A Theory of Post-Stall Transients in Axial Compression Systems: Part II—Application

1986 ◽  
Vol 108 (2) ◽  
pp. 231-239 ◽  
Author(s):  
E. M. Greitzer ◽  
F. K. Moore
Keyword(s):  
Axial Compression ◽  
Parametric Study ◽  
Pressure Rise ◽  
Transient Behavior ◽  
Rotating Stall ◽  
Future Research ◽  
System Response ◽  
System Behavior ◽  
Flow Pressure ◽  
The Impact

Using the theory developed in Part I, calculations have been carried out to show the evolution of the mass flow, pressure rise, and rotating-stall cell amplitude during compression system post-stall transients. In particular, it is shown that the unsteady growth or decay of the stall cell can have a significant effect on the instantaneous compressor pumping characteristic and hence on the overall system behavior. A limited parametric study is carried out to illustrate the impact of different system features on transient behavior. It is shown, for example, that the ultimate mode of system response, surge or stable rotating stall, depends not only on the B parameter, but also on the compressor length-to-radius ratio. Small values of the latter quantity tend to favor the occurrence of surge, as do large values of B. Based on the analytical and numerical results, some specific topics are suggested for future research on post-stall transients.

Generalized Cause-and-Effect Analyses for the Prototypic Nonlinear Mass–Spring–Damper System Using Volterra Kernels

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Ashraf Omran ◽  
Brett Newman
Keyword(s):  
Parametric Study ◽  
Volterra Series ◽  
System Response ◽  
System Behavior ◽  
Volterra Kernels ◽  
Numerical Examples ◽  
Frequency Domains ◽  
Variational Expansion ◽  
Mass Spring ◽  
Bilinear Terms

This paper develops generalized analytical first and second Volterra kernels for the prototypic nonlinear mass–spring–damper system. The nonlinearity herein is mathematically considered in quadratic and bilinear terms. A variational expansion methodology, one of the most efficient analytical Volterra techniques, is used to develop an analytical two-term Volterra series. The resultant analytical first and second kernels are visualized in both the time and the frequency domains followed by a parametric study to understanding the influence of each nonlinear/linear term appearing in the kernel structure. An analytical nonlinear step and periodic responses are also conducted to characterize the overall system response from the fundamental components. The developed analytical responses provide an illumination for the source of differences between nonlinear and linear responses. Feasibility of the proposed implementation is assessed by numerical examples. The developed kernel-based model shows the ability to predict, understand, and analyze the system behavior beyond that attainable by the linear-based model.

An Investigation of Rotating Stall and Surge of a 10-Stage Subsonic Compressor

1985 ◽  
Author(s):  
Xie Jinan ◽  
Bai Xiaoxu
Keyword(s):  
Transient Process ◽  
Phase Plane ◽  
Performance Test ◽  
Pressure Rise ◽  
Calculation Model ◽  
Rotating Stall ◽  
Stationary Condition ◽  
Process Pattern ◽  
Flow Pressure ◽  
Rise Phase

This article covers the analysis and study of the surge characteristic in a full-scale 10-stage subsonic compressor under the condition of performance test. The transient responses which arised after the compressor enters in non-stationary condition range are estimated through an improved nonlinear calculation model. There are two different kinds of response (or transient processe) model: stall pattern and surge pattern. The calculated results coincide with the test very well. When relative turning speed ñ ≤ 0.5, the system transient process is shown in stall pattern; when ñ ≥ 0.6, it is surge pattern. The obtainted calculation result has been drawn as a system transient process locus in the nondimensional flow-pressure rise phase plane. The nondimensional parameters affecting system transient process pattern were analysed and compared with the results made by E.M. Greitzer.

A Theory of Post-Stall Transients in Axial Compression Systems: Part I—Development of Equations

1986 ◽  
Vol 108 (1) ◽  
pp. 68-76 ◽  
Author(s):  
F. K. Moore ◽  
E. M. Greitzer
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Angular Dependence ◽  
Axial Compression ◽  
Pressure Rise ◽  
Rotating Stall ◽  
Flow Coefficient ◽  
Approximate Theory ◽  
Third Order ◽  
First Order

An approximate theory is presented for post-stall transients in multistage axial compression systems. The theory leads to a set of three simultaneous nonlinear third-order partial differential equations for pressure rise, and average and disturbed values of flow coefficient, as functions of time and angle around the compressor. By a Galerkin procedure, angular dependence is averaged, and the equations become first order in time. These final equations are capable of describing the growth and possible decay of a rotating-stall cell during a compressor mass-flow transient. It is shown how rotating-stall-like and surgelike motions are coupled through these equations, and also how the instantaneous compressor pumping characteristic changes during the transient stall process.

scholarly journals An Investigation of Post Stall Transients and Recoverability of Axial Compression Systems: Part I — A Simplified Method

1992 ◽  
Author(s):  
Hu Jun ◽  
Tang Guo Cai ◽  
Zhang Hui Min
Keyword(s):  
Pressure Rise ◽  
Recovery Process ◽  
Rotating Stall ◽  
Flow Instabilities ◽  
First Order ◽  
Proposed Model ◽  
Time Marching ◽  
Flow Pressure ◽  
Marching Method ◽  
Made In

