Limit Of Incompressible Flow Research Articles

The Effect of Laminated Layers on the Flutter Speed of Composite Wing

The paper presents an investigation to the flutter speed of composite wing for different ply orientation. Structurally the composite wing was idealized as a composite beam load carrying structure. Theodorsen’s expression was used to get the 2- dimension unsteady lifting force and pitching moment in the limit of incompressible flow and subsonic speed which were integrated over the wing span. A free vibration analysis was first carried out to get the natural frequencies and mode shapes .The velocity-damping (V-g) method was used to calculate the flutter speed and the flutter frequency. A wing of unmanned aerial vehicle was manufactured from woven glass and polyester resin where the flutter speed was calculated experimentally by the wind tunnel test .The flutter speed was calculated analytically for different ply orientation, it is found that the increasing in torsion rigidity leads to increase in the flutter speed, the fiber combination with high torsion rigidity and relatively low coupling rigidity give higher flutter speed.

Developing a physical influence upwind scheme for pressure‐based cell‐centered finite volume methods

SummaryIn the framework of a cell‐centered finite volume method (FVM), the advection scheme plays the most important role in developing FVMs to solve complicated fluid flow problems for a wide range of Reynolds numbers. Advection schemes have been widely developed for FVMs employing pressure‐velocity coupling methodology in the incompressible flow limit. In this regard, the physical influence upwind scheme (PIS) is developed for a cell‐centered finite volume coupled solver (FVCS) using a pressure‐weighted interpolation method for linking the pressure and velocity fields. The well‐known exponential differencing scheme and skew upwind differencing scheme are also deployed in the current FVCS and their numerical results are presented. The accuracy and convergence of the present PIS are evaluated solving flow in a lid‐driven square cavity, a lid‐driven skewed cavity, and over a backward‐facing step (BFS). The flow within the lid‐driven square cavity is numerically solved at Reynolds numbers from 400 to 10 000 on a relatively coarse mesh with respect to other reported solutions. The lid‐driven skewed cavity test case at Reynolds number of 1000 demonstrates the numerical performance of the present PIS on nonorthogonal grids. The flow over a BFS at Reynolds number of 800 is numerically solved to examine capabilities of current FVCS employing the current PIS in inlet‐outlet flow computations. The numerical results obtained by the current PIS are in excellent agreement with those of benchmark solutions of corresponding test cases. Incorporating implicit role of pressure terms in a pressure‐weighted interpolation method and development of PIS provides satisfactory solution convergence alongside the numerical accuracy for the current FVCS. A particular numerical verification is performed for the V velocity calculation within the BFS flow field, which confirms the reliability of present PIS.

Influence of gas compression on flame acceleration in the early stage of burning in tubes

The mechanism of finger flame acceleration at the early stage of burning in tubes was studied experimentally by Clanet and Searby [Combust. Flame 105 (1996) 225] for slow propane-air flames, and elucidated analytically and computationally by Bychkov et al. [Combust. Flame 150 (2007) 263] in the limit of incompressible flow. We have now analytically, experimentally and computationally studied the finger flame acceleration for fast burning flames, when the gas compressibility assumes an important role. Specifically, we have first developed a theory through small Mach number expansion up to the first-order terms, demonstrating that gas compression reduces the acceleration rate and the maximum flame tip velocity, and thereby moderates the finger flame acceleration noticeably. This is an important quantitative correction to previous theoretical analysis. We have also conducted experiments for hydrogen–oxygen mixtures with considerable initial values of the Mach number, showing finger flame acceleration with the acceleration rate much smaller than those obtained previously for hydrocarbon flames. Furthermore, we have performed numerical simulations for a wide range of initial laminar flame velocities, with the results substantiating the experiments. It is shown that the theory is in good quantitative agreement with numerical simulations for small gas compression (small initial flame velocities). Similar to previous works, the numerical simulation shows that finger flame acceleration is followed by the formation of the “tulip” flame, which indicates termination of the early acceleration process.

Quasiequilibrium lattice Boltzmann models with tunable bulk viscosity for enhancing stability

Taking advantage of a closed-form generalized Maxwell distribution function [P. Asinari and I. V. Karlin, Phys. Rev. E 79, 036703 (2009)] and splitting the relaxation to the equilibrium in two steps, an entropic quasiequilibrium (EQE) kinetic model is proposed for the simulation of low Mach number flows, which enjoys both the H theorem and a free-tunable parameter for controlling the bulk viscosity in such a way as to enhance numerical stability in the incompressible flow limit. Moreover, the proposed model admits a simplification based on a proper expansion in the low Mach number limit (LQE model). The lattice Boltzmann implementation of both the EQE and LQE is as simple as that of the standard lattice Bhatnagar-Gross-Krook (LBGK) method, and practical details are reported. Extensive numerical testing with the lid driven cavity flow in two dimensions is presented in order to verify the enhancement of the stability region. The proposed models achieve the same accuracy as the LBGK method with much rougher meshes, leading to an effective computational speed-up of almost three times for EQE and of more than four times for the LQE. Three-dimensional extension of EQE and LQE is also discussed.

