scholarly journals Centrifugal Compressor Polytropic Performance—Improved Rapid Calculation Results—Cubic Polynomial Methods

2021 ◽  
Vol 6 (2) ◽  
pp. 15
Author(s):  
Matt Taher ◽  
Fred Evans
Keyword(s):  
Performance Test ◽  
Ease Of Use ◽  
Solution Technique ◽  
Test Duration ◽  
Calculation Results ◽  
Cubic Polynomial ◽  
Compressor Performance ◽  
Cubic Polynomials ◽  
Slope Constraints ◽  
Polynomial Methods

This paper presents a new improved approach to calculation of polytropic performance of centrifugal compressors. This rapid solution technique is based upon a constant efficiency, temperature-entropy polytropic path represented by cubic polynomials. New thermodynamic path slope constraints have been developed that yield highly accurate results while requiring fewer computing resources and reducing computing elapsed time. Applying this thermodynamically sound cubic polynomial model would improve accuracy and shorten compressor performance test duration at a vendor’s shop. A broad range of example case results verify the accuracy and ease of use of the method. The example cases confirm the cubic polynomial methods result in lower calculation uncertainty than other methods.

Centrifugal Compressor Polytropic Performance Evaluation Using Cubic Polynomial Approximation for the Temperature-Entropy Polytropic Path

2021 ◽  
Author(s):  
Matt Taher ◽  
B. F. Evans
Keyword(s):  
Performance Evaluation ◽  
High Precision ◽  
Centrifugal Compressor ◽  
Approximation Method ◽  
Performance Testing ◽  
Ease Of Use ◽  
Continuous Path ◽  
State Variables ◽  
Cubic Polynomial ◽  
Compressor Performance

Abstract A highly accurate centrifugal compressor polytropic performance approximation method has been developed that is easy to employ. The method is based upon a constant efficiency, temperature-entropy path for real gases. The elegance of this method is its exceedingly simple way of calculating polytropic efficiency with sufficiently high precision as required for compressor performance testing. A constant efficiency polytropic path can be modeled as either a single or several sequential cubic polynomial segments affording solutions that allow for determining thermodynamic state variables along a continuous path. New analytic terms have been developed for slope and curvature of temperature versus entropy along the constant efficiency polytropic path. A broad range of example case results verify the accuracy and ease of use of the method.

Mathematical Modeling of the Polytropic Process Using the Sequential Cubic Polynomial Approximation

2021 ◽  
Author(s):  
Matt Taher
Keyword(s):  
Performance Testing ◽  
Operating Conditions ◽  
Solution Technique ◽  
Polynomial Method ◽  
Compression Process ◽  
Energy Degradation ◽  
Cubic Polynomial ◽  
Compressor Performance ◽  
Path Dependent ◽  
Polytropic Process

Abstract The polytropic process is used to signify the effect of “energy degradation” associated with the equipment losses, which is as an inherent irreversibility in a compression process. The polytropic process is path dependent, which entails the irreversibility associated with the system. The change of gas composition and operating conditions affect the energy degradation. In this paper the polytropic process of real gas is explained and thermodynamics and mathematical model used in Taher-Evans Cubic Polynomial Method [1], [2] is presented. The elegance of Taher-Evans Cubic Polynomial Method is its rapid solution technique and high precision for calculating polytropic efficiency as required for compressor performance testing by the ASME PTC-10 [3].

scholarly journals An Invariant Regarding Waring’s Problem for Cubic Polynomials

2009 ◽  
Vol 193 ◽  
pp. 95-110 ◽  
Author(s):  
Giorgio Ottaviani
Keyword(s):  
Secant Variety ◽  
Waring’S Problem ◽  
Waring Problem ◽  
Veronese Variety ◽  
Waring's Problem ◽  
Cubic Polynomial ◽  
Cubic Polynomials

