Blade Row Interaction Research Articles

Efficient Forced Response Minimization Using a Full-Viscosity Discrete Adjoint Harmonic Balance Method

A forced response induced by inlet distortion and blade row interactions can lead to high-cycle fatigue failure, especially when the unsteady excitation frequency is close to the natural vibration frequency of a blade. This paper presents the study of forced response sensitivity analysis and minimization using a full-viscosity unsteady discrete adjoint method. The goal is to improve the aeroelastic performances of turbomachinery blades and simultaneously constrain/improve aerodynamic performances. The decoupled modal reduction method is used to compute the forced response, which is considered the objective function in adjoint-based design optimization. To analyze aeroforcing and aerodamping flow and adjoint fields efficiently, the harmonic balance method and its adjoint counterpart developed by an automatic differentiation tool are applied. Two cases—the NASA Rotor 67 with inlet distortion and a three-row configuration with multiple fundamental frequencies in the second row—are used to demonstrate the effectiveness of the aerodynamic and aeroelastic coupled design optimization system developed in this work. For the latter case, the Fourier-transform-based method that first decomposes and then matches the time and space modes at two sides of an interface is used for interface coupling. The almost-periodic Fourier transform method is used to determine the time instances for cases with multiple fundamental frequencies.

Resolving nonuniform flow in gas turbines: challenges, progress, and moving forward

Abstract The flow in gas turbines exhibits a highly unsteady, complex and nonuniform manner, which presents two main challenges. Firstly, it introduces instrumentation errors, contributing to uncertainties when calculating one-dimensional performance metrics during rig or engine tests using fixed-location rakes. Secondly, it raises mechanical concerns, including high-cycle fatigue due to blade row interactions in turbomachines and thermal fatigue caused by hot-streaks at the combustor exit. Experimental characterisation of the flow nonuniformity in gas turbines is highly challenging due to the confined space and harsh environment for instrumentation. This paper presents recent efforts to address this issue by resolving the nonuniform flow in gas turbines using spatially under-sampled measurements. The proposed approach utilises discrete probe data and leverages a ‘Fourier-based approximation’ method developed by the author. The technique has undergone preliminary experimental validation involving reconstruction of the total pressure distribution in a multi-stage axial compressor and the total temperature field at the exit of the combustor and high-pressure turbine. Results show that, in the multi-stage axial compressor environment, reconstruction of inter-stage total pressure is achieved using a reduced dataset covering less than 20% of the annulus with reasonably good accuracy. The reconstructed total pressure yields almost identical mean total pressure values at all spanwise locations, with a maximum deviation of less than 0.02%. Additionally, reconstruction of the total temperature distribution at an engine-representative full annulus combustor is achieved using measurements at ten carefully selected circumferential locations. Results show that the reconstructed temperature field successfully captures the primary features associated with combustor exit temperature flow. The reconstructed temperature field yields excellent agreement in the magnitude of radial temperature distribution factor (RTDF) and overall temperature distribution factor (OTDF) predictions to the experiment, with a deviation of less than 0.5% for RTDF and less than 2.5% for OTDF. Lastly, reconstruction of the total temperature distribution at the exit of the GE E3 high-pressure turbine (HPT) is achieved using measurements at eight carefully selected circumferential locations. Results demonstrate remarkable robustness in resolving the temperature profile at the HPT exit with high fidelity, irrespective of the HPT inlet conditions. The initial validation results are promising, demonstrating that the new probe layout scheme and the Fourier-based approximation method enable effective characterisation of flow nonuniformity in gas turbines, thereby providing valuable insights into the complex flow of gas turbine engines.

