Inlet Section Research Articles

Experimental evaluation of isentropic efficiency in turbocharger twin-entry turbines

Turbocharging plays a fundamental role not only in improving the performance of automotive engines, but also in reducing the fuel consumption and exhaust emissions of spark-ignited biofuel, diesel, liquid, and gaseous engines. Dedicated experimental investigations on turbochargers are therefore needed to evaluate a better understanding of its performance. The availability of experimental information on the steady flow performance of the turbocharger is an essential requirement to optimize the matching calculation. It is interesting to know the isentropic efficiency of the turbine in order to improve the coupling with the engine, in particular it is difficult to identify the definition of the turbine efficiency through a direct evaluation. In a radial turbine, the isentropic efficiency, evaluated directly starting from the measurement of the thermodynamic quantities at the inlet and outlet sections, can be affected by significant errors. This inaccuracy is mainly related to the incorrect evaluation of the turbine outlet temperature, due to the non-uniform distribution of the flow field in the measurement section. For this purpose, a flow conditioner was installed downstream the turbine. Tests were performed at different values of the rotational speed, and in quasi-adiabatic conditions. The flow field downstream the de-coupler was analysed through a hand-made three-hole probe with an exposed junction thermocouple inserted in the pipe with different protrusions. Thanks to this experimental campaign, it was possible to measure pressure, velocity, mass flow and temperature profiles necessary to examine the homogeneity of the flow field. As the turbocharger is fitted with a twin entry turbine, the thermodynamic quantities have been properly taken into account referring to each sector.

Soot combustion characteristics of oxygen concentration and regeneration temperature effect on continuous pulsation regeneration in diesel particulate filter for heavy-duty truck

The effects of oxygen concentration and regeneration temperature on continuous pulsation regeneration of DPF (diesel particulate filter) for heavy-duty truck are crucial. The regeneration performance characteristics of the oxygen concentration of 7.2%, 8.2% and 9.4% and regeneration temperature of 823 K, 873 K and 923 K are investigated in this paper. The pressure trend, temperature field change, regeneration reaction rate and the dynamic regeneration oxygen concentration are analyzed. The complete soot regeneration can be achieved of all the simulation cases with different oxygen concentration and regeneration temperature. Under the same oxygen concentration conditions, the higher the regeneration temperature has the wider range of high-pressure pressure region. The highest and the lowest pressure appear at the regeneration temperature/oxygen concentration condition of 923 K/7.2% and 823 K/9.4%. The maximum temperature is 1792.5 K under the condition of 923 K/9.4%. The dynamic reaction rates of the 9 simulation cases are diverse significantly in the inlet and outlet sections of the DPF. The difference between the maximum and minimum reaction rates is less than 0.001. The study results is able to determine the regeneration oxygen concentration and regeneration temperature for achieving complete regeneration of DPF.

Large-Eddy Simulation of Hydrodynamic Structure in a Strongly Curved Bank

Advances in computer technology have facilitated the use of large-eddy simulation (LES) as a numerical simulation method in fluid mechanics. In this study, LES was used for the numerical simulation of curved water flow with a large curvature. The simulation results show that water separation occurs near the convex bank of the bend transverse section while the separation area increases and then decreases along the water depth direction, where the peak is at half-depth. As the water surface is affected by air shear stress, the velocity decreases. However, as the gradient increases, the vorticity is larger and the vorticity distribution is more even. Reflux occurs in the inlet and outlet sections of the bend but does not occur on the surfaces of z/H = 0.5 and z/H = 0.2, where the vorticity distribution is uneven. In the narrow corridor of the concave and convex banks, notably near the curved top, vorticity distribution is concentrated with a high intensity. At the center of the curve, the vorticity intensity is weak but 10 times higher at the concave and convex banks. A strong correlation exists between circulation structure and vorticity distribution: the vorticity is large where the circulation is intense and the structure is complex.

