the nozzle. In recent years, significant progress has been made in CFD-based nozzle structure optimization research. By adopting optimization algorithms such as the response surface methodology, the working efficiency of the nozzle can be further improved while ensuring its performance. Furthermore, considering the special requirements of specific application scenarios, such as the application of cavitation nozzles in enhancing jet cleaning effects, new ideas for nozzle design have been provided.

Given this background, this paper will systematically review the basic principles of nozzle design by comprehensively analyzing existing literature and research results. The current application status of CFD in nozzle design will be summarized, and a scientific and reasonable structural optimization scheme for medical injection pump nozzles will be proposed based on their characteristics. It is hoped that this research will provide theoretical support and practical guidance for the development of medical injection pump technology, bringing safer and more effective treatment options to patients.

2

State of the art

With the continuous development and maturation of CFD technology, it has become an effective tool for studying fluid mechanics problems and optimizing fluid devices. In the biomedical field, researchers have begun to rigorously validate their CFD models through comparisons with in vitro [1-4], in vivo [5,6], or clinical data [7,8]. Sankaran et al. [9] employed a stochastic collocation method for uncertainty quantification in cardiovascular simulations, applying it to sample problems such as abdominal aortic aneurysms and both idealized and patient-specific Fontan surgery scenarios. Schiavazzi et al. [10] utilized uncertainty quantification techniques to predict clinical outcomes in single-ventricle shunt surgery, determining the input parameters of their CFD model (e.g., pulmonary artery pressure and flow split ratio) and associated uncertainties using an inverse problem approach based on preoperative clinical data. They then propagated the uncertainties in the input parameters to the CFD outputs (pressure, velocity, and wall shear stress) using sparse grid stochastic collocation. Similarly, Tran et al. [11] employed a Monte Carlo sampling method to investigate coronary artery stenosis, quantifying the uncertainty in patient-specific hemodynamic parameters like time-averaged wall shear stress (TAWSS) and oscillatory shear index (OSI) based on fluctuations in noninvasively measured clinical input data. A few other research teams have also used similar types of uncertainty quantification methods for cardiovascular and intracranial aneurysm modeling [12-14]. Li Zhen et al. [15] used a two-dimensional axisymmetric model for modeling and simulation. They conducted numerical simulations of nozzle jets using the single-factor control method and found that the contraction angle, aspect ratio, contraction section length, and nozzle diameter of the nozzle can all have significant effects on the jet flow field. Regarding injection effects, Chen Bo et al. [16] used the CFD method to simulate the entire process of jet injection by a needle-free injector. They obtained the results of jet penetration and diffusion under the skin at different velocities, which agreed well with experimental results. Yu C et al. [17] conducted experimental analyses on needle-free injectors with different stagnation pressures and found that when the stagnation pressure reached 24 MPa, the drug solution could reach the subcutaneous layer but not enter the muscle layer. When the stagnation pressure reached 32 MPa, the drug solution could enter the muscle layer, and the injection depth increased with increasing stagnation pressure. In summary, the injection effect of needle-free injectors is related to the nozzle structure and its geometric parameters.

CFD technology can be used to accurately simulate and analyze the internal flow field of medical injection pump nozzles, revealing the motion patterns and pressure distribution of fluids inside the nozzle. This provides a reliable theoretical basis for the optimization and design of nozzle structures, not only improving the performance and stability of the nozzle but also providing important technical support for the research, development, and clinical application of medical injection pumps.

3

Methodology

3.1

Nozzle model

The structure of a traditional medical injector is shown in Figure 1. Traditional designs often fail to fully consider the challenges posed by the characteristics of different drugs and individual patient differences, limiting the applicability of the nozzle and potentially leading to inaccurate and unstable drug delivery in certain situations [18]. Moreover, traditional designs often do not adequately consider fluid dynamics characteristics, resulting in non-uniform internal flow field distribution and unstable flow velocity in the nozzle. This affects the precision and controllability of drug delivery, causing fluctuations in the delivered drug amount and increasing the noise and vibration generated by the injection pump during the delivery process, which reduces the patient's treatment experience.

