A Comprehensive Analytical Shock Loss Model for Axial Compressor Cascades

The approach applied in various research papers that model compressor shock losses is valid only for certain types of airfoil cascades operating in a narrow range of working conditions. Lately, more general shock loss models have been established that cover a wider variety of airfoils and operating regimes. However, owing to the complexity of the studied matter, the majority of such models are, to a certain extent, presented only in a descriptive manner. The lack of specific details can affect the end results when such a model is utilized since improvisation cannot be avoided. Some models also apply complex numerical procedures that can slow the calculations and be a source of computational instability. In this research, an attempt has been made to produce an analytical shock loss model that is simple enough to be described in detail while being universal and robust enough to find wide application in the fields of design and performance analysis of transonic compressors and fans. The flexible description of airfoil geometry encompasses a variety of blade shapes. Both unchoked and choked operating regimes are covered, including a precise prediction of choke occurrence. The model was validated using a number of numerical test cases.

Study of the Greitzer Model for Centrifugal Compressors: Variable Lc Parameter and Two Types of Surge

In this paper, the Greitzer surge model was systematically analysed with the model compressor duct length Lc as the tuning parameter. The surge phenomenon is known to induce a serious risk to centrifugal compressor operation. The two-dimensional Greitzer model is a well-established way of modelling this dangerous instability, but the determination and changes of the model parameters are still being discussed. In this paper an automated procedure determines the Lc value providing the best fit with the experimental data has been presented. The algorithm was tested on five valve positions and revealed that the best fit was obtained for different Lc values following a linear trend against the mass flow rate. The study has also shown that the Greitzer model has two solutions for a given pressure oscillation amplitude: one similar to the deep surge (low Lc) and one similar to the mild surge (low Lc). This suggests that this model can be used to simulate both types of the phenomenon known from the experimental analyses. The study proposes the dimensionless average pressure as the parameter allowing to distinguish which surge cycle was observed at a given instance. Past papers were analysed to observe the surge type that appeared in different experiments. It was found that most researchers obtained low Lc surge. The results show that both deep and mild surge could be simulated with the Greitzer model. It also revealed that the Lc should not be treated as a constant value for a given machine and that it changes with the mass flow rate.

A Reduced Complexity Model for the Compressor Power of an Automotive Turbocharger

Control-oriented models for automotive turbocharger (TC) compressors typically describe the compressor power assuming an isentropic thermodynamic process with fixed isentropic and mechanical efficiencies for power transmission between the turbine and the compressor. Although these simplifications make the control-oriented model tractable, they also introduce additional errors due to unmodeled dynamics. This is especially true for map-based approaches since the manufacture-provided maps tend to be sparse and often incomplete at the operational boundaries, especially at operational conditions with low mass flow rate and low speed. Extrapolation scheme is often used when the compressor is operated outside the mapped regions, which introduces additional errors. Furthermore, the manufacture-provided compressor maps, based on steady-flow bench tests, could be quite different from those under pulsating engine flow. In this paper, a physics-based model of compressor power is developed using Euler equations for turbomachinery, where the mass flow rate and the compressor rotational speed are used as model inputs. Two new coefficients, speed and power coefficients, are defined. As a result, this makes it possible to directly estimate the compressor power over the entire compressor operational range based on a single analytic relationship. The proposed modeling approach is validated against test data from standard TC flow bench tests, standard supercharger tests, steady-state, and certain transient engine dynamometer tests. Model validation results show that the proposed model has acceptable accuracy for model-based control design and also reduces the dimension of the parameter space typically needed to model compressor dynamics.

Investigation of Bypass Valve Positions on Performance of Closed Brayton Cycle

HTR-10GT is a closed Brayton cycle with two-stage compression and heat recuperation. Bypass control was adopted for rapid power regulation and safety protection. A bypass valve could be set between any two positions at different pressure levels, there would be in total 21 setting possibilities, whose regulating behaviors remained to be fully clarified. The dynamic characteristics of these settings were thus analyzed by implementing numerical simulation on the integrated system model. The reactor was modeled with point-kinetics and 1D thermal-hydraulics model; compressor performance calculation was based on digitization of the performance map and Reynolds number correlation; Flügel formula was chosen to calculate turbine performance. The system was modeled with Modelica, and the DASSL code was used to solve the Differential and Algebraic Equations. The results showed that only 6 choices among the 21 remained acceptable for engineering practice. The degree and rate on power output reduction, anti-surge effect and long-term thermal effects at reactor inlet and along recuperator’s metal wall were evaluated and compared among these choices to give out proposals. This research clarified the characteristics of bypass valves at different positions to give a reference on the final design of the control methods, and proposed a combination of valves for multi-valve cooperative regulation.

