CFD studies on burner secondary airflow

In many fossil power plants operating today, there is insufficient means to assure the proper balancing of the secondary airflows between the individual burners of wall-fired units. This mismatch leads to decreased boiler efficiency and increased emissions. In this study, a computational fluid dynamics (CFD) modeling of a fossil power plant wind box was performed. The model solved the three-dimensional Reynolds averaged Navier–Stokes equations with the k–ε turbulence model. The CFD results were validated by the experimental data taken from a 1/8th scale model of a wall-fired fossil unit. Simulations under various mass flow rates specified at inlet, various baffle positions and two opening conditions of the burners were obtained to identify the optimum design in terms of the equalization of the secondary airflow through the burners. This study demonstrated that the combination of experimental and CFD approach can be an effective tool in the research of burner secondary airflow balancing.     

Numerical study of the effect of changing the cyclone cone length on the gas flow field

Models of six different cyclone separator designs have been investigated numerically to study the effect of changing cone length on the gas flow field. The cone length was changed in two ways, one by fixing the cone diameter and the other by fixing the cone angle. The Reynolds stress model was applied to predict the turbulence of gas flow. The model was validated by comparing the numerical results to published experimental data. The results show that, for the cyclone without cylindrical part, the pressure drop and the value of tangential and axial velocity components increase with increasing cone length with fixed cone angle until they reach maximum value. It was found that increasing the cone length with the same cone diameter increases the back flow and the lip leakage below the vortex finder. The back flow and the lip leakage phenomena was observed to be reduced by increasing cone length with fixed cone angle. The effect of contraction ratio D_x/D, which is defined as the ratio between the vortex finder diameter and the cone diameter, on the turbulent kinetic energy and the velocity components also was investigated. As the contraction ratio decreases, the maximum value of the turbulent kinetic energy and the tangential and axial velocity components increases. The pressure drop was fitted into a correlation as a function of dimensionless quantities (Re, D_x/D, and l_c/D) for each design, so that the designers could select the appropriate dimensions according to their design limitations.     

An Experimental/Numerical Investigation on Drag Reduction by Dimples

The paper is concerned with experimental and numerical investigations of the turbulent flow over dimpled surfaces. Shallow dimples distributed regularly over the wall of a plane channel with large aspect ratio are used to study their effect on the skin-friction drag. The resulting pressure drop in the channel was measured for smooth and dimpled walls. In addition to these investigations on internal flows, an external flow study was performed and boundary-layer profiles were measured using a Pitot-tube rake. Complementary to the measurements, direct numerical simulations for the internal flow configuration with and without dimples were carried out for two different grid resolutions and analyzed in detail. The objective was to clarify whether or not dimples cause reduction of the skin-friction drag. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Polynomial entropies for Bott integrable Hamiltonian systems

In this paper, we study the entropy of a Hamiltonian flow in restriction to an energy level where it admits a first integral which is nondegenerate in the sense of Bott. It is easy to see that for such a flow, the topological entropy vanishes. We focus on the polynomial and the weak polynomial entropies h_pol and h _pol ^* . We show that, under natural conditions on the critical levels of the Bott first integral and on the Hamiltonian function H, h _pol ^* ∈ {0, 1} and h_pol ∈ {0, 1, 2}. To prove this result, our main tool is a semi-global desingularization of the Hamiltonian system in the neighborhood of a polycycle.     

Stability and omitting types

We give a complete solution to the following question: when does a superstable theory have a model of powerκ omitting a partial typeq? In particular, for fixedq, if there is such a model of power ?₁ then there is one of power 2^? ₀; and if there is a model omittingq of power ?₁, then there are arbitrarily large ones. For stable theories, a model of power ? _ω ⁺ , omittingq implies one of power 2^? ₀, and this is sharp. Several improvements and some negative results are listed in the introduction.     

新型降压槽结构设计及流动特性分析

针对三元复合驱分注过程中低视粘度损失和高压降不能同时实现的问题,设计出了一种新型降压槽,运用CFD软件对其环空流道的流动特性进行数值模拟,研究了新型降压槽内的压力、速度、湍动能、视粘度和应变率分布情况.同时将其与环形降压槽进行对比,结果表明,相同长度的降压槽,新型降压槽的压差更大,视粘度损失更小.     

Fractional integrals and weakly singular integral equations of the first kind in then-dimensional ball

The purpose of the paper is to introduce and to investigate a new class of fractional integrals connected with balls in ?ⁿ. A Riesz potentialI _Ω ^α ρ over a ball Ω is represented by a composition of such integrals. Using this representation we obtain necessary and sufficient solvability conditions for the equationI _Ω ^α ρ =f in the space L_p(Ωw) with a power weight w(x) and solve the equation in a closed form. The investigation is based on a special Fourier analysis adopted for operators commuting with rotations and dilations in ?ⁿ.     