3.2

Establishment of the computational model

In this study, ANSYS FLUENT is used for flow field analysis. The main algorithm for fluid numerical simulation is to describe the expression of an incompressible liquid in a spatial rectangular coordinate system as the continuity equation: (1) $\frac{\partial ρ}{\partial t} + \frac{\partial (ρ v_{x})}{\partial x} + \frac{\partial (ρ v_{y})}{\partial y} + \frac{\partial (ρ v_{z})}{\partial z} = 0$ \[\frac{\partial \rho }{\partial t}+\frac{\partial \left( \rho {{v}_{x}} \right)}{\partial x}+\frac{\partial \left( \rho {{v}_{y}} \right)}{\partial y}+\frac{\partial \left( \rho {{v}_{z}} \right)}{\partial z}=0\]

Where: ρ represents fluid density;

t represents time;

v_x represents the velocity vector v in the x direction;

v_y represents the velocity vector v in the y direction;

v_z represents the velocity vector v in the z direction;

In the Reynolds-averaged equation, the velocity components are decomposed into time-averaged and fluctuating components: (2) $v_{i} = {\bar{v}}_{i} + v_{i}^{'}$ \[{{v}_{i}}={{\bar{v}}_{i}}+v_{i}^{\prime }\]

Where: v_i represents the velocity vector v in the i direction, ;

${\bar{v}}_{i}$ \[{{\bar{v}}_{i}}\] represents the time-averaged velocity component in the i direction;

$v_{i}^{'}$ \[v_{i}^{\prime }\] represents the pulsating velocity component in the i direction;

Substituting into the equation yields: (3) $ρ \frac{\partial \bar{u}}{\partial t} = - \bar{\nabla} p + μ {\bar{\nabla}}^{2} u + ρ \bar{g}$ \[\rho \frac{\partial \bar{u}}{\partial t}=-\bar{\nabla }p+\mu {{\bar{\nabla }}^{2}}u+\rho \bar{g}\] (4) $ρ \cdot \bar{u} = 0$ \[\rho \cdot \bar{u}=0\]

Directly solving the above equations would consume a large amount of resources. For solving the turbulence model of the above equations, the k-ω SST is suitable for solving this type of working condition for the internal flow field simulation of the injector. The k–ε equations are as follows:

k equation: (5) $\frac{\partial (ρ k)}{\partial t} + \frac{\partial (ρ k u_{i})}{\partial x_{i}} = \frac{\partial}{\partial x_{j}} [(μ + \frac{μ_{t}}{σ_{k}}) \frac{\partial k}{\partial x_{j}}] + G_{k} + G_{b} - ρ ε - Y_{M} + S_{k}$ \[\frac{\partial (\rho k)}{\partial t}+\frac{\partial \left( \rho k{{u}_{i}} \right)}{\partial {{x}_{i}}}=\frac{\partial }{\partial {{x}_{j}}}\left[ \left( \mu +\frac{{{\mu }_{t}}}{{{\sigma }_{k}}} \right)\frac{\partial k}{\partial {{x}_{j}}} \right]+{{G}_{k}}+{{G}_{b}}-\rho \varepsilon -{{Y}_{M}}+{{S}_{k}}\] equation: (6) $\frac{\partial (ρ ε)}{\partial t} + \frac{\partial (ρ ε u_{i})}{\partial x_{i}} = \frac{\partial}{\partial x_{j}} [(μ + \frac{μ_{t}}{σ_{k}}) \frac{\partial ε}{\partial x_{j}}] + C_{1 ε} \frac{ε}{K} (G_{k} + C_{3 ε} G_{b}) - C_{2 ε} ρ \frac{ε^{2}}{k} + S_{ε}$ \[\frac{\partial (\rho \varepsilon )}{\partial t}+\frac{\partial \left( \rho \varepsilon {{u}_{i}} \right)}{\partial {{x}_{i}}}=\frac{\partial }{\partial {{x}_{j}}}\left[ \left( \mu +\frac{{{\mu }_{t}}}{{{\sigma }_{k}}} \right)\frac{\partial \varepsilon }{\partial {{x}_{j}}} \right]+{{C}_{1\varepsilon }}\frac{\varepsilon }{K}\left( {{G}_{k}}+{{C}_{3\varepsilon }}{{G}_{b}} \right)-{{C}_{2\varepsilon }}\rho \frac{{{\varepsilon }^{2}}}{k}+{{S}_{\varepsilon }}\]

