ON SUBSONIC AND SUBSONIC-SONIC FLOWS IN THE INFINITY LONG NOZZLE WITH GENERAL CONSERVATIVES FORCE

In this article, we study irrotational subsonic and subsonic-sonic flows with gen- eral conservative forces in the infinity long nozzle. For the subsonic case, the varified Bernoulli law leads a modified cut-off system. Because of the local average estimate, conservative forces do not need any decay condition. Afterwards, the subsonic-sonic limit solutions are constructed by taking the extract subsonic solutions as the approximate sequences.

On the Existence and Stability of a Global Subsonic Flow in a 3D Infinitely Long Cylindrical Nozzle

This paper is concerned with the problem on the global existence and stability of a subsonic flow in an infinitely long cylindrical nozzle for the 3D steady potential flow equation. Such a problem was indicated by Courant-Friedrichs in [8, p. 377]： A flow through a duct should be considered as a cal symmetry and should be determined steady, isentropic, irrotational flow with cylindriby solving the 3D potential flow equations with appropriate boundary conditions. By introducing some suitably weighted HSlder spaces and establishing a priori estimates, the authors prove the global existence and stability of a subsonic potential flow in a 3D nozzle when the state of subsonic flow at negative infinity is given.

TWO DIMENSIONAL SUBSONIC AND SUBSONIC-SONIC SPIRAL FLOWS OUTSIDE A POROUS BODY

In this paper,we investigate two dimensional subsonic and subsonic-sonic spiral flows outside a porous body.The existence and uniqueness of the subsonic spiral flow are obtained via variational formulation,which tends to a given radially symmetric subsonic spiral flow at far field.The optimal decay rate at far field is also derived by Kelvin ’s transformation and some elliptic estimates.By extracting spiral subsonic solutions as the approximate sequences,we obtain the spiral subsonic-sonic limit solution by utilizing the compensated compactness.The main ingredients of our analysis are methods of calculus of variations,the theory of second-order quasilinear equations and the compensated compactness framework.

Feature identification in complex fluid flows by convolutional neural networks

Recent advancements have established machine learning's utility in predicting nonlinear fluid dynamics,with predictive accuracy being a central motivation for employing neural networks.However,the pattern recognition central to the networks function is equally valuable for enhancing our dynamical insight into the complex fluid dynamics.In this paper,a single-layer convolutional neural network(CNN)was trained to recognize three qualitatively different subsonic buffet flows(periodic,quasi-periodic and chaotic)over a high-incidence airfoil,and a near-perfect accuracy was obtained with only a small training dataset.The convolutional kernels and corresponding feature maps,developed by the model with no temporal information provided,identified large-scale coherent structures in agreement with those known to be associated with buffet flows.Sensitivity to hyperparameters including network architecture and convolutional kernel size was also explored.The coherent structures identified by these models enhance our dynamical understanding of subsonic buffet over high-incidence airfoils over a wide range of Reynolds numbers.

COMPUTATION OF COMPRESSIBLE FLOW PAST SLENDER WING－BODY USING FULL－POTENTIAL EQUATION

The H-O grid is suggested to compute compressible flow past highly swept slender wing-body combinations. Full-potential equation, finite difference method and approximate factorization scheme are used. The computations for the AGARD-B wing-body show that the code developed can apply to the cases from subsonic up to low supersonic free stream. The computed lift and pitching moment are in good agreement with the experimental results.

REVIEW OF THE GREEN＇S FUNCTION METHOD FOR STEADY ＆UNSTEADY，SUBSONIC，TRANSONIC ＆SUPERSONIC AERODYNAMICS AROUND COMPLEX CONFIGURATIONS

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CONSTRUCTION OF MODIFIED TAYLOR－GALERKIN FINITE ELEMENTS AND ITS APPLICATION IN COMPRESSIBLE FLOW COMPUTATION

In this paper we begin with Taylor-Galerkin Finite Elements,then n improve it completely and finally construct Modified Taylor-Galerkin Finite Elements.Computation is done by two methods to study two kinds of subsonic and supersonic flow.field.The results show that the new one is much better than the old one.

On the nature of tip clearance flow in subsonic centrifugal impellers

Increasing demand for downsizing of engines to improve CO2 emissions has resulted in renewed efforts to improve the efficiency and expend the stable operating range of the centrifugal compressors used in petro-chemical equipment and turbochargers. The losses in these compressors are dominated by tip clearance flow. In this paper, the tip clearance flow in the subsonic impeller is numerically investigated. The nature of the tip clearance in inducer, axial to radial bend and exducer are studied in detail at design and off-design conditions by examining the detailed flow field through the clearance and the interaction of the clearance flow with the shear effect with the endwalls. The correlation between blade loading and span wise geometry and clearance flow at different locations are presented.

