scholarly journals Quantifying non-linearity in planar supersonic potential flows

2017 ◽  
Vol 121 (1237) ◽  
pp. 372-394 ◽  
Author(s):  
M.-C. Meijer ◽  
L. Dala ◽  
L. Dala
Keyword(s):  
Mach Number ◽  
Small Body ◽  
A Priori ◽  
Flow Equation ◽  
Full Potential ◽  
Linear Potential ◽  
Curvature Perturbation ◽  
Turning Angle ◽  
Potential Flows ◽  
Planar Flows

ABSTRACTAn analysis is presented which allows the engineer to quantitatively estimate the validity bounds of aerodynamic methods based in linear potential flows a-priori. The development is limited to quasi-steady planar flows with attached shocks and small body curvature. Perturbation velocities are parameterised in terms of Mach number and flow turning angle by means of a series-expansion for flow velocity based in the method of characteristics. The parameterisation is used to assess the magnitude of non-linear term-groupings relative to linear groups in the full potential equation. This quantification is used to identify dominant nonlinear terms and to estimate the validity of linearising the potential flow equation at a given Mach number and flow turning angle. Example applications include the a-priori estimation of the validity bounds for linear aerodynamic models for supersonic aeroelastic analysis of lifting surfaces and panels.

scholarly journals Experimental Investigation of Tandem Blade Cascades With Double-Circular ARC Profiles

1985 ◽  
Author(s):  
Wu Guochuan ◽  
Zhuang Biaonan ◽  
Guo Bingheng
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Mach Number ◽  
Total Pressure ◽  
Incidence Angle ◽  
Axial Direction ◽  
Geometrical Parameters ◽  
Optimal Conditions ◽  
Turning Angle ◽  
Circular Arc

24 double circular are tandem blade cascades of three different chord-ratios were investigated under different displacements in peripheral and axial direction. The inlet Mach number was 0.3. The Reynolds number based on blade chord was 2.7×105. The characteristics of the tandem blade cascades, such as the dependence of turning angle and coefficient of total pressure loss on incidence angle were obtained. The ranges of main geometrical parameters under optimal conditions were recommended.

Mach Number Influence on Reduced-Order Models of Inviscid Potential Flows in Turbomachinery

2002 ◽  
Vol 124 (4) ◽  
pp. 977-987 ◽  
Author(s):  
Bogdan I. Epureanu ◽  
Earl H. Dowell ◽  
Kenneth C. Hall
Keyword(s):  
Mach Number ◽  
Steady Flow ◽  
Inviscid Flow ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Spatial Gradients ◽  
Potential Flows ◽  
Proper Orthogonal Decomposition Technique ◽  
Flow Through ◽  
Phase Angles

An unsteady inviscid flow through a cascade of oscillating airfoils is investigated. An inviscid nonlinear subsonic and transonic model is used to compute the steady flow solution. Then a small amplitude motion of the airfoils about their steady flow configuration is considered. The unsteady flow is linearized about the nonlinear steady response based on the observation that in many practical cases the unsteadiness in the flow has a substantially smaller magnitude than the steady component. Several reduced-order modal models are constructed in the frequency domain using the proper orthogonal decomposition technique. The dependency of the required number of aerodynamic modes in a reduced-order model on the far-field upstream Mach number is investigated. It is shown that the transonic reduced-order models require a larger number of modes than the subsonic models for a similar geometry, range of reduced frequencies and interblade phase angles. The increased number of modes may be due to the increased Mach number per se, or the presence of the strong spatial gradients in the region of the shock. These two possible causes are investigated. Also, the geometry of the cascade is shown to influence strongly the shape of the aerodynamic modes, but only weakly the required dimension of the reduced-order models.

