Numerical Simulation and Experimental Study of the Rotor–Stator Interaction of a Turbine Under Variable Flow Coefficients
https://doi.org/10.1007/s11804-024-00453-y
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Abstract
Clarifying the gas ingestion mechanism in the turbine disc cavity of marine gas turbines is crucial for ensuring the normal operation of turbines. However, the ingestion is influenced by factors such as the rotational pumping effect, mainstream pressure asymmetry, rotor–stator interaction, and unsteady flow structures, complicating the flow. To investigate the impact of rotor–stator interaction on ingestion, this paper decouples the model to include only the mainstream. This research employs experiments and numerical simulations to examine the effects of varying the flow coefficient through changes in rotational speed and mainstream flow rate. The main objective is to understand the influence of different rotor–stator interactions on the mainstream pressure field, accompanied by mechanistic explanations. The findings reveal inconsistent effects of the two methods for changing the flow coefficient on the mainstream pressure field. Particularly, the pressure distribution on the vane side primarily depends on the mainstream flow rate, while the pressure on the blade side is influenced by the mainstream flow rate and the attack angle represented by the flow coefficient. A larger angle of attack angle can increase pressure on the blade side, even surpassing the pressure on the vane side. Assessing the degree of mainstream pressure unevenness solely based on the pressure difference on the vane side is insufficient. This research provides a basis for subsequent studies on the influence of coupled real turbine rotor–stator interaction on gas ingestion.Article Highlights● To ensure the proper operation of marine gas turbines, elucidating the mechanism of gas ingestion into the turbine is crucial.● To investigate the impact of rotor-stator interaction on ingestion, a simplified model with only the mainstream passage is chosen to analyze the mainstream pressure distribution under different flow coefficients.● Using a combined approach of experimental and numerical simulation methods, the pressure distribution patterns under various flow coefficients obtained by altering the mainstream flow rate and rotational speed are mechanistically explained.● These efforts lay the groundwork for studying gas ingestion in complex turbine disc cavities by establishing boundary conditions. -
1 Introduction
The turbine rotor disk cavity in marine gas turbines faces the challenge of high-temperature gas ingestion. To prevent the detrimental effects of gas ingestion on the lifespan of the turbine rotor disk, a sealing flow is introduced to seal the turbine disk cavity. To ensure an appropriate sealing flow rate, the mechanism of gas ingestion must be understood.
Previous studies have identified three mechanisms that induce gas ingestion in the turbine disk cavity: rotational induction (Owen, 2011a; Sangan et al., 2013b), external pressure induction (Owen, 2011b; Sangan et al., 2013a), and unsteady effects (Beard et al., 2017; Gao et al., 2020). Subsequent research revealed that the circumferential pressure asymmetries caused by the turbine vanes and blades in the mainstream play a dominant role in gas ingestion. A series of studies has been conducted to investigate this phenomenon further. Green and Turn (1994) conducted the first experimental study to examine the combined effect of vanes and blades on ingress, finding that the presence of blades decreases the ingestion. Hills et al. (2002) used unsteady CFD with the model, including vanes and rotating pegs instead of blades, and found that lower circumferential pressure from the pegs than from the vanes can cause more substantial ingestion. Bohn et al. (2003) performed laser Doppler velocimetry (LDV) experiments and found that vanes and blades strongly influenced ingestion. Roy et al. (2001; 2005) measured mainstream time-averaged and transient pressure distributions and found that the blades had the same influence as the vanes on the mainstream asymmetrical pressure distribution. Furthermore, researchers have investigated different mainstream flow coefficients. Bru Revert et al. (2021) investigated the influence of a range of flow coefficients on ingestion by keeping the mainstream flow constant and varying the rotational speed, finding that the sealing effectiveness inside the wheel-space was reduced for increased rotor speeds at constant purge flow rates under axisymmetric conditions, while the inverse phenomenon was observed when the stator vanes were introduced. Palermo et al. (2019) conducted a CFD study with different flow coefficients by fixing the rotational speed and varying the mainstream flow, finding that the vane improved sealing effectiveness compared to the vane-free case at the same mainstream flow. However, the sealing effectiveness of the vane case at high mainstream flow is higher than the vane-free case at low mainstream flow. Scobie et al. (2014) conducted experimental research over a wide range of flow coefficients ranging from 0 to 0.9 and found that the circumferential pressure difference is directly proportional to the flow coefficient, but at lower flow coefficients, severe gas ingestion occurs because of the "blade effect." The study of gas ingestion with mainstream vanes couples the joint influence of rotationally induced, external pressure induced, and rotor–stator interaction effects under complex flow but has not yet reached a unified conclusion. To simplify the problem, it is necessary to decouple the influence of the disk cavity and clarify the pressure distribution and unsteady flow mechanism of the main flow.