Compressible Subsonic Potential Flow Past a 2D Given Sharp Angular Unbounded Domain

In this paper, we focus on the two-dimensional subsonic flow problem around an infinite long ramp. The flow is assumed to be steady, isentropic and irrotational, namely, the movement of the flow is described by a second elliptic equation. By the use of a separation variable method, Strum- Liouville theorem and scaling technique, we show that a nontriviM subsonic flow around the infinite long ramp does not exist under some certain assumptions on the potential flow with a low Mach number.

A Study on High Subsonic Airfoil Flows in Relatively High Reynolds Number by Using OpenFOAM

In the present study,numerical calculations of the flow-field around the airfoil model are performed by using the OpenFOAM in high subsonic flows.The airfoil model is NACA 64A010.The maximum thickness is 10 % of the chord length.The SonicFOAM and the RhoCentralFOAM are selected as the solver in high subsonic flows.The grid point is 158,000 and the Mach numbers are 0.277 and 0.569 respectively.The CFD data are compared with the experimental data performed by the cryogenic wind tunnel in the past.The results are as follows.The numerical results of the pressure coefficient distribution on the model surface calculated by the SonicFOAM solver showed good agreement with the experimental data measured by the cryogenic wind tunnel.And the data calculated by the SonicFOAM have the capability for the quantitative comparison of the experimental data at low angle of attack.

An implicit algorithm based on iterative modified approximate factorization method coupling with characteristic boundary conditions for solving subsonic viscous flows

An algorithm composed of an iterative modified approximate factorization(MAF(k)) method with Navier-Stokes characteristic boundary conditions(NSCBC) is proposed for solving subsonic viscous flows.A transformation on the matrix equation in MAF(k) is made in order to impose the implicit boundary conditions properly.To be in consistent with the implicit solver for the interior domain,an implicit scheme for NSCBC is formulated.The performance of the developed algorithm is investigated using spatially evolving zero pressure gradient boundary layer over a flat plate and a wall jet mixing with a cross flow over a flat plate with a square hole as the test cases.The numerical results are compared to the existing experimental datasets and a number of general correlations,together with other available numerical solutions,which demonstrate that the developed algorithm possesses promising capacity for simulating the subsonic viscous flows with large CFL number.

On the existence and stability of 2-D perturbed steady subsonic circulatory flows

In this paper, under the generalized conservation condition of mass flux in a unbounded domain, we are concerned with the global existence and stability of a perturbed subsonic circulatory flow for the two-dimensional steady Euler equation, which is assumed to be isentropic and irrotational. Such a problem can be reduced into a second order quasi-linear elliptic equation on the stream function in an exterior domain with a Dirichlet boundary value condition on the circular body and a stability condition at infinity. The key ingredient is establishing delicate weighted Hlder estimates to obtain the infinite behaviors of the flow under physical assumption.

Subsonic impulsively starting flow at a high angle of attack with shock wave and vortex interaction

Impulsively starting flow, by a sudden attainment of a large angle of attack, has been well studied for incompressible and supersonic flows, but less studied for subsonic flow. Recently,a preliminary numerical study for subsonic starting flow at a high angle of attack displays an advance of stall around a Mach number of 0.5, when compared to other Mach numbers. To see what happens in this special case, we conduct here in this paper a further study for this case, to display and analyze the full flow structures. We find that for a Mach number around 0.5, a local supersonic flow region repeatedly splits and merges, and a pair of left-going and right-going unsteady shock waves are embedded inside the leading edge vortex once it is sufficiently grown up and detached from the leading edge. The flow evolution during the formation of shock waves is displayed in detail. The reason for the formation of these shock waves is explained here using the Laval nozzle flow theory. The existence of this shock pair inside the vortex, for a Mach number only close to 0.5, may help the growing of the trailing edge vortex responsible for the advance of stall observed previously.

THE UNIQUENESS OF A TRANSONIC SHOCK IN A NOZZLE FOR THE 2-D COMPLETE EULER SYSTEM WITH THE VARIABLE END PRESSURE

In this paper, by use of the methods in [1-3], we establish the uniqueness of a 2-D transonic shock solution in a nozzle when the end pressure in the diverging part of the nozzle lies in an appropriate scope. Especially, we remove the crucial but unnatural assumption in recent references which the transonic shock must be assumed to go through a fixed point in advance.