A theory for Langmuir solitons

1982 ◽  
Vol 27 (1) ◽  
pp. 95-120 ◽  
Author(s):  
N. Nagesha Rao ◽  
Ram K. Varma
Keyword(s):  
Mach Number ◽  
A Priori ◽  
Low Frequency ◽  
Analytic Solutions ◽  
Smooth Transition ◽  
Langmuir Waves ◽  
Method Of Solution ◽  
Mach Numbers ◽  
Ion Waves ◽  
Langmuir Solitons

A systematic and self-consistent analysis of the problem of Langmuir solitons in the entire range of Mach numbers (0 < M < 1) has been presented. A coupled set of nonlinear equations for the amplitude of the modulated, high-frequency Langmuir waves and the associated low-frequency ion waves is derived without using the charge neutrality condition or any a priori ordering schemes. A technique has been developed for obtaining analytic solutions of these equations where any arbitrary degree of ion nonlinearity consistent with the nonlinearity retained in the Langmuir field can be taken into account self-consistently. A class of solutions with non-zero Langmuir field intensity at the centre (ξ = 0) are found for intermediate values of the Mach number. Using these solutions, a smooth transition from single-hump solitons to the double-hump solitons with respect to the Mach number has been established through the definitions of critical and cut-off Mach numbers. Further, under appropriate limiting conditions, various solutions discussed by other authors are obtained. Sagdeev potential analyses of the solutions for the Langmuir field as well as the ion field are carried out. These analyses confirm the transition from single-hump solitons to the double-hump solitons with respect to the Mach number. The existence of many-hump solitons for higher-order nonlinearities in the low-frequency ion wave potential has been conjectured. The method of solution developed here can be applied to similar equations in other fields.

Meshless numerical simulation of (full) potential flows in a nozzle by genetic algorithms

2003 ◽  
Vol 43 (10-11) ◽  
pp. 1167-1176 ◽  
Author(s):  
G. Winter ◽  
J. C. Abderramán ◽  
J. A. Jiménez ◽  
B. González ◽  
E. Benitez ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Genetic Algorithms ◽  
Full Potential ◽  
Potential Flows

scholarly journals Finite element error estimates for subsonic flow

1987 ◽  
Vol 29 (1) ◽  
pp. 88-102 ◽  
Author(s):  
S. S. Chow ◽  
G. F. Carey
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Subsonic Flow ◽  
Full Potential ◽  
Linear Potential ◽  
Element Analysis ◽  
Subsonic Flows ◽  
Potential Equation ◽  
Dual Formulation ◽  
Element Error

AbstractError estimates are derived for a finite element analysis of plane steady subsonic flows described by the full potential equation. The analysis is based on the use of the theory of variational inequalities to accomodate the subsonic flow constraint and leads to a suboptimal estimate relative to that obtained for linear potential flow. We then consider an alternative dual formulation of the problem and obtain an optimal estimate subject to reasonable regularity assumptions.

A Parametric Analysis of Reduced Order Models of Potential Flows in Turbomachinery Using Proper Orthogonal Decomposition

2001 ◽  
Author(s):  
Bogdan I. Epureanu ◽  
Earl H. Dowell ◽  
Kenneth C. Hall
Keyword(s):  
Mach Number ◽  
Proper Orthogonal Decomposition ◽  
Steady Flow ◽  
Inviscid Flow ◽  
Orthogonal Decomposition ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Spatial Gradients ◽  
Potential Flows ◽  
Proper Orthogonal

An unsteady inviscid flow through a cascade of oscillating airfoils is investigated. An inviscid nonlinear subsonic and transonic model is used to compute the steady flow solution. Then a small amplitude motion of the airfoils about their steady flow configuration is considered. The unsteady flow is linearized about the nonlinear steady response based on the observation that in many practical cases the unsteadiness in the flow has a substantially smaller magnitude than the steady component. Several reduced order modal models are constructed in the frequency domain using the proper orthogonal decomposition technique. The dependency of the required number of aerodynamic modes in a reduced order model on the far-field upstream Mach number is investigated. It is shown that the transonic reduced order models require a larger number of modes than the subsonic models for a similar geometry, range of reduced frequencies and interblade phase angles. The increased number of modes may be due to the increased Mach number per se, or the presence of the strong spatial gradients in the region of the shock. These two possible causes are investigated. Also, the geometry of the cascade is shown to influence strongly the shape of the aerodynamic modes, but only weakly the required dimension of the reduced order models.

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