scholarly journals Numerical Simulation of Rotor–Wing Transient Interaction for a Tiltrotor in the Transition Mode

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 116 ◽  
Author(s):  
Zhenlong Wu ◽  
Can Li ◽  
Yihua Cao
Keyword(s):  
Numerical Simulation ◽  
Momentum Equation ◽  
Navier Stokes ◽  
Transition Mode ◽  
Rans Equations ◽  
Design And Optimization ◽  
Aerodynamic Interaction ◽  
Rotor Wing ◽  
Transition Modes ◽  
The Right

Tiltrotor aerodynamic interaction, especially in the transition mode, is a necessary consideration for tiltrotor aerodynamics, and structural design and optimization. Previous studies have paid much attention to the helicopter mode. However, due to the substantial complexity of the problem, only a small amount of work on the transition mode has been done so far. In this paper, the rotor–wing aerodynamic interaction of a scaled V-22 Osprey tiltrotor, both in the helicopter and transition modes, are studied by computational fluid dynamics (CFD) numerical simulation. The flow field is discretized via the chimera mesh technique and then solved with the Reynolds-averaged Navier–Stokes (RANS) equations. The rotational acceleration of the rotor is considered as a source term added on the right side of the momentum equation of the RANS equations. Both a quasi-steady and a fully transient method are employed to simulate the tilt motion of the rotor in the transition mode. Both qualitative and quantitative results are presented and discussed on the aerodynamic forces, flow physics, and mechanisms. The applicability of the extensively used quasi-steady method for rotor tilt simulation is revealed.

scholarly journals EXISTENCE AND EQUILIBRATION OF GLOBAL WEAK SOLUTIONS TO KINETIC MODELS FOR DILUTE POLYMERS II: HOOKEAN-TYPE MODELS

2012 ◽  
Vol 22 (05) ◽  
pp. 1150024 ◽  
Author(s):  
JOHN W. BARRETT ◽  
ENDRE SÜLI
Keyword(s):  
Center Of Mass ◽  
Planck Equation ◽  
Momentum Equation ◽  
Polymer Chains ◽  
Navier Stokes ◽  
Extra Stress Tensor ◽  
The Right ◽  
Extra Stress ◽  
Drag Term ◽  
Fokker Planck

We show the existence of global-in-time weak solutions to a general class of coupled Hookean-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier–Stokes equations in a bounded domain in ℝd, d = 2 or 3, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined by the Kramers expression through the associated probability density function that satisfies a Fokker–Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term. We require no structural assumptions on the drag term in the Fokker–Planck equation; in particular, the drag term need not be corotational. With a square-integrable and divergence-free initial velocity datum ṵ0 for the Navier–Stokes equation and a non-negative initial probability density function ψ0 for the Fokker–Planck equation, which has finite relative entropy with respect to the Maxwellian M, we prove, via a limiting procedure on certain regularization parameters, the existence of a global-in-time weak solution t ↦ (ṵ(t), ψ(t)) to the coupled Navier–Stokes–Fokker–Planck system, satisfying the initial condition (ṵ(0), ψ(0)) = (ṵ0, ψ0), such that t ↦ ṵ(t) belongs to the classical Leray space and t ↦ ψ(t) has bounded relative entropy with respect to M and t ↦ ψ(t)/M has integrable Fisher information (with respect to the measure [Formula: see text]) over any time interval [0, T], T>0. If the density of body forces [Formula: see text] on the right-hand side of the Navier–Stokes momentum equation vanishes, then a weak solution constructed as above is such that t ↦ (ṵ(t), ψ(t)) decays exponentially in time to [Formula: see text] in the [Formula: see text]-norm, at a rate that is independent of (ṵ0, ψ0) and of the center-of-mass diffusion coefficient. Our arguments rely on new compact embedding theorems in Maxwellian-weighted Sobolev spaces and a new extension of the Kolmogorov–Riesz theorem to Banach-space-valued Sobolev spaces.

scholarly journals EXISTENCE AND EQUILIBRATION OF GLOBAL WEAK SOLUTIONS TO KINETIC MODELS FOR DILUTE POLYMERS I: FINITELY EXTENSIBLE NONLINEAR BEAD-SPRING CHAINS

2011 ◽  
Vol 21 (06) ◽  
pp. 1211-1289 ◽  
Author(s):  
JOHN W. BARRETT ◽  
ENDRE SÜLI
Keyword(s):  
Planck Equation ◽  
Momentum Equation ◽  
Polymer Chains ◽  
Navier Stokes ◽  
Centre Of Mass ◽  
Extra Stress Tensor ◽  
The Right ◽  
Extra Stress ◽  
Drag Term ◽  
Fokker Planck

