Subsonic Compressor Research Articles

Resolvent Analysis for Subsonic Compressor With Impedance Boundary Condition Casing Treatment

Abstract A resolvent analysis framework for the axial compressor is established, and the impedance optimization is achieved based on the resolvent analysis framework for the impedance boundary condition casing treatment. This framework is derived by treating the nonlinearity in the perturbation equations as an unknown forcing, the linear relationship between wall impedance and energy gains is obtained. The validity of this framework is confirmed through experiments on rotating inlet distortion, which captures the most susceptible frequency for the stall points of the compressor. The resolvent analysis framework further confirms that the first-order circumferential mode exhibits the highest energy in the given cases. Subsequently, the proposed impedance optimization method is tested under throttling operating conditions, especially focusing on the first-order circumferential mode. The introduction of a favorable impedance boundary condition notably reduces energy gain within the low-order circumferential mode and in the range of the rotor rotating frequency, particularly in near-stall operating conditions. The energy suppression mechanism of the impedance boundary condition casing treatment is investigated, demonstrating that the impedance boundary condition, with an optimal impedance value, significantly suppresses perturbations compared to the case with the solid wall boundary condition. Lastly, a design method for the impedance boundary condition casing treatment is discussed, offering a reliable theoretical design tool for enhancing the stall margin of axial compressors.

Investigation of irreversible losses in subsonic compressor cascade flow field: A study on viscous dissipation and temperature gradient term in entropy production rate

The entropy generation rate is a widely employed loss characterization approach in the design and optimization of fluid machinery. This approach is utilized to quantitatively determine various types of losses in the flow field, and it is considered that the temperature gradient term in the entropy generation rate can characterize irreversible losses. This research paper aims to address the question of whether the temperature gradient term in entropy production rate can represent the irreversible losses in a flow field. By employing the Reynolds-Averaged Navier-Stokes (RANS) numerical simulation method, the flow field of a subsonic compressor cascade, both with and without wall heating, was investigated. Statistical analysis was conducted to examine the contributions of viscous dissipation, the temperature gradient term in entropy production rate, wall shear stress work, and global power loss. The study reveals the distribution differences of viscous dissipation and the temperature gradient term in entropy production rate within the separated flow region. The research results demonstrate that, under wall heating conditions, viscous dissipation increased by approximately 45%, and the ratio of the temperature gradient term to global power loss increased from 4% to 125%, exceeding the mechanical energy loss in the flow field. The distribution of the temperature gradient term within the separated flow region cannot be explained by irreversible losses, and it exhibits significant discrepancies with the distribution of viscous dissipation losses. Therefore, the temperature gradient term in entropy production rate cannot represent the local irreversible losses, whereas viscous dissipation serves as an accurate measure of local irreversible losses. The research results provide theoretical support for accurately determining the irreversible losses in the flow field.

Influence of Herringbone Grooves Inspired by Bird Feathers on Aerodynamics of Compressor Cascade under Different Reynolds Number Conditions

Nowadays, high aerodynamic load has made blade separation an issue for compact axial compressors under high-altitude low-Reynolds-number conditions. In this study, herringbone grooves inspired by bird feathers were applied to suppress the suction side separation and reduce loss. To study the effect of bio-inspired herringbone grooves on the aerodynamic performance of compressor cascades, a high subsonic compressor cascade was taken as the research object. Under the conditions of different Reynolds numbers, the effects of herringbone grooves of different depths on the flow separation were numerically studied. The research results show that at a high-Reynolds-number condition (Re = 5.6 × 105), the sawtooth-shaped wake induced by herringbone grooves increases the turbulent mixing loss near the suction surface, and the blade performance deteriorates. At a low-Reynolds-number condition (Re = 1.3 × 105), the span-wise secondary flow and micro-vortex structure induced by the herringbone grooves effectively suppress the laminar separation on the suction surface of the blade, and there is an optimal depth for the herringbone grooves that reduces the profile loss by 8.33% and increases the static pressure ratio by 0.55%. The selection principle of the optimal groove depth with the Re is discussed based on the research results under six low-Reynolds-number conditions.

