Influence Mechanism of Ambient Air Parameters on the Rotational Stall of an Axial Fan

Abstract

This study investigates a dual-stage axial-flow fan within a specific power plant context. Numerical simulations encompassing both steady-state and stall conditions were conducted utilizing the Reynolds-averaged Navier–Stokes (RANS) equations coupled with the Realizable k–ε turbulence model. The findings reveal that, under normal operating conditions, there exists a positive correlation between the mass flow rate and outlet pressure with gas density while displaying a negative correlation with dynamic viscosity. Regardless of the changes in air density, the volumetric flow rate at the maximum outlet pressure of the fan remains essentially the same. When a stall occurs, the volumetric flow rate rapidly decreases to a specific value and then decreases slowly. The analysis of the three-dimensional flow field within the first-stage rotor was performed before and after the rotational stall occurrence. Notably, stall inception predominantly manifests at the blade tip. As the flow rate diminishes, the leakage area at the blade tip within a passage expands, directing the trajectory of the leakage vortex toward the leading edge of the blade. Upon reaching a critical flow rate, the backflow induced by the blade tip leakage vortex obstructs the entire passage at the blade tip, progressively evolving into a stall cell, thereby affecting flow within both passages concurrently.

1. Introduction

With the escalating demands for the stringent regulation of thermal power units’ peak performance, instability manifests in the rotating machinery during rapid load fluctuations when there exists a disparity between the fan pressure and flow [1]. When the flow rate descends to a critical threshold, the flow field within the fan transitions from stability to instability, initiating the rotational stall. Numerous factors contribute to the rotational stall in rotating machinery, resulting in fluctuating stresses that exacerbate the flow field, diminish the lifespan of rotor blades, and disrupt the fans’ normal operation [2,3]. Consequently, a comprehensive examination of the inducing mechanism behind the rotational stall and its assorted influencing factors becomes imperative. This facilitates the anticipation or detection of stall inception and enables the timely mitigation or postponement of fan instability, thereby optimizing fan operational modalities.

A typical feature of modern high-speed rotating machinery is the appearance of short-length scale unsteady aerodynamic disturbances near the casing before the formation of classic rotating stall cells, propagating circumferentially. These disturbances are usually referred to as “spike”, a phenomenon where a small vortex rotates at nearly the same angular velocity as the blades, known as “rotating instability” (RI). These flow disturbances occur at stable operating points between the peak pressure rise and stall boundary [4]. Day [1] defined it in a review article as “small in circumferential extent (one or two blade pitches wide), rotate at about half rotor speed, in the same direction, have a high circumferential count (up to half the number of blades) and are always changing in intensity, wave number and frequency”. Measured from a stationary reference frame, these phenomena manifest as a series of frequency peaks at a fraction of the blade passing frequency, commonly referred to as “broadband humps” in pressure spectra [5]. The spectrum not only shows broadband disturbances (humps) at around 30% of the blade passing frequency (BPF) but also exhibits individual peaks with narrow spacing. Modulation with the blade passing frequency and its harmonics is also present. The physical sources of these broadband disturbances are explained as boundary layer separation [6], tip vortex oscillations [7], axial reverse flow, tip leakage flow [8], and vortices formed by the interaction of tip leakage flows.

Detection of stall inception in fans and compressors can be approached through two main avenues: experiments and numerical simulations. Ljevar [9] suggested that a narrow diffuser stall is related to the instability of the three-dimensional wall boundary layer, while a broad diffuser stall is related to the instability of the two-dimensional core flow. Salunkhe [10] used the Morlet wavelet transform to analyze the stall generation mechanism of a single-stage axial fan under undistorted and distorted inflow conditions. Dazin [11] experimentally determined the variation in the number of stall cells with decreasing flow rates over the entire flow range. Flow instability not only degrades compressor performance but also causes mechanical damage due to dynamic excitation, especially in high-pressure, high-mass flow applications [12]. In the study of active stall control, one of the most successful active methods to reduce the rotating stall is jet injection. The idea of jet injection is to introduce relatively high-speed flow into the high-stall regions of the bladeless area to address these low-speed regions, preventing the diffuser from recirculating into the impeller [13]. In Zhang et al.’s [14] experiments, the effect of different injection flow rates on the onset of stall was studied, and 110 m/s was found to be the optimal injection speed for suppressing the onset of stall. Brandstetter et al. [15] conducted a study on composite fans, where they examined the effects of sensor placement and post-processing techniques. They specifically focused on spectrum averaging, the isolation of non-synchronous phenomena, and multi-sensor cross-correlation methods. Their findings suggested that explanations relying solely on spectral peaks and their spacing might be misleading, as the characteristics of rotating unstable spectra do not always correlate with unstable pulsating disturbances. Choi et al. [13] utilized high-frequency Kulite sensors positioned upstream and downstream of the fan casing to measure unsteady static pressure. Both numerical and experimental results consistently revealed the eventual formation of a large stall cell post-stall inception, regardless of the fan speed.

Various factors exert influence on stall occurrence in fans and compressors. Investigations conducted by Subbarao [4] on axial-flow fans, Ummiti [12] on 1½-stage axial flow turbines, and Tavoulari [5] on transonic, single-stage, high-pressure axial flow turbines collectively emphasize the significance of axial spacing in their performance, encompassing stall inception and development. Zhang [14,16] noted that a single blade exhibiting an abnormal deflection angle significantly affects the three-dimensional unsteady evolution process from stall inception to the formation of stall cells in two rotors. Manas et al. [17] explored phenomena leading to stalling in a low aspect ratio rotor fan stage operated under various speed combinations amidst radial distortion inflow. Initially, fluid structures leading to stall are linked to the blade passing frequency (BPF). Toge et al. [18] elucidated stall inception and propagation phenomena in low-speed contra-rotating axial flow fan stages subjected to circumferential inlet distortion. Khaleghi et al. [10] artificially induced stall inception by increasing the tip clearance of a blade in a semicircular computational domain, observing the growth of low-speed regions near the pressure surface and leading edge of the blade, leading to leading-edge vortex spillage. Tan et al. [19] identified potential mechanisms for spike formation through the three-dimensional studies of flow in the rotor tip region, proposing that effective stall control techniques must suppress the recirculation of blade tip clearance and forward spillage of leading edge tip leakage flow. Hu et al. [7] conducted experiments on a transonic compressor and discovered a novel stall inception phenomenon induced by the stator hub area, with further discussion on the radial distribution of loads indicating that local critical loads are pivotal in the premature flow breakdown in the stator hub region. Xu et al. [20] investigated the effect of rotor blade sweep on the flow stability of low-speed axial flow compressors, noting that forward sweep reduces the diffusion factor, base work, and blade loading in the rotor blade tip region, while aft sweep enhances the interaction between tip leakage flow and the primary flow, thus influencing flow stability.