In equations (3) and (4), G_k,G_b represent the generation terms of turbulent kinetic energy k caused by the mean velocity gradient and buoyancy, respectively; Y_M is the influence of compressible turbulence pulsation expansion on the total dissipation rate; C_1ε,C_2ε is an empirical constant; σ_k and σ_ε represent the Prandtl numbers that correspond to the turbulent kinetic energy k as well as dissipation rate ε, respectively; S_k and S_ε represent user-defined source terms; is the turbulent viscosity coefficient $μ_{t} = ρ C_{μ} \frac{k^{2}}{ε}$ \[{{\mu }_{t}}=\rho {{C}_{\mu }}\frac{{{k}^{2}}}{\varepsilon }\].

Therefore, this turbulence model is used for flow field solving in this study. The pressure-velocity solving algorithm adopts the SIMPLEC algorithm, which can quickly solve fluid pressure-velocity coupling problems. The discretization method uses the default second-order format, and the minimum residual for iteration is set to 10e-4. When there is no significant change in the residual, the calculation can be considered converged. The computational resources used are AMD Epyc 7532 two-node 64-core.

3.3

Mesh generation and boundary condition settings

In this study, FLUENT MESHING software is used for the structural optimization and flow field simulation of medical injection pump nozzles. FLUENT MESHING can efficiently generate high-quality mesh models. Its flexibility and powerful mesh generation capabilities enable it to accurately capture the complex structure of the nozzle, ensuring accurate and reliable flow field data during the optimization process.

The mesh parameters are shown in Table 1. The generated mesh system is shown in Figure 2, with three layers of boundary layer mesh encryption to improve the accuracy of flow calculations.

Table 1.

Computational mesh parameters

Mesh	Mesh quantity/10,000	Mesh orthogonal quality
(a) Conventional medical injection pump nozzle	2	0.78
(b) Small inclination angle injection pump nozzle	2.3	0.8
(c) Three-stage nozzle structure	3	0.76

Boundary condition settings: Inlet is the velocity inlet, set to 0.3mm/s. Outlet is the pressure outlet, set to atmospheric pressure of 0Pa. The remaining walls are set as Wall boundary conditions. The main parameters are shown in Tables 1-3.

Table 2.

Water parameters

Density/(kg/m³)	Surface tension/(N/m)	Viscosity/(Pa·s)
998.2	0.0719404	0.00298

Table 3.

Boundary conditions of the nozzle model

Inlet velocity/(m/s)	Turbulence intensity/%	Turbulent viscosity ratio	Initial total pressure/MPa	Contact angle/(°)	Inlet water volume fraction/%
0.3mm/s	2	10	20	70	100

3.4

Structural optimization

This study optimizes the structure of conventional medical injection pump nozzles, as shown in Figure 3. The dimensional data are mainly derived from the appearance of conventional injector nozzles. The key dimensions are the drug storage injection tube (Syringe) with an inner diameter of 20mm, the nozzle diameter of 3mm, and the internal transition angle of 120°.

Considering drug deposition and changes in fluid viscosity, empirical improvements are made to the nozzle structure to reduce local resistance to internal flow. Based on Figure 4, the transition angle of the internal cross-section of the injector is improved to 30°, which minimizes the local resistance to flow at this inclination angle. This makes the internal cross-section of the injector more streamlined, which is beneficial for flow from a fluid mechanics perspective.