Unsteady Flows and Component Interaction in Turbomachinery

Unsteady component interaction represents a crucial topic in turbomachinery design and analysis. Combustor/turbine interaction is one of the most widely studied topics both using experimental and numerical methods due to the risk of failure of high-pressure turbine blades by unexpected deviation of hot flow trajectory and local heat transfer characteristics. Compressor/combustor interaction is also of interest since it has been demonstrated that, under certain conditions, a non-uniform flow field feeds the primary zone of the combustor where the high-pressure compressor blade passing frequency can be clearly individuated. At the integral scale, the relative motion between vanes and blades in compressor and turbine stages governs the aerothermal performance of the gas turbine, especially in the presence of shocks. At the inertial scale, high turbulence levels generated in the combustion chamber govern wall heat transfer in the high-pressure turbine stage, and wakes generated by low-pressure turbine vanes interact with separation bubbles at low-Reynolds conditions by suppressing them. The necessity to correctly analyze these phenomena obliges the scientific community, the industry, and public funding bodies to cooperate and continuously build new test rigs equipped with highly accurate instrumentation to account for real machine effects. In computational fluid dynamics, researchers developed fast and reliable methods to analyze unsteady blade-row interaction in the case of uneven blade count conditions as well as component interaction by using different closures for turbulence in each domain using high-performance computing. This research effort results in countless publications that contribute to unveiling the actual behavior of turbomachinery flow. However, the great number of publications also results in fragmented information that risks being useless in a practical situation. Therefore, it is useful to collect the most relevant outcomes and derive general conclusions that may help the design of next-gen turbomachines. In fact, the necessity to meet the emission limits defined by the Paris agreement in 2015 obliges the turbomachinery community to consider revolutionary cycles in which component interaction plays a crucial role. In the present paper, the authors try to summarize almost 40 years of experimental and numerical research in the component interaction field, aiming at both providing a comprehensive overview and defining the most relevant conclusions obtained in this demanding research field.

Analysis of the thermal insulation performance of turbine blade thermal barrier coatings considering inlet non-uniformity

The gases discharged from the new generation of lean-burn combustors usually have hot streaks (HS) and swirls. The thermal performance of rotor thermal barrier coatings (TBCs) exhibits significant non-constant behavior due to inlet non-uniformity and blade row interaction. To investigate the non-constant thermal insulation performance of the blade TBCs, non-constant numerical simulations were carried out for the first stage vane and blade of the High-pressure turbine of the GE-E3 engine. The normalized temperature results for the HS and the combination of HS and swirl cases were compared with the uniform inlet case to investigate the effect of inlet non-uniformity on the surface temperature and thermal insulation effect of the blade TBCs. The results show that a credible investigation of rotor TBCs should consider the unsteady blade row interaction. HS causes high-temperature hot spots on the surface of the TBCs and redistributes them with the change in the direction of the swirl. HS and swirl significantly reduce the turbine blade cooling effectiveness and thermal insulation effectiveness of TBCs. The lowest overall cooling performance of the blades was observed during the 1/4 T stator period. The added swirl reduces the insulation effectiveness's fluctuation value by reducing positive swirl (PSW) by 52.6 % and negative swirl (NSW) by 57.8 %. Therefore, applications and designs of TBCs should consider the effects of HS and swirl.

CFD Analysis of a Transient Rotor-Stator Axial Steam Turbine Stage

An axial steam turbine stage has both stationary and rotating components, which are coupled together in a CFD model by multiple frames of reference. There are three types of interface techniques available to exchange the information between the different frames of reference namely frozen rotor, stage, transient stator rotor. Both frozen rotor and stage interfaces are used in steady state analysis. The operation of axial turbine is inherently an unsteady process. The aerodynamic interaction between the rotating part and the stationary parts are the important contributor to the unsteadiness of the flow present in the turbine. Neither of the two interfaces implemented in the steady state CFD analysis is capable of predicting the unsteady effects resulting from the rotor-stator interaction due to their relative position change. The third type of interface, the transient stator-rotor interface, is available to simulate the fluid motion caused by the relative movement between a rotor and stationary components in axial turbine. Although enormous computer resources are needed for this modelling, it simulates real flow physics best of all, while steady or quasi-steady numerical approaches only approximate the real flow, because they neglect important effects of blade row interactions. The paper presents the CFD analysis carried out for an axial steam turbine stage with three different interface techniques and compares the results.

Accounting for Circumferential Flow Nonuniformity in a Multistage Axial Compressor

AbstractThe flow field in a compressor is circumferentially nonuniform due to geometric imperfections, inlet flow nonuniformities, and blade row interactions. Therefore, the flow field, as represented by measurements from discrete stationary instrumentation, can be skewed and contributes to uncertainties in both calculated one-dimensional performance parameters and aerodynamic forcing functions needed for aeromechanics analyses. Considering this challenge, this article documents a continued effort to account for compressor circumferential flow nonuniformities based on discrete, undersampled measurements. First, the total pressure field downstream of the first two stators in a three-stage axial compressor was measured across half of the annulus. The circumferential nonuniformities in the stator exit flow, including vane wake variability, were characterized. In addition, the influence of wake variation on stage performance calculations and aerodynamic forcing functions were investigated. In the present study for the compressor with an approximate pressure ratio of 1.3 at the design point, the circumferential nonuniformity in total pressure yields an approximate 2.4-point variation in isentropic efficiency and 54% variation in spectral magnitudes of the fundamental forcing frequency for the embedded stage. Furthermore, the stator exit circumferential flow nonuniformity is accounted for by reconstructing the full-annulus flow using a novel multiwavelet approximation method. Strong agreement was achieved between experiment and the reconstructed total pressure field from a small segment of measurements representing 20% coverage of the annulus. The analysis shows the wake–wake interactions from the upstream vane rows dominate the circumferentially nonuniform distributions in the total pressure field downstream of stators. The features associated with wake–wake interactions accounting for passage-to-passage variations are resolved in the reconstructed total pressure profile, yielding representative mean flow properties and aerodynamic forcing functions.