Upon comprehending the mechanism underlying stall inception and the factors influencing its generation, various methodologies have been proposed to forecast and mitigate rotating stalls. Chattopadhyay et al. [21] addressed rotating stall and surge suppression by scrutinizing unstable phenomena and implementing diverse control systems to expand the stable operating range of compressors. Li et al. [22] determined that substantial stall margin enhancement is achievable solely with tip air injection in the initial stage. Hence, their proposed automatic stability control, compared to steady injection, conserves energy during compressor stability and offers protection near the stall point to extend the stall margin. Lu et al. [23] introduced a design approach centered on recirculation flow control to enhance the efficacy of Axial Slot Casing Treatments (ASCTs) for tip-critical transonic rotors via unsteady computational parameter analyses. Liu [24] and Kozakiewicz [25] utilized a novel flow diagnostic technique based on vortex dynamics theory to elucidate the factors contributing to the enhanced aerodynamic performance of optimized transonic fans. In this established aerodynamic optimization approach, the curvature of the blade camber line and its leading-edge metal angle serve as optimization variables, with optimization conducted by modifying their control point coordinates and incorporating genetic algorithms.

This paper performs numerical simulations on an axial flow fan employed for deep peak shaving within a specific thermal power plant. It investigates the fan’s operational dynamics across various working conditions, aiming to identify the moment and mechanism of stall inception. The objective is to forecast the minimum flow rate required for fan stall, thus enabling the broad threshold operation of the axial flow fan during deep peak shaving.

2. Materials and Methods

2.1. Geometric Model and Grid Division

This study investigates the axial flow fan employed in the air supply fan and the induced draft fan of a power plant. Its structure includes the inlet collector, two-stage moving blades (Rotor1 and Rotor2), two-stage static blades (Stator1 and Stator2), and the outlet section. The geometric model is shown in Figure 1.

Here, Rotor1 and Rotor2 represent the first and second stages of moving blades, while Stator1 and Stator2 represent the first and second stages of stator blades. The specific structural parameters are given in

Table 1. Key structural parameters of the axial fan.

Structural Parameters	Numerical
Rotation speed (r/min)	1490
Number of moving blades	24
Number of static blades	23
Inlet diameter (m)	2.312
Outlet diameter (m)	2.305
Rotor diameter (m)	1.778
Hub ratio	0.668

.

The grid division employs a strategy of block partitioning, partitioning different computational regions for the inlet, impeller region, stator region, and outlet diffuser section, respectively [26]. In the impeller and stator regions, an adaptively strong unstructured grid is used for grid generation. In other regions, a hexahedral structured grid is employed. Additionally, a boundary layer grid is applied to the impeller surface, and a size function is used to grid refine local areas such as the leading and trailing edges of the blades and the gap at the blade tip. The grids in the impeller–stator regions and the impeller blade tip region are illustrated in Figure 2.

When conducting CFD simulations using Fluent (https://www.ansys.com/products/fluids/ansys-fluent, accessed on 6 May 2024), it is essential to perform a grid independence test to ensure the accuracy of the simulation results and reduce the workload. The main task is to find the minimum number of grid elements that make the CFD results independent of the grid size. As shown in Figure 3, six different grid sizes were set. It can be seen that, when the grid numbers reach 6.76 million, the numerical results agree well with the experimental results obtained by the fan manufacturer. In the grid independence calculation, we obtained the number of elements by varying the number of internal points on the edge of the blades and the maximum size from 10 to 30 mm.

2.2. Governing Equations and Turbulence Model

Axial-flow fans, as structurally complex rotating machinery, exhibit intricate characteristics in their internal flow fields. Complex and unstable flow phenomena such as blade tip clearance flow, secondary flow, and wake–jet interactions exist in the flow field. To achieve numerical simulations of axial-flow fans with less computational resources while ensuring calculation accuracy, it is necessary to reasonably simplify the computational conditions. Due to the small temperature difference at the inlet and outlet of the fan, and minimal heat exchange between the gas inside the fan and the external environment, the internal flow is considered incompressible. Simultaneously, variations in gas density, viscosity, temperature, and other parameters are neglected, and the energy equation is not considered.

In this paper, fluent software is used for numerical simulation. The numerical simulations in this paper involve the Reynolds-averaged Navier–Stokes mass conservation equation and the momentum conservation equation:

$${\displaystyle \frac{\partial {\overline{u}}_i}{\partial x_i}}=0$$

(1)

$${\displaystyle \frac{\partial {\overline{u}}_i}{\partial t}}+{\displaystyle \frac{\partial \left({\overline{u}}_i{\overline{u}}_j\right)}{\partial x_j}}=-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial \overline{p}}{\partial x_i}}+v{\displaystyle \frac{{\partial }^2{\overline{u}}_i}{\partial x_j\partial x_j}}-{\displaystyle \frac{\partial \left(\overline{u_i^{\prime }{u}_j^{\prime }}\right)}{\partial x_j}}$$

(2)

where ${\overline{u}}_i$ is the time-averaged velocity in the i direction; $u_i^{\prime }$ is the fluctuating velocity in the I direction; p is pressure; $\nu$ is the dynamic viscosity coefficient.

In this paper, a two-equation turbulence model is employed for numerical simulations, meeting the requirements for calculation accuracy while saving computational resources [27]. The k–ε two-equation model adds an equation for the turbulent dissipation rate based on a single-equation model. The Realizable k–ε model, which includes a swirl modification, introduces a turbulent viscosity correction formula and a dissipation rate transport equation [28]. It provides a more accurate prediction of the divergence ratio for flat plate and cylindrical jets and performs well in situations involving rotational flow, flow separation, and secondary flow [29]. Considering the requirements of numerical calculations and aiming for an accurate representation of phenomena such as rotational flow, flow separation, and secondary flow, the realizable k–ε model is applied to numerically simulate the three-dimensional flow field of the fan [30].

