Buoyancy effect on heat transfer in rotating smooth square U-duct at high rotation number

The buoyancy effect on heat transfer in a rotating,two-pass,square channel is experimentally investigated in curent work.The classical copper plate technique is performed to measure the regional averaged heat transfer cofficients.In order to perform a fundamental research,all turbulators are removed away.Two approaches of altering Buoyancy numbers are selected:varying rotation number from 0 to 2.08 at Reynolds number ranges of 10000 to 70000,and varying inlet density ratio from 0.07 to 0.16 at Reynolds number of 10000.And thus,Buoyancy numbers range from 0 to 12.9 for both cases.According to the experimental results,the relationships between heat transfer and Buoyancy numbers are in accord with those obtained under different rotation numbers.For both leading and trailing surface,a critical Buoyancy number exists for each X/D location.Before the critical point,the effect of Buoyancy number on heat transfer is limited;but after that,the Nusselt number ratios show different increase rate.Given the same rotation number,higher wall temperature ratios with its corresponding higher Buoyancy numbers substantially enhance heat transfer on both passages.And the critical exceed-point that heat transfer from trailing surface higher than leading surface happens at the same Buoyancy number for different wall temperature ratios in the second passage.Thus,the stronger buoyancy effect promotes heat transfer enhancement at high rotation number condition.

Effect of Coriolis and centrifugal forces on flow and heat transfer at high rotation number and high density ratio in non orthogonally internal cooling channel

Numerical predictions of three-dimensional flow and heat transfer are performed for a two-pass square channel with 45° staggered ribs in non-orthogonally mode-rotation using the second moment closure model. At Reynolds number of 25,000, the rotation numbers studied were 0,0.24, 0.35 and 1.00. The density ratios were 0.13, 0.23 and 0.50. The results show that at high buoyancy parameter and high rotation number with a low density ratio, the flow in the first passage is governed by the secondary flow induced by the rotation whereas the secondary flow induced by the skewed ribs was almost distorted. As a result the heat transfer rate is enhanced on both co-trailing and co-leading sides compared to low and medium rotation number. In contrast, for the second passage, the rotation slightly reduces the heat transfer rate on co-leading side at high rotation number with a low density ratio and degrades it significantly on both co-trailing and co-leading sides at high buoyancy parameter compared to the stationary, low and medium rotation numbers. The numerical results are in fair agreement with available experimental data in the bend region and the second passage, while in the first passage were overestimated at low and medium rotation numbers.

Effect of Blockage Ratio on Heat Transfer and Pressure Drop in Rotating Ribbed Channels at High Rotation Numbers

At high rotation numbers,the rotational effects on heat transfer and flow could be diverse among the channels with different blockage ratios.However,most studies are conducted under low rotation number(less than 0.25)and selected blockage ratio.This paper experimentally investigates the effect of rib blockage ratio(ranges from 0 to 0.3)on pressure loss and heat transfer in a rotating square channel under high rotation number(up to 0.81).The ribs staggered on leading and trailing walls were oriented 90°to the mainstream flow.The Reynolds number and the wall-to-fluid temperature ratio varied from 20000 to 40000 and 0.08 to 0.2,respectively.The results showed that a larger blockage ratio resulted in a better heat transfer but a higher pressure drop.The optimum blockage ratio was 0.1 for the best thermal performance.The rotational effects were weakened in the passage with a higher blockage ratio,where the critical rotation number could not be observed.Moreover,the heat transfer enhancement induced by rotation was more significant when the temperature ratio increased.Finally,the correlations were developed for the pressure drop and the convective heat transfer on the leading and trailing edges.

LYAPUNOV EXPONENT AND ROTATION NUMBER FOR STOCHASTIC DIRAC OPERATORS

In this paper, we consider the stochastic Dirac operatoron a polish space (Ω,β, P). The relation between the Lyapunov index, rotation number andthe spectrum of Lis discussed. The existence of the Lyapunov index and rotation number isshown. By using the W-T functions and W-function we prove the theorems for Las in Kotani[1], [2] for Schrodinger operatorB, and in Johnson [5] for Dirac operators on compact space.