Numerical investigation of the effect of helix angle and leaf margin on the flow pattern and the performance of the axial flow cyclone separator

A two-stage turbulence model based on the RNG κ–ε model combined with the Reynolds stress model is developed in this paper to analyze the gas flow in an axial flow cyclone separator. Five representative simulation cases are obtained by changing the helix angle and leaf margins of the cyclone. The pressure field and velocity field of the five cases are simulated, and then the effects of helix angle and leaf margins on the internal flow field of the cyclone are analyzed. When the continuum fluid (air) flow is relatively convergent, the discrete particle phase is added into the continuous phase and the gas-solid two-phase flow is simulated. One-way coupling method is used to solve the two-phase flow and a stochastic trajectory model is implemented for simulation of the particle phase. Finally, the pressure drop and separation efficiency of one case are measured and compare quantitatively well with the numerical results, which validates the reliability and accuracy of the simulation method based on the two-stage turbulence model.     

A dimension series for multivariate splines

For a polyhedral subdivision Δ of a region in Euclideand-space, we consider the vector spaceC _k ^r (Δ) consisting of allC ^r piecewise polynomial functions over Δ of degree at mostk. We consider the formal power series ∑ _k≥0 dim_? C _k ^r (Δ)λ^k and show, under mild conditions on Δ, that this always has the formP(λ)/(1?λ) ^d+1, whereP(λ) is a polynomial in λ with integral coefficients which satisfiesP(0)=1,P(1)=f _d (Δ), andP′(1)=(r+1)f _d?1 ⁰ (Δ). We discuss how the polynomialP(λ) and bases for the spacesC _k ^r (Δ) can be effectively calculated by use of Gröbner basis techniques of computational commutative algebra. A further application is given to the theory of hyperplane arrangements.     

On best approximations by analogs of “proper” and “improper” hyperbolic crosses

The exact approximation orders for the classes H _q ^Ω are calculated for the case in which Ω(t) contains both power and logarithmic multipliers. For these classes, the exact orders of best approximation by analogs of “improper” hyperbolic crosses are also obtained.     

Products of powers in finite simple groups

LetG be a group. For a natural numberd≥1 letG ^d denote the subgroup ofG generated by all powersa ^d ,a∈G. A. Shalev raised the question if there exists a functionN=N(m, d) such that for anm-generated finite groupG an arbitrary element fromG ^d can be represented asa ₁ ^d ...a _N ^d ,a _i ∈G. The positive answer to this question would imply that in a finitely generated profinite groupG all power subgroupsG ^d are closed and that an arbitrary subgroup of finite index inG is closed. In [5,6] the first author proved the existence of such a function for nilpotent groups and for finite solvable groups of bounded Fitting height. Another interpretation of the existence ofN(m, d) is definability of power subgroupsG ^d (see [10]). In this paper we address the question for finite simple groups. All finite simple groups are known to be 2-generated. Thus, we prove the following: THEOREM:There exists a function N=N(d) such that for an arbitrary finite simple group G either G ^d =1 orG={a ₁ ^d ...a _N ^d |a _i ∈G}. The proof is based on the Classification of finite simple groups and sometimes resorts to a case-by-case analysis.     

ON possible Turán densities

The Turán density π(F) of a family F of k-graphs is the limit as n → ∞ of the maximum edge density of an F-free k-graph on n vertices. Let Π _∞ ^(k) consist of all possible Turán densities and let Π _fin ^(k) ? Π _∞ ^(k) be the set of Turán densities of finite k-graph families. Here we prove that Π _fin ^(k) contains every density obtained from an arbitrary finite construction by optimally blowing it up and using recursion inside the specified set of parts. As an application, we show that Π _fin ^(k) contains an irrational number for each k ≥ 3. Also, we show that Π _∞ ^(k) has cardinality of the continuum. In particular, Π _∞ ^(k) ≠ Π _fin ^(k) .     

Patterson-Sullivan-type measures on Riccati foliations with quasi-Fuchsian holonomy

We consider Riccati foliations ?_ρ with hyperbolic leaves, over a finite hyperbolic Riemann Surface S, constructed by suspending a representation ρ: π ₁(S) → PSL(2,?) in a quasi-Fuchsian group. The foliated geodesic flow has a repeller-attractor dynamic with generic statistics µ⁺ and µ^? for positive and negative times, respectively. These measures have a common projection to a harmonic measure μ_ρ for the Riccati foliation. We describe μ _ρ ⁺ , μ _ρ ^- and μ_ρ in terms of the Patterson-Sullivan construction, and we show that the measures μ_ρ provide examples of the conformal harmonic measures introduced by M. Brunella.     