The standard k–ε equation is established based on the turbulent kinetic energy k equation by introducing an empirical equation for the turbulent kinetic energy dissipation rate ε. It achieves high accuracy when calculating fully turbulent flow fields [31]. It should be noted that there is a term in the e equation that cannot be directly calculated at the wall, requiring the introduction of a wall function to resolve it. Additionally, for anisotropic turbulence, such as strong swirling or buoyancy-driven flows, the calculation results may deviate from reality. The realizable k–ε model addresses the issue of negative normal stress that appears in the standard k–ε model when dealing with high mean strain rates by introducing certain mathematical constraints.

The transport equations for k and ϵ are as follows:

$${\displaystyle \frac{\partial \left(\rho K\right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho \overline{u_j}K\right)}{\partial x_j}}={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{P{r}_K}}\right){\displaystyle \frac{\partial K}{\partial x_j}}\right]+P_K+G_b-\rho \epsilon -Y_M+S_K$$

(3)

$${\displaystyle \frac{\partial \left(\rho \epsilon \right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho \overline{u_j}\epsilon \right)}{\partial x_j}}={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{P{r}_{\epsilon }}}\right){\displaystyle \frac{\partial \epsilon }{\partial x_j}}\right]-C_{\epsilon 2}\rho {\displaystyle \frac{{\epsilon }^2}{K+\sqrt{\nu \epsilon }}}+\rho C_1\overline{S}\epsilon +S_{\epsilon }$$

(4)

where K is the turbulent kinetic energy; ε is the turbulent dissipation rate; u_j is the mean velocity component in the j direction; μ is the kinematic viscosity of the fluid; μ_t is the turbulent viscosity; P_K is the production of turbulent kinetic energy; Pr_K and Prε are the turbulent Prandtl numbers for k and ε, respectively. Typical values are Pr_K = 1.0 and Prε = 1.2. C₁ and Cε₂ are model constants. C₁ ≈ 1.44, Cε₂ ≈ 1.9.

2.3. Boundary Conditions

In the numerical simulation process, the inlet and outlet of the fan calculation domain are chosen as the inlet and outlet sections at the collector and diffuser exits, respectively [30]. The inlet boundary condition is set as a pressure inlet with a reference pressure of 0 Pa. The outlet boundary condition is set as a pressure outlet, with a specified outlet pressure reference value for steady-state calculations. For unsteady-state calculations, a throttle valve model is applied at the outlet, and iteration is implemented using a custom user-defined function (UDF) written for this purpose. In the impeller region, for steady-state calculations, a multiple reference frame (MRF) approach is employed with a rotating wall speed set at 1490 rpm. For unsteady-state calculations, a moving mesh model is utilized. Interface boundary conditions are used to connect different sections of the fan, while the remaining areas utilize wall boundaries with no slip.

In this study, the numerical computation results of the stall condition are obtained by gradually increasing the outlet back pressure, approaching the stall point. This approach is intuitive and allows for the easy determination of the stall point on the performance curve, facilitating the observation of stall occurrence and development. Because the performance curve is relatively flat near the stall point of the highest static pressure, the calculation results are highly sensitive to the back pressure value. By introducing a throttle valve model at the outlet, it becomes convenient to control the operating conditions of the fan near and after the stall. This enables a semi-automated numerical simulation, reducing the need for extensive manual intervention. Therefore, in this paper, the numerical stall is implemented by loading the throttle valve function at the outlet. The expression for the throttle valve model [6] is as follows:

$$P{s}_{out}(t)=P{i}_{in}+{\displaystyle \frac{1}{2}}{\displaystyle \frac{k_0}{k}}\rho U^2$$

(5)

where $P{s}_{out}$ and $P{i}_{in}$ represent the outlet back pressure and atmospheric pressure, respectively; $k_0$ and $k$ are constants and valve opening; $\rho$ is the air density; $U$ is the axial airflow velocity at the outlet.

3. Results

3.1. Overall Characteristics of Axial-Flow Fan

To simulate the occurrence of rotational stall in an axial-flow fan, the numerical simulation is divided into three stages: Firstly, the inlet pressure of the fan is initially specified, and the outlet pressure is gradually increased until the performance parameters of the fan no longer converge in the steady-state simulation phase. Secondly, based on the converged solution of the maximum back pressure from the steady-state numerical simulation, an unsteady-state numerical simulation is conducted until the key parameters of the fan converge, and the flow field of the fan becomes relatively stable at that back pressure. Thirdly, based on the results of the above simulations, a throttle valve model is applied at the outlet with the current opening set to k = 1.0. The valve opening is gradually decreased to obtain stable solutions at each opening until the fan enters a numerical stall.

Table 2. Working fluid thermophysical properties.

Working Fluid	Temperature (°C)	Density (kg/m3)	Specific Heat Capacity (kJ/(kg⋅K))	Thermal Conductivity(W/(m⋅K))	Dynamic Viscosity (10−6 Pa⋅s)
Air	−25	1.4235	1.0058	0.0221	15.9789
	−20	1.3953	1.0058	0.0225	16.2385
	−15	1.3681	1.0058	0.0229	16.4962
	−10	1.342	1.0058	0.0232	16.7519
	−5	1.3169	1.0059	0.0236	17.0057
	0	1.2927	1.0059	0.024	17.2576
	5	1.2694	1.006	0.0244	17.5076
	10	1.2469	1.0061	0.0248	17.7558
	15	1.2252	1.0063	0.0251	18.0023
	20	1.2043	1.0064	0.0255	18.247
	25	1.184	1.0066	0.0259	18.4899
	30	1.1644	1.0067	0.0262	18.7312
	35	1.1455	1.0069	0.0266	18.9708
	40	1.1272	1.0072	0.027	19.2088
	45	1.1094	1.0074	0.0273	19.4452
	50	1.0922	1.0077	0.0277	19.6807
	60	1.0594	1.0083	0.0284	20.1452
	70	1.0284	1.0089	0.0291	20.6043
	80	0.9993	1.0097	0.0298	21.0577
	90	0.9717	1.0105	0.0305	21.5055
	100	0.9456	1.0115	0.0312	21.9479
	110	0.9209	1.0125	0.0318	22.3851
	120	0.8975	1.0136	0.0325	22.8173
	130	0.8752	1.0148	0.0332	23.2447
	140	0.854	1.016	0.0338	23.6673
	150	0.8338	1.0174	0.0345	24.0853
Flue gas	150	0.8206	1.2186	0.368	24.5014
	160	0.1310	1.3325	0.381	24.9186