However, since the flow on this inclined surface is a high adverse pressure gradient flow, if the drug solution is a highly viscous liquid, driving the injector requires more work, which is not conducive to the injection functionality. Therefore, this study adopts a three-stage stepped design, with a streamlined transition in the transition section, which helps reduce drug accumulation during the injection process and ensures smooth internal flow. This prevents backflow caused by cross-sectional changes in flow corners, which would prevent drug particles from being injected. The internal flow cross-sectional area of the injector undergoes a stepped change, combined with the transition of the cross-sectional change angle in Figure 4. The middle section adopts a zero-slope design to reduce the pressure gradient and internal flow resistance, which is beneficial for drug injection. The three-stage nozzle structure is shown in Figure 4, dividing the nozzle structure into a three-stage design, each with its unique functions and advantages. The first stage is mainly the drug storage area, and its design capacity can be adjusted according to the drug requirements to ensure that the drug does not settle due to insufficient capacity during the delivery process. The second stage is the drug transmission area, and its special structure enables stable drug delivery, reducing flow losses during transmission and drug accumulation in flow dead corners. The third stage is the injection acceleration area, designed to allow the drug to be rapidly injected into the body.

As shown in Figure 5, the first stage maintains the same dimensions as the structure in Figure 3. The transition to the second stage has a flow inclination angle of 57°, and the second stage has a length of 15mm. It then transitions to the third stage injection acceleration area with an inclination angle of 30°. These dimensions are adjusted based on actual sizes.

This study mainly focuses on optimizing the structure of the injector nozzle through fluid mechanics theory to achieve excellent internal flow characteristics, which is beneficial for drug injection and delivery. It provides a certain optimization design direction for the design of injectors.

4

Result Analysis and Discussion

In the design of the nozzle structure, two key indicators need to be considered: velocity residual and continuity residual. The velocity residual refers to the difference between the actual velocity and the theoretical velocity in the flow field. The continuity residual, on the other hand, refers to whether the continuity boundary conditions of physical quantities such as density and pressure are satisfied in the flow field. When these two residuals are stable and meet the design requirements, the nozzle structure can be considered to have reached a convergence state.

Simulation results reveal that conventional nozzle structures (as shown in Figure 6(a)) have lower flow velocities in the corners of their internal flow field, leading to the accumulation of drug molecules and hindering smooth injection. This may cause the drug to adhere to the wall, further resulting in nozzle blockage. Such blockage severely affects the precise control of drug delivery by the injector.

As shown in Figure 6(b), increasing the corner angle of the conventional nozzle brings significant optimization effects. Enlarging the corner angle is conducive to drug delivery inside the nozzle, reducing drug accumulation and waste in the corners. It also makes the velocity at the nozzle tip more uniform, improving the injectability of the injector.

To further enhance the performance of the injector, a three-stage injector is designed, and its velocity cloud diagram is shown in Figure 6(c). It not only inherits the advantages of the increased corner angle but also strengthens the flow field velocity at the nozzle tip. This is beneficial for enhancing the flow of drug particles inside the injector, indicating smoother drug delivery within the injector and further reduction of drug accumulation in the corners. By comparing the velocity cloud diagrams, it is evident that the innovative three-stage injector designed in this study outperforms traditional injectors in terms of drug delivery. The three-stage injector not only improves drug delivery efficiency but also reduces drug waste. This design makes the injector more precise during the drug delivery process, helping to improve the localization effect of the drug in the patient's body.

In the three-stage injector, after the fluid passes through the first and second contraction sections, as shown in Figure 7, according to the continuity equation, it can be seen that after two contractions and accelerations, the drug particles have good followability in the liquid and will not cause excessive drug particle accumulation. Therefore, this streamlined injector tip contour based on two interconnected nozzles is conducive to enhancing the flow of microparticles in the injector. The proposed injector design method based on the multi-stage concept can be applied to the design of similar drug delivery devices (e.g., needle-free injectors).

Although the streamlined tip of the injector largely optimizes the injection process and reduces the adhesion of drug particles during injection, the issue of particle adhesion zones is not completely resolved despite this design.