Coupling optimization design of configuration and swept-bowed effects in highly loaded subsonic compressor tandem cascades with tip clearance

The coupling optimization design for swept-bowed effects and configuration of tandem cascade is conducted in a highly loaded subsonic compressor tandem cascade, in which the novelty lies in considering the spanwise distribution of configuration parameters and exploring the coupling relationship between them and swept-bowed design. Research results show that, compared with the original one, the loss coefficient of the optimal tandem cascade is decreased by 38.7% at the 4° incidence angle and the range of available incidence angle expands by 25%. For the distribution of the configuration parameters, parameters at the hub are significantly different from those near the tip, which confirms the tandem blade design in compressors is complex and needs to consider 3D flow effect. Forward swept and positive bowed design are beneficial for reducing loss at tip and alleviating the blockage, which cannot be achieved by the optimization only for configuration parameters. In terms of the weak coupling relationship between configuration parameters distribution and swept-bowed effects, the former should be considered first in practical engineering.

Extraction of geometric features and analysis of flow mechanism of high loaded compressor airfoils at low Reynolds number

When the aircraft cruising at high altitude, the aerodynamic performance of the compressor sharply decreases due to the enhanced boundary layer separation loss. Therefore, it is of great significance to design the high-performance airfoils suitable for low Reynolds numbers (Re) to improve the aerodynamic performance of compressor. In this paper, numerical simulations were carried out on a high-loaded subsonic compressor cascade V103 at low Re. Meanwhile, a multi-objective optimization of blade profile was performed to get optimal solutions, and data mining techniques were applied to extract valuable design knowledge from the optimal database. The results show that the Pareto-optimal airfoils achieve a maximum reduction of 27.32% in total pressure loss coefficient under design condition and 36.71% under near stall condition. Compared with the original airfoil, the curvature distribution law of the camber line with larger values at both ends and smaller values in the middle is advantageous for the performance of the compressor cascade under design condition. This distribution pattern causes a forward shift for the loading distribution of airfoils, accompanied by an earlier transition onset. Additionally, it reduces adverse pressure gradient at the rear part of suction surface, which suppresses the development and growth of laminar separation bubble and delays the separation of turbulent boundary layer. Under near stall condition, maintaining larger leading edge angle and uniform flow diffusion is beneficial for improving the performance of compressor cascade. This is because the larger leading edge angle reduces incidence angle, while the uniform flow diffusion inhibits a great flow separation.

A data-driven polynomial chaos method for uncertainty quantification of a subsonic compressor cascade with stagger angle errors

The probability-based uncertainty quantification (UQ) methods require a large amount of sampled data to construct the probability distribution of uncertain input parameters. However, it is a common situation that only limited and scarce sampled data are available in engineering applications due to expensive tests. In the present paper, the Data-Driven Polynomial Chaos (DDPC) method is adopted, which can propagate input uncertainty in the case of scarce sampled data. The calculation accuracy and convergence of the self-developed DDPC method are validated by a nonlinear test function. Subsequently, the DDPC method is applied to investigate the uncertain impact of stagger angle errors on the aerodynamic performance of a subsonic compressor cascade. A family of manufacturing error data of stagger angles was obtained from the real compressor blades. Based on the limited measurement data, the DDPC method combined with Computational Fluid Dynamics (CFD) simulation is employed to quantify the performance impact of the compressor cascade. The results show that the performance dispersion under off-design conditions is more prominent than that under design conditions. The actual aerodynamic performance deviating from the nominal performance is not a small probability event, and the probability of deviating from the nominal loss coefficient and exit flow angle by more than 1% can reach up to 47.6% and 36.8% under high incidence i = 7°. Detailed analysis shows that stagger angle errors have a significant effect on the flow state near the leading edge, resulting in variations in separation bubble size and boundary layer thickness.

