Comment on: “Variational principle for two-dimensional incompressible inviscid flow” [Phys. Lett. A 371 (2007) 39]

2008 ◽  
Vol 372 (36) ◽  
pp. 5857 ◽  
Author(s):  
Markus Scholle ◽  
Christian Heining ◽  
Andre Haas
Keyword(s):  
Variational Principle ◽  
Inviscid Flow ◽  
Two Dimensional

A Viscous-Inviscid Interaction Procedure—Part 1: Method for Computing Two-Dimensional Incompressible Separated Channel Flows

1986 ◽  
Vol 108 (1) ◽  
pp. 64-70 ◽  
Author(s):  
O. K. Kwon ◽  
R. H. Pletcher
Keyword(s):  
Experimental Data ◽  
Finite Difference ◽  
Turbulent Flows ◽  
Inviscid Flow ◽  
Companion Paper ◽  
Separated Flows ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Interaction Scheme ◽  
Laminar And Turbulent Flows

A viscous-inviscid interaction scheme has been developed for computing steady incompressible laminar and turbulent flows in two-dimensional duct expansions. The viscous flow solutions are obtained by solving the boundary-layer equations inversely in a coupled manner by a finite-difference scheme; the inviscid flow is computed by numerically solving the Laplace equation for streamfunction using an ADI finite-difference procedure. The viscous and inviscid solutions are matched iteratively along displacement surfaces. Details of the procedure are presented in the present paper (Part 1), along with example applications to separated flows. The results compare favorably with experimental data. Applications to turbulent flows over a rearward-facing step are described in a companion paper (Part 2).

Unsteady transonic flows in two-dimensional channels

1972 ◽  
Vol 52 (3) ◽  
pp. 437-449 ◽  
Author(s):  
T. C. Adamson
Keyword(s):  
Inviscid Flow ◽  
Time Varying ◽  
Two Dimensional ◽  
Perfect Gas ◽  
Flow Disturbance ◽  
Specific Heats ◽  
Isentropic Flow ◽  
Perturbation Potential ◽  
Temporal Flow ◽  
Nozzle Flows

A two-dimensional, unsteady, transonic, irrotational, inviscid flow of a perfect gas with constant specific heats is considered. The analysis involves perturbations from a uniform sonic isentropic flow. The governing perturbation potential equations are derived for various orders of the ratio of the characteristic time associated with a temporal flow disturbance to the time taken by a sonic disturbance to traverse the transonicregime. The case where this ratio is large compared to one is studied in detail. A similarity solution involving an arbitrary function of time is found and it is shown that this solution corresponds to unsteady chimel flows with either stationary or time-varying wall shapes. Numerical computations are presented showing the temporal changes in flow structure as a disturbance dies out exponentially for the following typical nozzle flows: simple accelerating (Meyer) flow and flow with supersonic pockets (Taylor and limiting Taylor flow).

Study of Vaneless Diffuser Rotating Stall Based on Two-Dimensional Inviscid Flow Analysis

1996 ◽  
Vol 118 (1) ◽  
pp. 123-127 ◽  
Author(s):  
Yoshinobu Tsujimoto ◽  
Yoshiki Yoshida ◽  
Yasumasa Mori
Keyword(s):  
Propagation Velocity ◽  
Flow Instability ◽  
Present Report ◽  
Inviscid Flow ◽  
Rotating Stall ◽  
Critical Flow ◽  
Two Dimensional ◽  
Vaneless Diffuser ◽  
Flow Angle ◽  
Pressure Disturbance

Rotating stalls in vaneless diffusers are studied from the viewpoint that they are basically two-dimensional inviscid flow instability under the boundary conditions of vanishing velocity disturbance at the diffuser inlet and of vanishing pressure disturbance at the diffuser outlet. The linear analysis in the present report shows that the critical flow angle and the propagation velocity are functions of only the diffuser radius ratio. It is shown that the present analysis can reproduce most of the general characteristics observed in experiments: critical flow angle, propagation velocity, velocity, and pressure disturbance fields. It is shown that the vanishing velocity disturbance at the diffuser inlet is caused by the nature of impellers as a “resistance” and an “inertial resistance,” which is generally strong enough to suppress the velocity disturbance at the diffuser inlet. This explains the general experimental observations that vaneless diffuser rotating stalls are not largely affected by the impeller.