AbstractWe compute the equation of the 7-secant variety to the Veronese variety (P4,O(3)), its degree is 15. This is the last missing invariant in the Alexander-Hirschowitz classification. It gives the condition to express a homogeneous cubic polynomial in 5 variables as the sum of 7 cubes (Waring problem). The interesting side in the construction is that it comes from the determinant of a matrix of order 45 with linear entries, which is a cube. The same technique allows to express the classical Aronhold invariant of plane cubics as a pfaffian.

scholarly journals Elements of Bi-cubic Polynomial Natural Spline Interpolation for Scattered Data: Boundary Conditions Meet Partition of Unity Technique

2020 ◽  
Vol 8 (4) ◽  
pp. 994-1010
Author(s):  
Weizhi Xu
Keyword(s):  
Boundary Conditions ◽  
Spline Interpolation ◽  
Partition Of Unity ◽  
Scattered Data ◽  
Rectangular Domain ◽  
Natural Boundary ◽  
Natural Spline ◽  
Cubic Polynomial ◽  
Natural Boundary Conditions ◽  
Cubic Polynomials

This paper investigates one kind of interpolation for scattered data by bi-cubic polynomial natural spline, in which the integral of square of partial derivative of two orders to x and to y for the interpolating function is minimal (with natural boundary conditions). Firstly, bi-cubic polynomial natural spline interpolations with four kinds of boundary conditions are studied. By the spline function methods of Hilbert space, their solutions are constructed as the sum of bi-linear polynomials and piecewise bi-cubic polynomials. Some properties of the solutions are also studied. In fact, bi-cubic natural spline interpolation on a rectangular domain is a generalization of the cubic natural spline interpolation on an interval. Secondly, based on bi-cubic polynomial natural spline interpolations of four kinds of boundary conditions, and using partition of unity technique, a Partition of Unity Interpolation Element Method (PUIEM) for fitting scattered data is proposed. Numerical experiments show that the PUIEM is adaptive and outperforms state-of-the-art competitions, such as the thin plate spline interpolation and the bi-cubic polynomial natural spline interpolations for scattered data.

Cubic polynomials with the same residues (mod p)

1968 ◽  
Vol 64 (3) ◽  
pp. 655-658 ◽  
Author(s):  
K. McCann ◽  
K. S. Williams
Keyword(s):  
Recent Work ◽  
Linear Transformation ◽  
Integer Coefficients ◽  
Cubic Polynomial ◽  
Cubic Polynomials ◽  
Mod P

Some recent work by the authors (1) on the distribution of the residues of a cubic polynomial modulo an odd prime p led to the conjecture that, in general, two cubic polynomials with integer coefficients possessing the same residues modulo p (not necessarily occurring to the same multiplicity) are equivalent, that is are related by a linear transformation modulo p. The purpose of the present paper is to prove this conjecture. We establish the following theorem.

An Analysis of Axial Compressor Fouling and a Blade Cleaning Method

1998 ◽  
Vol 120 (2) ◽  
pp. 256-261 ◽  
Author(s):  
A. P. Tarabrin ◽  
V. A. Schurovsky ◽  
A. I. Bodrov ◽  
J.-P. Stalder
Keyword(s):  
Mathematical Model ◽  
Axial Compressor ◽  
Axial Compressors ◽  
Cleaning Method ◽  
Engine Efficiency ◽  
Calculation Results ◽  
On Line ◽  
Compressor Performance ◽  
High Level ◽  
Industrial Gas Turbine

The paper describes the phenomenon of axial compressor fouling due to aerosols contained in the air. Key parameters having effect on the level of fouling are determined. A mathematical model of a progressive compressor fouling using the stage-by-stage calculation method is developed. Calculation results on the influence of fouling on the compressor performance are presented. A new index of sensitivity of axial compressors to fouling is suggested. The paper gives information about Turbotect’s deposit cleaning method of compressor blading and the results of its application on an operating industrial gas turbine. Regular on-line and off-line washings of the compressor flow path make it possible to maintain a high level of engine efficiency and output.