Uncertainty quantification of blade geometric deviation on compressor stability

PurposeThe geometric parameters of the compressor blade have a noteworthy influence on compressor stability, which should be meticulously designed. However, machining inaccuracies cause the blade geometric parameters to deviate from the ideal design, and the geometric deviation exhibits high randomness. Therefore, the purpose of this study is to quantify the uncertainty and analyze the sensitivity of the impact of blade geometric deviation on compressor stability.Design/methodology/approachIn this work, the influence of blade geometric deviation is analyzed based on a subsonic compressor rotor stage, and three-dimensional numerical simulations are used to compute samples with different geometric features. A method of combining Halton sequence and non-intrusive polynomial chaos is adopted to carry out uncertainty quantitative analysis. Sobol’ index and Spearman correlation coefficient are used to analysis the sensitivity and correlation between compressor stability and blade geometric deviation, respectively.FindingsThe results show that the compressor stability is most sensitive to the tip clearance deviation, whereas deviations in the leading edge radius, trailing edge radius and chord length have minimal impact on the compressor stability. And, the effects of various blade geometric deviations on the compressor stability are basically independent and linearly superimposed.Originality/valueThis work provided a new approach for uncertainty quantification in compressor stability analysis. The conclusions obtained in this work provide some reference value for the manufacturing and maintenance of rotor blades.

The unsteadiness of tip leakage vortex breakdown and its role in rotating instability

The unsteadiness due to tip leakage vortex (TLV) breakdown was studied using a special experimental test campaign in parallel with numerical simulations. The back flow vortex (BFV), an isolated vortex caused by TLV spiral-type breakdown, was found to play a key role in rotating instability (RI). High-speed pressure transducers were used to measure the unsteady pressure field at the casing end wall of the blade in an isolated subsonic compressor rotor, which identified a low-frequency fluctuation at the near stall condition. A single-passage unsteady Reynolds-averaged Navier–Stokes simulation was used to study the evolution of unsteady flow structures, validated by the experimental measurements. Two distinct kinds of periodically unsteady flow were revealed by the simulations. A high-frequency fluctuation corresponding to 1.0 blade pass frequency (BPF) was caused by the spiral-type breakdown of the TLV. The other low-frequency fluctuation corresponding to 0.5BPF was caused by the feedback interaction between the BFV and the blade loading. The BFV was generated by the TLV breakdown, which was separated from the twisted vortex core of the TLV, and it moved downstream along the pressure side of the adjacent blade. A larger sized BFV reduced the local loading of the adjacent blade. The TLV was weakened as a consequence of the reduced loading, resulting in a smaller sized BFV. The blade tip loading was relatively less affected by the small sized BFV rather than the larger sized BFV. Therefore, the blade loading recovered and the size of the BFV increased, repeating the cycle. This feedback mechanism produced a pressure fluctuation with a frequency equal to 0.5BPF, which was closely related to RI.

A New Influence Mechanism of Clocking Effect in Subsonic Compressor

This paper investigates the clocking effect in subsonic compressor element stages and the influence of design parameters on the flow mechanism. We focus on the relationship between the wake-induced separation loss and wake mixing loss and the unsteady mechanism in the wake flow process without considering the transition through several steady and unsteady numerical simulations aimed at a series of subsonic compressor element stages. The simulation results indicate that the performance difference at various indexing positions depends on the relationship between wake mixing loss and wake-induced separation loss for different compressor designs and operating conditions. Furthermore, the pressure transport caused by the negative jet of the Stator 0 wake in Rotor 1 creates a local acceleration region called SFAF, and a decrease in its absolute flow angle reduces the Stator 1 separation. Sufficient rim work of the rotor at highly loaded operating conditions is the basis for generating an effective SFAF. Furthermore, the fore-loading blade of Rotor 1 significantly reduces suction surface pressure drop, and a small angle between the stagger angles of Stator 0 and Rotor 1 increases the unsteady rotor load caused by the upstream wake to the total rotor load, both of which enhance SFAF.

Quasi-three-dimensional loss prediction model of subsonic compressor cascade based on bidirectional long short-term memory networks and multi-head self-attention

