A Rational Analysis of Periodic Flow Perturbation in Supersonic Two-Dimensional Cascade

1979 ◽  
Vol 101 (3) ◽  
pp. 431-439 ◽  
Author(s):  
Ron-Ho Ni
Keyword(s):  
Flow Equation ◽  
Two Dimensional ◽  
Rational Analysis ◽  
Axial Velocity Component ◽  
Flow Perturbation ◽  
Supersonic Inlet ◽  
Previous Solution ◽  
Inlet Conditions ◽  
Unsteady Loading ◽  
Physical Phenomena

An analytical formulation which can be applied to obtain unsteady aerodynamic solutions for a cascade of flat plate blades oscillating in subsonic or supersonic flow with either subsonic or supersonic axial velocity component is presented. In the analysis, the flow is assumed to be two-dimensional and isentropic and the blades are undergoing small amplitude harmonic oscillations. The method of superposition of basic wave solutions of the linearized unsteady flow equation is used to construct the flow field induced by the harmonic motion of blades in cascade. This method leads to an integral equation from which the unsteady loading on a blade can be determined. Since the equation applied to both subsonic and supersonic inlet conditions, the present approach provides a unified basis for analyzing and understanding the complex physical phenomena associated with flow past vibrating cascades. The technique used to determine a solution for an unsteady supersonic cascade is also described and the results obtained are shown to agree with those from previous solution.

scholarly journals Deformed $$\sigma $$-models, Ricci flow and Toda field theories

2021 ◽  
Vol 111 (6) ◽  
Author(s):  
Dmitri Bykov ◽  
Dieter Lüst
Keyword(s):  
Sigma Models ◽  
Ricci Flow ◽  
Flag Manifold ◽  
Flow Equation ◽  
Target Space ◽  
Field Theories ◽  
Two Dimensional

AbstractIt is shown that the Pohlmeyer map of a $$\sigma $$ σ -model with a toric two-dimensional target space naturally leads to the ‘sausage’ metric. We then elaborate the trigonometric deformation of the $$\mathbb {CP}^{n-1}$$ CP n - 1 -model, proving that its T-dual metric is Kähler and solves the Ricci flow equation. Finally, we discuss a relation between flag manifold $$\sigma $$ σ -models and Toda field theories.

RENORMALIZATION GROUP ANALYSIS OF A TWO-DIMENSIONAL INTERACTING ELECTRON SYSTEM

2001 ◽  
Vol 16 (11) ◽  
pp. 1889-1898
Author(s):  
WALTER METZNER
Keyword(s):  
Renormalization Group ◽  
Group Analysis ◽  
Interaction Strength ◽  
Electron System ◽  
Flow Equation ◽  
Group Method ◽  
Model Parameters ◽  
Two Dimensional ◽  
Renormalization Group Analysis ◽  
Effective Interactions

We describe a Wick ordered functional renormalization group method for interacting Fermi systems, where the complete flow from the bare action of the microscopic model to the effective low-energy action is obtained from a differential flow equation. We apply this renormalization group approach to a prototypical two-dimensional lattice electron system, the Hubbard model on a square lattice. The flow equation for the effective interactions is evaluated numerically on 1-loop level. The effective interactions diverge at a finite energy scale which is exponentially small for small bare interactions. To analyze the nature of the instabilities signalled by the diverging interactions we compute the flow of the singlet superconducting susceptibilities for various pairing symmetries and also charge and spin density susceptibilities. Depending on the choice of the model parameters (hopping amplitudes, interaction strength and band-filling) we find antiferromagnetic order or d-wave superconductivity as leading symmetry breaking instability.

