Supersonic Cascade Research Articles

Aerodynamic design of supersonic compressor cascade and vorticity dynamic diagnosis of flow field structure

High-load counter-rotating compressor plays a crucial role in reducing the axial length and weight of the compressor and increasing the thrust-to-weight ratio of the aero-engine. However, the boundary layer flow separation induced by shock waves in the channel of high adverse pressure gradient also brings more aerodynamic losses. This paper proposed a supersonic compressor cascade modeling method based on the unique inlet angle theory and the superimposing thickness on the suction surface method. It carried out aerodynamic optimization design of cascade with inlet Mach number of 1.85 combined with numerical optimization technology, vorticity dynamics diagnosis, and planar cascade experiment. The results show that multiple shock wave combination pressurization can be realized in the supersonic cascade channel. At the design point, the static pressure ratio is 3.285, and the total pressure recovery coefficient reaches 86.82%, and the experimental results of planar cascade also verify the correctness of the simulation method. In addition, the correlation laws between the distribution of the vorticity dynamic parameter, shock wave structure, and aerodynamic performance of cascade were analyzed by the vorticity dynamic flow field diagnosis method, which provides a beneficial reference for the subsequent compressor design.

Control on SWBLI by vortex generator in a supersonic cascade

In order to control the SWBLI separation in supersonic cascade and widen its working range, VG array is set on the suction surface and numerically explored. VG can redistribute the passage flow to suppress the separation near the blade wall. Through the analysis on the effects of typical geometry parameters, the chord position of VG trailing edge should be set at the middle position between the blade leading edge and passage shock wave, the height of VG leading edge should be set to nearly 80 % thickness of boundary layer at SWBLI position at near-stall condition, and the array distance of VG should be large as much as possible on the premise of ensuring stable and ordered flow. With the parameter design of VG, at the cost of increasing flow loss from 0.209 to 0.222, the stall margin of cascade is improved from 0.068 to 0.167.

Research on time sequence prediction of supersonic cascade flow field based on compressed sensing artificial neural network

The aviation engine that achieves efficient energy conversion is the core power equipment for low-carbon navigation, and the thermal components represented by the combustion chamber greatly affect the stable state of the compressor cascade flow field. Accurate, comprehensive and promptly monitoring of the compressor cascade flow state is related to the safe operation of the engine. A flow field time sequence prediction framework named compressed convolutional gate recurrent unit (CC-GRU) was proposed in this study to predict future supersonic cascade flow parameters based on the flow field at previous moments. CC-GRU embedded convolution into gate recurrent unit (GRU) to deal with the complex spatial-temporal behavior of supersonic cascade flow field. Firstly, unsteady numerical simulations driven by linear changes in back pressure were carried out, and the dataset for model training and validation was obtained to verify the feasibility of time sequence prediction of the cascade flow field. The verification results indicate that the framework can comprehensively predict the flow field with high back pressure in the future according to the flow field with low back pressure in the past period, and further validated the effectiveness of the proposed time sequence prediction model in ground wind tunnel experiments. The CC-GRU model can accurately capture the fine shock wave structure and flow separation zone, with a relative error of less than 10% in predicting the pressure field, and is mainly concentrated within the shock wave structure. Therefore, this research provides new research perspective and technical support for comprehensive and promptly condition monitoring of supersonic cascade flow field.

Nitrogen Experiments on a Supersonic Linear Cascade For ORC Applications

A novel experiment has been conceived at Politecnico di Milano for the study of the flow within and downstream of supersonic cascades of Organic Rankine Cycle (ORC) turbines. This paper documents the first phase of the research, focused on the preliminary tests and studies performed by operating the facility with nitrogen as working fluid, to demonstrate the technical relevance of the experiment and the validity of the measurement system in a simplified thermodynamic condition. The set of measured data includes, beside the inlet total thermodynamic state, eight static pressure values obtained via taps manufactured on the test section rear end-wall, both within the bladed and semi-bladed region of the cascade, as well as a total pressure probe to retrieve the cascade performance. A double-passage Schlieren equipment was also employed to visualize the density gradients. Experiments show an outstanding repeatability, indicate a quasi-steady cascade operation during the blow-down process for all the pressure signal considered, and demonstrate a remarkable periodicity among two consecutive channels also in off-design conditions. Experimental data were also compared with CFD simulations, resulting in an excellent agreement for the pressure data acquired both within and downstream of the cascade.