The prediction of compressor cascade loss is a crucial aspect of compressor design. Flow separation is an important flow structure and the main source of loss in subsonic cascades. In order to capture the flow separation and accurately evaluate flow loss, a data-driven quasi-three-dimensional (quasi-3D) subsonic compressor cascade loss prediction model based on bidirectional long short-term memory (BiLSTM) and multi-head self-attention is proposed. The model contains four sub-models to predict the pressure, temperature, axial velocity, and total pressure loss coefficient in two-dimensional slices along the axial direction, using Mach number, curved blade angle, solidity, camber angle, and incidence as inputs, respectively. For the purpose of adapting to cascade geometrical change, geometric reformulation is adopted before the model training. The model is trained and tested by validated computational fluid dynamics results, which contain symmetric separation and asymmetric separation samples. It is proved that the model is able to accurately predict flow parameters value in each slice. Then, four typical cases are mainly discussed, which shows that the model can effectively capture the characteristics of flow separation formation and development. Afterward, different models are compared, and it is found that the BiLSTM with multi-head self-attention model achieved the lowest mean squared error, which is because of its outstanding predicting ability in asymmetric separation cases. The work of this paper indicates that the quasi-3D loss prediction model proposed in this paper will be beneficial to the flow separation structure rapid prediction and cascade loss accurate evaluation in compressor design.

A New Segmented Suction Slot Design Based on the Performance of Compressor Cascade

To develop an effective suction slot arrangement, computational fluid dynamics simulation software and a high subsonic compressor cascade were used to simulate different suction slots. Based on the effects of various suction slots on the cascade performance under various operating conditions, a novel segmented suction slot structure Seg3 was proposed. The results of the study revealed that in the vicinity of the operating conditions ( incidence ≤ 4 ° ), a full-blade height suction slot should be installed at least 5% of the chord length downstream of the corner separation point to effectively remove the separation. For small and medium incidences, the best performance was observed for suction slot SS5, which was located at 60% of the chord length downstream of the leading edge. Analyzing the effects of SS5 and Seg3 on the cascade performance revealed that when the incidence was less than 4°, the reductions in the total pressure loss coefficients for ζsuc of SS5 and Seg3 both exceeded 8.2%. When the incidence was 4° or greater, the ζsuc increased slightly for SS5, whereas it decreased for Seg3, and the ζsuc was reduced. For a 3° incidence, for example, Seg3 reduced the ζsuc and passage blockage by 12.74% and 8.41%, respectively, and increased the static pressure rise coefficient by 18.55% from the baseline values. Thus, the segmented suction slot proposed in this paper outperformed conventional full-blade height suction slots.

Optimization of impedance boundary-controlled casing treatment on subsonic compressors

Optimization of impedance boundary-controlled casing treatment on subsonic compressors

Numerical investigations of vortex dynamics and loss generation in the corner separation region of a high subsonic compressor blade

Three-dimensional corner separation seriously deteriorates the aerodynamic performance of a compressor blade. In this study, the complicated vortex dynamics and loss mechanism in the corner region of a high subsonic compressor blade (the inlet Mach number is 0.67) are investigated using large eddy simulations (LESs) at a Reynolds number (Re) of 5.6 × 105. The results show that the predicted total pressure loss and outlet flow angle match well with the experimental data, indicating that the LES method can accurately predict the size and strength of corner separation in the compressor blade. With the passage vortex rolling up and further interacting with the low-momentum fluids originating from the end wall boundary layers and the local blade boundary layers, strong shear strain induces a large-scale concentrated shedding vortex (CSV) near the spanwise location of x/H = 0.3. The formation and rolling-up of the CSV not only cause the strongest flow blockage but also strengthen the turbulence anisotropy. As the CSV moves toward the trailing edge, the strong interaction with a pair of counter-rotating vortices shed in the wake region (wake shedding vortex) further accelerates the local generation of turbulent kinetic energy (TKE). Detailed TKE budget analysis shows that the streamwise Reynolds normal stress (w′w′¯) plays the most decisive role in the TKE production term. Furthermore, we demonstrate that the strength of turbulence anisotropy is positively correlated with the TKE budget. Therefore, turbulence anisotropy should be considered carefully in predicting the loss level in the corner region of a compressor blade.

