Low Pressure Region Research Articles

Explosion limits of binary mixtures of ammonia and additives (hydrogen, natural gas, and diethyl ether)

This study investigates the explosion limits of ammonia (NH3) and the effect of three different active fuels, hydrogen (H2), natural gas (NG), and diethyl ether (C2H5OC2H5, DEE), on the explosive characteristics of NH3 through comprehensive chemical kinetics analysis. The results reveal that the explosion limits of NH3 exhibit the narrowest explosive range and display comparatively weakest explosive reactivity among the four fuels, presenting a monotonic changing trend. Reaction pathway analysis unveils that with increasing temperature, NH2 tends to oxidize more predominantly through the NH-N2H2-NNH-N2 pathway, while the conversion of NH2 to H2NO pathway decreases. Therefore, the introduction of active fuels significantly enhances the explosive reactivity of NH3. However, their impact under various temperature-pressure conditions presents nuanced and diversified characteristics. When a 0.5 % mole fraction of active fuel is added to NH3, DEE exhibits the most significant enhancement in medium to high-pressure conditions, while H2 predominates at low pressure, with NG consistently demonstrating the least pronounced enhancement. Upon the active fuel proportion being increased to 20 %, the promoting effect of DEE remains the most significant in the medium to high-pressure region, while NG has surpassed H2 as the secondary dominant fuel. In the low-pressure region, NH3-H2 still demonstrates the highest reactivity, followed by NH3-DEE, while NH3-NG exhibits the least reactivity. These findings provide valuable insights into the widespread utilization and scientific exploration of ammonia as a fuel source.

Simulating the Rising Air Bubbles Stream through Heavy Fuel Oil Residue Bubble Column Reactor using COMSOL

Several industrial operations rely on the rise of air bubbles through heavy fuel oil residue (HFOr), including oil recovery and wastewater treatment. In order to increase efficiency and decrease expenses, it is necessary to understand the peculiarities of this process. With the help of COMSOL Multiphysics, we numerically simulate the ascent of a single air bubble via HFOr in this article. The dimensions of the container used in the simulations were (100) mm in diameter and (200) mm in height, with an air bubble diameter of 4.5 mm. For an air bubble ascending through an HFOr column, the predicted numerical outcomes are contrasted with nine experimental versions. As the bubble rose higher, the region with the greatest number of vortices was located on its side. The remaining vortex is contained inside the bubble. In addition, since drag decreases the flow, a lighter fluid usually exhibits a region of strong vortex and low pressure. Because of the oscillation effect, the results reveal that the rising velocity initially rises and then gradually falls between 0.6 and 0.65 s. The air bubbles' wavy motion is caused by the high fluid density, which becomes worse as the air velocity gets higher. The values of the drag coefficient rise sharply with decreasing air extrusion speed. It turns out that the height of the fluid has an inverse relationship with the pressure.

Flame propagation, explosion hazard, and pollutant emission characterization of typical clean fuels leaks in plateau low-pressure region

To accelerate energy transformation and sustainable development, various countries are rushing to lay hydrogen doped natural gas pipelines. However, the installation of pipelines will pass through plateau low-pressure region, and the impact of low-pressure environments on the flame propagation, explosion hazards, and pollutant emission characteristics of hydrogen doped natural gas is not yet clear. To solve this problem, a combination of constant volume combustion experiment and numerical simulations is used. The characterization parameters of flame, explosion and pollutant concentration of natural gas/H2/air under low-pressure environment are obtained, and their chemical reaction kinetics are analyzed. When the pressure drops, the laminar burning velocity (LBV) of them increases, and the Lewis number (Le) gradually increases by more than 1. Thermal diffusion is stronger than mass diffusion, and the growth rate of flame thickness exceeds 26 %. The effect of hydrodynamic instability enhances, causing an increment in the average size of flame cells, the critical instability radius, and the Markstein length (Lu). At the equivalent ratio (φ) of 1, there is a change from negative to positive in the Lu, and flame stability continuously strengthens. The explosion overpressure is reduced by 78 % to 90 %, the explosion temperature by 16 % to 20 %. As the φ increases, the LBV exhibits an inverted U-shaped relationship, reaching its maximum value near “φ = 1″. The flame stability first weakens and then strengthens. The explosion hazard is strongest in the range of ”φ = 1–1.2″. With a decrease in pressure, the total reaction rate of fuel consumption is reduced by more than 50 %. The continuous reaction distance is extended by 12 %. Changes in pressure have a relatively weak impact on the content of CO and CO2. The increase in the φ results in an increase in CO content of over 7 %. The content of CO2 reaches its maximum value around “φ = 1″. It is an essential reference for the safe delivery of hydrogen energy and the reduction of environmental pollution.