However, previous studies on the mainstream rotor–stator interaction have focused more on cascades and flow structure. Mahallati and Sjolander (2013) found limited inhibition of blade flow separation by wake trails in their study on the cascade. Förster et al. (2012) found strong non-stationarity in the passage vortices in the cascade. Matsunuma (2006) analyzed the details of the flow in the channel at a low Reynolds number and found that the wake was bent and deformed at the blade inlet. Rose et al. (2013) found a considerable nonstationary flow in the inlet and outlet of the blade in the Class 1.5 low-speed axial turbine due to the wake interference. Maclsaac (2010) measured the time-averaged and turbulent flow fields downstream of low-speed turbine cascades and explained the secondary flow loss formation mechanism. Miller et al. (2003) found a complex three-dimensional interaction between the high-pressure stage and the downstream guide vane, in which the guide vane wake and hub passage vortex interactions dominate. Eymann et al. (2002) and Gier et al. (2002) used experiments and numerical simulations to investigate the unsteady effect on low-pressure turbines and to analyze the beneficial effect of secondary flow on losses. Wang et al. (2023) studied the unsteady flow characteristics of the tip leakage flow under the stator–rotor interaction and analyzed the influence of this interaction on pressure oscillations, mixing, and vortex evolution within the tip leakage flow. Touil and Ghenaiet (2021) investigated the unsteady flow through a two-stage high-pressure axial turbine with analyses of the rotor–stator interaction effects on the aerothermodynamic performance. Zheng et al. (2023) investigated the forced response of an embedded compressor rotor induced by upstream and downstream stator disturbances and rotor–stator interactions through full-annulus unsteady calculations with decoupled and coupled configurations. Duda et al. (2021) investigated the interaction of the rotor blade wakes with the stator ones by changing the stator wheel's angle using the particle image velocimetry (PIV) technique. Gaetani (2018) analyzed the flow physics for high- and low-pressure turbines and commented on the effects of three-dimensional design on the interaction. Hu et al. (2023) and Yang et al. (2022) investigated the pressure fluctuations of the rotor–stator interaction in a pump–turbine.
Previous studies have extensively investigated the gas ingestion induced by mainstream pressure variations. However, some conclusions remain unclear, such as the inconsistent impact of the blade on gas ingestion and the non-monotonic effect of the flow coefficient on pressure distribution and gas ingestion. To further clarify these conclusions, clarifying the pressure distribution and unsteady flow characteristics initially under only the mainstream rotor–stator interaction is necessary, but most previous studies on the mainstream rotor–stator interaction have ignored the pressure distribution between vanes and blades. Hence, rotor–stator interaction must be studied at different flow coefficients in the turbine stage as a basis for the influence of subsequent rotor–stator interaction on ingestion.
2 Experimental and numerical methods
2.1 Experimental method
2.1.1 Experimental facility
The experimental rig used in this study is an autonomously designed single-stage turbine rotor disk cavity experimental rig at the Institute of Engineering Thermophysics, Chinese Academy of Sciences. An overall schematic of the experimental rig is shown in Figure 1.
Figure 1 Configuration of the rotating disk cavity experimental rigThe experimental rig is driven by an ABB QABP160M2B electric motor manufactured by ABB company, with a maximum rotational speed of 4 700 r/min and a rated power of 15 kW. The mainstream annulus is supplied by an MJL300 Roots blower, capable of delivering a maximum flow rate of 97 m3/min. In contrast, an MJA100 Roots blower provides the secondary airflow, whose maximum flow rate is 13 m3/min. Because this experiment focuses on the pressure distribution of the mainstream under different operating conditions, the secondary airflow is sealed to prevent any interference from sealing flow and disk pump effects.
The test section comprises a stationary disk with 33 guide vanes and a rotating disk with 66 blades. The diameter of the disk is 500 mm, and the blade passage height is 10 mm. The test section allows for measuring the pressure at the trailing edge of the vanes in the mainstream, as well as the pressure inside the rotor disk cavity and the sealing effectiveness. This experiment aims to focus simply on the pressure field distribution of the mainstream under different operating conditions and to serve as a study of the external boundary conditions for gas ingestion. Therefore, the measurement is solely focused on the pressure at the trailing edge of the vanes.