Enhancement of Rotor Loading and Suppression of Stator Separation through Reduction of the Blade–Row Gap

An immersed boundary (IB) method is applied to study the effect of the blade–row gap in a low-speed single-stage compressor. The advantage of using an IB method is that the rotor/stator interface can be eliminated and, thus, the blade–row interaction can be considered at an extremely small gap. The IB method was modified to internal-flow problems, and the adaptive mesh refinement (AMR) technique, together with a wall model, used to facilitate the simulations for high Reynolds-number flows. The results showed that both the pressure rise and the efficiency were observed to be higher in the smaller-gap cases. Comparisons between the results of two gaps, 35%ca and 3.5%ca, are highlighted and further analysis at a specific flow coefficient showed that the increase of the stage performance was contributed to by the enhancement of rotor loading and the suppression to the flow separation of the stator. Correspondingly, the increases of the total pressure rise on the rotor and the stator outlets were observed to be 0.5% and 4.3%, respectively. Although the increase on the rotor outlet is much lower than that on the stator outlet, its significance is that a higher level of static pressure is formed near the hub of the gap, which, thus, reduces the adverse pressure gradient of this region in the stator passage. This improvement suppresses the flow separation near the hub of the stator and, thereby, results in a considerable increase to the pressure rise on the stator outlet as a consequence. The effect of the gap on unsteady pressure fluctuation is also presented.

Investigation of Unsteady Rotor–Stator Interaction and Deterministic Correlation Analysis in a Transonic Compressor Stage

Abstract Unsteady blade row interaction (UBRI) has a large impact on performance in high-speed axial compressors. Thus, the influence of UBRI should be accurately predicted in compressor routine design. In this study, the unsteady rotor–stator interaction in a transonic single-stage compressor, NASA Stage 35, is studied by steady and unsteady Reynolds-Averaged Navier–Stokes methods. First, the UBRI is analyzed. Periodic separation bubbles on the stator suction surface induced by the rotor wake are observed. Comparisons between steady and unsteady results show that the radial distribution of flow angle near the hub and tip region of the stator is strongly influenced by UBRI. Second, deterministic correlations are analyzed based on the average-passage equation system. The distribution of deterministic stress and the relationship between spatial correlations and deterministic correlations are analyzed. Results show that a strong nonlinear interaction caused by the rotor wake and the stator potential field is found in the rotor–stator gap, which is responsible for the generation of spatial–time correlation. Then, the anisotropy of deterministic correlations is analyzed using the Lumley triangle. Results show that the deterministic stress is highly anisotropic in the stator passage, which can be considered in the modeling using a similar strategy of turbulence modeling. At last, the relationships between the harmonics and decay rate of deterministic correlations are analyzed. The decay rate of deterministic correlation is highly related to the corresponding harmonics, and the higher-order harmonic exhibits a higher decay rate. A modified exponential decay model is proposed for deterministic correlation based on harmonics, which provides improved performance.

Numerical study on unsteady film cooling performance of turbine rotor considering influences of inlet non-uniformities and upstream coolant