Numerical Investigation of Inlet Boundary Layer in an Axial Compressor Tandem Cascade

To explore the inlet boundary layer (IBL) influence on the tandem cascade aerodynamic performance, this paper took the high subsonic compressor NACA65 K48 cascade and its modified tandem cascade as the research object. The effects of the IBL thickness and the skewed IBL on the aerodynamic performance of the original cascade and tandem cascade were analyzed based on the numerical method. The results show that the tandem cascade effective design makes it better than the original cascade in the aerodynamic performance under different IBL conditions. Compared with the collateral IBL, the skewed IBL can effectively improve the aerodynamic performance of the original cascade and tandem cascade by suppressing the endwall cross flow, but an increase in the IBL thickness will suppress this advantage. In addition, the increase of incidence angle or the IBL thickness will make the tandem cascade forward blade corner separation more serious and cause the flow passage to be blocked, which seriously affects the rear blade diffusing capacity. In general, the IBL thickness is positively correlated with the tandem cascade total pressure loss and negatively correlated with the static pressure rise (except for the −6° incidence angle). The skewed IBL can effectively reduce the total pressure loss and increase the static pressure rise within −4°~7° incidence angle, but the law is opposite at a −6° incidence angle. At a 0° or 2° incidence angle, the performance improvement effect of the skewed IBL on the tandem cascade is the best, and this positive effect diminishes as it tends towards a larger positive incidence angle or a smaller negative incidence angle.

A data-driven non-intrusive polynomial chaos for performance impact of high subsonic compressor cascades with stagger angle and profile errors

The impact of geometric variations due to manufacturing errors on the aerodynamic performance of compressor blades is considerable in engineering practice. Accurate uncertainty quantification (UQ) of aerodynamic performance based on actual statistical information of manufacturing errors is helpful for error detection, aerodynamic shape design, etc. However, the actual manufacturing errors may not be independent of each other, and their marginal distributions are often not standard. To apply UQ to dependent input variables with arbitrary distributions, the present paper first introduced a decorrelation algorithm and proposed a novel data-driven Non-Intrusive Polynomial Chaos (DNIPC) model. The subsequent tests based on high-dimensional function experiments and UQ of the performance for a high subsonic compressor cascade have validated its generality, effectiveness, and efficiency. Then, the simultaneous impact of stagger angle and profile errors on the performance of the compressor cascade was investigated by the proposed DNIPC and Sobol's sensitivity analysis. The distributions of manufacturing error were determined by kernel density estimation based on finite measurement data, then using the parametric B-spline and Bezier curves to build the manufactured geometry of the cascade. Finally, the influence of the manufacturing errors on aerodynamic performance was further discussed through the UQ of the cascade flow field. The results show that the performance impact in the off-design conditions, especially for those below the design incidence, is the most important. It suggested that the uncertainty of profile error should be checked carefully in the process of detecting machining error when the operation condition is at or below the design incidence; in contrast, the influence of stagger angle error calls for more attention when the cascade works at high incidences. The fluctuation of the overall aerodynamic loss is mainly associated with the manufacturing error near the leading edge, for it affects the velocity spike and the development of its downstream boundary layer. Therefore, the leading edge error should be the top focus.

Influence of uncertain inflow conditions on a subsonic compressor cascade based on wind tunnel experiment

The intended inflow condition of compressors is subject to the uncertain inflow Mach number ( Ma1) and incidence angle ( i). To quantify the effects of uncertain inflow conditions, real-time measuring experiments of Ma1 and i are performed under various operating conditions to extract the statistical characteristics of the uncertainties. Statistical analysis shows that Ma1 and i follow Gaussian distribution. 0.005 and 0.125 are chosen as the standard deviation of Ma1 and i, respectively. Based on these data, an in-house code of non-intrusive polynomial chaos and Sobol’ indices are employed to quantify the variability in the aerodynamic performance of a compressor cascade caused by uncertain Ma1 and i. The results show that the inflow uncertainties narrow the steady working range of the compressor cascade and lead to fluctuation in the aerodynamic performance. The fluctuation amplitude of the total pressure loss coefficient increases about 15.8 times and tenfold while the static pressure ratio increases just double and 1.3 times under various Ma1 and i conditions, respectively. An analysis of flow field under various operating conditions shows that the uncertainties change the peak isentropic Mach number on the suction surface alter the location and size of the boundary layer separation and reattachment, and shift the interference between the wake and suction surface separation vortex. The sensitivity analysis reveals that as Ma1 increases from 0.5 to 0.6, the dominant parameter affecting the uncertainty of the flow field changes from i to Ma1. When Ma1 increases to 0.75, the coupling effect of Ma1 and i dominates the flow field.