Using the theory developed by Moore and Greitzer, a simplified approximate method is proposed to calculate the evolution of the mass flow, pressure rise, and the growth and decay of rotating stall cell during post stall transients or recovery process in multistage arial compression systems. The method leads to a set of three simultaneous nonlinear first order partial differential equations, and for the numerical solution, a simple explicit time marching method can be used. It is shewa that a study of rotating-statt-like and surge-like motion, recoverability from rotating stall or surge, and limited parameters can be carried out through this method. It has been found that, except the two general types of distinct flow instabilities (rotating stall and surge), there is another type of instability in arial compression systems, which has the basic characteristic of both rotating stall and surge. Some qualitative comparisons with available experimental results and some qualitative comparisons with test data are made in this paper. It shows that the proposed model is very simple, accurate and dependable.

A theory for rotating stall in contra-rotating fans

2020 ◽  
pp. 095440622096253
Author(s):  
Hossein Khaleghi ◽  
Mohammad Javad Shahriyari ◽  
Martin Heinrich
Keyword(s):  
Single Cell ◽  
Critical Role ◽  
Pressure Rise ◽  
Transient Behavior ◽  
Rotating Stall ◽  
Speed Ratio ◽  
Rotor Speed ◽  
Modified Model ◽  
Stall Cells ◽  
Stagger Angle

This paper reports on a theory of rotating stall in contra-rotating fans and compressors. The theory is developed from Moore’s theory. A second-order hysteresis is used in the current study for the pressure rise of the counter-rotating rows. This enables the model to predict the transient behavior of the stall cell. Comparing the experimental results with the theory shows that the modified model can predict the speed of the stall cells fairly accurately. Results show that the rotor speed ratio plays a critical role in the stall cell speed and its direction of rotation. Furthermore, the developed model makes it possible to study the effects of stagger angle and number of stall cells. The conditions under which pure rotating stall can occur in contra-rotating fans are also discussed in this paper. It is shown that the stall cells merge to form a single cell before a stable fully-developed rotating stall is established.

A Model for System Instability Analysis in a Multi-Stage Intercooled Industrial Compressor

2019 ◽  
Author(s):  
Jiaye Gan ◽  
Ahmed Abdelwahab ◽  
Viktor Kilchyk
Keyword(s):  
Guide Vane ◽  
Transient Behavior ◽  
Industrial Applications ◽  
Operating Conditions ◽  
System Response ◽  
Stable Operation ◽  
System Behavior ◽  
Multi Stage ◽  
Performance Reduction ◽  
Inlet Conditions

Abstract Compression equipment used for industrial applications are typically comprised of multi-stage intercooled compressor stages. The presence of large volume intercoolers between individual stages adds a layer of complexity currently not present in publicly available surge models both in terms of system behavior and recovery analysis. In this work a compressible, temporal, and spatial model is developed in which the conservation equations are solved numerically for each of the system components, i.e. pipes, plenums and heat exchangers, valves, and individual compressor stages. The model can identify the onset of instability on an individual stage basis as well as the switching that can occur between the controlling stages of the instability onset when the operating conditions change, e.g. changes in inlet conditions, intercooler fouling or cooling tower performance reduction, and speed or guide vane changes. The model is therefore used both as a stage stacking model during the compressor stable operation as well as a model of the transient behavior of the system past the stable operation. An inertial model of the compressor drive train is also incorporated to analyze the effects of power transients, e.g. emergency shut down (ESD), on the system behavior. In this article details of the developed model are provided. Several test cases are presented. The model is then used to demonstrate the proper sizing of a vent valve of a base load compressor to meet the required system response specification in a surge event. The developed model represents an improvement over available transient system models in terms of predicting the post stable behavior of multi-stage intercooled compressors.

Impact of Inter-Stage Dynamics on Stalling Stage Identification

2011 ◽  
Author(s):  
Manuj Dhingra ◽  
J. V. R. Prasad ◽  
Prashant Tiwari ◽  
Tsuguji Nakano ◽  
Andy Breeze-Stringfellow
Keyword(s):  
Test Data ◽  
Fluid Dynamic ◽  
Pressure Rise ◽  
State Equation ◽  
Rotating Stall ◽  
Expansion Waves ◽  
Upstream Pressure ◽  
Compression And Expansion ◽  
Suitable Framework ◽  
The Impact