We show the existence of global-in-time weak solutions to a general class of coupled FENE-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier–Stokes equations in a bounded domain in ℝd, d = 2 or 3, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined by the Kramers expression through the associated probability density function that satisfies a Fokker–Planck-type parabolic equation, a crucial feature of which is the presence of a centre-of-mass diffusion term. We require no structural assumptions on the drag term in the Fokker–Planck equation; in particular, the drag term needs not be corotational. With a square-integrable and divergence-free initial velocity datum ṵ0 for the Navier–Stokes equation and a non-negative initial probability density function ψ0 for the Fokker–Planck equation, which has finite relative entropy with respect to the Maxwellian M, we prove, via a limiting procedure on certain regularisation parameters, the existence of a global-in-time weak solution t ↦ (ṵ(t), ψ(t)) to the coupled Navier–Stokes–Fokker–Planck system, satisfying the initial condition (ṵ(0), ψ(0)) = (ṵ0, ψ0), such that t ↦ ṵ(t) belongs to the classical Leray space and t ↦ ψ(t) has bounded relative entropy with respect to M and t ↦ ψ(t)/M has integrable Fisher information (w.r.t. the measure [Formula: see text] over any time interval [0, T], T > 0. If the density of body forces [Formula: see text] on the right-hand side of the Navier–Stokes momentum equation vanishes, then a weak solution constructed as above is such that t ↦ (ṵ(t), ψ(t)) decays exponentially in time to [Formula: see text] in the [Formula: see text] norm, at a rate that is independent of (ṵ0, ψ0) and of the centre-of-mass diffusion coefficient.

Numerical Study of Wave Slamming on a Rectangular Slab

2012 ◽  
Vol 204-208 ◽  
pp. 4971-4977
Author(s):  
Ya Mei Lan ◽  
Wen Hua Guo ◽  
Yong Guo Li
Keyword(s):  
Numerical Study ◽  
Navier Stokes ◽  
Governing Equations ◽  
Reflected Waves ◽  
Rans Equations ◽  
Numerical Wave Flume ◽  
Wave Flume ◽  
Wave Slamming ◽  
Numerical Wave ◽  
Rectangular Slab

The CFD software FLUENT was used as the foundation to develop the numerical wave flume, in which the governing equations are the Reynolds-averaged Navier-Stokes (RANS) equations and the standard k~ε turbulence model. The wave generating and absorbing were introduced into the RANS equations as the source terms using the relaxation approach. A new module of the wave generating and absorbing function, which is suitable for FLUENT based on the volume of fluid method (VOF), was established. Within the numerical wave flume, the reflected waves from the model within the computation domain can be absorbed effectively before second reflection appears due to the wave generating boundary. The computational results of the wave pressures on the bottom of the rectangular slab were validated for the different relative clearance by the experimental data. Good agreements were found.

Numerical Simulation of Muzzle Flow Field of Gun Based on CFD

2013 ◽  
Vol 291-294 ◽  
pp. 1981-1984
Author(s):  
Zhang Xia Guo ◽  
Yu Tian Pan ◽  
Yong Cun Wang ◽  
Hai Yan Zhang
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Stokes Equation ◽  
Wave Structure ◽  
Flow Fields ◽  
Single Equation ◽  
Navier Stokes ◽  
Turbulent Model ◽  
Navier Stokes Equation ◽  
Numerical Simulation Result

Gunpowder was released in an instant when the pill fly out of the shell during the firing, and then formed a complicated flow fields about the muzzle when the gas expanded sharply. Using the 2 d axisymmetric Navier-Stokes equation combined with single equation turbulent model to conduct the numerical simulation of the process of gunpowder gass evacuating out of the shell without muzzle regardless of the pill’s movement. The numerical simulation result was identical with the experimental. Then simulated the evacuating process of gunpowder gass of an artillery with muzzle brake. The result showed complicated wave structure of the flow fields with the muzzle brake and analysed the influence of muzzle brake to the gass flow field distribution.

Multiple Vortex Body Vortex Numerical Simulation

2011 ◽  
Vol 328-330 ◽  
pp. 1755-1758
Author(s):  
Han Xiao Liu ◽  
Zhong Liu ◽  
Huai Liang Li ◽  
Xin Xin Feng ◽  
Zhen Zhong Xing
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Turbulence Intensity ◽  
Continuity Equation ◽  
Momentum Equation ◽  
Turbulent Intensity ◽  
Good Effect ◽  
Train Of Thought

In this paper, the continuity equation, momentum equation and the k-ε turbulence equation were introduced to simulate the flow field of the multiple vortex bodies in different spacing cases. Found that each vortex body had good effect in producing vortex, and the greater flow field spacing, the smaller the highest velocity; the turbulence intensity is increasing gradually from the former vortex body to the next one, and there may be a best spacing between the vortex bodies which makes the best turbulent intensity. All of these theories provide a train of thought for the turbulent coalescence mechanism.

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