High-pressure turbine (HPT) rotor blades work in a harsh environment with high temperature and rotational speed. Affected by blade row interaction and inlet non-uniformities, the rotor flow field behaves with significant unsteady characteristics. In order to study the unsteady film cooling performance of the rotor blade, unsteady numerical simulations were conducted on the film-cooled first stage vane and blade of GE-E3 engine HPT. Time-resolved results of cases with hot streak (HS) and combined HS and swirl were compared to the case with uniform inlet total temperature and velocity to investigate the effect of inlet non-uniformities. A simulation with non-film-cooled stator vane (NFCS) was also studied to reveal the impact of stator film coolant. The results showed that unsteady film cooling effectiveness fluctuations at the leading edge (LE) region are the most significant, with the mean-to-peak fluctuation amplitude reaching over ±100%. LE cooling air unsteady excursion induced by the stagnation line oscillation is the main cause of this behavior. Vane coolant and inlet non-uniformities have shown a distinguished influence on the coolant attachment and migration at LE, thus affecting the film cooling effectiveness. At blade pressure side (PS) and suction side (SS), vane coolant and inlet non-uniformities affect the fluctuation amplitude of film cooling effectiveness by changing the static pressure perturbation behavior. Simultaneously, the existence of HS will decrease the SS time-averaged film effectiveness by a factor of 10%. In comparison, swirl has shown a negative effect on PS film effectiveness by a factor of 6%.

Characteristics of fluid exciting force due to blade row interaction of a propeller turbine

As the use of renewable energy is promoted, much researches on propeller-type turbines are carried out. To improve reliability, it is important to evaluate the fluid exciting force due to blade row interaction that may cause vibration or fatigue fracture. In this paper, CFD(URANS) simulations and experimental studies were conducted to understand the characteristics of the fluid exciting force due to blade row interaction of a propeller turbine. To evaluate the fluid exciting force, strain gauges and pressure sensors were used in the closed-loop water channel. The fluid exciting force acting on the rotor due to the stator was measured by changing stator load type and the rotor-stator distance. Based on the difference in the attenuation tendency of potential interaction and wake interaction due to changes in the rotor-stator distance, the influences of these interactions could be distinguished. As results of experiments and computation, wake interaction affecting pressure fluctuation was hardly attenuated due to the swirling flow and changing the rotor-stator distance has little effect on the attenuation of blade row interaction.

Reconstructing Compressor Non-Uniform Circumferential Flow Field From Spatially Undersampled Data—Part 1: Methodology and Sensitivity Analysis

Abstract The flow field in a compressor is circumferentially non-uniform due to the wakes from upstream stators, the potential field from both upstream and downstream stators, and blade row interactions. This non-uniform flow impacts stage performance as well as blade forced vibrations. Historically, experimental characterization of the circumferential flow variation is achieved by circumferentially traversing either a probe or the stator rows. This involves the design of complex traverse mechanisms and can be costly. To address this challenge, a novel method is proposed to reconstruct compressor non-uniform circumferential flow field using spatially under-sampled data points from a few probes at fixed circumferential locations. The paper is organized into two parts. In the present part of the paper, details of the multi-wavelet approximation for the reconstruction of circumferential flow and use of the particle swarm optimization algorithm for selection of probe positions are presented. Validation of the method is performed using the total pressure field in a multi-stage compressor representative of small core compressors in aero engines. The circumferential total pressure field is reconstructed from eight spatially distributed data points using a triple-wavelet approximation method. Results show good agreement between the reconstructed and the true total pressure fields. Also, a sensitivity analysis of the method is conducted to investigate the influence of probe spacing on the errors in the reconstructed signal.

Reconstructing Compressor Nonuniform Circumferential Flow Field From Spatially Undersampled Data—Part 2: Practical Application for Experiments

Abstract In the previous part of the paper, a novel method to reconstruct the compressor nonuniform circumferential flow field using spatially undersampled data points is developed. In this part of the paper, the method is applied to two compressor research articles to further demonstrate the potential of the novel method in resolving the important flow features associated with these circumferential nonuniformities. In the first experiment, the static pressure field at the leading edge of a vaned diffuser in a high-speed centrifugal compressor is reconstructed using pressure readings from nine static pressure taps placed on the hub of the diffuser. The magnitude and phase information for the first three dominant wavelets are characterized. Additionally, the method shows significant advantages over the traditional averaging methods for calculating repeatable mean values of the static pressure. While using the multi-wavelet approximation method, the errors in the mean static pressure with one dropout measurement are 70% less than the pitchwise-averaging method. In the second experiment, the full annulus total pressure field downstream of Stator 2 in a three-stage axial compressor is reconstructed from a small segment of data representing 20% coverage of the annulus. Results show very good agreement between the reconstructed total pressure profile and the experiment at a variety of spanwise locations from near hub to near shroud. The features associated with blade row interactions accounting for passage-to-passage variations are resolved in the reconstructed total pressure profile.