Numerical study on comprehensive performance of flow and heat transfer coupled with ortho-para hydrogen conversion

The energy consumption of hydrogen liquefaction can be effectively reduced by filling the plate-fin heat exchanger with the catalyst to achieve continuous conversion of ortho-para hydrogen while cooling. In this study, a three-dimensional numerical model of heat transfer and flow coupled with ortho-para hydrogen conversion is established, and the simulation results are verified by the experimental data. Both the temperature field and the outlet parahydrogen fraction demonstrate better accuracy of the local thermal non-equilibrium model results compared to the local thermal equilibrium model results, and the thermal non-equilibrium effect is most significant at the inlet of the porous medium, where the temperature difference between the fluid and the solid exceeds 2 K. Furthermore, it is indicated that two typical stages exist in the hot channel: the heat transfer dominates in the inlet section and the ortho-para hydrogen conversion efficiency decreases significantly, even once falling below 30%. In the thermal fully developed section, the catalytic performance is effectively improved along with the decay of velocity, with a 10% improvement compared to the lowest point of performance. Finally, an integrated comprehensive performance evaluation criterion is summarized regarding the overall performance of heat transfer, flow and catalysis, with excellent comprehensive performance being achieved at Reynolds numbers of 170 to 300. This research can provide a reference for the comprehensive performance study of catalyst-filled plate-fin heat exchanger for hydrogen.

Effect of Mixing Section Acoustics on Combustion Instability in a Swirl-Stabilized Combustor

An experimental study was performed to investigate the characteristics of two different combustion instability modes in a swirl-stabilized combustor. The first is the eigenfrequency corresponding to the half-wave of the combustion chamber section, and the second is the quarter-wave eigenmode of the inlet mixing section. The purpose of this study is to understand the effects of the swirl number on each combustion instability mode and analyze their generalized characteristics. Premixed gases composed of hydrocarbon fuels (C2H4 and CH4) and air were burned by independently varying the experimental conditions. Three dynamic pressure transducers and a photomultiplier tube were installed to detect pressure oscillations and heat release fluctuations in the inlet and combustion chamber sections, respectively. A high-speed camera was used to capture the instantaneous flame structures. In the swirl-stabilized combustor, the bands of the dominant frequencies were strongly dependent on the swirl number of the swirler vane. When the swirl number was low, the entire combustion system was often coupled with the quarter-wave eigenmode of the inlet mixing section. However, as the swirl number increased, the combustion instability mode was almost independent of the mixing section acoustics. Analysis of the phase difference and flame structure clearly demonstrated the differences between each eigenmode. The results provide new insights into the effect of the resonance mode in the inlet mixing section on combustion instability, depending on the swirl number in the swirl-stabilized combustor.

Analysis at cell scale of porosity effect on forced convection with nanofluids in porous structures with Kelvin cells

• The study is provided with Kelvin cell structure for different porosity values. • Pressure and temperature have periodic trends inside the structures. • Highest velocities are recorded at lower porosities between two cells. • Highest temperature differences are detected between outlet and inlet sections. In this paper a numerical investigation in metal porous structures with Kelvin cell model is carried out on water/Al 2 O 3 nanofluids using the single-phase model. The employed foams are characterized by a fixed value of cells per inch (CPI) equal to 10 for porosity ɛ equal to 0.85, 0.90, 0.92, 0.95, 0.97. For porosity of 0.95 structures at 5, 20 and 40 CPI are also analyzed. Three different values of Al 2 O 3 nanoparticle volume concentrations ϕ , equal to 0, 2 and 4% are used. Results are showed and discussed in terms of pressure drop and temperature profiles, velocity and temperature fields. Correlations for the evaluation of permeability K and drag coefficient C F and their values are also shown. Furthermore, dimensionless entropy generation as function of Reynolds number has been evaluated. The results reveal that both the pressure and the temperature have a periodic trend with oscillations that vary both for the geometric aspects and for the properties of the fluids used. The velocity and temperature fields then serve to understand the dynamic and thermal characteristics: the highest velocities are recorded at lower porosities and at the contact zones from between two cells, as well as the highest temperature differences between outlet and inlet sections. The correlations with which permeability and drag coefficient are obtained reveal that they depend only on the foam used and not on the fluid considered. Finally, the trend of the dimensionless entropy generation as a function of the Reynolds number is decreasing and reducing with increasing porosity.

Simulation and optimization design of hydrogen ejector in proton exchange membrane fuel cell system

The optimization of structural parameters in ejector design is a problem of optimization of multivariate nonlinear unsteady flow field, in this paper, the numerical model of the ejector is established by using the computational fluid dynamics (CFD) method. The CFD model is used to study the influence law of the structural parameters of the mixing section, diffuser section and fluid inlet of the ejector, optimize the structure of the ejector, and find out the best scheme for the structural optimization design of the hydrogen ejector, so as to broaden the available load range of the ejector.