lists various fluid properties, which are the parameters needed for the numerical simulations of fluid. These parameters, such as density, specific heat capacity, thermal conductivity, and dynamic viscosity, primarily vary within a temperature range of −25 –150 °C. The specific values are calculated based on the REFPROP model of the National Institute of Standards and Technology (NIST) in the United States. In practical situations, when the fluid is air, the temperature ranges from −25 °C to 50 °C, and when the fluid is flue gas, the temperature ranges from 150 °C to 160 °C. In order to make the curve graph coherent, the calculated air temperature range is set to −25–150 °C. Figure 4 shows the curves of fluid density, fan mass flow rate, fan volumetric flow rate, and fan outlet pressure as functions of the fluid temperature under the condition where the throttle valve of the axial-flow fan used in the power plant is fully open. Under constant fan speed conditions, as the fluid temperature rises, the fluid density gradually decreases. Consequently, the mass flow rate of fluid within the fan gradually decreases, leading to a synchronous decline in outlet pressure. However, the volumetric flow rate of fluid exhibits an increasing trend. This indicates that the changes in various monitored parameters are interrelated. The decrease in fluid mass flow rate is insufficient to offset the impact of reduced density, resulting in an upward trend in the volumetric flow rate.

From Figure 4, it can be seen that there is a functional relationship between independent and dependent variables. The variation should be explored from the perspective of influencing mechanisms and should not be merely represented as a change in temperature. To investigate the impact of air parameters on the operation of an axial flow fan, density, specific heat capacity, thermal conductivity, and dynamic viscosity are individually used as independent variables for numerical simulation. Under the condition of changing only one independent variable, with 20 °C air as the 100% initial state, each variable is changed by 10% of the initial state. The outlet pressure and mass flow characteristic curves are shown in Figure 5. It should be noted that the gas may not exist under this condition; it is solely for numerical simulation exploration.

From Figure 5, it can be observed that, when each parameter changes individually, the characteristic curves of outlet pressure and mass flow rate are similar. Specifically, an increasing trend is observed with increasing density and dynamic viscosity. However, the trends with specific heat capacity and thermal conductivity remain essentially unchanged, with a change magnitude of less than 0.5% and minimal impact. It can be inferred that density and dynamic viscosity have an impact on airflow, while specific heat capacity and thermal conductivity affect the air heat transfer but have a relatively small influence on airflow. Therefore, density and dynamic viscosity are chosen as independent variables, and volume flow rate and outlet pressure are selected as dependent variables. Data fitting is performed using a neural network model. Additionally, a comparison is made with data fitting using temperature as an independent variable.

The following are the results of the data fitting. Due to the simplicity of the curves and the absence of complex variations, a cubic function curve fitting is performed when temperature is taken as the independent variable. The objective function is:

$$f(MT)=a+b*t+c*t^2+d*t^3$$

(6)

where MT is the monitoring target; a, b, c and d represent the 0th, 1st, 2nd, and 3rd power terms of the independent variable temperature (t), and their specific numerical values are listed in

Table 3. Parameter values with temperature as its independent variable.

Monitoring Target	a	b	c	d	R-Square
Mass flow rate	109.4	−0.2653	4.755 × 104	−2.198 × 10−7	0.999
Volume flow rate	84.65	0.1053	−3.678 × 104	9.748 × 10−7	0.998
Outlet pressure	1.303 × 104	−63.86	0.1475	5.29 × 10−6	0.996

. R-square is the square of the correlation coefficient between the measured and predicted data; a value closer to 1 is desirable.

When density and dynamic viscosity are taken as the independent variables, the objective function is:

$$f(MT)=p_{00}+p_{10}*\rho +p_{01}\ast \nu +p_{20}*{\rho }^2+p_{11}\ast \rho \nu +p_{02}\ast {\nu }^2$$

(7)

where $p_{00}$ represents the constant term of the function, $p_{10}$ and $p_{01}$ represent the first power term of the independent variable density and dynamic viscosity, $p_{20}$ and $p_{02}$ represent the second power term of the independent variable density and dynamic viscosity, and $p_{11}$ represents the cross-impact term between density and dynamic viscosity. The specific numerical values are listed in

Table 4. Parameter values with density and dynamic viscosity as its independent variables.

Monitoring Target		${\mathit{p}}_{10}$	${\mathit{p}}_{01}$	${\mathit{p}}_{20}$	${\mathit{p}}_{11}$	${\mathit{p}}_{02}$	R-Square
Mass flow rate	−1046	359.7	27.35	−71.68	18.91	−0.2813	0.991
Volume flow rate	−0.6882	−28.14	−1.205	−2.389	5.783	0.05878	0.989
Outlet pressure	71,310	48,240	−2146	−11,780	−3406	40.53	0.993

.

It can be observed that the coefficient before density is larger than that of dynamic viscosity, which aligns with the trends and magnitudes shown in Figure 4. When applying the thermophysical parameters of the working substance as flue gas into the formula, the numerical calculation results show an error within 3% compared to the formula calculation results. It can be considered that the fitting formula applies to both flue gas and air. The distinction between flue gas and air lies in the differences in density and dynamic viscosity caused by the varying types and quantities of molecules. These two factors play a significant role in numerical calculations. The fan flow rate and outlet pressure are related to the working substance’s temperature and type. On a deeper level, this is associated with the molecular composition of the working substance, specifically related to its density and dynamic viscosity. The fan mass flow rate and outlet pressure are positively correlated with the working substance’s density and negatively correlated with dynamic viscosity.

Figure 6 shows the total pressure-volume flow rate characteristics obtained through the transient and steady-state numerical calculations of the fan under different working temperatures with air and flue gas as the working fluid. In thermal power plants, axial flow fans are used for both the forced draft fan and the induced draft fan. The forced draft fan supplies combustion air to the boiler, while the induced draft fan extracts the flue gas after combustion from the furnace. Therefore, when the working fluid is air, temperatures of −25 °C, 0 °C, 25 °C, and 50 °C are selected, and when the working fluid is flue gas, a temperature of 150 °C is chosen. The characteristic curves corresponding to each working fluid are discontinuous. The left side interruption in the middle represents transient conditions under different control valve openings, while the right side represents steady-state numerical calculations under different back pressures when the control valve is fully open.