Effect of Blade Row Interaction on Rotor Film Cooling

Abstract The mechanisms of blade row interaction affecting rotor film cooling are identified to make recommendations for the design of film cooling in the real, unsteady turbine environment. Present design practice makes the simplifying assumption of steady boundary conditions despite intrinsic unsteadiness due to blade row interaction; we argue that if film cooling responds nonlinearly to unsteadiness, the time-averaged performance will then be in error. Nonlinear behavior is confirmed using experimental measurements of flat-plate cylindrical film cooling holes, mainstream unsteadiness causing a reduction in film effectiveness of up to 31% at constant time-averaged boundary condition. Unsteady computations are used to identify the blade row interaction mechanisms in a high-pressure turbine rotor: a “negative jet” associated with the upstream vane wake, and frozen and propagating vane potential field interactions. A quasi-steady model is used to predict unsteady excursions in momentum flux ratio of rotor cooling holes, with fluctuations of at least ±30% observed for all hole locations. Computations with modified upstream vanes are used to vary the relative strength of wake and potential field interactions. In general, both mechanisms contribute to rotor film cooling unsteadiness. It is recommended that the designer should choose a cooling configuration that behaves linearly over the expected unsteady excursions in momentum flux ratio as predicted by a quasi-steady hole model.

Reducing Instrumentation Errors Caused by Circumferential Flow-Field Variations in Multistage Axial Compressors

Abstract The effects of blade row interactions on stator-mounted instrumentation in axial compressors are investigated using unsteady numerical calculations. The test compressor is an eight-stage machine representative of an aero-engine core compressor. For the unsteady calculations, a 180-deg sector (half-annulus) model of the compressor is used. It is shown that the time-mean flow field in the stator leading edge planes is circumferentially nonuniform. The circumferential variations in stagnation pressure and stagnation temperature, respectively, reach 4.2% and 1.1% of the local mean. Using spatial wave number analysis, the incoming wakes from the upstream stator rows are identified as the dominant source of the circumferential variations in the front and middle of the compressor, while toward the rear of the compressor, the upstream influence of the eight struts in the exit duct becomes dominant. Based on three circumferential probes, the sampling errors for stagnation pressure and stagnation temperature are calculated as a function of the probe locations. Optimization of the probe locations shows that the sampling error can be reduced by up to 77% by circumferentially redistributing the individual probes. The reductions in the sampling errors translate to reductions in the uncertainties of the overall compressor efficiency and inlet flow capacity by up to 50%. Recognizing that data from large-scale unsteady calculations are rarely available in the instrumentation phase for a new test rig or engine, a method for approximating the circumferential variations with single harmonics is presented. The construction of the harmonics is based solely on the knowledge of the number of stators in each row and a small number of equispaced probes. It is shown how excursions in the sampling error are reduced by increasing the number of circumferential probes.

An improved inverse method for multirow blades of turbomachinery

A three-dimensional viscous inverse design method is improved and extended to multirow blades environment. The inverse method takes load distribution as optimization objective and is implemented into the time-marching finite-volume Reynolds-averaged Navier–Stokes solver. The camber line of rotor blade is updated by virtual displacement, which is calculated by characteristic compatibility relations according to the difference between target and actual load so as to control the location and intensity of shock wave, and realize the optimization of flow structure and reduction flow separation. The inlet and outlet geometry angles of stator blade are adjusted in real time according to the inlet and outlet flow angles. Thus, it is computationally ensured that the blade row interactions are accounted and optimization process is carried out under the design condition. To preserve the robustness of calculation, the maximum virtual displacement is limited by Y+ <10 and the camber line is smoothed via cubic B-spline interpolation. The complete blade profile is then generated by adding the prescribed blade thickness distribution to the camber line. The effectiveness of the method is demonstrated in the optimization of Stage35 compressor stage. Numerical results showed that this inverse method can effectively improve the internal flow structure and optimize the matching between blade rows, and this method is robust, efficient, and flexible.