Trailing-edge shock loss control with self-sustaining synthetic jet in a supersonic compressor cascade

To effectively reduce the loss of strong shock wave at the trailing edge of the supersonic cascade under high backpressure, a shock wave control method based on self-sustaining synthetic jet was proposed. The self-sustaining synthetic jet was applied on the pressure side of the blade with the blow slot and the bleed slot arranged upstream and downstream of the trailing-edge shock, respectively. The flow control mechanism and effects of parameters were investigated by numerical simulation. The results show that the self-sustaining synthetic jet forms an oblique shock wave in the cascade passage which slows down and pressurizes the airflow, and the expansion wave downstream of the blow slot weakens the shock strength which can effectively change the Mach reflection to regular reflection and thus weaken the shock loss. And the suction effect can reduce loss near blade surface. Compared with the baseline cascade, the self-sustaining jet actuator can reduce flow losses by 6.73% with proper location design and vibration of diaphragm.

Aerodynamic Characteristics of Morphing Supersonic Cascade Under Low-Upstream-Mach-Number Condition

For fans of a variable-cycle engine, a good aerodynamic performance over a wide range of rotating speeds is essential. However, when supersonic cascades designed for a high upstream Mach number operate under a low upstream Mach number, a starting problem may occur, which significantly decreases the aerodynamic performance of fan blades. As a result, the operating range of the supersonic cascades is severely limited. To solve the starting problem caused by the mismatch between geometry of supersonic cascades and upstream Mach number, a morphing supersonic cascade is developed. Thus, this study mainly focuses on the effect of the static deformation of supersonic cascades driven by smart materials on aerodynamic characteristics under a low upstream Mach number. To investigate this issue, numerous simulations are conducted on an S-type cascade by finite element method and computational fluid dynamics. As demonstrated by flow structure analysis, the morphing cascades are started under certain morphing configurations while the original cascade operates at nonstarted state. The results show that the deformation driven by smart materials alters the shock wave structures under a low upstream Mach number by adjusting key cascade geometric parameters. Specifically, the morphing cascades achieve 80% reduction of detached shock loss compared with the original cascades.

The Influence of Steady Air Jet on the Trailing-Edge Shock Loss in a Supersonic Compressor Cascade

To effectively reduce shock wave loss at the trailing edge of a supersonic cascade under high back-pressure, a shock wave control method based on air jets is proposed. The air jet was arranged on the pressure side of the blade in the upstream of the trailing-edge shock. The flow control mechanism and effects of parameters were analyzed by computational methods. The results show that the air jet formed an oblique shock wave in the cascade passage which decelerated and pressurized the airflow. The resulting expansion wave downstream of the jet slot weakened the strength of the trailing-edge shock. This could effectively change the normal shock into oblique shock and thus weaken the shock loss. Optimal control effect was achieved when the mass flow rate ratio of the jet to the passage airflow remained 0.35–1.11% and the distance from the jet slot to the shock foot of the trailing-edge shock was about five times the thickness of the boundary layer. The proposed method can reduce the total pressure loss of a supersonic cascade, with the maximum improvement effect reaching 7.29% compared to the no-control state.