scholarly journals A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion

2019 ◽  
Vol 475 (2224) ◽  
pp. 20180642 ◽  
Author(s):  
H. Alemi Ardakani ◽  
T. J. Bridges ◽  
F. Gay-Balmaz ◽  
Y. H. Huang ◽  
C. Tronci
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Variational Principle ◽  
Stream Function ◽  
Fluid Motion ◽  
Two Dimensional ◽  
Euclidean Group ◽  
Fluid Sloshing ◽  
Pressure Boundary Condition ◽  
Vessel Motion

A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and the vessel motion is represented by a path in the planar Euclidean group. Novelties in the formulation include how the pressure boundary condition is treated, the introduction of a stream function into the Euler–Poincaré variations, the derivation of free surface variations and how the equations for the vessel path in the Euclidean group, coupled to the fluid motion, are generated automatically.

Application of a Two-Dimensional Supersonic Passage Analysis to the Design of Compressor Rotors

1974 ◽  
Author(s):  
R. G. Hantman ◽  
A. A. Mikolajczak ◽  
F. J. Camarata
Keyword(s):  
Leading Edge ◽  
Inviscid Flow ◽  
Two Dimensional ◽  
Compressor Rotor ◽  
Pressure Distributions ◽  
Displacement Thickness ◽  
Blade Section ◽  
Comparison Of The Results ◽  
Rotational Method ◽  
Good Agreement

A description of a two-dimensional supersonic cascade passage analysis and its application to the design of a high hub-to-tip ratio supersonic compressor rotor is presented. The analysis, applicable to the case in which the inviscid flow is everywhere supersonic, includes an entrance region calculation which accounts for blade leading edge bluntness effects, and a passage and wake region calculation. The inviscid part of the analysis is solved using a rotational method of characteristics. The effect of the blade boundary layer displacement thickness is taken into consideration. Comparison of the results of the analysis with supersonic cascade data is made, showing good agreement in overall performance prediction, in blade surface static pressure distributions, and in achievement of the desired shock wave patterns. A comparison of the results of the analysis is made also with the performance of a blade section of a high hub-to-tip ratio supersonic compressor and acceptable agreement obtained.

On the existence and ‘blow-up’ of solutions to a two-dimensional nonlinear boundary-value problem arising in corrosion modelling

2003 ◽  
Vol 133 (1) ◽  
pp. 119-149 ◽  
Author(s):  
Otared Kavian ◽  
Michael Vogelius
Keyword(s):  
Variational Principle ◽  
Boundary Value Problem ◽  
Finite Number ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Boundary Value ◽  
Classical Solutions ◽  
Two Dimensional ◽  
Limiting Behaviour ◽  
Corrosion Modelling

Let Ω be a bounded C2,α domain in R2. We prove that the boundary-value problem Δυ = 0 in Ω, ∂υ/∂n = λsinh(υ) on ∂Ω, has infinitely many (classical) solutions for any given λ > 0. These solutions are constructed by means of a variational principle. We also investigate the limiting behaviour as λ → 0+; indeed, we prove that each of our solutions, as λ → 0+, after passing to a subsequence, develops a finite number of singularities located on ∂Ω.

A Two-Dimensional Multibody Integral Approach for Forces in Inviscid Flow With Free Vortices and Vortex Production

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Juan Li ◽  
Chen-Yuan Bai ◽  
Zi-Niu Wu
Keyword(s):  
Flat Plate ◽  
Lift Force ◽  
Vortex Sheet ◽  
Inviscid Flow ◽  
The Body ◽  
Integral Approach ◽  
Two Dimensional ◽  
Middle Point ◽  
Dependent Behavior ◽  
The Individual

In this paper, we propose an integral force approach for potential flow around two-dimensional bodies with external free vortices and with vortex production. The method can be considered as an extension of the generalized Lagally theorem to the case with continuous distributed vortices inside and outside of the body and is capable of giving the individual force of each body in the case of multiple bodies. The lift force formulas are validated against two examples. One is the Wagner problem with vortex production and with moving vortices in the form of a vortex sheet. The other is the lift of a flat plate when there is a standing vortex over its middle point. As a first application, the integral approach is applied to study the lift force of a flat plate induced by a bounded vortex above the plate. This bounded vortex may represent a second small airfoil at incidence. For this illustrative example, the lift force is found to display an interesting distance-dependent behavior: for a clockwise circulation, the lift force acting on the main airfoil is attractive for small distance and repulsive for large distance.

Sign in / Sign up

Export Citation Format

Share Document