2.1.2 Operating conditions
Studying the flow mechanisms in the mainstream under various rotational speeds and inlet flow conditions is crucial for gas turbine engines, as they often operate under non-design conditions during start-up, maximum power, acceleration, and deceleration phases. This research aims to provide insights into the flow mechanisms at different mainstream operating conditions, which will serve as vital boundary conditions for investigating gas ingestion. The annulus flow in a turbine is commonly characterized by the flow coefficient CF. Equation (1) defines CF. Figure 2 illustrates a schematic of the velocity triangles between turbine stages. C, V, Ωb, and W represent the vane exit velocity, relative velocity at the blade inlet, rotational speed of the rotor, and axial velocity. α and β represent the flow angles at the vane exit and the blade inlet, respectively. According to the design condition of the vane exit airflow angle and the blade inlet airflow angle given in Table 3, the CF value for the design condition can be obtained from the velocity triangle as 0.64.
$$ C_F=\frac{W}{\varOmega b} $$ (1) 
Figure 2 Turbine interstage velocity triangleAccording to the velocity triangles between turbine stages and the definition of the flow coefficient CF, different values of CF result in variations in the velocity triangles between stages. Altering the mainstream flow and rotational speed impacts CF. To investigate the influence of different CF values obtained by independently changing the mainstream flow and rotational speed of the mainstream pressure field, the following experiments were conducted: (1) experiments under variable operating conditions with a fixed rotational speed of 4 000 r/min and varying the mainstream flow rate; and (2) experiments under variable operating conditions with fixed mainstream flow rates of 1.272 5 kg/s and 0.994 12 kg/s and varying the rotational speed. The specific operating conditions corresponding to each experiment are outlined in Tables 1 and 2.
Table 1 Operating conditions at a fixed speed at 4 000 r/minRotational reynolds number, Reφ 1.69×106 Axial reynolds number, Rew (0.507−1.3)×106 Flow coefficient, CF 0.3−0.77 Table 2 Operating conditions at a fixed mainstream flowMass flow (kg/s) 1.272 5 0.994 12 Axial reynolds number, Rew 1.08×106 8.45×105 Rotational reynolds number, Reφ (0.847−1.69)×106 (0.847−1.69)×106 Flow coefficient, CF (0.64−1.28) (0.5−1) 2.2 Numerical method
2.2.1 Computational models
To investigate the unsteady flow mechanisms related to rotor–stator interaction, the numerical study chooses the single-stage turbine without the disk cavity based on the dimensions of the experimental rig. Figure 3 shows the computational domain model of the mainstream passage for the single-stage turbine. The vane profile is derived from the root section of a self-designed engine guide vane model developed at the Institute of Engineering Thermophysics, Chinese Academy of Sciences. The blade profile is NACA0018, a symmetric airfoil with zero lift. Table 3 provides the relevant parameters for the blade profiles.
Figure 3 Single-stage turbine mainstream computational domain modelTable 3 Vane and blade parametersParameters Value Number of vanes/blades 33/66 Vane inlet mach number 0.2 Vane exit mach number 0.65 Vane inlet airflow angle (°) 0 Vane exit airflow angle (°) 67.04 Blade inlet airflow angle (°) 38.41 Blade exit airflow angle (°) 44.71 Vane/blade chord (mm) 46.5/33.10 Distance between vane and blade (mm) 15 To balance computational accuracy and resource requirements, the 10.909° sector model (1/33 of the annulus) of the mainstream passage is chosen for the computation. The mesh for the mainstream passage is generated using ANSYS TurboGrid 19.0. The first layer thickness of the mesh is set to 0.005 mm with a stretching ratio of 1.3. Figure 4 shows the mesh configuration for the vane and blade passages.
Figure 4 Mesh configuration for the vane and blade passages2.2.2 Computational setups and conditions
In this study, ANSYS CFX 19 commercial software is employed for simulation purposes. The shear stress transport turbulence model is used. The URANS (unsteady Reynolds-averaged Navier–Stokes) numerical simulation method is employed, with the RANS (Reynolds-averaged Navier–Stokes) results serving as the initial field. The boundaries are defined as the mass flow rate inlet and the pressure outlet. The interface between the guide vane and blade regions is treated differently by RANS and URANS calculations, employing the mix-plane and transient rotor–stator methods, respectively.
According to the velocity triangles, CF is determined to be 0.64 at the design condition. According to the definition of CF, the rotational speed and the mainstream flow rate can affect its value. The effects of the mainstream flow rate and the rotational speed on the mainstream pressure were investigated by performing the following numerical simulations: (1) Four numerical simulations were performed by keeping the rotational speed fixed at 4 000 r/min and varying the mainstream flow rate. The flow coefficients considered were CF = 0.3, 0.5, 0.64, and 0.83. (2) Four numerical simulations were conducted by keeping the mainstream flow rate constant at 1.272 5 kg/s and varying the rotational speed. The flow coefficients considered were CF = 0.43, 0.5, 0.64, and 0.85. Tables 4 and 5 show the numerical boundary conditions.