A Bayesian data assimilation method to enhance the time sequence prediction ability of data-driven models

The generalization ability and robustness of data-driven models deteriorate when samples are scarce or input features are outside the training sample space. This research focuses on building a data assimilation (DA) framework that embeds the time sequence prediction model and improves the prediction results by constructing an enhanced system state vector that incorporates model bias parameters and new observation data to achieve the deviation correction and improve the robustness of the model. The DA framework proposed in this study includes three steps: prediction model inference, ensemble Kalman filter (EnKF) online deployment, and model parameter update. Wind tunnel experiments of a supersonic cascade are performed to obtain the original data for training the prediction model and optimizing the DA framework. Long short-term memory network (LSTM) was chosen as the prediction model. The testing set is distributed outside the sample space of the training set to verify the effectiveness of the DA framework for enhancing the time sequence prediction model. The improvement effects of the EnKF-enhanced LSTM model on the time sequence prediction results of the wall pressure in the oscillating flow field and the non-oscillating flow field are studied. The optimization results indicate that the LSTM model embedded in the DA framework can significantly improve the wall pressure prediction results. Thus, the results of this study lay a solid foundation for the condition monitoring and margin determination of the supersonic cascade flow field.

Research on the Influence of Surface Roughness on the Flow Field in the Cascade

Fouling, corrosion, and icing are common causes of increased compressor blade roughness due to special operating conditions and natural environment. Roughness increase would influence on flow field, especially in supersonic compressor cascades where incident waves can interact with reflected shock waves. Studies have shown that the boundary layer condition of the blade varies with wall roughness, which affects both the incident shock wave and the reflected shock wave. In order to study the effect of the distribution of roughness, the flow field under different roughness settings is simulated. The results show that flow loss is reduced with increasing roughness at the incidence point of an incident wave and the trailing edge of the suction side.

Research on time sequence prediction of the flow field structure of supersonic cascade channels in wide range based on artificial neural network

Accurate and comprehensive flow field prediction is indispensable for promptly monitoring the flow state of supersonic cascades. This paper proposes a time sequence prediction architecture based on the full convolutional neural network (FCNN) to predict the future flow parameters of supersonic cascades based on the wall pressure at the previous moment. Considering the complicated spatial-temporal characteristics of the time sequence prediction of flow field structures, FCNN embeds the convolution into the long short-term memory (LSTM) and replaces the fully connected layer with a convolution in the output layer. Wind tunnel experiments with different flap rotation rates were performed to obtain the dataset required for model training and verification. For pressure-to-schlieren time sequence prediction, FCNN takes the cascade wall pressure at the previous moment as input and the future schlieren of the flow field structure captured by a high-speed camera as its output. The experimental results show that FCNN can accurately predict the position of the leading edge and that the maximum relative error is less than 4.4%. Moreover, for pressure-to-pressure time sequence prediction, the bidirectional LSTM (BiLSTM) was used to predict the wall pressure of the cascade channel. Results show that the BiLSTM can accurately capture the nonlinear characteristics of the wall pressure changing over time. Thus, the results of this study lay a solid foundation for the subsequent determination of the stability margin of flow fields.

Throttling process of a supersonic cascade studied by high-frequency response pressure and high-speed schlieren

In this study, a single-channel supersonic cascade model is investigated experimentally at a freestream Mach number of 2.4 to obtain a better understanding of the flow field evolution during the throttling process. A flap is placed at the channel exit to choke the flow linearly. Measurements include 1-kHz schlieren imaging and 10-kHz simultaneous fast-response wall pressure. Three stages, namely attached flow, separated flow, and oscillatory flow, are identified in the throttling process. The joint time–frequency analysis and wall pressure spectrum contour exhibit the time evolution and spatial distribution of the pressure fluctuation. With the increase in backpressure, the pressure fluctuation in the low-frequency shock oscillation range of 40–400 Hz on the suction surface located in the separated flow gradually enhances. The power spectral, coherence, and phase analyses of the schlieren images describe the dominant oscillation structure and its relationship with other regions. During the separated flow, the pressure change in the subsonic separated region first lead to a change in the state of the separated shear layer, after which the shock waves in the shock train, move. The oscillatory flow is a process wherein the upstream shock wave oscillates, causing the entire downstream channel to fluctuate.