A Discussion on Generation Mechanism of Higher Harmonic Noise Due to Blade Rows Interaction in a Torque Converter

A Discussion on Generation Mechanism of Higher Harmonic Noise Due to Blade Rows Interaction in a Torque Converter

Blade stacking and clocking effects in two-stage high-pressure axial turbine

Purpose The purpose of this paper is to characterize the blade–row interaction and investigate the effects of axial spacing and clocking in a two-stage high-pressure axial turbine. Design/methodology/approach Flow simulations were performed by means of Ansys-CFX code. First, the effects of blade–row stacking on the expansion performance were investigated by considering the stage interface. Second the axial spacing and the clocking positions between successive blade–rows were varied, the flow field considering the frozen interface was solved, and the flow interaction was assessed. Findings The axial spacing seems affecting the turbine isentropic efficiency in both design and off-design operating conditions. Besides, there are differences in aerodynamic loading and isentropic efficiency between the maximum efficiency clocking positions where the wakes of the first-stage vanes impinge around the leading edge of the second-stage vanes, compared to the clocking position of minimum efficiency where the ingested wakes pass halfway of the second-stage vanes. Research limitations/implications Research implications include understanding the effects of stacking, axial spacing and clocking in axial turbine stages, improving the expansion properties by determining the adequate spacing and locating the leading edge of vanes and blades in both first and second stages with respect to the maximum efficiency clocking positions. Practical implications Practical implications include improving the aerodynamic design of high-pressure axial turbine stages. Originality/value The expansion process in a two-stage high-pressure axial turbine and the effects of blade–row spacing and clocking are elucidated thoroughly.

Separation of Up and Downstream Forced Response Excitations of an Embedded Compressor Rotor

The aerodynamic interaction of upstream and downstream blade rows can have a significant impact on the forced response of the compressor. Previously, the authors carried out the forced response analysis of a three-row stator-rotor-stator (S1-R2-S2) configuration from a 3.5-stage compressor. However, since the stator vane counts in both the stators (S1 and S2) were the same, it was not possible to separate the excitations from both the rows as they excited the rotor at the same frequency. Hence, a new configuration was developed and tested in which the stator 1 blade count was changed to 38 and stator 2 blade count was maintained at 44 in order to study the individual influences of the stator on the embedded rotor. By using this method, the excitations from both rows can be determined, and the excitations can be quantified to determine the row having the maximum influence on the overall forcing. To achieve this, two sets of simulations were carried out. The three-row stator-rotor (S1-R2-S2) simulation was carried out at both the 38EO (engine order) and 44EO crossings at the peak efficiency (PE) operating condition. The two-row stator-rotor analysis (S1-R2) was carried out at the 38EO crossing, and the other two-Row (R2-S2) analyses were carried out at the 44EO crossing. The steady aerodynamics was preserved in both the cases. A study was done to determine the contribution of wave reflections from the stator inlet and exit planes to the forcing function. Two conclusions drawn from this study are as follows: (1) the modal force value decreased after the upstream stator was removed, which proved that wave reflections from this stator were significant and (2) the increase in modal force was in-line with experimental observations.

Characterization of the Unsteady Aerodynamics of Optimized Turbine Blade Tips through Modal Decomposition Analysis

The present research focused on the analysis of the leakage flows developing from advanced blade tip geometries. The aerodynamic field of a contoured blade tip and of a high-performance rimmed blade were investigated against a baseline squealer rotor. Time-resolved numerical predictions were combined with high-frequency pressure measurements to characterize the tip leakage flow of each tip design. High spatial and temporal resolution measurements provided a detailed representation of the unsteady flow in the near-tip region and at the stage outlet. Numerical computations, based on the nonlinear harmonic method, were employed to assess the unsteady blade row interactions and identify the loss generation mechanisms depending on the tip design. The space- and time-resolved flow field was analysed by modal decomposition to identify the main periodicities of the near-tip and outlet flow and classify the most relevant sources of aerodynamic unsteadiness and entropy generation across the stage.

An Exponential Decay Model for the Deterministic Correlations in Axial Compressors

The unsteady blade row interaction (UBRI) is inherent and usually has a large effect on performance in multistage axial compressors. The effect could be considered by using the average-passage equation system (APES) in steady-state environment by introducing the deterministic correlations (DC). How to model the DC is the key in APES method. The primary purpose of this study is to develop a DC model for compressor routine design. The APES technique is investigated by using a 3D viscous unsteady and time-averaging Computational fluid dynamics (CFD) flow solver developed in our previous studies. Based on DC characteristics and its effects on time-averaged flow, an exponential decay DC model is proposed and implemented into the developed time-averaging solver. Steady, unsteady, and time-averaging simulations are conducted on the investigation of the UBRI and the DC model in the first transonic stage of NASA 67 and the first two stages of a multistage compressor. The DC distributions and mean flow fields from the DC model are compared with the unsteady simulations. The comparison indicates that the proposed model can take into account the major part of UBRI and provide significant improvements for predicting compressor characteristics and spanwise distributions of flow properties in axial compressors, compared with the steady mixing plane method.