Table 4 Numerical conditions at a fixed speed at 4 000 r/minRotational reynolds number, Reφ 1.69×106 Axial reynolds number, Rew 0.507×106, 0.845×106, 1.08×106, 1.4×106 Flow coefficient, CF 0.3, 0.5, 0.64, 0.83 Table 5 Numerical conditions at a fixed mainstream flowMass flow (kg/s) 1.272 5 Axial reynolds number, Rew 1.08×106 Rotational reynolds number, Reφ 3.61×106, 2.12×106, 1.69×106, 1.27×106 Flow coefficient, CF 0.43, 0.5, 0.64, 0.83 2.2.3 Grid and timestep independence validation
To ensure that the calculation results are grid-independent the, CF =0.64 working condition is chosen, and the grid-independence of 1, 2, 3, 4 million cells is verified. Figure 5 presents the circumferential distribution of dimensionless pressure at the 1.5 mm positions of the vane trailing edge and the blade leading edge for different grids. Dimensionless pressure Cp (note: when studying the flow coefficients of a fixed mainstream, the mainstream dynamic pressure head is dimensionless) is defined using Equation (2). The figure shows that when the number of grid cells reaches 3 million, further increasing the number of cells minimally affects the peak pressure values at the vane trailing edge and the blade leading edge. Therefore, a grid comprising 3 million cells was selected for the numerical simulations in this study.
$$ C_p=\left(p-p_{\text {avg }}\right) / 0.5 \rho \varOmega^2 b^2 $$ (2) 
Figure 5 Dimensionless pressure circumferential distribution at the vane trailing edge and blade leading edgeConsidering the inherent instability of the rotor – stator interaction flow in the annulus, a sufficiently small timestep must be selected to resolve all relevant time scales. This decision can be made using the physical CFL. Two different timesteps were tested, 40 steps and 20 steps, to cover one blade passage revolution. Correspondingly, the timestep sizes were set to 5.682×10−6 and 1.136×10−5, respectively. The domain-averaged CFL numbers for these two cases are 1.75 and 3.49, respectively. Both CFL numbers are relatively small and close to 1. Considering the computational time and accuracy, the timestep size of 1.136×10−5 is chosen for the numerical simulations.
2.2.4 Experimental validation
The experiments conducted on the single-stage turbine rotor disk cavity rig, varying the flow coefficient by two methods, are used to validate the numerical approach. Figure 6 presents the distribution of measurement points at the location 1 mm downstream of the vane trailing edge in the experimental setup. Figure 7 compares the experimental and URANS time-averaged results at the location 1 mm downstream of the vane trailing edge for two different mainstream flow rates with a fixed rotational speed of 4 000 r/min. Figure 8 compares the experimental values of pressure distribution and the URANS time-averaged results for two speed conditions with a fixed main flow rate of 1.27 kg/s. For the two types of variable conditions varying CF, the simulation and experimental results are in good overall agreement, and the difference between the peak and valley values of interest and the experimental values is small, verifying the accuracy of the numerical simulation.
Figure 6 Distribution of pressure measurement points at the 1 mm position of the vane trailing edge
Figure 7 Dimensionless pressure distribution in the annulus compared to experimental data at a fixed rotational speed
Figure 8 Dimensionless pressure distribution in the annulus compared to experimental data at a fixed mass flow3 Results and discussion
3.1 Effect of rotor–stator interaction on mainstream pressure
The mechanism of unsteady flow and its influence on the annulus pressure distribution due to rotor–stator interaction is investigated by analyzing a specific operating condition. The chosen operating condition for analysis is a mainstream mass flow rate of 1.272 5 kg/s, a rotational speed of 3 000 r/min, and a flow coefficient of 0.85.
3.1.1 Mainstream pressure distribution
The circumferential variation in annulus pressure is considered a key factor determining the ingestion. Therefore, the annulus circumferential pressure difference must be focused on for the subsequent gas ingestion study. Figure 9 shows the axial distribution of the dimensionless circumferential pressure difference from the vane trailing edge downstream 1 mm to the blade leading edge upstream 1 mm at the 5% span for RANS, time-averaged URANS, and different instants URANS. T represents the blade passing period. The dimensionless circumferential pressure difference is denoted by ΔCp and defined by Equation 3.
$$ \Delta C_p=C_{p \max }-C_{p \min } $$ (3) 
Figure 9 Differential pressure distribution of different simulation methods from the vane trailing edge downstream 1 mm to the blade leading edge upstream 1 mmOn the side of the vane trailing edge, ΔCp obtained by the RANS calculation is lower than the time-averaged and instantaneous URANS results because the RANS method cannot capture the trailing edge vortex and flow on the vane suction surface well. On the side of the blade leading edge, RANS and time-averaged URANS are similar and lower than the instantaneous URANS results. These values are lower because the RANS and time-averaged URANS methods mitigate the influence of the wake at the interface, which is weaker than the mainstream flow. As the flow passes downstream, it is averaged with the mainstream, leading to unsubstantial differences in stagnation pressure ahead of different blades. For the instantaneous URANS results, the influence of the mainstream and vane wake on the blade varies as the blade rotates relative to the vane. This behavior leads to considerable time variation in the pressure distribution on the blade side. For the chosen condition, the blade potential flow pressure field slightly influences the vane, resulting in little difference in pressure on the vane side.