An efficient deep learning framework to reconstruct the flow field sequences of the supersonic cascade channel

Accurate and comprehensive flow field reconstruction is essential for promptly monitoring the flow state of the supersonic cascade. This paper proposes a novel data-driven method for reconstructing the slices of the two-dimensional (2D) pressure field in three-dimensional (3D) flow of the supersonic cascade by using deep neural networks. Considering the complicated spatial effects of 2D pressure field slices, the architecture embeds the convolution into the long short-term memory (LSTM) network to realize the purpose of using the upstream pressure to reconstruct downstream pressure. Numerical simulations of the supersonic cascade under different back pressures are performed to establish the database capturing the complex relationship between the upstream and downstream flow. The pressure of different upstream slices can be used as a spatial-dependent sequence as the input of the model to reconstruct the pressure of different downstream slices. A deep neural network including special convolutional LSTM layers and convolutional layers is designed. The trained model is then tested under different back pressures. The reconstruction results are in good agreement with the computational fluid dynamics, especially for the identification of shock wave position changes and the recognition of complex curved shock waves in 3D flow with high accuracy. Moreover, analyzing the frequency distribution of reconstructed pressure at different positions can clearly distinguish the flow separated zone, which will further improve the accuracy of the state monitoring. Specifically, it is of great significance for identifying the stall of the flow field promptly.

Mechanism and detection of oscillatory flow in a supersonic cascade

The throttling process in a supersonic cascade is investigated in a free-jet wind tunnel at Mach 2.4. High-speed schlieren imaging and high-resonance frequency pressure measurements are used to capture the flow features. A flap is placed at the channel exit to choke the flow linearly. In the throttling process before the onset of oscillatory flow, the shock train leading shock leads to large area of flow separation near the suction surface and high total pressure loss. The oscillatory flow is triggered by the expansion of the flow separation induced by the impingement of the shock train leading shock onto the suction surface, which belongs to the Dailey criterion. The alarm is triggered during oscillatory flow detection, based on the pressure data at the optimal S5 transducer, either before the large-amplitude pressure fluctuation begins or after it ends. Comparing with other algorithms, the derivative-based algorithm has no data to be stored and no expensive calculation is the best technique for detection. To adjust the alarm margin, three detection points are set upstream of the S5 transducer and detection is performed based on the schlieren images. All algorithms detect the sudden drop in light intensity caused by the arrival of the shock train leading shock at the detection location. The alarm margin is the largest at point C, which is farthest from the suction surface tip, and smallest at point A, which is closest to the suction surface tip.

The sonic scale of interstellar turbulence

Understanding the physics of turbulence is crucial for many applications, including weather, industry, and astrophysics. In the interstellar medium (ISM), supersonic turbulence plays a crucial role in controlling the gas density and velocity structure, and ultimately the birth of stars. Here we present a simulation of interstellar turbulence with a grid resolution of 10048^3 cells that allows us to determine the position and width of the sonic scale (l_s) - the transition from supersonic to subsonic turbulence. The simulation simultaneously resolves the supersonic and subsonic cascade, v(l) ~ l^p, where we measure p_sup = 0.49 +/- 0.01 and p_sub = 0.39 +/- 0.02, respectively. We find that l_s agrees with the relation l_s / L = phi_s Mach^(-1/p_sup), where Mach is the three-dimensional Mach number, and L is either the driving scale of turbulence or the diameter of a molecular cloud. If L is the driving scale, we measure phi_s = 0.42 (+0.12) (-0.09), primarily because of the separation between the driving scale and the start of the supersonic cascade. For a supersonic cascade extending beyond the cloud scale, we get phi_s = 0.91 (+0.25) (-0.20). In both cases, phi_s < 1, because we find that the supersonic cascade transitions smoothly to the subsonic cascade over a factor of 3 in scale, instead of a sharp transition. Our measurements provide quantitative input for turbulence-regulated models of filament structure and star formation in molecular clouds.

