Circumferential Asymmetry in Axial Flow Compressors

1966 ◽  
Vol 70 (670) ◽  
pp. 953-957
Author(s):  
M. D. C. Doyle ◽  
J. H. Horlock
Keyword(s):  
Mathematical Model ◽  
Velocity Profile ◽  
Small Perturbation ◽  
Axial Flow ◽  
Inlet Distortion ◽  
Non Linear ◽  
Axial Flow Compressors

In this paper we are restricting our attention to those cases of circumferential inlet distortion where the distortion of the velocity profile is too large to be described as a small perturbation. Thus any theory describing the flow must use a mathematical model which is non-linear.

The Prediction of Steady, Circumferential Pressure and Temperature Distortions in Multistage Axial Flow Compressors

1979 ◽  
Author(s):  
H. Mokelke
Keyword(s):  
Perturbation Theory ◽  
Small Perturbation ◽  
Axial Flow ◽  
Two Dimensional ◽  
Stream Surface ◽  
Efficient Calculation ◽  
Two Dimensional Flow ◽  
The Mathematical Model ◽  
Circumferential Pressure ◽  
Axial Flow Compressors

A small perturbation theory is presented for the prediction of the decay of steady circumferential pressure, temperature and velocity distortions in multistage axial flow compressors. The mathematical model which is employed replaces the blade rows of the compressor by actuator discs. A closed solution for the linearized equations describing the two-dimensional, inviscid and compressible flow between the discs is derived and appropriate matching conditions at the discs (assuming a quasi-steady blade response) are determined. An efficient calculation procedure is presented which allows the rapid computation of the distortion development through any compressor configuration, i.e., through any combination of rotors, stators, and axial clearances including the core engine compression system. The theory can be applied to the mean section of the compressor or separately from stream surface to stream surface. Due to the assumption of a two-dimensional flow, however, it is restricted to purely circumferential distortions in compressors with sufficiently high hub-to-tip ratios where radial flow redistributions can be expected to be small. The validity of the small perturbation theory is demonstrated by comparing the theoretical results with experimental data. In addition, the theory is used to study the effect of Mach-number and flow rate on the decay of the distortions through two compressor configurations. Suggestions are made on how to utilize the theory for the design of distortion-tolerant compressors.

Active Control of Surge in Multi-Stage Axial-Flow Compressors

1995 ◽  
Vol 209 (4) ◽  
pp. 249-258 ◽  
Author(s):  
J-F Escuret ◽  
R L Elder
Keyword(s):  
Frequency Response ◽  
Active Control ◽  
Flow Model ◽  
Axial Flow ◽  
Normal Operation ◽  
Linear Controller ◽  
Multi Stage ◽  
Non Linear ◽  
Axial Flow Compressors ◽  
Sensor Locations

Non-linear simulations of a surge model with and without control are investigated using a Runge-Kutta scheme. This shows how some non-linearities in the flow model can affect the normal operation of a linear controller and the problem of actuatop sensor locations. Also, the amplitudes and frequency response required of the actuator to retain stability can sometimes be found to exceed the practical limitations.

The Prediction of Steady, Circumferential Pressure and Temperature Distortions in Multistage Axial Flow Compressors

1980 ◽  
Vol 102 (2) ◽  
pp. 448-458
Author(s):  
H. Mokelke
Keyword(s):  
Perturbation Theory ◽  
Small Perturbation ◽  
Axial Flow ◽  
Two Dimensional ◽  
Stream Surface ◽  
Efficient Calculation ◽  
Two Dimensional Flow ◽  
The Mathematical Model ◽  
Circumferential Pressure ◽  
Axial Flow Compressors

A small perturbation theory is presented for the prediction of the decay of steady circumferential pressure, temperature and velocity distortions in multistage axial flow compressors. The mathematical model which is employed replaces the blade rows of the compressor by actuator disks. A closed solution for the linearized equations describing the two-dimensional, inviscid and compressible flow between the disks is derived and appropriate matching conditions at the disks (assuming a quasi-steady blade response) are determined. An efficient calculation procedure is presented which allows the rapid computation of the distortion development through any compressor configuration, i.e., through any combination of rotors, stators and axial clearances including the core engine compression system. The theory can be applied to the mean section of the compressor or separately from stream surface to stream surface. Due to the assumption of a two-dimensional flow, however, it is restricted to purely circumferential distortions in compressors with sufficiently high hub-to-tip ratios where radial flow redistributions can be expected to be small. The validity of the small perturbation theory is demonstrated by comparing the theoretical results with experimental data. In addition, the theory is used to study the effect of Mach-number and flow rate on the decay of the distortions through two compressor configurations. Suggestions are made how to utilize the theory for the design of distortion-tolerant compressors.

Imprecision of Laboratory Determinations and Diagnostic Accuracy: Theoretical Considerations

1974 ◽  
Vol 13 (03) ◽  
pp. 151-158 ◽  
Author(s):  
D. A. B. Lindbebo ◽  
Fr. R. Watson
Keyword(s):  
Mathematical Model ◽  
Diagnostic Accuracy ◽  
Diagnostic Process ◽  
Clinical Laboratories ◽  
Non Linear ◽  
Theoretical Considerations ◽  
Made In

Recent studies suggest the determinations of clinical laboratories must be made more precise than at present. This paper presents a means of examining benefits of improvement in precision. To do this we use a mathematical model of the effect upon the diagnostic process of imprecision in measurements and the influence upon these two of Importance of Diagnosis and Prevalence of Disease. The interaction of these effects is grossly non-linear. There is therefore no proper intuitive answer to questions involving these matters. The effects can always, however, be calculated.Including a great many assumptions the modeling suggests that improvements in precision of any determination ought probably to be made in hospital rather than screening laboratories, unless Importance of Diagnosis is extremely high.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

scholarly journals MODELING AND PRODUCTIVITY PREDICTION OF THE COMPANIES-INTERNAL CROWDSOURCING-BASED IDEATION

2021 ◽  
Vol 1 ◽  
pp. 2147-2156
Author(s):  
Pavel Livotov
Keyword(s):  
Mathematical Model ◽  
Finite Number ◽  
Research Question ◽  
Performance Function ◽  
Non Linear ◽  
Series Of Experiments ◽  
Productivity Prediction ◽  
A Company

AbstractThe internal crowdsourcing-based ideation within a company can be defined as an involvement of its staff, specialists, managers, and other employees, to propose solution ideas for a pre-defined problem. This paper addresses a question, how many participants of the company-internal ideation process are required to nearly reach the ideation limit for the problems with a finite number of workable solutions. To answer the research question, the author proposes a set of metrics and a non-linear ideation performance function with a positive decreasing slope and ideation limit for the closed-ended problems. Three series of experiments helped to explore relationships between the metric attributes and resulted in a mathematical model which allows companies to predict the productivity metrics of their crowdsourcing ideation activities such as quantity of different ideas and ideation limit as a function of the number of contributors, their average personal creativity and ideation efficiency of a contributors’ group.

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