Coanda Effect Displayed in a Giant Intracranial Aneurysm.

The Coanda effect is a fluid dynamics phenomenon in which a fluid jet adheres to a convex or flat surface. This effect occurs when a liquid or gas jet emerging from an orifice clings to an adjacent surface and entrains the surrounding fluid, creating a lower-pressure region along its path that maintains its attachment to the surface. The Coanda effect accounts for the behavior of blood flow in the fetal right atrium and the dispersion of eccentric mitral regurgitation jets along atrial walls. This series of interesting images depicting a large 4 × 3.75 cm saccular intracranial aneurysm suggests that the Coanda effect may play a role in the pathophysiology of intracranial aneurysms and could be an underlying factor in their formation, progression, or rupture.

Exploring cavitation dynamics and noise reduction in hydraulic machinery with bionic leading edge impeller

Cavitation and induced noise are common issues in the operation of mixed-flow pumps, affecting their stability. Studying these phenomena is of both academic and engineering interest. Previous research has mainly focused on modifying the impeller blade profile or optimizing the pump structure to reduce cavitation and noise. In this paper, we apply a bionic design to the mixed-flow pump impeller by mimicking the natural shape of a humpback whale's pectoral fin on the leading edge of the blade. We compare the cavitation suppression and noise reduction effects of this design with those of a conventional mixed-flow pump. Unsteady flow calculations for the original pump at different flow rates revealed that at its rated speed, increasing flow rates led to lower pressure in the low-pressure region on the suction surface of the impeller, expanding the cavitation-prone area. By applying the bionic design, we studied the unsteady cavitation flow and its induced noise. Results showed that the impeller and guide vane experienced larger pressure pulsations at the rotation frequency and its multiples. The bionic modification increased the cavitation initiation speed and reduced the cavity volume within the runner. With an NPSH (net positive suction head) of 6.76, the void volume in the bionic pump was only 79% of that in the original pump, and the head increased by 16%. Additionally, the bionic design reduced the maximum far-field sound pressure level by 12.5%, achieving significant noise reduction. This study demonstrates that the bionic design effectively controls dynamic flow separation, reduces flow-induced noise, and enhances the mixed-flow pump's performance. These findings have important theoretical and practical implications for optimizing mixed-flow pump design, improving energy efficiency, and reducing noise.

Numerical investigation of vehicle water entry with angle of attack

This paper investigates the water entry of a vehicle with angle of attack (AOA) through numerical methods, employing the volume-of-fluid multiphase flow model and overset grid technique. The validity of the numerical model is confirmed through experimental verification. Building upon this, the study analyzes the motion characteristics, cavity evolution, and flow field distribution of the vehicle during water entry, considering the influence of AOA and falling velocity. Numerical findings indicate that the collapse of the right side of the cavity induces a transient lateral force on the vehicle, resulting in vehicle tilting. Moreover, an increase in initial velocity delays vehicle tilt, while an increase in AOA reduces vehicle motion stability, leading to earlier tilting. Initially, the vehicle rotates counterclockwise around the Oz axis of the projectile coordinate system. Subsequent to cavity collapse, the vehicle experiences an opposing moment, leading to a reduction in rotation speed and eventual rotation in the opposite direction. Water impact triggers sudden changes in the vehicle's lift and drag coefficients, while cavity sticking induces a minor abrupt change in the lift coefficient. Following cavity collapse, both lift and drag coefficients exhibit significant oscillations. Unlike typical cavity collapse phenomena, the flow field on the right side of the vehicle undergoes alternating high-pressure and low-pressure regions.