Two-Dimensional Numerical Model for Studies of Collective Beam-Plasma Interaction

2010 ◽  
Vol 5 (2) ◽  
pp. 85-97
Author(s):  
Andrey V. Terekhov ◽  
Igor V. Timofeev ◽  
Konstantin V. Lotov
Keyword(s):  
Numerical Model ◽  
Electron Beams ◽  
Modulational Instability ◽  
Two Dimensional ◽  
Particle In Cell ◽  
Plasma Energy ◽  
Proposed Model ◽  
The Laplace Operator ◽  
Physical Phenomena ◽  
Powerful Electron

A two-dimensional particle-in-cell numerical model is developed to simulate collective relaxation of powerful electron beams in plasmas. To increase the efficiency of parallel particle-in-cell simulations on supercomputers, the Dichotomy Algorithm is used for inversion of the Laplace operator. The proposed model is tested with several well-known physical phenomena and is shown to adequately simulate basic effects of the beam driven turbulence. Also, the modulational instability is studied in the regime when the energy of pumping wave significantly exceeds the thermal plasma energy

scholarly journals Double Hopf Bifurcation in Microbubble Oscillators with Delay Coupling

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Jinbin Wang ◽  
Rui Zhang ◽  
Lifenq Ma
Keyword(s):  
Hopf Bifurcation ◽  
Center Manifold ◽  
Two Dimensional ◽  
Main Attention ◽  
Dimensional Parameter ◽  
Center Manifold Reduction ◽  
Double Hopf Bifurcation ◽  
Physical Phenomena ◽  
Manifold Reduction ◽  
Theoretical Results

Using center manifold reduction methodswe investigate the double Hopf bifurcation in the dynamics of microbubble with delay couplingwith main attention focused on nonresonant double Hopf bifurcation. We obtain the normal form of the system in the vicinity of the double Hopf point and classify the bifurcations in a two-dimensional parameter space near the critical point. Some numerical simulations support the applicability of the theoretical results. In particularwe give the explanation for some physical phenomena of the system using the obtained mathematical results.

scholarly journals Dichotomy between frustrated local spins and conjugated electrons in a two-dimensional metal–organic framework

Nanoscale ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 955-961 ◽  
Author(s):  
Wei Jiang ◽  
Zheng Liu ◽  
Jia-Wei Mei ◽  
Bin Cui ◽  
Feng Liu
Keyword(s):  
Metal Organic Framework ◽  
Electronic States ◽  
Two Dimensional ◽  
Metal Organic ◽  
Physical Phenomena ◽  
Organic Framework

Dichotomy between local spins and conjugated electrons spawns various exotic physical phenomena. We discover a 2D MOF dichotomy system and propose to characterize the exotic electronic states using STM.

scholarly journals Interpreting Aerodynamics of a Transonic Impeller from Static Pressure Measurements

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Fangyuan Lou ◽  
John Charles Fabian ◽  
Nicole Leanne Key
Keyword(s):  
Flow Field ◽  
High Speed ◽  
Static Pressure ◽  
Pressure Ratio ◽  
Leading Edge ◽  
Pressure Measurements ◽  
High Loss ◽  
Supersonic Inlet ◽  
Mach Numbers ◽  
Inlet Conditions

This paper investigates the aerodynamics of a transonic impeller using static pressure measurements. The impeller is a high-speed, high-pressure-ratio wheel used in small gas turbine engines. The experiment was conducted on the single stage centrifugal compressor facility in the compressor research laboratory at Purdue University. Data were acquired from choke to near-surge at four different corrected speeds (Nc) from 80% to 100% design speed, which covers both subsonic and supersonic inlet conditions. Details of the impeller flow field are discussed using data acquired from both steady and time-resolved static pressure measurements along the impeller shroud. The flow field is compared at different loading conditions, from subsonic to supersonic inlet conditions. The impeller performance was strongly dependent on the inducer, where the majority of relative diffusion occurs. The inducer diffuses flow more efficiently for inlet tip relative Mach numbers close to unity, and the performance diminishes at other Mach numbers. Shock waves emerging upstream of the impeller leading edge were observed from 90% to 100% corrected speed, and they move towards the impeller trailing edge as the inlet tip relative Mach number increases. There is no shock wave present in the inducer at 80% corrected speed. However, a high-loss region near the inducer throat was observed at 80% corrected speed resulting in a lower impeller efficiency at subsonic inlet conditions.

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