Figure 10 shows the pressure and velocity distribution contours at the 5% span. From the pressure contour, the time-averaged URANS and RANS results in the blade of the pressure distribution are identical without the vane wake, as shown by the dotted circle in the figure. For the 0T moment, the blade affected by different wakes and mainstream will stagnate to form different pressures; as in the figure, the blade pressure is higher at the circle position than at the rectangle position. The velocity contour shows the effect of different vane wakes. The blades of time-averaged URANS and RANS results are in the uniform velocity field without a vane wake. At 0T, the blades are located in the wake and mainstream velocity fields with different velocities, as shown in the figure, and the pressure is higher at the blade leading edge located in the mainstream velocity field than at the blade leading edge in the wake velocity field after the velocity–pressure transformation. Figure 11 gives the Cp distribution at the blade leading edge upstream 1 mm for the RANS, time-averaged URANS, and 0T URANS results, which shows the difference in pressure distribution at the blade leading edge due to the presence of the wake. The RANS calculation method does not apply to studying the mainstream rotor–stator interaction, and the URANS method is needed.
Figure 10 Pressure and velocity contours at the 5% span of the annulus
Figure 11 Cp circumferential distribution at the 1 mm position of the blade leading edge3.1.2 Pressure distribution in one blade passing period
To investigate the effects of rotor – stator interaction on the pressure distribution along the end walls over time, the pressure contours at 0T, 0.2T, 0.4T, 0.6T, and 0.8T in one blade passing period are plotted. Figure 12 shows the pressure, velocity, and radial vortex contours at a 5% span position at different times in one blade passing period, where the velocity and radial vortex contours reflect the trajectory of the vane wake. The blade, indicated by the black circle, experiences a diminishing influence from the vane wake and an increasing influence from the mainstream flow during the time interval from 0T to 0.4T. Consequently, the stagnation pressure at the blade's leading edge gradually increases. From 0.4T to 0.8T, the rotation of the blade gradually decreases the influence of the mainstream flow on the blade and increases the influence of the downstream vane wake. Thus, the stagnation pressure at the blade's leading edge gradually decreases.
Figure 12 Pressure, velocity, and radial vortex contours at the 5% span of the annulusTo more clearly represent the influence of the rotor–stator interaction on the vane trailing edge and the blade leading edge, Figure 13 shows the dimensionless circumferential pressure distributions at the vane trailing edge downstream 1 mm and the blade leading edge upstream 1 mm. The pressure potential field of the blade at different times has a relatively minor impact on the region near the vane trailing edge. However, the effect is slightly greater on the low-pressure region than on the high-pressure region near the vane trailing edge, as shown in the red circle. The wakes from the vane and the mainstream flow considerably impact the blade pressure field at different times. The pressure near the blade's leading edge exhibits distinct variations over time, influenced by the blade's position within the mainstream flow. When the blade aligns with the mainstream flow, the stagnation effect increases the pressure on the blade side (0T–0.4T). As the blade moves from the mainstream and encounters the wake, the stagnation pressure on the blade's leading edge gradually decreases (0.4T–0.8T).
Figure 13 Cp circumferential distribution of the 1 mm position at the vane trailing edge and blade leading edgeFigure 14 shows the distribution of the inlet circumferential average relative airflow angle along the blade height direction at the blade inlet. The blade is influenced by different mainstream and vane wakes at different times, resulting in different pressure distributions, which corresponds to different inlet airflow angles at the blade inlet (attack angles). Figure 13 shows that the different times correspond to different inlet airflow angles, and the most obvious difference is at the 0.15–0.8 blade height position.
Figure 14 Distribution of the mean relative airflow angle of the blade inlet at different times along the blade height3.1.3 Mainstream flow field
Figure 15 shows the evolution of the flow field within the vane passage. The oncoming mainstream boundary layer is arrested at the vane leading edge, creating a radial pressure gradient. Under the influence of this radial pressure gradient, the fluid near the end wall rolls up to form a horseshoe vortex. Subsequently, under the pressure gradient along the end wall, horseshoe vortices with opposite directions are formed on the suction side (Vsh) and pressure side (Vph) of the vane. Because of the transverse pressure gradient within the passage, the Vph migrates toward the vane suction side, intersecting with the Vsh to form a shroud passage vortex. Unlike other high aspect ratio blade profiles, end-wall passage vortices and a wide range of wake vortices are present at the vane exit. Because this particular blade has an extremely low aspect ratio, the upper and lower end-wall passage vortices fill the entire blade passage and mix with the shed vortices to form a trailing shedding vortex.