Spatial correlations and risk transmission of virtual water flow at city scale: A case study of the Yellow River Basin

By introducing virtual water (VW) flow correlation coefficients and risk indicators, this study examines the VW transmission relationship between urban agglomerations and cities in the Yellow River Basin (YRB) and its impact on regional water resources pressure. The results show that: except for the Shandong Peninsula Urban Agglomeration (SPUA) and Central Plains Urban Agglomeration (CPUA), the other urban agglomerations primarily act as VW exporting regions, while virtual water-importing cities are concentrated in the eastern regions. Notably, the Ningxia Urban Agglomeration (NUA) demonstrates significantly higher values in VW impact and sensitivity coefficients than the remaining six urban agglomerations. First-tier cities generally display lower virtual water impact and sensitivity coefficients, whereas emerging cities exhibit the opposite trend. Additionally, we observe uneven risk variations between VW importing and exporting regions. Taking NUA as an example, the risk increase resulting from VW exports significantly exceeds the risk reduction associated with VW imports in the corresponding regions. It's important to highlight that first-tier cities consistently decrease water resource risk through VW imports in both study years. However, among second and third-tier cities, only 38.9% experience reduced water resource risk through VW imports. Therefore, we recommend a focused examination of VW imports and exports in western region urban agglomerations, cities, and second and third-tier cities within the watershed. Leveraging virtual water's asymmetric and high-value transfer can alleviate water resource pressure and scarcity risks in high-pressure regions by shifting them to lower-pressure regions, thus mitigating water resource stress across regions.

A coordination polymer based on ionic-type ligand for efficient separation of C2H2/C2H4 and C3H4/C3H6 mixtures

C2–C3 alkyne/alkene adsorption and separation is a critical process in industrial production, but it remains challenging due to the similar size of gas molecules. Herein, based on an ionic-type ligand, a porous coordination polymer with inherent positive charged sites has been successfully constructed by 1D chains through non-conventional CH···O hydrogen bonds. The flexible framework shows adsorption ability for C2H2 while negligible adsorption of C2H4; and a much earlier steep increase for C3H4 isotherm compared to C3H6 isotherm in the low-pressure region. Ideal adsorbed solution theory further illustrated that the framework has the ability to separate C2H2/C2H4 and C3H4/C3H6 mixtures.

Analysis on the Influence of Duct Casing Geometry on the Performance of a Ducted Fan

This paper aims to evaluate the influence of an electric ducted fan’s (EDF) geometry on its performance through parameter correlation analysis. Sample data was first built by generating new EDF models with varying duct casing geometries through optimal space-filling (OSF) sampling method. Afterwards, each model was numerically solved with computational fluid dynamics (CFD) analysis to obtain each model’s thrust, required power, and efficiency. It is found that the casing’s inlet lip diameter displays the greatest influence on the EDF’s total thrust, as the inlet diameter determines the casing’s surface area affected by the low-pressure region ahead of the rotating fan blades. Additionally, it is found that length of the casing’s exhaust lip affects the EDF’s efficiency, while the exhaust lip diameter displays the highest correlation with the fan’s required power.

Dynamics of a single cavitation bubble near a cylindrical blind hole

Cavitation bubble dynamics, such as microjets and moving shock waves, are strongly influenced by their surroundings. We investigated the complex bubble behavior during the growth and collapse stages near a blind hole. The simultaneous study, which is a combination of experiment and numerical methods, was performed. The single bubble was induced by a laser focus beam near a blind hole in the cuvette and measured by a high-speed camera with an image processing method. Numerical predictions were conducted for a detailed further investigation of the pressure and velocity fields near and inside the bubble. A fully compressible two-phase Navier-Stokes solver based on the homogeneous flow assumption was used. Both experimental and numerical results showed good agreement with each other. Strong deformation of the bottom bubble surface evolution was observed at low standoffs above the hole entrance. An extremely high-velocity microjet with a mushroom cap-shaped bubble was predicted under high standoffs below the hole entrance. Secondary cavitation in the blind hole was observed experimentally, and we discussed the low-pressure region caused by the interaction among the shock wave, bubble, and blind hole. Consequently, the tendencies of maximum microjet velocity and time-dependent surface pressure in the collapse phase are suggested.