The overall trend of each curve is similar. During the steady-state calculation phase, as the flow rate decreases, the total pressure gradually increases, indicating that the fan is in normal operating conditions. In the transient calculation phase, with a decrease in fan flow rate, the total pressure initially slightly rises. After the flow rate decreases to 78 m³/s, the total pressure reaches its maximum. Subsequently, a sudden change occurs in both fan flow rate and total pressure, with the flow rate rapidly decreasing to 55 m³/s. The total pressure correspondingly decreases by varying degrees, indicating that the fan enters a state of rotational stall. Each breakpoint on the curve represents the transition between steady-state and transient calculations. From the graph, it can be observed that, with an increase in temperature, the volume flow rate at the breakpoint also increases. Meanwhile, the corresponding outlet total pressure is decreasing. The outlet pressure at the point of maximum pressure and stall occurrence decreases, resulting in a decrease in mass flow rate and a reduction in impeller efficiency, leading to a decrease in stall margin.

Figure 7 illustrates the characteristic curves of throttle valve opening versus volumetric flow rate obtained through the transient simulations of the fan under different working temperatures for air and flue gas. In the transient calculation phase, as the valve opening decreases, the fan flow rate decreases. After the flow rate decreases to 78 m³/s, with a further reduction in the valve opening, the flow rate rapidly drops to 55 m³/s, indicating that the fan enters a state of rotational stall. Combined with the figure, although the valve opening values corresponding to the occurrence of stall differ for different temperatures, the fan flow rate at the stall is consistently 78 m³/s. The valve opening coefficients (k values) corresponding to the stall for air temperatures of −25 °C, 0 °C, 25 °C, and 50 °C are 0.895, 0.825, 0.752, and 0.693, respectively. For flue gas at 150 °C, the corresponding k value at stall is 0.514.

3.2. Time-Domain Characteristics of Fan Outlet Static Pressure

By monitoring the fan’s outlet static pressure, the presence of periodic fluctuations can be verified, serving as an indicator of whether the fan has entered the rotational stall. Figure 8a illustrates the variations in fan outlet static pressure over time at different valve opening coefficients (k values) for an air temperature of −25 °C. At k = 0.896, corresponding to a fan flow rate of 78.0 m³/s, the outlet static pressure rapidly decreases and quickly stabilizes at 14,939 Pa. As the valve opening decreases further to k = 0.895, the flow rate significantly decreases to 52.7 m³/s. After approximately seven rotor cycles, the fan achieves a stable outlet static pressure. However, around the 45th rotor cycle, the outlet static pressure struggles to maintain stability, experiencing a sharp drop. Subsequently, after approximately 25 rotor cycles, it enters a new stable state with pressure fluctuations ranging between 6850 Pa and 7480 Pa. At the adjacent valve opening of k = 0.894, there is no significant change in flow rate compared to the previous opening. However, a pressure drop occurs in a shorter time, around the 36th rotor cycle, and eventually enters a state of pressure fluctuations, with the maximum fluctuation equal to that at k = 0.895 and a minimum of 6278 Pa. At k = 0.8, the fan cannot reach a stable state, experiencing a rapid decrease in outlet static pressure. Around the 17th cycle, it reaches the first extreme point, gradually entering a periodical fluctuation state. In all three rotational stall states, after a rapid decline in outlet static pressure, there is a small increase followed by irregular oscillations. As k decreases, the range of stall-induced fluctuations gradually diminishes.

Figure 8b–d depict the variations of fan outlet static pressure over time at air temperatures of 0 °C, 25 °C, and 50 °C, respectively. Figure 8e represents the variation in fan outlet static pressure over time at flue gas temperatures of 150 °C. A comparison of these figures reveals that the overall shapes of the curves depicting the process of the fan entering the stall under different valve opening coefficients (k values) are similar for both air and flue gas. As the valve opening decreases, the fan transitions from a stable state to stall, and the five sets of curves are sorted in descending order of fluid density. With decreasing density, the k value at which the fan first enters the stall gradually decreases. The number of rotor cycles from maintaining a stable state to entering stall decreases, becoming 45, 40, 34, 30, and 11 cycles. The intervals between two stall curves decrease when k further decreases by 0.001, becoming 14, 11, 11, 9, and 3 cycles. Before stall, the mass flow rates for the fan under stable conditions are 111.3 kg/s, 94.2 kg/s, 92.4 kg/s, 85.3 kg/s, and 63.1 kg/s, with corresponding volumetric flow rates of 78.2 m³/s, 78.1 m³/s, 78.0 m³/s, 78.3 m³/s, and 78.7 m³/s. All fan conditions before stall fall within the approximate range of 78.2 m³/s. Subsequently, as k decreases slightly, the throttle valve experiences a stall. The decrease in fluid density causes a simultaneous decrease in the fan’s mass flow rate, but the volumetric flow rate remains essentially unchanged. The volumetric flow rate of the fan is a crucial indicator for determining whether a stall occurs.

This study focuses on the complete process of the fan evolving from stall inception to a fully developed stall cell condition. It aims to identify the minimum flow rate at which the fan enters the stall and uses this as a criterion for assessing the stability of the unit. Therefore, the relevant flow field data for the valve opening coefficient k = 0.752 at common room temperature 25 °C are primarily selected for analysis.

3.3. Dynamic Characteristics of the Flow Field inside the Moving Blade before and after Rotational Stall Occurs

To analyze the flow field characteristics inside the impeller before and after rotational stall, and observe the manifestations of stall inception and stall cells within the blade, four different valve opening coefficients and time points were selected. In Yuan’s study [28], it was found that stall precursors first occur in the second-stage rotor blades and then propagate to the first-stage rotor blades. This study investigates the evolution process of the stall and the mechanism of stall precursors. Since Yuan’s paper has already studied the second-stage rotor blades, this paper focuses on the changes in the first-stage rotor blades. A comparative analysis was conducted on the static pressure distribution, transient streamlines, and turbulent kinetic energy distribution on the midsection of the first-stage moving blade. Specific operational conditions are described in

Table 5. Detailed description of four typical operational conditions.

