Naoki Yamada

Multi-intensity-layer particle-image velocimetry for spray measurement

A new particle-image-velocimetry (PIV)-data-processing method called multi-intensity-layer PIV is developed and applied for injector spray analysis. It uses the principle that the light intensity scattered from a small particle is proportional to its diameter squared at a certain angle. The light-intensity information was used to provide diameter information from PIV data. There are two methods of uncertainty analysis: intensity weighted and number-density weighted. The measurement results demonstrated that the droplet dynamics for droplets of various diameters can be described by this multi-intensity-layer PIV, that is, small droplets followed the vortex shearing and highly turbulent flows, whereas larger droplets penetrated the shear flow. It was found that this multi-intensity-layer PIV would be a useful method for describing spatial droplet-spray behaviour in a practical spray diagnostic.

Spray combustion characteristics in a highly pressurized swirl-stabilized combustor

Flame structure and droplet behavior in a swirl-stabilized gas turbine combustor at elevated pressure were investigated. The combustion chamber was specially designed and optimized for laser diagnostics, such as phase Doppler anemometry and laser-sheet visualization. Direct observation and CH* chemiluminescence measurements were used to investigate the flame structure and its dependence on ambient pressure. The setup parameters of phase Doppler anemometer were optimized for high-pressure flow field measurements and this considered the thickness of the optical windows and the refractive index of the ambient air in the combustor were taken into account, respectively. The parameter to be discussed in the study is the pressure dependence of droplet velocity, slip velocity, size distribution, and mass flux. This study concentrated on a spray pilot flame burner in order to have stable flame holding but reduce soot and NOx at elevated pressure, then we focused on flame shape, spray droplet size, and velocity, which were measured directly using a high-speed camera and phase Doppler anemometer (PDA). The pressure dependencies of these characteristics are discussed. Image analysis of flame shape indicated that the spray angle narrowed and the flame lengthened as ambient pressure increased. The same tendency was observed with the PDA measurements. The axial velocity difference was not very large, although the fuel flow rate was increased in the high-pressure condition. These results are due to centrifugal force and the variation in the size of the recirculation region within the hollow cone.

The Hamilton-Jacobi-Bellman equation with a gradient constraint

Abstract : As the first order Hamilton Jacobi equation is related to a control problem associated with ordinary differential equations, the Hamilton Jacobi Bellman (HJB) equation arises from a control problem with random noise. In the stationary problem, the HJB equation has the form sup when alpha is an element of A of (L superscript alpha)u - (f superscript and alpha = 0 where L superscript alpha are second order linear elliptic operators with parameter alpha an element of A. In this paper, we are concerned with the HJB equation of the form maxL superscript 1 u - (f superscript 1,...,(L superscript m u)) - (f superscript m), (absolute value of Du) - g. We prove the existence of solutions which satisfy the equation almost everywhere. Using the notion of weak solution (so called viscosity solution) we prove the uniqueness of the solution in the class of continuously differentiable functions. The method of the uniqueness proof is also applicable to other obstacle problems. We prove uniqueness results in the class of continuous functions for two model problems. Keywords: Obstacle problem; Minimax equations; Variational inequalities; and Viscosity solutions.

Existence of non-radially symmetric viscosity solutions to semilinear degenerate elliptic equations with radially symmetric coefficients in the plane, Part II

We study continuous viscosity solutions for a semilinear degenerate elliptic equation with radially symmetric coefficients in the plane. If the equation satisfies certain relations with respect to the behavior of coefficients at the infinity, then it is known that there exist many solutions. Our purpose is to construct many non radially symmetric solutions satisfying the similar behavior with radial symmetric solutions at the infinity. The solutions are obtained as a small perturbation from a radially symmetric solution. We construct superand sub-solution by using the series expansion of rα− jβ cosnθ ( j,n = 1,2, . . .) , where (r,θ ) is the polar coordinate and α and β are certain positive constants.