Low-Speed Model Testing Studies for an Exit Stage of High Pressure Compressor

This paper discusses detailed experimental studies of a low-speed large-scale axial compressor, which is typical of an exit stage of HPC. Numerous measuring techniques were performed, and detailed experimental results were obtained, including inlet boundary layer total pressure distributions, overall compressor and model-stage performance, traverse flow field between blade rows and inside the stator for the model stage, static pressure on the stator blade and casing dynamic pressure of the rotor. The objective of the study is to assess the low-speed model compressor design and verify 3D computational fluid dynamics (CFD) code. Results show that inlet endwall blockage requirement of HPC exit stage is achieved; the low-speed model compressor design is fundamentally successful; the flow rate and pressure rise requirements are met at the design operating point, although the flow loss is relatively larger than design values for the lower half span, which can be attributed to a certain hub-corner separation. Furthermore, the reliability of adopted 3D commercial CFD code is validated. It is proved that the low-speed model testing technique is still a prospective way for the design of high performance HPC.

Study on the Effect of Asymmetric Vane Spacing on Vibratory Stress of Blade

It is well known that asymmetric vane spacing can result in decreased levels of the excitation at specific frequencies. In this paper, the resonant response reduction of compressor blades due to asymmetric vane spacing is studied both theoretically and experimentally for the most probable asymmetric vane in which the vane count of the upper and lower half is slightly different. First, a method for predicting the vibratory stress of the blade for the asymmetric spacing vane is proposed. Secondly, using a simple model of the asymmetric vane, a parametric study is carried out to clarify the influence of blade damping and vane count on the blade resonant response reduction. Finally, experiments are carried out to verify the validity of the proposed method and the effect of asymmetric vane spacing on resonant stress response using a 3 stage scaled-model compressor.

Development of a Transonic Front Stage of an Axial Flow Compressor for Industrial Gas Turbines

This paper describes the aerodynamic blade design of a highly loaded three-stage compressor, which is a model compressor for the front stage of an industrial gas turbine. Test results are presented that confirm design performance. Some surge and rotating stall measurement results are also discussed. The first stator blade in this test compressor operates in the high subsonic range at the inlet. To reduce the pressure loss due to blade surface shock waves, a shock-free airfoil is designed to replace the first stator blade in an NACA-65 airfoil in a three-stage compressor. Comparison of the performance of both blades shows that the shock-free airfoil blade reduces pressure loss. This paper also presents some experimental results for MCA (multicircular arc) airfoils, which are used for first rotor blades.

Development of a Transonic Front Stage of an Axial Flow Compressor for Industrial Gas Turbines

This paper describes the aerodynamic blade design of a highly-loaded three-stage compressor, which is a model compressor for the front stage of an industrial gas turbine. Test results are presented that confirm design performance. Some surge and rotating stall measurement results are also discussed. The first stator blade in this test compressor operates in the high subsonic range at the inlet. To reduce the pressure loss due to blade surface shock waves, a shock-free airfoil is designed to replace the first stator blade in an NACA-65 airfoil in a three-stage compressor. Comparison of the performance of both blades shows that the shock-free airfoil blade reduces pressure loss. This paper also presents some experimental results for MCA (multi-circular arc) airfoils, which are used for first rotor blades.

Similarity Transformations for Compressor Blading

Improving the performance of high-speed axial compressors through low-speed model compressor testing has proved to be economical and effective (Wisler, 1985). The key to this technique is to design low-speed blade profiles that are aerodynamically similar to their high-speed counterparts. The conventional aerodynamic similarity transformation involves the small disturbance potential flow assumption; therefore, its application is severely limited and generally not used in practical design. In this paper, a set of higher order transformation rules are presented that can accommodate large disturbances at transonic speed and are therefore applicable to similar transformations between the high-speed high-pressure compressor and its low-speed model. Local linearization is used in the nonlinear equations and the transformation is obtained in an iterative process. The transformation gives the global blading parameters such as camber, incidence, and solidity as well as the blade profile. Both numerical and experimental validations of the transformation show that the nonlinear similarity transformations do retain satisfactory accuracy for highly loaded blades up to low transonic speeds. Further improvement can be made by only slightly modifying profiles numerically without altering the global similarity parameters.