Operational Condition	Description
k = 1	Flow state approaching the design flow rate and far from the occurrence of rotational stall
k = 0.752, T = 30	State of incipient stall characterized by the appearance of stall inception
k = 0.752, T = 50	State in the process where stall inception develops into mature stall cells
k = 0.752, T = 80	State where the stall inception has developed into mature stall cells and stabilized flow

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3.3.1. Static Pressure Distribution Patterns inside the First-Stage Impeller before and after Stall

Figure 9 shows the cloud maps of static pressure distribution at five typical moments within the first-stage impeller before and after the occurrence of the rotational stall at the Z = 0 section. The shown sections represent the impeller’s rotation in the clockwise direction. As indicated in Figure 9a, under the design conditions, the internal flow field of the impeller is in a stable state, and the static pressure distribution is uniform in each channel. There is a negative pressure region near the top of the blade suction surface. Along the direction of decreasing radial height and the direction from the blade suction surface to the pressure surface, the pressure in the channel gradually increases. When it develops close to the blade pressure surface, the overall pressure in the channel is at a higher state, and the highest pressure value is generated on the surface of the blade’s top pressure surface. This is because, on the blade suction surface, there is a significant angle of attack between the leading edge of the blade and the fluid, resulting in a substantial favorable pressure gradient. Subsequently, as the fluid flows along the blade profile, the channel widens, causing a gradual reduction in velocity. This leads to an adverse pressure gradient, causing an increase in pressure and the potential occurrence of boundary layer separation and other phenomena.

Figure 9b illustrates the internal pressure distribution within the impeller at the 30th rotor cycle moment when the valve opening is k = 0.752, representing the initial state of fan stall occurrence. It can be observed from the graph that stall first occurs at the top of the blade suction surface. In the adjacent regions of the two blades, the negative pressure area at the top of blade A’s suction surface expands, gradually extending from the root to the midsection of the blade. In the clockwise adjacent blade B, the expansion trend of the suction surface’s negative pressure area is similar to A, but the pressure value of the negative pressure area decreases, approaching 0 Pa pressure. In the clockwise adjacent blade C, the negative pressure region on the suction surface decreases, and the minimum pressure area of −4000 Pa disappears. The high-pressure region on the pressure surface expands to three-quarters of the entire blade surface. There is a significant static pressure difference compared to the first two blades, causing abnormal airflow due to the pressure gradient. In the AB channels, the originally small negative pressure area near the top of the suction surface has developed into a large area of negative pressure with relatively high pressure values from the root to 80% of the radial height, resulting in nearly half of the channel being blocked.

As the impeller continues to rotate, the flow field gradually evolves to the state shown in Figure 9c at the 50th rotor cycle. At this point, a widespread stall region begins to appear within the impeller. It can be observed from the figure that each channel within the impeller is affected by stall inception, resulting in a noticeable uneven circumferential distribution. In this, the pressure distribution in the upper-right part of the channel at this moment is similar to the steady-state flow, with an overall decrease in pressure values. The pressure distribution in the left part of the channel differs the most from the steady state, indicating the most severe disruption in the flow field, which is the region where stall occurs. In the upper-left part of the channels affected by stall, there is a trend of negative pressure regions developing towards the blade root. At the same time, the high-pressure region near the blade pressure surface is suppressed, especially the significant reduction in the high-pressure region near the blade’s top area, indicating a trend of deteriorating flow field. In the lower-left channels adjacent to it, influenced by stall, the pressure gradient distribution on the blade changes from the suction surface to the pressure surface direction towards the along-blade-height direction. The pressure near the suction surface increases along the entire blade height direction, and the high-pressure region originally near the blade’s pressure surface moves to the 50% blade camber line. The pressure field exhibits a vortex-like transformation on the suction surface side of the blade. In the lower-right channels, the pressure distribution is similar to the blades ABC in Figure 9b. The stall cell has a relatively lower rotational speed compared to the impeller speed, and stall inception rotates counterclockwise in the circumferential direction. Thus, influenced by stall inception blocking the channels, the flow field in the direction of stall inception propagation is negatively affected, gradually deteriorating into the development of a new stall cell.

As the flow field develops to the state shown in Figure 9d at the 80th rotor cycle, the stall inception has evolved into a complete stalls cell and rotates along the impeller at a stable speed. At this point, it can be seen from the figure that the radial non-uniformity of the flow field within the impeller is more severe under the influence of the stall cells, and the pressure distribution trend resembles the steady-state design conditions even in the absence of channels. The majority of the pressure gradients in the channels shift towards the along-blade-height direction, and the overall static pressure in the impeller transitions to another form of stable state. Low-pressure regions are distributed near the suction surface at the blade root, while high-pressure regions are distributed near the pressure surface at the blade tip. In the left channels at the snapshot moment, negative pressure regions near the leading edge of the blade primarily exist in the range from the blade root to 50% of the blade height, while high-pressure regions near the blade pressure surface only exist in a small range near the blade tip. In the counterclockwise direction, the pressure values of the negative pressure regions gradually strengthen, and the pressure in the high-pressure regions near the pressure surface gradually decreases. In the adjacent 13 channels along the direction of stall cell propagation, the stall cells fully develop, leading to a more uneven pressure distribution, and the flow field tends to deteriorate. In the continuous distribution of six channels on the right at the snapshot moment, the flow characteristics tend to be similar. The high-pressure region near the blade pressure surface has disappeared, indicating severe disruption, characteristic of fully stalled channels. Simultaneously, as the stall inception develops into stall cells within the impeller, the scale gradually increases, and this change occurs in a very short period. Subsequently, the stall wave propagates at a lower speed and with a larger wavelength.

3.3.2. Distribution Patterns of Relative Velocity Streamlines before and after Stall

Figure 8 depicts the distribution of relative velocity streamlines in the axial section at Z = 0 for four typical moments before and after the stall in the first stage impeller. As shown in Figure 10a, when the fan is far from the stall state, the relative velocity inside the impeller is in a uniform state. Streamlines in each channel develop circumferentially, and there is no relative velocity along the radial height of the blades. Due to the influence of circumferential velocity, the relative velocity values gradually increase from the hub to the blade tip. From the graph, it can be observed that the maximum relative velocity occurs in the region near the suction surface close to the blade tip, reaching approximately 160 m/s, while the relative velocity values near the pressure surface are smaller. This is because, on the blade suction surface, there is a significant angle of attack between the leading edge of the blade and the fluid, resulting in a substantial favorable pressure gradient. As a result, the relative velocity is high. Subsequently, as the fluid flows along the blade profile, the channel widens, causing a gradual reduction in velocity.

