Computational study of hole shape effect on film cooling performance

Film cooling effectiveness has been studied by using a computational approach based on solving the Reynolds-averaged Navier–Stokes equations. A wind tunnel test configuration is considered with a total of four cooling hole geometries as a cylindrical hole, a cylindrical hole with an upstream wedge (called ‘ramp’ thereafter), a shaped diffuser, and a double console slot. In all cases, the hole centreline has an inclination angle of 35° against the mainstream airflow and the blowing ratio is unity. Choosing the cylindrical model as a baseline, simulations have been carried out for grid convergence and turbulence model influence studies. Results are compared with available experimental data and other numerical predictions and good agreement has been achieved. Further computations continue with three remaining geometries, using the baseline flow conditions and configuration. Comparing to the results from the baseline model, it was found that the centreline adiabatic cooling effectiveness has shown incremental increases for the ‘ramp’ model, while results from the console slot model and the shape diffuser model have exhibited significant improvements by a factor of 1.5 and 2, respectively. The reason for such a step change in cooling effectiveness is mainly due to the weakening of the vortex structures in the vicinity of the hole exit, thus significantly reducing the entrainment of surrounding ‘hot’ fluids

Zero-sum linear quadratic stochastic integral games and BSVIEs

This paper formulates and studies a linear quadratic (LQ for short) game problem governed by linear stochastic Volterra integral equation. Sufficient and necessary condition of the existence of saddle points for this problem are derived. As a consequence we solve the problems left by Chen and Yong in [3]. Firstly, in our framework, the term GX^2(T) is allowed to be appear in the cost functional and the coefficients are allowed to be random. Secondly we study the unique solvability for certain coupled forward-backward stochastic Volterra integral equations (FBSVIEs for short) involved in this game problem. To characterize the condition aforementioned explicitly, some other useful tools, such as backward stochastic Fredholm-Volterra integral equations (BSFVIEs for short) and stochastic Fredholm integral equations (FSVIEs for short) are introduced. Some relations between them are investigated. As a application, a linear quadratic stochastic differential game with finite delay in the state variable and control variables is studied.Comment: 27 page

Generalized Projective Representations for sl(n+1)

It is well known that $n$-dimensional projective group gives rise to a non-homogenous representation of the Lie algebra $sl(n+1)$ on the polynomial functions of the projective space. Using Shen's mixed product for Witt algebras (also known as Larsson functor), we generalize the above representation of $sl(n+1)$ to a non-homogenous representation on the tensor space of any finite-dimensional irreducible $gl(n)$-module with the polynomial space. Moreover, the structure of such a representation is completely determined by employing projection operator techniques and well-known Kostant's characteristic identities for certain matrices with entries in the universal enveloping algebra. In particular, we obtain a new one parameter family of infinite-dimensional irreducible $sl(n+1)$-modules, which are in general not highest-weight type, for any given finite-dimensional irreducible $sl(n)$-module. The results could also be used to study the quantum field theory with the projective group as the symmetry.Comment: 24page

Maximum principle for a stochastic delayed system involving terminal state constraints

We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an equivalent backward delayed system depicted as a time-delayed backward stochastic differential equation. Then a stochastic maximum principle is obtained by virtue of Ekeland's variational principle. Finally, applications to a state constrained stochastic delayed linear-quadratic control model and a production-consumption choice problem are studied to illustrate the main obtained result.Comment: 16 page

The Equivalence between Uniqueness and Continuous Dependence of Solution for BDSDEs

In this paper, we prove that, if the coefficient f = f(t; y; z) of backward doubly stochastic differential equations (BDSDEs for short) is assumed to be continuous and linear growth in (y; z); then the uniqueness of solution and continuous dependence with respect to the coefficients f, g and the terminal value are equivalent.Comment: 11 page