Figure 15 Flow field development in the vane passageThe flow structure in the vane passage affects the blade side. Different blades located at different circumferential positions downstream of the vane experience varying influences from the upstream flow field. This variation results in different pressures at their leading edges. Figure 16 shows the flow field distribution at the blade side at time 0T and the corresponding pressure contour. The pressure is obviously smaller for the blade leading edge, mainly influenced by the vane wake, than for that mainly influenced by the mainstream. The pressure at the blade leading edge, influenced by the vane wake, is lower than the pressure influenced by the mainstream flow.
Figure 16 Flow field and pressure contours at the blade leading edge at 0T3.2 Influence of CF (changing the speed) on mainstream pressure
On the basis of the analysis of the rotor–stator interaction mechanism under specific operating conditions, the pressure field caused by rotor–stator interaction under different flow coefficients is investigated. Initially, the pressure field is analyzed for different flow coefficients obtained by changing the rotational speed at a fixed mainstream flow rate.
Although the pressure differs between the time-averaged and instantaneous URANS results under a given operating condition, the time-averaged URANS results can still reflect the trend of pressure changes under different operating conditions. Figure 17 presents the time-averaged URANS results of the axial distribution of the dimensionless circumferential pressure difference ΔCp between the vane trailing edge and the blade leading edge at the 5% span for different flow coefficients. It is observed that when the mainstream flow rate is kept constant, the pressure on the vane side remains relatively unchanged between rotational speeds. However, the pressure on the blade side initially decreases and then increases as the rotational speed increases. The change in CF changes the airflow angle at the blade inlet, which changes the pressure at the blade leading edge. Figure 18 shows the distribution of the airflow angle at blades of different CF values along the blade height direction. As CF decreases, the blade inlet airflow angle gradually increases, and at CF=0.43, the angle increases considerably or even becomes positive. Figure 19 shows the relative velocity contour in front of the blade for different CF values. It is seen that the change in the airflow angle changes the stagnation area in front of the blade. The sharp increase in the stagnation area at CF=0.5 and 0.43 increases the pressure at the blade leading edge.
Figure 17 ΔCp axial distribution of time-averaged URANS from the vane trailing edge to the blade leading edge at different CF values and a fixed mass flow
Figure 18 Distribution of the airflow angle at the blade along the blade height direction for different CF values
Figure 19 Relative velocity contour at the blade leading edge for different CF values of time-averaged URANS resultsTo compare the impact of rotational speed on the transient pressure field, the results at 0T for different flow coefficients are analyzed. Figure 20 displays the distribution of ΔCp at 0T for various flow coefficients. The axial distribution patterns of transient ΔCp and time-averaged ΔCp are closely aligned, except in the rim seal region. At CF=0.43, the larger inlet airflow angle amplifies the influence of the blade potential flow pressure field. However, the impact on the vane side pressure remains minimal. Figure 21 shows the circumferential pressure distribution of the vane trailing edge and the blade leading edge at different CF values at 0T. It is seen that the speed has less influence on the pressure on the side of the vane compared to the side of the blade.
Figure 20 Axial distribution of ΔCp at time 0T for different CF values
Figure 21 Cp circumferential distribution at the vane trailing edge and blade leading edge at different CF valuesFigure 22 displays the axial distribution of ΔCp at different times within one blade passing period for different CF values, using time-averaged URANS as a reference. When CF=0.85 and 0.64, the pressure distribution on the vane side is almost constant over time; this result indicates that the blade potential flow pressure field has minimal influence on the upstream vane. However, on the blade side, distinct variations in pressure are observed over time due to the effects of rotor–stator interaction. For the case of CF=0.43, where the airflow angle at the blade inlet is larger, the mainstream and the wake are stalled on the larger surface area of the blade suction side. Thus, the pressure values on the rotor side vary slightly over time. However, because of the different relative circumferential positions of the rotor and vane, the blade pressure field has varying effects on the vane side.
