A Mixed-Flow Cascade Passage Design Procedure Based on a Power Series Expansion

1983 ◽  
Vol 105 (2) ◽  
pp. 231-242 ◽  
Author(s):  
R. A. Novak ◽  
G. Haymann-Haber
Keyword(s):  
Experimental Data ◽  
Power Series ◽  
Series Expansion ◽  
Taylor Series ◽  
Power Series Expansion ◽  
Design Procedure ◽  
Taylor Series Expansion ◽  
Analytic Solutions ◽  
Mixed Flow ◽  
Flow Passage

Flow passage design and analysis procedures employing a TAYLOR series expansion across the flow field were first suggested as far back as 1908. With very few exceptions the early work addressed only the problem of symmetrical convergent-divergent passages. A generalization and an extension of the approach permits it to be used for the design of arbitrary cascade passages in subsonic, supersonic, or mixed-flow regimes. The method will give fast, realistic solutions in situations where shock-free flow is meaningful, and where the cascade gap-chord ratio is not excessive. It assumes inviscid, irrotational flow and employs a fourth-order TAYLOR series expansion across the cascade passage. Numerous examples are given, with comparisons with experimental data and other analytic solutions.

A Mixed-Flow Cascade Passage Design Procedure Based on a Power Series Expansion

1982 ◽  
Author(s):  
R. A. Novak ◽  
G. Haymann-Haber
Keyword(s):  
Experimental Data ◽  
Power Series ◽  
Series Expansion ◽  
Taylor Series ◽  
Power Series Expansion ◽  
Design Procedure ◽  
Taylor Series Expansion ◽  
Analytic Solutions ◽  
Mixed Flow ◽  
Flow Passage

Flow passage design and analysis procedures employing a Taylor series expansion across the flow field were first suggested as far back as 1908. With very few exceptions the early work addressed only the problem of symmetrical convergent-divergent passages. A generalization and an extension of the approach permits it to be used for the design of arbitrary cascade passages in subsonic, supersonic, or mixed-flow regimes. The method will give fast, realistic solutions in situations where shock-freeflow is meaningful, and where the cascade gap-chord ratio is not excessive. It assumes inviscid, irrotational flow and employs a fourth-order Taylor series expansion across the cascade passage. Numerous examples are given, with comparisons with experimental data and other analytic solutions.

scholarly journals A Generalized Fractional Power Series for Solving a Class of Nonlinear Fractional Integro-Differential Equation

2018 ◽  
Author(s):  
Sirunya Thanompolkrang ◽  
Duangkamol Poltem
Keyword(s):  
Differential Equation ◽  
Power Series ◽  
Series Expansion ◽  
Fractional Derivatives ◽  
Power Series Expansion ◽  
Fractional Power ◽  
Taylor Series Expansion ◽  
New Approach ◽  
Integro Differential Equation ◽  
Fractional Power Series

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

scholarly journals Convergent Power Series of sech⁡(x) and Solutions to Nonlinear Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
U. Al Khawaja ◽  
Qasem M. Al-Mdallal
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Series Expansion ◽  
Taylor Series ◽  
Nonlinear Differential Equations ◽  
Series Representation ◽  
Power Series Expansion ◽  
Detailed Comparison ◽  
Radius Of Convergence ◽  
Finite Radius

It is known that power series expansion of certain functions such as sech⁡(x) diverges beyond a finite radius of convergence. We present here an iterative power series expansion (IPS) to obtain a power series representation of sech⁡(x) that is convergent for all x. The convergent series is a sum of the Taylor series of sech⁡(x) and a complementary series that cancels the divergence of the Taylor series for x≥π/2. The method is general and can be applied to other functions known to have finite radius of convergence, such as 1/(1+x2). A straightforward application of this method is to solve analytically nonlinear differential equations, which we also illustrate here. The method provides also a robust and very efficient numerical algorithm for solving nonlinear differential equations numerically. A detailed comparison with the fourth-order Runge-Kutta method and extensive analysis of the behavior of the error and CPU time are performed.

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