A key objective of compressor rig tests is the identification of compressor stall boundary. A complementary goal is the identification of the stalling stage based on test data. This serves two purposes: 1) Validate the pre-test prediction of the stage loading distribution, and 2) identify the weak stages, should improvements in operating range be desired in subsequent design iterations. Typically the pertinent test data is in the form of static pressure measurements. Many engineers believe that a stalling stage is accompanied by a transient upstream pressure rise coupled with a downstream pressure loss. However, inter-stage dynamics may cloud the identification of the stalling stage. To this end, an analysis of inter-stage dynamics, immediately preceding the stall event, could provide an alternate assessment of the stalling stage. This work reviews existing stall models for studying compressor dynamics. The main focus of this work is to develop ability to capture inter-stage dynamics. A 3-state equation lumped Moore-Greitzer (MG3) model is widely used to study the dynamic compressor response during surge and rotating stall transients. However the evolution of MG3 model may not provide a suitable framework for the investigation of inter-stage dynamics. On the other hand, an unsteady time marching 1-D fluid dynamic model (e.g. similar to the DynTECC formulation which includes body forces), while unable to capture the rotating stall dynamics, is sufficient for this purpose. A numerical simulation has been developed to investigate the impact of stage characteristics, as well as load distribution on the compression and expansion waves that develop prior to a surge event. Through a controlled weakening of selected stages, the time evolution of these waves is related back to the stalling stage. It is found that the weakened stage is not necessarily the stalling stage as identified via the pressure rise and downstream pressure drop pattern.

scholarly journals Stalled Flow Performance for Axial Compressors: II — Rotating Stall Characteristic

1984 ◽  
Author(s):  
S. G. Koff
Keyword(s):  
Rotating Stall ◽  
Flow Mode ◽  
Thin Shells ◽  
System Behavior ◽  
Stall Inception ◽  
Compression System ◽  
Axial Compressors ◽  
System Parameters ◽  
Multistage Compressors ◽  
The Impact

This paper describes a study of stalled flow performance of multistage compressors. The study is focused on the performance in rotating stall, in particular, the impact on stall inception and stall recovery. It is argued that the recovery point measured in post-stall compressor tests results from a compression system instability, rather than from an unstable rotating stall flow. If so, recoverability from rotating stall may be improved by altering system parameters. Furthermore, the full-span rotating stall characteristic is extrapolated beyond the measured recovery point. On this basis, the compressor stall point is viewed as a bifurcation, where a change in flow mode exists, perhaps analogous to the critical point in the axial compression of thin shells. An application for the extended rotating stall characteristic is in a model of transient compression system behavior.

scholarly journals Multi-Time Scale Perspective in Analyzing Cardiovascular Data

2014 ◽  
pp. 439-456 ◽  
Author(s):  
H. K. LACKNER ◽  
J. J. BATZEL ◽  
A. RÖSSLER ◽  
H. HINGHOFER-SZALKAY ◽  
I. PAPOUSEK
Keyword(s):  
Transient Behavior ◽  
System Response ◽  
Fine Grained ◽  
Hemodynamic Variables ◽  
Physiological Processes ◽  
Specific Effects ◽  
Social Observation ◽  
Transient Variations ◽  
Time Frames ◽  
The Impact

Cardiovascular dynamic and variability data are commonly used in experimental protocols involving cognitive challenge. Usually, the analysis is based on a sometimes more and sometimes less well motivated single specific time resolution ranging from a few seconds to several minutes. The present paper aimed at investigating in detail the impact of different time resolutions of the cardiovascular data on the interpretation of effects. We compared three template tasks involving varying types of challenge, in order to provide a case study of specific effects and combinations of effects over different time frames and using different time resolutions. Averaged values of hemodynamic variables across an entire protocol confirmed typical findings regarding the effects of mental challenge and social observation. However, the hemodynamic response also incorporates transient variations in variables reflecting important features of the control system response. The fine-grained analysis of the transient behavior of hemodynamic variables demonstrates that information that is important for interpreting effects may be lost when only average values over the entire protocol are used as a representative of the system response. The study provides useful indications of how cardiovascular measures may be fruitfully used in experiments involving cognitive demands, allowing inferences on the physiological processes underlying the responses.

Self-Compassion and Quality of Life in Adults Who Stutter

2020 ◽  
Vol 29 (4) ◽  
pp. 2097-2108
Author(s):  
Robyn L. Croft ◽  
Courtney T. Byrd
Keyword(s):  
Quality Of Life ◽  
Social Connectedness ◽  
The Self ◽  
Future Research ◽  
Self Compassion ◽  
Adults Who Stutter ◽  
And Gender ◽  
Relationship Of ◽  
The Impact

Purpose The purpose of this study was to identify levels of self-compassion in adults who do and do not stutter and to determine whether self-compassion predicts the impact of stuttering on quality of life in adults who stutter. Method Participants included 140 adults who do and do not stutter matched for age and gender. All participants completed the Self-Compassion Scale. Adults who stutter also completed the Overall Assessment of the Speaker's Experience of Stuttering. Data were analyzed for self-compassion differences between and within adults who do and do not stutter and to predict self-compassion on quality of life in adults who stutter. Results Adults who do and do not stutter exhibited no significant differences in total self-compassion, regardless of participant gender. A simple linear regression of the total self-compassion score and total Overall Assessment of the Speaker's Experience of Stuttering score showed a significant, negative linear relationship of self-compassion predicting the impact of stuttering on quality of life. Conclusions Data suggest that higher levels of self-kindness, mindfulness, and social connectedness (i.e., self-compassion) are related to reduced negative reactions to stuttering, an increased participation in daily communication situations, and an improved overall quality of life. Future research should replicate current findings and identify moderators of the self-compassion–quality of life relationship.

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