Figure 22 Axial distribution of ΔCp at different CF values3.3 Influence of CF (changing the mass flow) on mainstream pressure
The pressure field is analyzed for the different flow coefficients caused by different mass flows with a fixed rotational speed. Figure 23 shows the time-averaged URANS results of the axial distribution of ΔCp at different CF values. For the vane side, ΔCp decreases with decreasing mass flow because the high-pressure area on this side originates from the velocity loss of vane trailing, and when the mainstream flow rate is larger, the total pressure is larger, and the static pressure value formed after the velocity loss is larger. On the blade side, ΔCp is not only determined by the mainstream flow rate but also influenced by the airflow angle at the blade inlet. For CF=0.85, 0.64, and 0.5, ΔCp decreases on the blade side as the mainstream flow rate decreases. However, when CF is 0.3, ΔCp suddenly increases on the blade side even higher than on the vane side. Referring to the analysis above of changing the rotational speed, the sharp increase in the airflow angle at the blade inlet can increase the pressure on the blade side.
Figure 23 ΔCp axial distribution of time-averaged URANS from the vane trailing edge to the blade leading edge at different CF values for a fixed rotational speedFigure 24 displays the axial distribution of ΔCp at different times within one blade passing period for different CF values. At small airflow angles at the blade leading edge, corresponding to CF=0.85, 0.64, and 0.5, the pressure distribution on the vane side is almost unchanged over time, indicating that the influence of the blade's potential flow pressure field on the upstream vane is small, and the pressure value on the vane side is larger than the pressure value on the blade. The influence of rotor–stator interaction on the blade side is large, and the blade side pressure varies considerably over time. At large airflow angles at the blade leading edge, corresponding to CF=0.3, the increased incoming flow angle increases the stagnation area on the blade side. This result increases the pressure on the blade side because of a greater amount of mainstream flow stagnation. Consequently, the pressure is higher on the blade side than on the stator side. Because of the larger airflow angle, the pressure variation on the blade side is relatively small over time. In contrast, the pressure distribution on the vane side is considerably influenced by the rotor-induced potential flow pressure field and thus shows noticeable time variation.
Figure 24 Axial distribution of ΔCp at different CF values3.4 Experimental results under variable operating conditions
Based on the analysis of the numerical simulation of the pressure field under different CF conditions obtained by changing the rotating speed or mass flow, an experimental study of changing CF in two ways is conducted. Because of the difficulty of measuring the pressure on the blade side, only the pressure on the vane side is measured. Figure 25 shows the circumferential distribution of the dimensionless pressure at the vane trailing edge for different CF values obtained by varying the mass flow at a fixed speed of 4 000 r/min. The high pressure and circumferential differential pressure at the vane trailing edge decrease gradually with decreasing mass flow, consistent with the trend of the numerical simulation. Figure 26 shows the experimental results of the dimensionless pressure distribution at the vane trailing edge for different rotating speeds at two main flow rates. For two fixed main flow rates, different rotating speeds have no effect on the pressure distribution at the vane trailing edge and essentially no effect on the circumferential pressure difference at this edge. When the mass flow is fixed, the vane trailing pressure distribution is unaffected by the rotating speed, consistent with the regularity of the numerical simulation results.
Figure 25 Circumferential distribution of Cp at the vane trailing edge under different mass flow rates at a fixed speed of 4 000 r/min
Figure 26 Circumferential distribution of Cp at the vane trailing edge under different rotating speeds at fixed mass flow ratesAlthough changing the mass flow and rotating speed can change CF, these two approaches affect the annulus pressure distribution differently. Experimentally measuring the pressure distribution on the vane trailing edge reveals that this pressure distribution is mainly determined by the mass flow rather than rotating speed. The regularity of the numerical simulation is experimentally derived and confirmed.
4 Conclusions
This paper analyzes the pressure field of the turbine interstage under the influence of rotor–stator interaction using numerical simulations and experiments for different CF conditions obtained by changing the mass flow rate or the rotational speed. The following main conclusions are drawn.
1) Among the numerical simulation methods, the URANS method is the most suitable. The pressure at the blade's leading edge is influenced by the trailing and mainstream stagnation degrees at different times. The mainstream stagnation has a greater impact than the trailing stagnation. In the determined working condition, the changes in pressure on the blade side are attributed to variations in the attack angle over time.
2) An analysis of the mainstream time-averaged pressure field under different flow coefficients shows that the mainstream pressure is primarily influenced by the mainstream flow rate and the angle of attack on the blade inlet. The vane side pressure decreases as the mainstream flow rate decreases. The blade side pressure is related to the mainstream flow rate and the angle of attack on the blade inlet. When the incidence angle is small, the blade side pressure decreases monotonically with decreasing mainstream flow rate. However, when the incidence angle is large, the blade side pressure sharply increases even at a low mainstream flow rate.
3) The analysis of the instantaneous pressure field shows that different flow coefficients obtained from the two methods lead to varying angles of attack on the blade inlet. For small incidence angles, the rotor–stator interaction causes substantial variations in the blade side pressure distribution over time while the vane side pressure remains relatively stable. For large incidence angles, the larger stagnation area reduces the temporal variations in blade side pressure and enhances the pressure potential field, varying the vane side pressure distribution.