Direct Numerical Simulation of Tandem-Wing Aerodynamic Interactions at Low Reynolds Number

A three-dimensional direct numerical simulation was conducted to investigate the vortex–wing interactions through two NACA 0012 stationary wings placed in tandem at a low Reynolds number Re=10,000. The aerodynamic characteristics and three-dimensional flow structures were analyzed for the tandem wings. The back wing disturbed by the upstream vortices gained an evident increase in aerodynamic performance, where the advantage is related to the suppression of the large-scale vortex formation near the trailing edge. The Liutex method was applied to visualize the vortical structures for investigating the three-dimensional evolution and instability when interacting with the back wing. The upstream wake triggered dual-secondary vortices and intensified the secondary instability on the back wing. The induced vortices contributed to the lift enhancement because they provided an extra low-pressure region when propagating downstream on the suction side of the back wing. Because of the three-dimensional destabilization, the vortex interaction in the evolution process accelerated the transition and injection of the high-momentum flow into the boundary layer attached to the back wing, energizing the turbulent boundary layer and eliminating the large-scale separation near the trailing edge. This study provided a new perspective on the enhanced aerodynamic performance of tandem layout.

Effect of shape and thermal conductivity of microstructured capillary-porous coatings on heat transfer during evaporation and boiling in thin horizontal liquid layers

Investigation results on heat transfer during evaporation and boiling in thin horizontal liquid layers on 2D modulated capillary-porous coatings with a sinusoidal profile in a wide range of relative pressures and layer heights are presented in this paper. Coatings were made on a 3D laser printer using the technology of additive selective laser sintering (SLS). One coating was made of bronze with a modulation wavelength equal to the Laplace constant of the working fluid and two coatings were made of stainless steel and bronze with a doubled wavelength. The experimental data obtained on the coatings were compared with each other and with the values obtained by evaporation and boiling of n-dodecane on a smooth surface under the same conditions. It is shown that in the region of low relative pressures in liquid layers with a height less than the Laplace constant, heat transfer intensification achieved on a sample made of a material with low thermal conductivity (stainless steel) was five times higher as compared to a smooth surface. In the range of relative pressures, when nucleate boiling was observed in the layers, the temperature difference reached on the bronze coatings was approximately 3–4 times less than on a smooth surface. The temperature difference for the stainless steel coating changed little with an increase in the heat flux. In pre-crisis conditions, the temperature difference during boiling on the stainless steel coating was less than on the bronze coatings in the entire range of relative pressures and layer heights. The highest critical heat fluxes were obtained on a bronze coating with a modulation wavelength equal to the Laplace constant.

Sampling of plasma plume from atmosphere into vacuum for reliable Langmuir probe diagnostics

Langmuir probes cannot be used to diagnose cold atmospheric plasma jet, because their presence in the high electric field after-glow region modifies the plasma parameters that they are intended to measure. Here, we propose a system to sample the plasma plume from ambient conditions into a low-pressure region, where probe analysis can be accomplished. The effect of such a sampling process on the number density and velocity of the gas has been studied through simulations and using analytical equations. Simulation results regarding the effect of chamber and orifice dimensions on these parameters, have been presented. Based on this study an experimental chamber was fabricated and Langmuir probe analysis of the sampled plasma was done. Continuum flowing plasma theory was applied and the plasma density and electron temperature were estimated to be 1.8 × 1020m−3 and 4.7 eV respectively for the operating condition of 3 W plasma power at 12 kHz.

On-Site Characterization of Automotive Diffuser Aerodynamics by 3D LPT

This investigation proposes a novel LPT facility featuring Helium-Filled Soap Bubbles flow tracers, LED illumination and two high-speed cameras to characterize the dominating flow patterns within automotive underbodies. A remote control (RC) car model, fitted with custom-made floor and diffusers, traverses a region of seeded air following the Ring of Fire methodology. Underground-placed cameras view the car through a transparent panel, providing unparalleled optical access to the underbody of the car. The on-site measurement setup and the interaction between car model and ground enhance the realism and fidelity of the experiments, while potentially reducing testing costs associated with wind tunnel operation. The setup is shown to be a valid alternative to conventional testing approaches to capture flow separation, 3D flow evolution and differences in the flow field between the four tested configurations, whereby the diffuser angle was varied in the range between 5° and 20°. The 15° diffuser led to the largest velocity and pressure peaks under the car, whereas the 10° diffuser produced the most downforce thanks to the diffuser “pumping” effect, leading to a large region of low pressure under the vehicle. Notably, the 20° diffuser featured the most prominent flow separation at the diffuser’s leading edge, heavily affecting its ability to sustain low pressures under the car. The results show that the wide tyres have a major impact on the underbody flow, because their large wakes induce mass flow leakage through the sides of the car, thus disrupting the mechanism of downforce generation and impairing the generation of streamwise vortices.