Pressure Fluctuation–Vorticity Interaction in the Volute of Centrifugal Pump as Hydraulic Turbines (PATs)

The pump as turbines (PATs) has been widely used in the petrochemical, seawater desalination, and mining industries. Volutes are critical components for flow guidance and energy conversion in the PATs. Therefore, its inner flow characteristic could significantly influence the hydraulic turbine system stability. To reveal the vortex evolution, pressure pulsation characteristics, and the interaction between the two in the volute of PATs, a single-stage cantilever hydraulic turbine is investigated by the numerical and experiment method. The effect of impeller rotation on vorticity distribution and pressure fluctuation intensity in volute is analyzed based on the numerical simulation results. By clarifying the frequency components corresponding to local high amplitude vorticity and pressure pulsations, the relationship between vortex evolution and pressure pulsations is established. The results showed that the dominant frequency of pressure pulsation in the circumferential direction of the volute is 6fn under different operating conditions, and the pressure pulsation characteristics in the inlet section of the volute were less affected by the rotor–stator interaction. Under Qb and 1.3Qb conditions, the vorticity pulsation near the walls in the circumferential direction of the volute had less effect on local pressure pulsation characteristics. The evolution of vorticity at the leading edge of the volute tongue intensified the local pressure pulsations as the flow rate increased. Under 0.7Qb conditions, the vorticity pulsation characteristics in the volute are complex and have a relatively significant influence on local pressure pulsation.

Numerical simulation study on the optimization of the central ejector intake tube

A CFD numerical simulation study was conducted for the primary flow non-axial inlet L/Y intake tube ejector. The effects of different configurations of the inlet piping on the secondary flow of the ejector were analyzed in terms of total pressure loss, separation zone volume, and velocity uniformity. The results showed that: the volume of the separation zone decreases with the increase of secondary flow total pressure. The L intake tube causes a larger separation zone under the same working condition. When the total pressure of secondary flow is 20kPa, the volume of the separation zone caused by the L intake tube reaches 15 times that of the Y intake tube, and the total pressure loss is 2.3 times that of the Y intake tube. A smaller separation zone has less effect on the flow field structure, resulting in better velocity uniformity in the mixing chamber inlet section of the Y intake tube ejector.

The impacts of near-bed flow characteristics on river bed sediment transport under ice-covered conditions in 2016–2021

Global climate change has been projected to affect hydrology, the ice-covered flow period and river morphology (including changed sediment transport conditions) in northern high-latitude regions. To understand the impact of the expected shortening of the ice-covered period on bedload transport, one needs to understand the present sediment transport in these high-latitude rivers with annually occurring ice cover. Thus, the aims are (1) to define the impacts of ice cover on near-bed flow characteristics during hydrologically varying years, and (2) to analyse the impacts of these mid-winter flow characteristics on the bed sediment transport potential. The analyses are based on Acoustic Doppler Current Profiler (ADCP: 2016–21) and Acoustic Doppler Velocimeter (ADV: 2020–21) measurements performed in mid-winter ice-covered conditions of the sandy and small (circa 20 m wide) Pulmanki River in northern Finnish Lapland.Despite the ice-covered river conditions in winter, sediment transport occurs even during these harshest mid-winter conditions. The critical velocities and shear velocities of mid-winter conditions were exceeded in winters 2016–2021, and bedload transport occurred according to bedload measurements. Three different situations occurred regarding the bed sediment transport and near-bed velocity conditions: (1) high measured mid-winter discharges indicate high velocities throughout the meander bend; (2) low measured mid-winter discharges cause low near-bed velocities throughout the meander bend; (3) winters having intermediate discharges indicate near-bed velocities and sediment transport potential being higher at the upstream inlet and apex sections of the meander bend but clearly lower downstream of the apex. The confinement by the river ice cover, i.e. bottom-fast ice, explains the velocity variation. The near-bed velocities were the highest at the upstream inlet section of a symmetrical meander bend, where the measurement cross-sections were narrower and shallower. The velocities were the lowest downstream of the apex, where the channel changed from relatively narrow to wider and deeper.