An Analysis of Axial Compressors Fouling and a Cleaning Method of Their Blading

1996 ◽  
Author(s):  
A. P. Tarabrin ◽  
V. A. Schurovsky ◽  
A. I. Bodrov ◽  
J.-P. Stalder
Keyword(s):  
Mathematical Model ◽  
Axial Compressor ◽  
Axial Compressors ◽  
Cleaning Method ◽  
Engine Efficiency ◽  
Calculation Results ◽  
On Line ◽  
Compressor Performance ◽  
High Level ◽  
Industrial Gas Turbine

The paper describes the phenomenon of axial compressor fouling due to aerosols contained in the air. Key parameters having effect on the level of fouling are determined. A mathematical model of a progressive compressor fouling using the stage-by-stage calculation method is developed. Calculation results on the influence of fouling on the compressor performance are presented. A new index of sensitivity of axial compressors to fouling is suggested. The paper gives information about the Turbotect’s deposit cleaning method of compressor blading and the results of its application on an operating industrial gas turbine. Regular on line and off line washings of compressor flow path make it possible to maintain a high level of engine efficiency and output.

The description of the rate of protein and lipid growth in pigs in relation to live weight

2002 ◽  
Vol 138 (4) ◽  
pp. 415-423 ◽  
Author(s):  
C. T. WHITTEMORE ◽  
D. M. GREEN
Keyword(s):  
Simple Form ◽  
Retention Rate ◽  
Live Weight ◽  
Logistic Function ◽  
Allometric Relationship ◽  
Gompertz Function ◽  
Protein Retention ◽  
Weight Range ◽  
Cubic Polynomial ◽  
Cubic Polynomials

The paper seeks to compare the effectiveness of various functions as appropriate to express protein retention and lipid retention as a function of pig live weight. Linear descriptors were adequate for protein growth over the 20 to 120 kg live weight range, but not adequate when higher live weights were included. Linear descriptors were not adequate for lipid growth over any weight range. Quadratic and cubic polynomials, and the logistic function, were faulted on their failure to describe the known biology. Augmentation of the allometric function added nothing to the simple form. The Gompertz function was consistently effective for the description of daily protein retention rate. The Bridges and Richards functions are more flexible than the Gompertz with respect to the point of inflection, but when applied they resembled the Gompertz and therefore did not materially influence the descriptive outcome. The cubic polynomial, augmented allometric, Bridges and Richards functions, although favoured in other reports, were found to add nothing to the more simple functions. It is concluded that protein retention can be well expressed in relation to live weight by linear and Gompertz functions. Lipid retention could be well described by an allometric relationship with pig mass.

Application of a Low-Solidity Cascade Diffuser to Transonic Centrifugal Compressor

1990 ◽  
Vol 112 (1) ◽  
pp. 25-29 ◽  
Author(s):  
H. Hayami ◽  
Y. Senoo ◽  
K. Utsunomiya
Keyword(s):  
Centrifugal Compressor ◽  
Performance Test ◽  
Pressure Ratio ◽  
Test Results ◽  
Vaneless Diffuser ◽  
Circular Arc ◽  
Transonic Centrifugal Compressor ◽  
Wide Range ◽  
Compressor Performance ◽  
Low Solidity Cascade Diffuser

Low-solidity circular cascades, conformally transformed from high-stagger linear cascades of double-circular-arc vanes with solidity 0.69, were used as a part of the diffuser system of a transonic centrifugal compressor. Performance test results were compared with data of the same compressor with a vaneless diffuser. Good compressor performance and a wider flow range as well as a higher pressure ratio and a higher efficiency, superior to those with a vaneless diffuser, where the flow range was limited by choke of the impeller, were demonstrated. The test circular cascade diffusers demonstrated a good pressure recovery over a wide range of flow angles, even when the inflow Mach number to the cascade was over unity.

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