Effect of Axial Clearance Variation on Dual-Rotor Flowmeter Performance.

This study examines the impact of axial clearance variations on the performance characteristics of a dual-rotor flowmeter (DRT-FM) through numerical simulations, with the validity of the numerical results verified by calibration experiments. The results indicate that within the range of 200 L/h to 1600 L/h, the K factors of different groups increase as clearance increases. The K factor of the 0.80 mm group is the largest, showing an average increase of around 6% compared to that of the 0.50 mm group. Additionally, Linearity E also decreased, with a minimum of 1.07% in the 0.65 mm group, significantly lower than the 3.33% in the 0.50 mm group. Furthermore, the pressure loss increased slightly, with the 0.65 mm group having the largest pressure loss; however, at a flow rate of 1600 L/h, the pressure loss only increases by 0.186 kPa compared to that of the 0.50 mm group. Flow field analysis reveals that changes in axial clearance predominantly affect pressure distribution. Larger clearances reduce low-pressure regions on upstream and downstream transition surfaces, thereby reducing energy loss due to pressure changes. Entropy analysis further demonstrates that higher axial clearance decreases energy loss in the upstream and downstream stationary domains, optimizing the DRT-FM's energy characteristics.

Optimal design of a combined Power-Heating-Oxygen system for plateau hotel buildings

The Qinghai–Tibet Plateau of China is a region of low atmospheric pressure and oxygen deficiency, with a high heating demand in the winter; therefore, plateau hotel buildings have a demand for comprehensive power-heating-oxygen loads. Solar energy resources are particularly abundant in plateau areas, where a combined multi-energy system based on solar energy can be designed to meet the demand of plateau hotel buildings for multiple loads. However, currently, there is a relative lack of methods for the optimal design and performance evaluation of combined power-heating-oxygen (CPHO) systems. Thus, this study proposes a CPHO system model for plateau hotels, and provides two operation strategies, i.e., power priority and oxygen priority. Taking the minimum total annual cost of the combined system as the optimization objective, an optimized CPHO system model for plateau hotels has been proposed, followed by a case study of a hotel in Qilian County, Qinghai Province. Results showed that: 1) Compared with the conventional combined power-heating (CCPH) system, the CPHO system saw reductions of 0.8% and 1.3% in its total annual cost under the operation strategies of power priority and oxygen priority, respectively. 2) The energy self-consumption (SC) rates of the CCPH system and CPHO system under the operation strategies of power priority and oxygen priority were 84.8%, 64.2%, and 89.8%, respectively; with power self-sufficiency (PSS) rates of 8.3%, 49.9%, and 29.5%, and oxygen self-sufficiency (OSS) rates of 0.0%, 3.2%, and 4.7%, respectively. 3) The total annual cost of the CPHO system was affected slightly by the cost of photovoltaics (PVs) and energy storage devices, and significantly by the price of oxygen. When the price of oxygen was 8 yuan per normal cubic meter(Nm3) or above, the CPHO system was economically efficient under the operation strategy of oxygen priority. When the price of oxygen was 10yuan/Nm3 or above, the system was economically efficient under both operation strategies.

Enhanced ammonia adsorption-desorption properties of synthesized zeolite-carbon composite with the effect of Si/Al ratio

Effective ammonia (NH3) adsorbent is crucial for removing undecomposed NH3 residue after splitting into N2 and H2 fuel. In this study, a zeolite-activated carbon (AC) hybrid was successfully synthesized with a trace AC amount and different Si/Al ratios via hydrothermal method. The NH3 adsorption–desorption properties and mechanisms were investigated through two major activity tests, employing high pressure adsorption isotherm analyzer and breakthrough set up. Incorporating AC at 1 wt%, effectively shortened the regeneration period of the pure zeolite by ∼50 % due to the AC’s pore-widening effect on zeolite network, reducing the trapping of adsorbed NH3 in the zeolite pores. Interestingly, an optimum Si/Al ratio of 1.6 led to the highest specific surface area of 977.57 m2/g by the formation of zeolite mixture with coexisting NaX (faujasite zeolite with high Al atoms per cell) and NaY (higher crystalline faujasite zeolite with low Al atoms per cell). These improved structural characteristics consequently exhibited the highest NH3 (99.9995 %) storage capacity of 15.6 mmol/g at a partial pressure of 300 kPa in isotherm analysis at 25 °C. Besides, the initial breakthrough adsorption capacity for dilute NH3 (5%/N2 balance) under atmospheric conditions reached 8.9 mmol/g, accurately equivalent to isotherm analysis result at 5 kPa. This reproducibility of consistent adsorption uptake within low pressure region in both tests was credited to the compositional presence of both acidic and alkaline surface functionalities in the optimum zeolite-AC hybrid as stable NH3 adsorption sites. These active sites also provided a uniform dynamic adsorption capacity of ∼4 mmol/g throughout 15 cycles. Conclusively, this work highlighted the importance of zeolite composition and AC-incorporated proportion for the H2 purification aspect.

