A New Slip Factor Model for Axial and Radial Impellers

2007 ◽  
Author(s):  
Xuwen Qiu ◽  
Chanaka Mallikarachchi ◽  
Mark Anderson
Keyword(s):  
Factor Model ◽  
Important Variable ◽  
Flow Coefficient ◽  
Slip Model ◽  
Mixed Flow ◽  
Velocity Difference ◽  
Blade Loading ◽  
Axial Compressors ◽  
Slip Factor ◽  
Proposed Model

This paper proposes a unified slip model for axial, radial, and mixed flow impellers. For many years, engineers designing axial and radial turbomachines have applied completely different deviation or slip factor models. For axial applications, the most commonly used deviation model has been Carter’s rule or its derivatives. For centrifugal impellers, Wiesner’s correlation has been the most popular choice. Is there a common thread linking these seemingly unrelated models? This question becomes particularly important when designing a mixed flow impeller where one has to choose between axial or radial slip models. The proposed model in this paper is based on blade loading, i.e., the velocity difference between the pressure and suction surfaces, near the discharge of the impeller. The loading function includes the effect of blade rotation, blade turning, and the passage area variation. This velocity difference is then used to calculate the slip velocity using Stodola’s assumption. The final slip model can then be related to Carter’s rule for axial impellers and Stodola’s slip model for radial impellers. This new slip model suggests that the flow coefficient at the impeller exit is an important variable for the slip factor when there is blade turning at the impeller discharge. This may explain the interesting slip factor trend observed from experiments, such as the rise of the slip factor with flow coefficient in Eckardt A impeller. Some validation results of this new model are presented for a variety of applications, such as radial compressors, axial compressors, pumps, and blowers.

Analysis and Validation of a Unified Slip Factor Model for Impellers at Design and Off-Design Conditions

2010 ◽  
Author(s):  
Xuwen Qiu ◽  
David Japikse ◽  
Jinhui Zhao ◽  
Mark R. Anderson
Keyword(s):  
Test Data ◽  
Slip Velocity ◽  
Factor Model ◽  
Flow Coefficient ◽  
Slip Model ◽  
Flow Conditions ◽  
Mixed Flow ◽  
Blade Loading ◽  
New Model ◽  
Slip Factor

This paper presents a unified slip model for axial, radial, and mixed-flow impellers. The core assumption of the model is that the flow deviation or slip velocity at impeller exit is mainly originated from the blade loading near the discharge of an impeller and its subsequent relative eddy in the impeller passage. The blade loading is estimated and then used to derive the slip velocity using Stodola’s assumption. The final form of the slip factor model can be successfully related to Carter’s rule [1] for axial impellers and Stodola’s [2] slip model for radial impellers, making the case for this model to be applicable to axial, radial, and mixed-flow impellers. Unlike conventional slip factor models for radial impellers, the new slip model suggests that the flow coefficient at the impeller exit is an important variable for the slip factor when there is significant blade turning at the impeller discharge. This explains the interesting off-design trends for slip factor observed from experiments, such as the rise of the slip factor with flow coefficient in the Eckardt A impeller [3]. Extensive validation results for this new model are presented in this paper. Several cases are studied in detail to demonstrate how this new model can capture the slip factor variation at the off-design conditions. Furthermore, a large number of test data from more than 90 different compressors, pumps, and blowers were collected. Most cases are radial impellers, but a few axial impellers are also included. The test data and model predictions of the slip factor are compared at both design and off-design flow conditions. In total, over 1,650 different flow conditions are evaluated. The unified model shows a clear advantage over the traditional slip factor correlations, such as the Busemann-Wiesner model [4], when off-design conditions are considered.

Analysis and Validation of a Unified Slip Factor Model for Impellers at Design and Off-Design Conditions

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Xuwen Qiu ◽  
David Japikse ◽  
Jinhui Zhao ◽  
Mark R. Anderson
Keyword(s):  
Test Data ◽  
Slip Velocity ◽  
Factor Model ◽  
Flow Coefficient ◽  
Slip Model ◽  
Flow Conditions ◽  
Mixed Flow ◽  
Blade Loading ◽  
New Model ◽  
Slip Factor

This paper presents a unified slip model for axial, radial, and mixed-flow impellers. The core assumption of the model is that the flow deviation or the slip velocity at the impeller exit is mainly originated from the blade loading near the discharge of an impeller and its subsequent relative eddy in the impeller passage. The blade loading is estimated and then used to derive the slip velocity using Stodola’s assumption. The final form of the slip factor model can be successfully related to Carter’s rule for axial impellers and Stodola’s slip model for radial impellers, making the case for this model applicable to axial, radial, and mixed-flow impellers. Unlike conventional slip factor models for radial impellers, the new slip model suggests that the flow coefficient at the impeller exit is an important variable for the slip factor when there is significant blade turning at the impeller discharge. This explains the interesting off-design trends for slip factor observed from experiments, such as the rise of the slip factor with flow coefficient in the Eckardt A impeller. Extensive validation results for this new model are presented in this paper. Several cases are studied in detail to demonstrate how this new model can capture the slip factor variation at the off-design conditions. Furthermore, a large number of test data from more than 90 different compressors, pumps, and blowers were collected. Most cases are radial impellers, but a few axial impellers are also included. The test data and model predictions of the slip factor are compared at both design and off-design flow conditions. In total, over 1650 different flow conditions are evaluated. The unified model shows a clear advantage over the traditional slip factor correlations, such as the Busemann–Wiesner model, when off-design conditions are considered.