The reconstruction problem for certain infinite graphs

We are concerned with the notion of the degree-type (D _G ⁱ )_i∈ω of a graphG, whereD _G ⁱ is defined to be the number of vertices inG with degreei. In the first section the following results are proven:

1. IfG is a connected, locally finite, countably infinite graph such that there exists ani so thatD _G ⁱ andD _G ⁱ⁺¹ are both finite and different from 0, thenG is reconstructible.
2. Locally finite, countably infinite graphsG, for which infinitely manyD _G ⁱ are different from 0 but only finitely manyD _G ⁱ are infinite, are reconstructible.

In the second section we give some results about the reconstructibility of certain locally finite countably infinite interval graphs and show that a reconstruction of a planar, infinite graph has to be planar too.     

Multi-neighboring grids schemes for solving PDE eigen-problems

Instead of most existing postprocessing schemes,a new preprocessing approach,called multineighboring grids(MNG),is proposed for solving PDE eigen-problems on an existing grid G(Δ).The linear or multi-linear element,based on box-splines,are taken as the frst stage Kh1Uh=λh1Mh1Uh.In this paper,the j-th stage neighboring-grid scheme is defned asKh jUh=λh j Mh jUh,where Kh j:=Mh j 1Kh1and Mh jUh is to be found as a better mass distribution over the j-th stage neighboring-gridG(Δ),and Kh jcan be seen as an expansion of Kh1on the j-th neighboring-grid with respect to the(j 1)-th mass distribution Mh j 1.It is shown that for an ODE model eigen-problem,the j-th stage scheme with 2j-th order B-spline basis can reach2j-th order accuracy and even(2j+2)-th order accuracy by perturbing the mass matrix.The argument can be extended to high dimensions with separable variable cases.For Laplace eigen-problems with some 2-D and 3-D structured uniform grids,some 2j-th order schemes are presented for j 3.     

Mathematical modelling and optimisation of a waste water treatment plant by combined oxygen electrode and biological waste water treatment model

Structured mathematical models of oxygen electrode and biological waste water treatment were combined to optimise the position of electrode in the bioreactor. Parameters sensibility testing of mathematical model has shown that the model was most sensitive to the change of these parameters (in decreasing order of significance): oxygen consumption per unit of BOD_5, specific consumption rate of adsorbed BOD₅, volumetric coefficient of oxygen transfer rate (k_La), and waste water inflow. Two positions of electrode were tested: in the bioreactor and in the bioreactors syphon outlet shaft. Results obtained for the exchange of the oxic/anoxic phase and sludge recycling plant indicated that a reduction of electrical power for the aeration could be achieved if O₂ electrode is placed in the bioreactor tank, compared to position in outlet shaft. Better positioning of electrode has resulted in shortening of the oxic/anoxic cycle by 13% and the daily working time of aerators for 0.5 h per day, respectively. In the same time, the number of oxic/anoxic cycles per day was increased by 29%. In addition, results obtained by mathematical modelling indicated no debasement of chemical composition in out coming purified water if new position will be used.     

О теореме Ч. Горовица о нулях функций иэ пространств Бергмана

Thedistribution of the absolute values of the zeros z _k (f) is studied, where f belongs to the Bergman space A _α ^p with the power weight t ^α α > ?1, or to near spaces of analytic n functions. The main object of the study is the estimate of the product $ \prod\limits_{k = 1}^n {\left| {z_k (f)} \right|^{ - 1} } $ . Estimates of such products for functions f ε A _α ^p , were given by Ch. Gorovic in 1974. However, a number of essential questions in connection with these estimates have not been answered so far. In the present paper, answers are be given for some of these questions.     

Thermodynamic formalism for null recurrent potentials

We extend Ruelle’s Perron-Frobenius theorem to the case of Hölder continuous functions on a topologically mixing topological Markov shift with a countable number of states. LetP(?) denote the Gurevic pressure of ? and letL _? be the corresponding Ruelle operator. We present a necessary and sufficient condition for the existence of a conservative measure ν and a continuous functionh such thatL _? ^* ν=e ^P(?)ν,L _? h=e ^P(?) h and characterize the case when ∝hdν<∞. In the case whendm=hdν is infinite, we discuss the asymptotic behaviour ofL _? ^k , and show how to interpretdm as an equilibrium measure. We show how the above properties reflect in the behaviour of a suitable dynamical zeta function. These resutls extend the results of [18] where the case ∝hdν<∞ was studied.     

Regular Submanifolds in Conformal Space ${\mathbb Q}^n_p$

The authors study the regular submanifolds in the conformal space Q_p~n and introduce the submanifold theory in the conformal space Q_p~n.The first variation formula of the Willmore volume functional of pseudo-Riemannian submanifolds in the conformal spaceQ_p~n is given.Finally,the conformal isotropic submanifolds in the conformal space Q_p~n are classified.