As shown in Figure 6(c), due to the relatively low velocity of the fluid near the injector wall, a velocity boundary layer is generated. Within this boundary layer, the fluid velocity is low, and the particle viscosity is high, leading to particle adhesion at the wall. This not only affects the injection effect of the drug but also impacts the accuracy of the drug dosage.

This study processes the flow velocity at the injection port using the average velocity processing method, as shown in Equation (7). The pressure gradient increases from the previous 5Pa/mm to 10Pa/mm.

(7)

\frac{\oint s_{v} d s}{s} = \bar{v}

\[\frac{\oint _{s}^{v}ds}{s}=\bar{v}\]

In Equation (7), S is the outlet cross-sectional area; V is the velocity; and $\bar{V}$ \[\bar{V}\] is the average outlet flow rate.

As shown in Table 4, it can be found that the injection port velocity of the (c) three-stage injector structure is far superior to the previous two nozzle structures, indicating that the three-stage nozzle design improves injection performance. The small inclination angle injection nozzle is also better than the traditional nozzle, demonstrating that designing the injector nozzle from a fluid mechanics perspective is correct.

Table 4.

Comparison of nozzle injection efficiency

Nozzle type	Nozzle outlet velocity (m/s)	Injection efficiency improvement
(a) Conventional nozzle	0.12
(b) Small flow inclination angle injection pump nozzle	0.14	16.67%
(c) Three-stage nozzle structure	0.18	50.00%

The tip of the injector needs to have a taper design, which can create a favorable pressure gradient during the injection process, thereby thinning the boundary layer. The thinning of the boundary layer means that the degree of drug particle adhesion at the wall is reduced, thus decreasing the adhesion phenomenon of drug particles.

Furthermore, this study analyzes the pressure gradient cloud diagram at the injection port, as shown in Figure 8. The pressure gradient at the injection port is significant, forming a clear Poiseuille flow pressure driving force. This part of the flow has a small Reynolds number and evident laminar flow effects, which are very beneficial for drug particle transport and injection.

5

Conclusion

Conventional nozzle structures have many issues, including unstable internal flow in the nozzle and uneven drug delivery, which directly affect the performance of the injection pump. These issues lead to inaccurate and unstable drug delivery and may even cause adverse treatment effects and safety hazards for patients.

Therefore, this study proposes an improved nozzle structure scheme and uses computational fluid dynamics simulation technology to verify and optimize it. The new nozzle structure is improved in terms of geometric shape and internal flow channel design to enhance the uniformity and delivery stability of the drug solution. Simulation results show that the improved nozzle structure can significantly reduce the turbulence level of the flow, improve the stability of the flow field, and make drug delivery more accurate and controllable. Finally, by comparing and analyzing the performance indicators of conventional nozzles and improved nozzles, the conclusion is drawn that the improved nozzle structure is superior to the conventional structure in terms of drug delivery effect and flow field stability.

In future work, a multi-objective optimization method will be adopted to comprehensively consider indicators such as the accuracy and stability of drug delivery and patient treatment comfort. A multi-objective optimization model will be established. By adjusting and optimizing the parameters of the multi-stage injector, it can achieve the best performance under different working conditions to meet the requirements of different clinical needs as well as personalized patient treatment.

Język:: Angielski

Częstotliwość wydawania:: 1 razy w roku
Dziedziny czasopisma:: Nauki biologiczne, Nauki biologiczne, inne, Matematyka, Matematyka stosowana, Matematyka ogólna, Fizyka, Fizyka, inne

Kanał RSS czasopisma

Optimization of Medical Injection Pump Nozzle Structure Based on CFD

Chao Xie

Data publikacji: 17 mar 2025

Otrzymano: 04 paź 2024

Przyjęty: 31 sty 2025

DOI: https://doi.org/10.2478/amns-2025-0838

Słowa kluczowemedical injection pump nozzle, computational fluid dynamics, optimization calculation

© 2025 Chao Xie, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Słowa kluczowe
medical injection pump nozzle, computational fluid dynamics, optimization calculation