Validations of Some Slip Factor Models for Mixed-Flow Impellers

2008 ◽  
Author(s):  
Shengqin Huang ◽  
Zhenxia Liu ◽  
Yaguo Lu ◽  
Yan Yan ◽  
Xiaochun Lian
Keyword(s):  
Inclination Angle ◽  
Factor Model ◽  
Critical Value ◽  
Factor Models ◽  
Flow Coefficient ◽  
Centrifugal Impeller ◽  
Correct Prediction ◽  
Mixed Flow ◽  
Blade Number ◽  
Slip Factor

Accurate modeling of the slip factor is essential for correct prediction of the mixed-flow impeller performance, but the slip factor model well-known for mixed-flow impeller is relatively rare. Two ways for calculating mixed-flow impeller slip factor are present in this paper: (1) Using impeller exit inclination angle correction to transform the slip factor for centrifugal impeller to mixed-flow machine. (2) Setting up model that can be used to mixed-flow machine directly. Based on these two ways, there are six slip factor models chosen for mixed-flow impeller, including models of Wiesner, Stodola, Staniz, Paeng, Backstrom and Qiu. And they are need to be validated by experiments data to find a proper method for mixed-flow machine. The test data are reproduced from Wiesner’s work and nine mixed-flow impellers are included. Experiment and simulation (including six slip factors) have been conducted and the results show that: (1) slip factor models of centrifugal impeller can be used to mixed-flow impeller while no proper mixed-flow slip factor models exist. If the impeller discharge inclination angle is greater than 45 degree, then these models can be used for mixed-flow impellers directly without transformation. (2) Equivalent blade number exists in mixed-flow impeller and it may have critical value. There are only little differences between results calculated by various slip factor models in the condition of equivalent blade number beyond the critical value. Otherwise it has to choose proper slip factor models as different situations while the equivalent blade number is less than the critical value. (3) Blade number, impeller exit inclination angle and exit blade angle of mixed-flow impeller are dominated over slip factor, but blade turning rate and flow coefficient have to be taken into account for more exact solution.

Experimental Study on the Influence of Casing Treatment on Near-Stall Unsteady Behavior of a Mixed-Flow Compressor

2019 ◽  
Author(s):  
Juan Du ◽  
Felix Kauth ◽  
Jichao Li ◽  
Qianfeng Zhang ◽  
Joerg R. Seume
Keyword(s):  
Stability Limit ◽  
Tip Clearance ◽  
Flow Coefficient ◽  
Surprising Result ◽  
Mixed Flow ◽  
Stall Inception ◽  
Casing Treatment ◽  
Axial Compressors ◽  
Flow Compressor ◽  
Unsteady Behavior

Abstract This paper aims at experimentally demonstrating the effects of axial slot casing treatment and tip gap variation on compressor performance, unsteady tip clearance flow, and stall inception features in a highly-loaded mixed-flow compressor at partspeed. Two tip gaps (0.32% and 0.64% of rotor blade chord at mid-span) were tested at three rotational speeds. A semicircular axial slot casing treatment improves compressor stability. The experimental results show that this casing treatment significantly moves the stability limit at partial speeds towards lower mass flow for both tip gaps, compared to the reference case without casing treatment. In the case of the compressor with casing treatment, efficiency increases for the large tip gap and decreases for the small tip gap. Dynamic pressure transducers installed in the casing upstream and along the rotor tip chord direction are used to detect the unsteady behavior of tip region flow and stall inception signals of the compressor. The characteristic frequency in the tip region decreases, and the oscillating amplitude first decreases and then increases during the throttling process, regardless of tip gap size or casing treatment. For axial compressors, by contrast, the observation in previous work has been an increase of the oscillating amplitude with decreasing flow coefficient. This is a surprising result of our work. Neither experiment nor CFD so far was able to explain why the trend in this mixed-flow compressor is different from the trend expected from axial compressors. The compressor stalls through the spike stall inception both with and without casing treatment. This observation also differs from recent studies on axial compressors, which demonstrated that casing treatments could change the type of stall inception. The unstable disturbance indicating initial stall inception initially appears in the blade tip region from blade mid-chord to trailing edge, and then propagates upstream towards the leading edge. This disturbance might be generated by the reversed flow separation near mid-chord.