4) The effects of rotational speed and mainstream flow rate on pressure are different and need to be clearly defined before studying the effect of flow coefficients on pressure. Since the differential pressure is sometimes higher on the blade side than the vane side, judging the degree of ingestion only by the vane side pressure is imperfect.
Acknowledgments: The authors wish to acknowledge the financial support of the National Natural Science Foundation Outstanding Youth Foundation (Grant No. 52122603), the National Science and Technology Major Project (J2019-Ⅲ-0003–0046), and the cloud computing supported by the Beijing Super Cloud Computing Center.Competing interest The authors have no competing interests to declare that are relevant to the content of this article. -
Figure 1 Configuration of the rotating disk cavity experimental rig
Figure 2 Turbine interstage velocity triangle
Figure 3 Single-stage turbine mainstream computational domain model
Figure 4 Mesh configuration for the vane and blade passages
Figure 5 Dimensionless pressure circumferential distribution at the vane trailing edge and blade leading edge
Figure 6 Distribution of pressure measurement points at the 1 mm position of the vane trailing edge
Figure 7 Dimensionless pressure distribution in the annulus compared to experimental data at a fixed rotational speed
Figure 8 Dimensionless pressure distribution in the annulus compared to experimental data at a fixed mass flow
Figure 9 Differential pressure distribution of different simulation methods from the vane trailing edge downstream 1 mm to the blade leading edge upstream 1 mm
Figure 10 Pressure and velocity contours at the 5% span of the annulus
Figure 11 Cp circumferential distribution at the 1 mm position of the blade leading edge
Figure 12 Pressure, velocity, and radial vortex contours at the 5% span of the annulus
Figure 13 Cp circumferential distribution of the 1 mm position at the vane trailing edge and blade leading edge
Figure 14 Distribution of the mean relative airflow angle of the blade inlet at different times along the blade height
Figure 15 Flow field development in the vane passage
Figure 16 Flow field and pressure contours at the blade leading edge at 0T
Figure 17 ΔCp axial distribution of time-averaged URANS from the vane trailing edge to the blade leading edge at different CF values and a fixed mass flow
Figure 18 Distribution of the airflow angle at the blade along the blade height direction for different CF values
Figure 19 Relative velocity contour at the blade leading edge for different CF values of time-averaged URANS results
Figure 20 Axial distribution of ΔCp at time 0T for different CF values
Figure 21 Cp circumferential distribution at the vane trailing edge and blade leading edge at different CF values
Figure 22 Axial distribution of ΔCp at different CF values
Figure 23 ΔCp axial distribution of time-averaged URANS from the vane trailing edge to the blade leading edge at different CF values for a fixed rotational speed
Figure 24 Axial distribution of ΔCp at different CF values
Figure 25 Circumferential distribution of Cp at the vane trailing edge under different mass flow rates at a fixed speed of 4 000 r/min
Figure 26 Circumferential distribution of Cp at the vane trailing edge under different rotating speeds at fixed mass flow rates
Table 1 Operating conditions at a fixed speed at 4 000 r/min
Rotational reynolds number, Reφ 1.69×106 Axial reynolds number, Rew (0.507−1.3)×106 Flow coefficient, CF 0.3−0.77 Table 2 Operating conditions at a fixed mainstream flow
Mass flow (kg/s) 1.272 5 0.994 12 Axial reynolds number, Rew 1.08×106 8.45×105 Rotational reynolds number, Reφ (0.847−1.69)×106 (0.847−1.69)×106 Flow coefficient, CF (0.64−1.28) (0.5−1) Table 3 Vane and blade parameters
Parameters Value Number of vanes/blades 33/66 Vane inlet mach number 0.2 Vane exit mach number 0.65 Vane inlet airflow angle (°) 0 Vane exit airflow angle (°) 67.04 Blade inlet airflow angle (°) 38.41 Blade exit airflow angle (°) 44.71 Vane/blade chord (mm) 46.5/33.10 Distance between vane and blade (mm) 15 Table 4 Numerical conditions at a fixed speed at 4 000 r/min
Rotational reynolds number, Reφ 1.69×106 Axial reynolds number, Rew 0.507×106, 0.845×106, 1.08×106, 1.4×106 Flow coefficient, CF 0.3, 0.5, 0.64, 0.83 Table 5 Numerical conditions at a fixed mainstream flow
Mass flow (kg/s) 1.272 5 Axial reynolds number, Rew 1.08×106 Rotational reynolds number, Reφ 3.61×106, 2.12×106, 1.69×106, 1.27×106 Flow coefficient, CF 0.43, 0.5, 0.64, 0.83 -
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