With the decrease in flow rate, as it develops into the stall inception stage depicted in Figure 10b, certain channels experience pronounced and severe disturbances. In the blade channels ABC corresponding to the pressure distribution, significant backflow occurs. In the middle B-blade channel, the backflow vortex is particularly prominent, occupying the entire region from the blade top area to 80% of the radial height. The relative velocity values within this region are very small, around 10 m/s, and the fluid is nearly stagnant. This backflow is directed from the blade suction surface towards the blade pressure surface and ultimately returns to the blade suction surface. In the adjacent channel along the direction of the stall inception propagation, the backflow region is smaller but shows a tendency to gradually increase. In the counterclockwise direction opposite to it, the backflow region in the adjacent channel is weak and shows a trend of continued weakening. In other channels less affected by the stall inception, the flow remains in a uniform state. This is consistent with the static pressure distribution described earlier. In the two channels adjacent to these three blades, the flow field remains relatively uniform, but there is a small radial velocity near the blade top area due to the enhanced leakage flow near the blade top, leading to small disturbances in the flow.

As the flow field develops to the state shown in Figure 10c at the 80th rotor cycle, the stall inception has evolved into complete stall cells, rotating along the impeller at a stable speed. It can be observed that the circumferential non-uniformity of the flow field within the impeller becomes more severe, with the number of channels experiencing backflow due to the influence of the stall cells increasing to 18. In the 10 channels closest to the stall cell, the backflow vortex within the channels has developed from the blade top to 60% of the blade height. The flow has been severely disrupted, and these channels’ stall cells have all developed to the leading edge position of the blade suction surface, forming mature stall cells. They exhibit a relatively stable flow with the impeller, and the velocity has increased to around 30 m/s. In the upper part of the snapshot moment, the position of the newly formed stall cell is shown, and the streamlined shape is similar to the region where the stall inception occurred in Figure 10b. It can be observed that the initial center of the stall cell is located in the middle section at the top of the blade, gradually developing towards the blade suction surface.

With a further reduction in the flow rate, in the deep stall state shown in Figure 10d, the number of channels affected by stall cell blockage increases to 13. The overall flow state remains consistent with Figure 10c, confirming the non-uniformity of the pressure distribution.

Figure 11 illustrates the distribution characteristics of the velocity streamlines between the blades. As can be seen from Figure 11a, the flow field inside the impeller exhibits uniform velocity streamline characteristics when the turbine is away from the stall condition. However, with the gradual decrease in flow rate, the flow field develops to the early stage of stall shown in Figure 11b, and the fluid in some flow channels starts to show obvious and violent disturbances, leading to a significant increase in the disturbance of the flow field inside the impeller. Entering the 80th rotor cycle shown in Figure 11c, the precursor of the stall has evolved into a complete stall mass that rotates along the impeller at a stable rotational speed, at which time the circumferential inhomogeneity of the flow field is further aggravated, and the flow structure is seriously damaged. Accompanied by the further reduction in flow rate, the deep stall state demonstrated in Figure 11d is basically the same as that in Figure 11c, which further confirms the serious inhomogeneity of the pressure distribution.

Figure 12 shows the vortex structures of the two-stage rotor and stator at four typical moments. From Figure 12a, it can be seen that, under design conditions, all vortices are distributed on the blade surface, and the internal flow of the fan is smooth. When it develops to the stall onset stage shown in Figure 12b, the recirculation zone caused by the breakdown of the tip leakage vortex is located near the trailing edge of the blade, the area of the tip separation vortex increases, and the tip vortex detaches from the surface. When the leakage vortex forms, the dimensionless helicity at the vortex core approaches 1, indicating a high entrainment capability and strong intensity of the leakage vortex. As the flow field gradually develops to the stall development stage shown in Figure 12c, the dimensionless helicity at the vortex core starts to decrease as the leakage vortex develops downward, especially during the breakdown of the leakage vortex. The fastest decrease in dimensionless helicity indicates that the breakdown of the leakage vortex causes the vortex structure to disappear, reducing the entrainment capability. Downstream of the first-stage blade passage exit, the dimensionless helicity begins to increase again as the vortex breakdown disappears, indicating that the vortex structure regenerates after the second-stage blades.

When the flow field develops to the full stall state shown in Figure 12d, the stall cell has already affected the entire passage and rotates along the impeller at a stable speed. The flow field experiences severe disturbances and flow separation, which is likely to cause the blockage of the passage. The vortex structures in the tip region are mainly distributed near the suction surface area. At the blade tip, there is a tip separation vortex, a tip leakage vortex near the suction surface, and a passage vortex adjacent to the leakage vortex. There is also a horseshoe vortex at the leading edge of the tip. The passage vortex mainly originates from two parts: one part is the interference between the secondary flow of low-energy fluid from the upper-end wall and the tip leakage vortex, causing the end wall secondary flow to merge and form a passage vortex; the other part originates from the leading edge of the tip, induced by the leakage vortex.

3.3.3. Distribution Patterns of Turbulent Kinetic Energy before and after Stall

Turbulent kinetic energy refers to the kinetic energy of unit mass in turbulent motion, specifically the energy associated with turbulent fluctuations in a turbulent flow field. It not only reflects the strength of the positive stress in Reynolds stress in a turbulent flow field but also serves as a crucial parameter characterizing the intensity of turbulent fluctuations. As shown in Figure 13, four typical moments of the turbulent kinetic energy distribution maps at the Z = 0 cross-section are presented. From Figure 13a, it can be observed that, under the design operating condition, the turbulent intensity in the impeller channels is very low. The turbulent kinetic energy is mainly concentrated in the circumferentially distributed region near the blade top, with high-turbulent-energy distributed near the suction surface blade top. This is significantly influenced by the unstable flow near the blade top, primarily caused by small leakage vortices in the blade top gap region. The turbulent kinetic energy values in most regions of the impeller channels are almost zero, indicating that in this operating condition, most regions in the channels do not exhibit turbulent fluctuations.

In the stall occurrence stage shown in Figure 13b, the turbulent kinetic energy in the blade channel ABC significantly increases. The small-range high-turbulent-energy area originally distributed near the blade top in the channel develops into a large-area region from the blade top to approximately 70% of the radial height. The distribution of turbulent kinetic energy in other blade channels is basically the same as in the design operating condition. This is because, with the reduction in flow rate, the positive incidence angle gradually increases, leading to an enlargement of the separation vortex area near the blade top and causing an increase in turbulent fluctuations. The low-turbulent-energy area in the middle of the channel develops towards the blade top, forming an elliptical distribution, and the area increases. This corresponds to the backflow region described in the streamline plot earlier, indicating that the intensity of turbulent fluctuations in the channels significantly increases, and the flow field undergoes severe disturbances during the occurrence of stall inception.