Investigation of shock wave control by suction in a supersonic cascade

The numerical simulation of suction control on a supersonic cascade is presented in this paper. The purpose of this study is to enhance the resistance backpressure characteristics of a flow field by suction control and demonstrate the evolution of shock structures and parameter distributions in the flow field controlled by suction. The study is based on the SAV21 supersonic cascade designed by the German Aerospace Centre and operated under an incoming Mach number of 2.4 and a flow turning angle of 45°. The three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations in a Cartesian coordinate system are successfully applied to the cascade flow. The two-equation shear-stress transport (SST) k-ω turbulence model of Menter is employed to model the turbulent velocity profile. The results show that when the backpressure is greater than the critical backpressure, the shock train leading edge crosses the throat, causing a decrease in the mass-capturing coefficient and the occurrence of stall. To control supersonic cascade by suction, the most effective location is at the interaction of the shock train leading edge and the suction surface boundary layer. By applying suction control at the key position, the shock train is stabilized at the downstream boundary of the suction slot with a small loss of suction mass flow. At mild backpressure ratio range, the increased backpressure is compensated by the local enhanced barrier wave. By increasing the pressure gradient downstream of the barrier wave, the maximum backpressure is improved by suction control. By using the improved combined suction scheme with one spanwise slot on the suction surface and one streamwise slot on the endwall, the maximum backpressure can be improved by 20% under a suction mass flow of 8% of the capture mass.

Flow field reconstruction and prediction of the supersonic cascade channel based on a symmetry neural network under complex and variable conditions

A data-driven model containing a symmetrical deep neural network is proposed to reconstruct the flow field structure in a cascade channel by measuring discrete pressure values on the wall of the supersonic cascade channel. The model designed is to demonstrate that the deep neural network can realize the reconstruction and prediction of the flow field structure in the supersonic cascade channel under complicated and changing working conditions. The dataset used for model training is derived from numerical simulation of the supersonic cascade channel. The symmetrical model includes a transposed convolution part and a conventional convolution part, which, respectively, implement up-sampling of the pressure data and further extraction of features. The generalization ability and scalability of the model are analyzed from the contour plots of the pressure and density gradient. In order to verify the ability of the model to reconstruct unknown operating conditions, the organizational form of the training set and testing set has been specially designed to achieve the ability of interpolating outwards. In the testing set, the symmetrical model has a certain ability to realize extrapolation and prediction, and the flow field structure can be accurately reconstructed by using the discrete pressure values on the wall surface of the cascade channel. Moreover, to accurately evaluate the regression model proposed by this study, the correlation analysis was also applied in this study. The results show that the worst linear correlation coefficient is 0.9848 in the testing set, indicating that the model has satisfactory ability to reconstruct and predict the flow field.

Inversion and reconstruction of supersonic cascade passage flow field based on a model comprising transposed network and residual network

A data-driven model comprising a transposed network and a residual network is proposed to predict the flow field structure of the supersonic cascade passage by measuring the wall pressure of the cascade passage. This model is based on the close relationship between the wall pressure values of the supersonic cascade passage and the flow field structure. Wind tunnel experiments of the supersonic cascade passage were conducted to obtain real experimental data. The transposed network, which is the first part of the model, consists of transposed convolution, normal convolution, and fully connected layers. However, the mapping ability of the transposed network between the wall pressure values and the cascade passage flow field structures was insufficient. The maximum relative error by the transposed network in predicting the position of the leading edge of the shock train was 8.5%. Therefore, the residual network was introduced as the second part of the model to achieve end-to-end super-resolution and improve the mapping ability of the model. After training, the residual network reduced the maximum relative error of the position prediction of the leading edge of the shock train to 3.5%. In the testing set, the prediction results of the model indicated that the movement of the leading edge of the shock train can be distinguished well. Furthermore, a combination of the two networks revealed the mapping relationship between the wall pressure of the supersonic cascade passage and the flow field structure. Thus, the results of this study lay a good foundation for the subsequent determination of the flow field stability margin.