Comparative Study of Tip Injection in a Transonic and Subsonic Compressor

Abstract Discrete tip injection is an effective method to enhance stability of compressors. This study compares the effects of injection parameters on compressor performance and underlying mechanisms in two different compressors. The transonic compressor is studied using unsteady simulations, and the subsonic compressor is mainly investigated with experiments. Results show that tip injection improves stable operating range by 35.6% and 77.9% for the transonic compressor and subsonic compressor, respectively, without decreasing compressor efficiency. The effects of circumferential coverage percentage and injector throat height on compressor stability are similar in the two compressors when the injection velocity is double the velocity of the main flow. The optimal injector throat height which is normalized by the tip clearance size is the same for the two compressors, and the best circumferential coverage percentage for the subsonic compressor is lower than that in the transonic compressor. For the two compressors, the adaption of the main flow to the discrete tip injection is unsteady, and the hysteresis effect that the recovery of tip blockage lags behind the recovery of tip leakage vortex accounts for the improved stability using partial coverage of injection. The injection efficiency, which is defined to quantify the improved quality of the flow field in the injection domain, is proven to determine the stall limits by studying the effects of different injection parameters. The guidelines built in the subsonic compressor can be used in the transonic compressor to design tip injection, but the optimal values of some injection parameters should be reconfirmed.

Variable Clearance Characteristics of High Subsonic Compressor Cascades with Blade Tip Winglets

Variable Clearance Characteristics of High Subsonic Compressor Cascades with Blade Tip Winglets

Stochastic aerodynamic analysis for compressor blades with manufacturing variability based on a mathematical dimensionality reduction method

It is essential for engineering manufacture and robust design to evaluate the impact of manufacturing variability on the aerodynamics of compressor blades efficiently and accurately. In the paper, a novel quadratic curve approximation method based on the scanning points of blade design profiles was introduced and combined with Karhunen–Loève expansion, a mathematical dimensionality reduction method for modeling manufacturing variability as truncated Normal process was proposed. Subsequently, Sparse Approximation of Moment-based Arbitrary Polynomial Chaos (SAMBA PC) and computational fluid dynamics (CFD) were applied to build a computational framework for stochastic aerodynamic analysis considering manufacturing variability. Finally, the framework was adopted to evaluate the aerodynamic variations of a high subsonic compressor cascade under the design incidence. The results illustrate that the SAMBA PC method is more efficient than the traditional methods such as Monte Carlo simulation (MCS) for stochastic aerodynamic analysis. Through uncertainty quantification, the impact of manufacturing variability on the global aerodynamic performance is primarily reflected in the fluctuation of aerodynamic losses, and the fluctuation of the total losses is mainly contributed by the fluctuation of the separation loss after the suction peak (a negative pressure spike near the leading edge (LE)) and the boundary-layer loss on the suction surface (SS). With sensitivity analysis, the most important geometric modes to aerodynamics can be revealed, which provides a useful reference for manufacturing inspection process and helps reduce computational cost in robust design.

Searching for the Most Suitable Loss Model Set for Subsonic Centrifugal Compressors Using an Improved Method for Off-Design Performance Prediction

This work investigates loss model sets based on empirical loss correlations for subsonic centrifugal compressors. These loss models in combination with off-design performance prediction algorithms make up an essential tool in predicting off-design behaviour of turbomachines. This is important since turbomachines rarely work under design conditions. This study employs an off-design performance prediction algorithm based on an iterative process from Galvas. Modelling of ten different loss mechanisms and physical phenomena is involved in this approach and is thoroughly described in this work. Geometries of two subsonic compressors were reconstructed and used in the evaluation of individual loss correlations in order to obtain a suitable loss model. Results of these variations are compared to experimental data. In addition, 4608 loss model sets were created by taking all possible combinations of individual loss estimations from which three promising candidates were selected for further investigation. Finally, off-design performance of both centrifugal compressors was computed. These results were compared to experimental data and to other loss model sets from literature. The newly composed loss model set No. 2137 approximates experimental data over a 21.2% better in relative error than the recent Zhang set and nearly a 36.7% better than the outdated Oh’s set. Therefore, set No. 2137 may contribute to higher precision of centrifugal turbomachines’ off-design predictions in the upcoming research.