As the impeller continues to rotate, the flow field gradually evolves to the state shown in Figure 13c, at which point widespread stall occurs inside the impeller. From the figure, it can be seen that the impeller channels are affected by the stall cell, resulting in non-uniform circumferential distribution. The flow field is significantly affected in 18 consecutive channels, with the 12 channels near the tail (considering the clockwise rotation of the impeller as positive) experiencing the most severe damage, indicating the region where the stall cell is generated. The small-range high-turbulent-energy area originally distributed near the blade top in the aforementioned channels develops into a large-area region from the blade top to approximately 50% of the radial height, and the turbulent kinetic energy values also significantly increase. In the channel affected by the stall cell in the counterclockwise direction, there is also a trend of an increasing high-turbulent-energy area. In contrast, the high-turbulent-energy area at the blade top in the seven channels affected by the stall inception in the clockwise direction (impeller rotation direction) is reduced compared to Figure 13b.

This phenomenon is due to the lower speed of the stall inception relative to the impeller speed and its rotation in the counterclockwise direction along the circumferential direction of the impeller. Therefore, the channels affected by the stall inception are blocked, and the flow field in the direction of stall inception propagation is negatively affected, gradually deteriorating into the development of a new stall cell. In the opposite direction, the channels experience improved flow conditions due to an increase in flow rate and a decrease in incidence angle.

As the flow field develops to the state shown in Figure 13d, the stall cell has affected all channels and is rotating along with the impeller at a stable speed. It can be observed from the figure that, under the influence of the stall cell, the circumferential non-uniformity of the flow field inside the impeller becomes more severe. High-turbulent-energy areas have appeared in a continuous set of 15 channels, corresponding to the channels affected by the stall cell. Compared with Figure 13c, it is evident that, although the numerical values of high-turbulent-energy areas in the aforementioned channels have not increased, the area of these high-turbulent-energy regions has significantly expanded. In particular, the high-turbulent-energy areas in three of the most severely affected channels have almost extended to 70% of the channels. The flow field undergoes severe disturbances and flow separation occurs, potentially leading to the blockage of the channels. In the three adjacent channels along the direction of stall cell propagation, the closer they are to the stall cell, the relatively larger the high-turbulent-energy areas near the blade top, and the flow field tends to deteriorate. In the two channels adjacent to the stall cell along the counterclockwise direction, the impeller channels improve and gradually recover from the stall state.

Figure 14 illustrates the characteristics of the Mach number distribution in the axial section at Z = 0 for four typical moments before and after the onset of impeller stall. From Figure 14a, it can be seen that, when the turbine is in a state far from stall, the relative velocity inside the impeller shows a uniform distribution of Mach number, and the flow lines develop in a circumferential direction along all flow paths, and no relative velocity change in the radial height of the blades is observed. Influenced by the circumferential velocity, the Mach number gradually increases from the hub to the tip of the blade. When the flow rate decreases to the initial stage of the stall shown in Figure 14b, a significant and violent disturbance of the fluid in part of the flow channel occurs, resulting in a significant decrease in the relative velocity of the fluid in this region, and the Mach number decreases significantly. Further developed to the 80th rotor cycle shown in Figure 14c, the circumferential inhomogeneity of the flow field inside the impeller is significantly intensified, the low Mach number region is continuously expanded, and the flow structure has been seriously damaged. When the flow rate is further reduced to the deep stall condition shown in Figure 14d, the low Mach number region has extended to the whole impeller, indicating that the flow performance has been fully destabilized. This process clearly reflects the drastic change in the flow state at the onset of stall and its significant impact on the impeller performance.

The above comparison analyzes the pressure axial cross-section, relative velocity streamlines, turbulent kinetic energy, and Mach number distributions of the fan’s first stage impeller at five typical moments before and after the stall. This provides insights into the evolution of the flow field properties during the stall initiation phase and the onset of the stall cell.

3.3.4. The Influence of Temperature Changes on Turbulent Kinetic Energy during Stall Occurrence

The contour plots of turbulent kinetic energy at Z = 0 corresponding to the occurrence of stall in axial flow fans under different air temperatures, as shown in Figure 15a–d. indicate that the initial location of stall occurrence is not fixed. Stall always initiates from a specific location and gradually expands, with no simultaneous occurrence at multiple locations. In comparison to locations where stall has not occurred, temperature variations have no impact on the normal flow conditions. High-turbulent kinetic energy is concentrated at the suction side of the blade tip, induced by blade tip leakage flow. As the flow rate decreases and stall occurs, disturbances in air flow are generated, and the leakage flow within the blade passage gradually intensifies. The fluid motion trajectory, formed by the mixture of blade leakage flow and the mainstream, undergoes significant changes, leading to the formation of a larger extent of stall under mutual influence.

4. Conclusions

(1).

Numerical simulations were performed on axial-flow fans employed within the plant, analyzing the flow rate and pressure variations under various temperatures at the fan’s design conditions. Through the manipulation of air parameters as individual variables and employing neural networks for data fitting, it was discerned that the fan’s flow rate and outlet pressure exhibit dependency on both temperature and the nature of the working fluid. Delving further, these dependencies are intricately linked to the density and dynamic viscosity of the working fluid. Specifically, the mass flow rate and outlet pressure of the fan demonstrate a positive correlation with the density of the working fluid, while displaying a negative correlation with its dynamic viscosity.

(2).

Unsteady simulations were used to achieve the phenomenon of rotating stalls in an axial flow fan at low flow rates, obtaining the total pressure and flow characteristics curves of the fan. The peak outlet pressure was reached at around 80 m³/s for air at various densities. When the flow was further reduced by adjusting the valve, a stall occurred after a slight decrease in flow rate, reducing the volumetric flow to 55 m³/s. As the air temperature increases (i.e., density decreases), both the maximum outlet pressure and the outlet pressure at the stall decrease, the mass flow rate decreases, the power output capability reduces, and the stall margin decreases.

(3).

An analysis of the internal flow field of the rotor was performed at various critical moments preceding and following stall occurrence, focusing on static pressure distribution, streamlines, and turbulent kinetic energy. Observations revealed that the stall cell initiates at the blade tip, propagating through the rotor passage. During this progression, a localized backflow phenomenon manifests at the blade tip region, aligning with the direction of propagation. Subsequently, the extent and intensity of the backflow gradually escalate, culminating in the complete obstruction of the passage. Eventually, the backflow induced by the stall cell weakens rapidly, allowing the passage to exit the stall, thereby restoring the flow field to its normal state.