Evolution of subsonic and supersonic corner vortices in a supersonic cascade

Numerical investigations on a supersonic cascade are conducted at the flow-through, high-backpressure, and low-speed modes to obtain a deeper understanding of the generation, development, and transformation of the subsonic and supersonic corner vortices. The geometry considered is the SAV21 supersonic cascade designed by the German Aerospace Centre operating under incoming Mach number of 2.4 and flow turning angle equal to 45 degrees. The corner vortex is generated by the impinging and glancing of shock waves on the boundary layer and drives the low-kinetic energy fluid moving spanwise. The cross-flow topology of the supersonic corner vortex follows Zhang's theory that considers flow with high Reynolds number and excludes the incorrect solutions generated by the expression of the velocity gradient along the vortex axis. The Hopf bifurcation position of the subsonic corner vortex can be accurately predicted by describing the velocity gradient along the vortex axis, while deviation occurs when using Zhang's theory. By observing the development process of corner vortices, the reason for the limitations in the range of application of Zhang's theory is analyzed. In general, the key factors for the evolution of the subsonic and supersonic corner vortices are the velocity gradient and pressure gradient along the vortex axis, respectively. The bifurcation processes of the corner vortex can be classified into four types. And the bifurcation principle can be summarized, the appearance of limit cycle does not immediately change the rotating direction of the vortex and the bifurcation process is gradual.

Experimental investigation of the throttling process and oscillation mechanism in a supersonic cascade

The structure and oscillation characteristics of the shock train during steady and oscillatory flows in a supersonic cascade was experimentally studied. The study was based on the SAV21 supersonic cascade designed by the German Aerospace Centre operating under incoming Mach number equal to 2.27 and flow turning angle of 45 degrees. Before the onset of stall, the expansion waves generated on the curved configuration of the suction surface (stage III) and the separation bubble (stage IV) suppresses the movement of the shock train. A striking feature of stage 1 of the oscillatory flows is that as the throttling ratio increases, the dominant frequency of the pressure fluctuation keeps decreasing and the high-energy oscillations take up more time and a wider frequency range. Then stage 2 (which is composed of large-amplitude oscillations and secondary oscillations) appears. With the enhancement of the throttling ratio, the occurrence probability of large-amplitude oscillations rises in stage 3. The shock train propagates into the upstream passage in stage 4, the final stage. Through cross-wavelet transform, it was discovered that the immediate change of the entrance local conditions leads to the in-phase fluctuation of pressure in the entire flowfield during the oscillatory flows, which is consistent with the observation of Dailey. Further analysis indicates that all the oscillation stages except stage 4, are triggered by the suction-surface flow separation, which belongs to the Dailey criterion. Furthermore, the feedback loop established by the communicating ways (acoustic wave propagation, shock movement, spillage, and separation bubble deformation) is brought forward.

Investigations on flowfield behavior and resistance backpressure characteristics of supersonic cascade with boundary layer suction

A numerical study aiming at the enhancement of the operating range of supersonic cascade via boundary layer suction is presented. The purpose of this paper is to improve the maximum backpressure ratio of the flowfield by suction control and to learn the flowfield behavior and characteristics with different suction control parameters. An S-shaped supersonic cascade developed and tested at DLR (DLR-PAV-1.5) that operates with a relative entrance Mach number of 1.5 is selected in this paper. A two-dimensional multiblock NS solver has been successfully applied to the cascade flow which is validated using the data of the experiment of Schreiber. An in-deep numerical study has been carried out to investigate the effects of suction locations, widths and angles by comparing the operating range and aerodynamic performance parameters of the supersonic cascade. The results indicate that the maximum backpressure ratio can be enhanced by 17.4% with a loss of 3% mainstream mass flow by suction slot in 60% or 70% length of the axial chord. As the width of the suction slot increases to 7 mm, the maximum backpressure ratio is enhanced by 24%, and the total pressure recovery coefficient is improved to 95.3%. The range of suction slot angle that can effectively improve the maximum backpressure ratio is 60–90° and −90 to −60°. This paper provides guidance for the supersonic cascade to improve its performance parameters through suction control.