Effect of air inlet and outlet cross sections on the cooling system of cylindrical lithium battery with segmental arrangement utilized in electric vehicles

This paper examines a three-dimensional analysis of the temperature of a battery pack (BYK) with 16 lithium-ion cylindrical batteries. Battery cells (BYC) placed in four rows in a segmental configuration in the BYK are cooled by a laminar airflow. The air inlet and outlet are located at the top and bottom of the pack, respectively. The effect of inlet and outlet dimensions on BYK temperature and air temperature (T-Air) is examined in this research. COMSOL Multiphysics software is used to simulate the BYK, and the FEM is employed to solve the equations. The results demonstrate that the impact of the inlet on the temperature of the batteries (T-BT) is much more than the outlet, which is due to the change in air velocity (V-Air) in the pack. An increment in the inlet causes the maximum (MXT) (1.56°) and average temperature (AVT) of the BYK (3.01°) to decrease. The dimensions of the inlet affect the AVT of the battery from the initial time. Larger air outlets slightly enhance the MXT and AVT of the BYK. Enhancing the inlet reduces the outlet T-Air. The BYCs located in the middle of the BYK need more cooling since they have a MXT.

STUDY OF CHANGES IN HYDRODYNAMIC PARAMETERS PATTERNS OF VISCOUS FLUID FLOW IN A FLAT DIFFUSER

The relevance. Diffusers, either as nozzles or constituent elements, are frequently used in many mechanisms and machines. In this regard, the study of viscous fluid flow in diffusers aims to discover patterns of changes in the flow's hydrodynamic parameters, allowing better understanding of the nature of flow as a function of Reynolds number. Following the results of the analysis of the study, conditions for the proper construction of the mechanism unit, ensuring its reliable and durable operation will be revealed. The main aim of this study is to determine the velocity profiles in the flat diffuser for a viscous incompressible fluid by integrating the simplified Navier–Stokes differential equations under the established initial and boundary conditions, as well as the bifurcation point's dependence on the opening angle and Reynolds number of the diffuser. Objects: a flat diffuser in which viscous incompressible fluid moves. At the same time, revealing the patterns of changes of the hydrodynamic parameters of the flow is of defining value when choosing the structural dimension of devices and mechanisms, the main part of which is the flat diffuser. Methods. To reveal the patterns of changes of the hydrodynamic parameters of the flow in a flat diffuser, the study is based on the fundamental nonlinear differential equations of viscous fluid mechanics, which in a general case are not subject to an exact mathematical solution. For integration in the nonlinear differential equations, due to the smallness, the nonlinear-convective terms are neglected, and the inertial terms are also partially simplified. Such a simplification is justified if the velocities are very small or if the dynamic coefficient of viscosity of the fluid is very large. A method for solving the boundary value problem was developed, and regularities for changing the flow parameters were obtained. According to the derived regularities, graphs of the change in velocity, pressure and shear stresses on the wall of the fixed channel were plotted and the coordinates of the separation point were determined. Results. Depending on the angle of the diffuser opening and the Reynolds number, a general solution of the approximating Navier–Stokes equations was given. In accordance with the nature of the motion, the boundary conditions of the problem were established and the boundary value problem was stated. A method for integrating a boundary value problem was developed, and regularities for the change in velocities along the length of the diffuser were obtained for a parabolic distribution of velocities in the inlet sections. Graphs of the change in radial velocities along the length and at a fixed value of the opening angle were constructed, a flow pattern and the transition of a single-mode flow to multimode operation were obtained. For a fixed opening angle and Reynolds number, the conditions for flow separation from a fixed wall were derived, where the flow velocity changes the sign.

Numerical Characterization of Mixing in a Kneading Element Channel of Dual‐Speed Corotating Non‐Twin Screws Using Lagrangian Statistics Method

AbstractA novel kind of dual‐speed corotating non‐twin kneading elements with a zero stagger angle is designed to improve mixing ability. The physical model considering several narrow gaps is developed where the inlet and outlet transition sections are also included. Finite element method associated with the mesh superposition technique is further applied to solve the time‐dependent flow field where fluid is assumed to obey the Carreau constitutive model. The tracers initially from different locations are tracked using a self‐developed fourth‐order Runge–Kutta scheme. Distributive mixing is evaluated through evolution of tracer droplets and decaying of variance index with time. In addition, a Lagrangian statistics method is used to characterize the dispersive mixing in terms of the statistical distributions of mixing index and their integration areas within the range of mixing index larger than 0.5. In contrast, the kneading elements of a conventional twin screw configuration are also modeled to show the mixing difference.