Surface Pressure Measurement of Truncated, Linear Aerospike Nozzles Utilising Secondary Injection for Aerodynamic Thrust Vectoring

A cold-gas test campaign has been conducted at the DLR’s P6.2 test bench in Lampoldshausen, with the objective of investigating the linear aerospike nozzle flow in interaction with secondary injection thrust vector control (SITVC). In this campaign, the influence of nozzle truncation, injection position and injection pressure on the nozzle surface and base pressure is analysed using pressure probes and Schlieren flow-visualisation techniques. The effects of injection position and truncation on the nozzle surface pressure development are comparable for all geometric variations, resulting in a locally increased static pressure upstream and a locally decreased static pressure downstream of the injection. The magnitude and dimension of these high- and low-pressure regions are correlated with the injection pressure. However, the influence of injection position and truncation on the base pressure is not entirely predictable by the named parameters, indicating an interdependence between both geometric parameters. Finally, the required pressure ratio of injection to the primary flow to ensure sonic injection has been analysed on TUD’s cold-gas test bench. This allows the respective injection position-dependent threshold to be identified. The analysis reveals that these experiments have been conducted under transsonic injection conditions.

Experimental and numerical analysis of cavitator angle effects on artificial cavitation characteristics under low ventilation coefficients, with prediction using optimized random forest and extreme gradient boosting models

Artificial cavitation, a complex two-phase phenomenon, involves cavity formation by injecting air into a low-pressure region behind the cavitator. Influenced by factors like cavitator shape and angle, ventilation coefficient, etc., its understanding is crucial. While past research primarily focused on large ventilation coefficients, this study explores the impact of cavitator angles on ventilated cavity characteristics at low ventilation coefficients. For this purpose, three experimental, numerical and machine learning methods have been used. Initially, three angles (0°, 12.5°, 25°) were experimentally investigated across ventilation coefficients of 0.017–0.085. Additionally, through numerical simulations, the effects of increasing the cavitator angle up to 40° at small ventilation coefficients were explored. By optimizing random forest (RF) and Extreme Gradient Boosting (XGB) using Bayesian Optimization Algoritm (BOA), the cavitation characteristics under varying cavitator angles were predicted. The results show the appropriate accuracy of the BOA-XGB model compared to the RF model in predicting the characteristics of cavitation. Results indicate at very small ventilation coefficients, the shape of the cavity is not affected by the cavitator angle. However, with the increase of the ventilation coefficient, in addition to its value, the cavitator angle also affects the shape of the cavity. Increasing the cavitator angle under constant ventilation coefficient induces asymmetry in the cavity's end, elongates the cavity, and reduces the cavitation number.

Numerical and Experimental Analysis of Vortex Pump with Various Axial Clearances

Axial clearance is a critical parameter affecting the performance of vortex pumps. In this study, numerical simulation and experimental validation methods are employed to establish four different clearance schemes. The analysis focuses on multiple aspects, including the internal flow field, clearance flow field, leakage flow, and recirculation flow, to investigate the impact of axial clearance on the internal flow field and the external characteristics of the vortex pump. The results indicate that under the pressure difference between the inlet and outlet, the main flow leaks from the high-pressure region at the outlet to the clearance flow channel, and the clearance flow returns to the main flow channel at the low-pressure region of the inlet. As the axial clearance increases, the intensity of the vortices inside the pump gradually decreases. This leads to a reduction in intensity of the momentum exchange between the fluid inside and outside the impeller, causing a decline in the pump performance curve. Simultaneously, the increase in clearance reduces the flow resistance in the clearance region, and the clearance flow gradually stabilizes. The interaction between the clearance flow and the main flow intensifies, causing the leakage flow and recirculation flow to increase rapidly, which results in significant energy loss.