On the unsteady inviscid force on cylinders and spheres in subcritical compressible flow

The unsteady inviscid force on cylinders and spheres in subcritical compressible flow is investigated. In the limit of incompressible flow, the unsteady inviscid force on a cylinder or sphere is the so-called added-mass force that is proportional to the product of the mass displaced by the body and the instantaneous acceleration. In compressible flow, the finite acoustic propagation speed means that the unsteady inviscid force arising from an instantaneously applied constant acceleration develops gradually and reaches steady values only for non-dimensional times c(infinity)t/R approximately >10, where c(infinity) is the freestream speed of sound and R is the radius of the cylinder or sphere. In this limit, an effective added-mass coefficient may be defined. The main conclusion of our study is that the freestream Mach number has a pronounced effect on both the peak value of the unsteady force and the effective added-mass coefficient. At a freestream Mach number of 0.5, the effective added-mass coefficient is about twice as large as the incompressible value for the sphere. Coupled with an impulsive acceleration, the unsteady inviscid force in compressible flow can be more than four times larger than that predicted from incompressible theory. Furthermore, the effect of the ratio of specific heats on the unsteady force becomes more pronounced as the Mach number increases.

Rayleigh-Bénard simulation using the gas-kinetic Bhatnagar-Gross-Krook scheme in the incompressible limit.

In this paper, a gas-kinetic Bhatnagar-Gross-Krook (BGK) model is constructed for the Rayleigh-Bénard thermal convection in the incompressible flow limit, where the flow field and temperature field are described by two coupled BGK models. Since the collision times in the corresponding BGK models can be different, the Prandtl number can be changed to any value instead of a fixed Pr=1 in the original BGK model [P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev. 94, 511 (1954)]. The two-dimensional Rayleigh-Bénard thermal convection is studied and numerical results are compared with theoretical ones as well as other simulation results.

Design Method for Turbomachine Blades With Finite Thickness by the Circulation Method

This paper presents a procedure to extend a recently developed three-dimensional inverse method for infinitely thin blades to handle blades with finite thickness. In this inverse method, the prescribed quantities are the blade pressure loading and the blade thickness distributions, and the calculated quantity is the blade mean camber line. The method is formulated in the fully inverse mode whereby the blade shape is determined iteratively using the flow-tangency condition along the blade surfaces. Design calculations are presented for an inlet guide vane, an impulse turbine blade, and a compressor blade in the two-dimensional inviscid- and incompressible-flow limit. Consistency checks are carried out for these design calculations using a panel analysis method and the analytical solution for the Gostelow profile.

Lagrangian Simulation of Diffusion Flames

Abstract Abstract-We develop a new Lagrangian numerical technique to investigate the interaction between fluid mechanics and chemical reaction in diffusion flames through volumetric expansion and baroclinic vorticity production. We base our numerical method on the mixture-fraction variable formulation and the Burke-Schumann limit of an infinitely thin flame sheet, In this way. we do not attempt to resolve the flame structure in detail, but instead are in a position to simulate combustion in more complex flow fields. The method employs Lagrangian blobs that carry gradients of the mixture-fraction variable. Other blobs act as sources to account for thermal expansion, while vortex blobs are introduced to represent the baroclinic vorticity production. These blobs deform as a result of diffusion, strain, and thermal expansion. In its Lagrangian nature, our approach to diffusion flames corresponds to the technique recently developed by Ghoniem for premixed flames. In the incompressible flow limit, we demonstrat...

Computation of inviscid incompressible flow with rotation

The standard hyperbolic methods used to solve the compressible Euler equations are not effective in the limit of incompressible flow. The sound waves dominate the system and it becomes poorly conditioned for numerical solution. For steady flow governed by the incompressible Euler equations, artificial compressibility is a technique that removes the troublesome sound waves. It leads to a hyperbolic system of equations that we solve by finite-volume differences centred in space, and explicit multistage time-stepping. The stability of this novel system is analysed, its allowable discontinuities are described, and appropriate far-field and solid-wall boundary conditions are introduced. Results are presented for both two- and three-dimensional flows, including vorticity shed from a delta wing. Whether vorticity is produced or not depends very strongly on the body geometry, the accuracy of the solution method, and the transient discontinuities that evolve in the flow field. The results are analysed for the total-pressure losses in the flow fields, and for the diffusion of the vortex sheets.

Rayleigh–Taylor instabilities of an accelerating, compressible, perfectly conducting plane layer

The stability of a plane stratified slab of perfectly conducting, compressible, inviscid plasma accelerated by a magnetic field is considered. Exact closed form solutions for the growth rates of the unstable modes are determined for a γ-law gas when the undisturbed equilibrium is an isothermal atmosphere of semi-infinite extent with no frozen-in field. It is shown that the fluid slab is always unstable at wavelengths long compared with the atmospheric scale height and that the corresponding growth rates agree with those calculated in the limit of incompressible flow.