Numerical Calculations of Liquid-Metal Magnetohydrodynamic Flows Through Circular Pipe in Magnetic Field Inlet Region and Outlet Region

Numerical calculations are conducted for liquid-metal magnetohydrodynamic flows through a circular pipe with an electrically conducting wall in both the magnetic field inlet region and the outlet region. Conservation equations of fluid mass and of fluid momentum and the Poisson equation for electrical potential are solved numerically. The calculations are performed by a cylindrical coordinate system using a staggered grid in order to obtain numerically stable solutions, covering Hartmann numbers up to the order of 10 000. As to the loss coefficient ζ for the pressure drop, the value of ζ/(Ha2/Re) does not depend on the Ha number, the Re number, and the wall conductance ratio very much for both the magnetic field inlet section and the outlet section. The value of ζ/(Ha2/Re) changes mainly with the gradient of the applied magnetic field for both the magnetic field inlet section and the outlet section.

Optimization design of the elbow draft tube of the hydraulic turbine

The draft tube of the hydraulic turbine serves to recover the kinetic energy of the water flow that leaves the runner. The amount of this energy depends on the turbine type, its specific speed and flow capacity. For high specific speed turbines, influence of the draft tube on the turbine efficiency is more essential. The height of the elbow-type draft tube has a considerable influence on its performance. Statistics show that increasing the height of the draft tube leads to a considerable increase of the turbine efficiency, but it also increases the scope and cost of civil works. The present paper presents the solution of the multi-objective optimization problem directed to minimization of the height of the toroidal elbow-type draft tube and maximization of the overall efficiency of the turbine. During optimization, 11-19 parameters that determine the shape and dimensions of the draft tube were subject to variation. In optimization, efficiency was maximized in two operating points: best efficiency point and full-load point. Cavitation qualities were defined as constraints. In order to correctly assess the turbine efficiency and cavitation, the computational domain included one channel of the distributor, one channel of the runner and draft tube; whereas losses in the spiral case and stay ring were determined using empiric formulae. Within the optimization the flow analysis was performed using 3D steady-state Reynolds averaged Navier Stokes equations closed by the k-ε turbulence model. On solid walls the method of wall functions was used. The turbine head, being the difference of specific energies in the inlet and outlet cross sections, was pre-set as a constant value, while the discharge was determined in the course of solution of the problem. A multi-objective genetic algorithm was used to solve the optimization problem. For the draft tube shapes obtained in the course of optimization, their performance characteristics and flow character were compared by means of CFD. It was found that it is possible to significantly reduce the height of the classical toroidal draft tubes without considerably affecting their performance characteristics.

Influence of Injection of the Thermal Shield Decomposition Products on the Flow Coefficient of a Recessed Nozzle Depending on the Inlet Section Shape

Influence of Injection of the Thermal Shield Decomposition Products on the Flow Coefficient of a Recessed Nozzle Depending on the Inlet Section Shape

Approach to sediment monitoring in Hydro Power Plant

The presence of mineral sediments in water led to significant erosion damage to a power plant in the Chilean Andes. The plant is operated by Enel and is equipped with three vertical Francis power units, with approximately 25 MW each operating under a net head of around 120 m. The overall machine condition with reported significant damage on the turbine caused by erosion led to a modernization project with runner replacement and output and efficiency increase. In order to ensure a proper sediment measurement and quantification during the turbine operation, Voith developed, supplied and installed a sediment monitoring system in power unit #01. The monitoring system, developed using the OnCare.Health Hydro platform, applies optical sensors installed directly in the spiral case inlet section to measure the water turbidity. Other operational parameters are recorded, processed and stored together in the same database. Two optical sensors were installed in the spiral case inlet section and provide turbidity readings. The first one is positioned directly flush to the flow. The second one is located in a sampling pipe that collects water from four different points of the same cross section. An automatic water sampler installed in the sampling pipe collects water periodically, which is sent to a laboratory for particle analysis. The laboratory results allow an identification of important parameters such as sediments concentration, particle sizes and materials that are used for correlation with the indicated turbidities. The main data analysis shows that the power unit operated most of the time close to the rated condition. A comparison between turbidities indicated by both sensors shows an offset, probably associated to the particles distribution along the cross section. A system calibration process successfully correlated suspended sediment concentration and turbidity values to allow online indications of the sediment concentration. The system has been operating for almost two years in a close cooperation with the engineering teams of the plant owner and system provider. Main results and system findings for this application will be presented and discussed in this paper.