A Transonic Mixed Flow Compressor for an Extreme Duty

2014 ◽  
Author(s):  
Hamid Hazby ◽  
Michael Casey ◽  
Ryusuke Numakura ◽  
Hideaki Tamaki
Keyword(s):  
Test Data ◽  
Pressure Rise ◽  
High Flow ◽  
Flow Coefficient ◽  
Compressor Stage ◽  
Aerodynamic Optimization ◽  
Mixed Flow ◽  
Axial Compressors ◽  
Blade Shape ◽  
Flow Compressor

This paper describes the design of a transonic mixed flow compressor stage for an extreme duty, with an extremely high flow coefficient (Φ) of 0.25 and a high isentropic pressure rise coefficient (ψ) of 0.56. The impeller design makes use of modern aerodynamic practice from radial and transonic axial compressors, whereby the aerodynamic blade shape involved arbitrary surfaces on several spanwise sections. Some aspects of the aerodynamic optimization of the design were limited by mechanical considerations, but nevertheless the test data obtained on a prototype stage demonstrates that acceptable performance levels can be achieved at these extreme design conditions, although map width enhancement devices were needed to obtain an acceptable operating range. The test data is compared with CFD predictions to demonstrate the validity of the design methods used.

A Transonic Mixed Flow Compressor for an Extreme Duty

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Hamid Hazby ◽  
Michael Casey ◽  
Ryusuke Numakura ◽  
Hideaki Tamaki
Keyword(s):  
Test Data ◽  
Pressure Rise ◽  
High Flow ◽  
Flow Coefficient ◽  
Aerodynamic Optimization ◽  
Mixed Flow ◽  
Axial Compressors ◽  
Blade Shape ◽  
Computational Fluid Dynamics Cfd ◽  
Flow Compressor

This paper describes the design of a transonic mixed flow compressor stage for an extreme duty, with an extremely high flow coefficient (φ) of 0.25 and a high isentropic pressure rise coefficient (ψ) of 0.56. The impeller design makes use of modern aerodynamic practice from radial and transonic axial compressors, whereby the aerodynamic blade shape involved arbitrary surfaces on several spanwise sections. Some aspects of the aerodynamic optimization of the design were limited by mechanical considerations, but nevertheless the test data obtained on a prototype stage demonstrates that acceptable performance levels can be achieved at these extreme design conditions, although map width enhancement (MWE) devices were needed to obtain an acceptable operating range. The test data are compared with computational fluid dynamics (CFD) predictions to demonstrate the validity of the design methods used.

An Validation on A New Slip Factor Model for Mixed-flow Impellers

2008 ◽  
Author(s):  
Shengqin Huang ◽  
Zhenxia Liu ◽  
Yaguo Lu ◽  
Yan Yan ◽  
Xiaochun Lian
Keyword(s):  
Factor Model ◽  
Mixed Flow ◽  
Slip Factor

scholarly journals One-factor model for default rates by loan type

Bankarstvo ◽  
2021 ◽  
Vol 50 (2) ◽  
pp. 88-100
Author(s):  
Miloš Božović
Keyword(s):  
Factor Model ◽  
Risk Measures ◽  
Loan Default ◽  
Macroeconomic Risk ◽  
Default Rates ◽  
Proposed Model ◽  
Default Rate ◽  
Systemic Component ◽  
Very High

This paper investigates the link between default rates by loan types and the systemic credit risk component. This link is described by a linear model that combines systemic and idiosyncratic contributions. The systemic component is a latent factor that depends directly on the aggregate loan default rate, while the idiosyncratic component drives specific variations of default rates across loan types. By transforming observable risk measures, the model can be econometrically represented as a mixed-effects model, where the systemic and idiosyncratic components represent, respectively, the slope and the intercept that are specific for each loan type individually. The proposed model is illustrated on a panel of defaulted loans of the Association of Serbian Banks. The obtained results show the model's very high power in explaining average default rates for all loan types. Thus, the aggregate default rate plays the role of a unique systemic component that mimics the influence of fundamental macroeconomic risk factors easily, without the necessity to model this relationship explicitly.

scholarly journals The Slip Factor Centrifugal and Mixed-Flow Comprssors

1967 ◽  
Vol 33 (249) ◽  
pp. 735-744 ◽  
Author(s):  
Toshimichi SAKAI ◽  
Ichiro WATANABE
Keyword(s):  
Mixed Flow ◽  
Slip Factor

scholarly journals An Exponential Decay Model for the Deterministic Correlations in Axial Compressors

2019 ◽  
Vol 141 (2) ◽  
Author(s):  
Yangwei Liu ◽  
Yumeng Tang ◽  
Baojie Liu ◽  
Lipeng Lu
Keyword(s):  
Exponential Decay ◽  
Equation System ◽  
Time Averaging ◽  
Mean Flow ◽  
Flow Solver ◽  
Axial Compressors ◽  
Routine Design ◽  
Proposed Model ◽  
Exponential Decay Model ◽  
Two Stages

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.

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