A study of hydrodynamic viscous fluid flow parameters change regularities in case of a conical diffuser

Studies of patterns of changes in hydrodynamic parameters of the viscous incompressible fluid in a conical diffuser were conducted. The specificity of the viscous liquid flow in a conical diffuser is that the kinetic energy of the flow, depending on the opening angle, is converted into pressure energy. Depending on Reynolds numbers and diffuser opening angles, the velocity vector field is stationary. With an increase in the Reynolds number, the symmetry of the flow relative to the axis of the diffuser is broken. A general solution to the approximate Navier-Stokes equations is given, based on the diffuser opening angle and the Reynolds number. A method for integrating the boundary value problem has been developed, and the patterns of velocity changes across the diffuser length at a parabolic distribution of velocities in the inlet section are obtained. By integrating partial differential equations that match all boundary conditions, the solution to the boundary value problem can be found. Graphs of changes in radial and axial velocities along the length and with a fixed value of the opening angle are shown; the flow pattern and the transition of a single-mode flow to multimode regimes are obtained. For a fixed opening angle and Reynolds number, the conditions for flow separation from a fixed wall are derived, where the flow velocity changes the sign. A mixing process is observed in the multi-mode region, which is accompanied by numerous pulsation phenomena and an unstable diffuser operation, where the resulting solutions are inappropriate. Based on the results of the studies obtained, it is possible to correctly design a conical diffuser, namely, under the condition of non-separated flow, to choose the opening angle and its length.

Improvement of the Flow Pattern of a Forebay with a Side-Intake Pumping Station by Diversion Piers Based on Orthogonal Test Method

The flow analysis of the forebay of a lateral intake pumping station with asymmetrical operating pumps was carried out with a realizable k-ε turbulent model and SIMPLEC (Semi Implicit Method for Pressure Linked Equations Consistent) algorithm. The Pressure Inlet boundary condition was adopted and the pressure between the top surface and the bottom surface was linear with the height of the inlet section. The Mass Flow Outlet boundary condition was also adopted to ensure the accuracy and precision of the CFD (Computational Fluid Dynamics) simulation. The diversion pier was selected as the optimization strategy based on the flow parameters. The layout of the diversion piers was designed with four parameters which are the relative length, relative height, width, and straight-line distance of the piers’ tail. Each parameter had three values. Based on the orthogonal test, nine groups of the numerical simulation on different layouts of diversion piers were analyzed with the uniformity of axial flow velocity and weighted average angle of the flow velocity of the inlet cross-section of each pump, reducing the number of tests from 64 (43) groups to 9 groups, improving work efficiency. The results show that the diversion piers had a significant adjustment of uniformity of axial flow velocity and weighted average angle of flow velocity. After optimization of the forebay, the uniformity of axial flow velocity of intake of No.1 pump was 80.26% and the weighted average angle of flow velocity was 77.68°. The above values of the No.2 pump were 98.74% and 87.84°, respectively. The values of the No.4 pump were 93.41% and 77.28°. The results of numerical simulation, which was carried out to estimate the rectification effect under the operation combination of the No.1, No.3, and No.4 pumps, showed that the uniformity and the angle of the No.1 pump were 92.65% and 72.66°, respectively, the uniformity and the angle of No.3 pump were 94.54% and 85.14°, and the uniformity and the angle of the No.4 pump were 75.81% and 78.21°. This research proves that the orthogonal test method, in a reasonable and convenient way, can be applied in hydraulic optimization for a lateral intake pumping station.

Unsteady flow analysis regarding stall flow and rotating cavitation in the first-stage of a multistage LNG cryogenic submerged pump

In this paper, the evolution of vortex structure and energy conversion process under the coupling of stall and cavitation flow (CSC) in the first-stage of a multistage LNG cryogenic submerged pump are numerically studied in detail, using a time-scale-driven hybrid URANS/LES turbulence model and a mushy interfacial dynamics cavitation model. The flow instability diagnostic parameter, PVS, is then established combining the first and second laws of thermodynamics. Further, the dynamic behaviors under CSC are analyzed by Liutex method and the fluctuations of vortex intensity are investigated in time-frequency domain. Results show that compared with the oscillation process of the pump head, PVS is more intuitive to depict the stall state. It is treated as light and deep stall as PVS drops to 0.2 and 0.15, while PVS is further reduced and finally locks at about 0.12. For the above conditions, vortices at the inlet section involves high-frequency cavity-shedding vortex and low-frequency impact vortex. The middle separation region absorbs the upstream shedding vortex and transports the separation vortex downstream, whereas vortices with the highest intensity locates at the outlet diffusion section in the helical shape. Among the vortex-vortex interaction, broadband oscillations get more significant under CSC.