Collisional Quantum Interference on Rotational Energy Transfer： Relation Between Integral Interference Angle and Rotational Quantum Number in Na2（A^1∑u^＋,ν=8～b^3∏0u,ν=14）-Na System

Collisional quantum interference （CQI） on rotational energy transfer was observed in Na2（A^1∑u^＋,ν=8～b^3∏0u,ν=14） system in collision with Na [Chem. Phys. Lett. 318 （2000） 107], and the degree of the interference was measured. The integral interference angle was obtaJned through theoretical calculation. We will research the factors that have effect on collisional quantum interference on rotational energy transfer in Na2（A^1∑u^＋,ν=8～b^3∏0u,ν=14）-Na system. Basing on the time-dependent first order Born approximation, and taking into account the anlsotroplc Lennard Jones interaction potentials and ＂straight-line＂ trajectory approximation, we obtain the factors that have effect on CQI in Na2-Na system, and obtain the relation between the integral interference angle and rotational quantum number.

Numerical Simulation of Aspect Ratio Effect on Turbulent Annular Flows

The control of energy in various industrial applications passes by the comprehension of the phenomena of transfers especially in complex flows. The structure of the turbulent flow in the cavities in rotation depends on several parameters like the Reynolds number of rotation Ra and the aspect ratio of the cavity. The purpose of this work is to simulate numerically the effect of the aspect ratio on the level of turbulence in the annular steady flow with an incompressible fluid for three different configurations. In the first, the interior cylinder is fixed and the external is moving. The second configuration is the reverse. The third is the contra-rotating cylinders. For all these configurations, we varied the aspect ratio from 0.5 to 2.5. The numerical tool is based on a statistical model in a point using the closing of the second order of the transport equations of the Reynolds stresses （Reynolds Stress Model： RSM）. The results of our numerical simulation show that this geometrical parameter can be an interesting factor to increase the level of turbulence that is often required in several industrial applications where the economy and the control of energy are always required.

Heat Transfer in Internal Channel of a Blade:Effects of Rotation in a Trailing Edge Cooling System

The aerothermal performance of a trailing edge （TE） internal cooling system of a high pressure gas turbine blade was evaluated under stationary and rotating conditions. The investigated geometry consists of a 30：1 scaled model reproducing a typical wedge shaped discharge duct with one row of enlarged pedestals. The airflow pattern inside the device simulates a highly loaded rotor blade cooling scheme with a 90 [deg] turning flow from the radial hub inlet to the tangential TE outlet. Two different tip configurations were tested, the first one with a completely closed section, the second one with a 5 holes outlet surfaces discharging at ambient pressure. In order to assess rotation effects, a rotating test rig, composed of a rotating ann holding both the PMMA TE model and the instru mentation, was purposely developed and manufactured. A thin Inconel heating foil and wide band Thermochromic Liquid Crystals are used to perform steady state heat transfer measurements on the blade pres sure side. A rotary joint ensures the pneumatic connection between the blower and the rotating apparatus; more over several slip rings are used for both instrumentation power supply and thermocouple connection. A parallel CFD analysis involving steadystate RANS modeling was conducted to allow an insight of the flow field inside the redirecting channel and the interpedestal ducts to better interpret the developing vortical structures. LowReynolds grid clustering permits to integrate up to the wall both the momentum and the thermal boundary layer. Calculations were performed by means of an inhouse developed pressure based solver exploiting the kco SST turbulence model implemented in the framework of the opensource finite volume discretization toolbox OpenFOAM~. Analyzed flow conditions correspond to Reynolds number of 20000 in the hub inlet section and angular speed varies to obtain rotation numbers in the range from 0 to 0.3. The orientation of the rotation axis is orthogonal to the heated surface as to resemble a 90 [deg] blade metal angle. Results are reported in terms of de tailed heat transfer coefficient 2D maps on the suction side surface as well as spanwise profiles inside the pedestal ducts.

Continuity in weak topology:higher order linear systems of ODE

We will introduce a type of Fredholm operators which are shown to have a certain con- tinuity in weak topologies.From this,we will prove that the fundamental matrix solutions of k-th, k≥2,order linear systems of ordinary differential equations are continuous in coefficient matrixes with weak topologies.Consequently,Floquet multipliers and Lyapunov exponents for periodic systems are continuous in weak topologies.Moreover,for the scalar Hill’s equations,Sturm-Liouville eigenvalues, periodic and anti-periodic eigenvalues,and rotation numbers are all continuous in potentials with weak topologies.These results will lead to many interesting variational problems.

Continuity in Weak Topology: First Order Linear Systems of ODE

In this paper we study important quantities defined from solutions of first order linear systems of ordinary differential equations. It will be proved that many quantities, such as solutions, eigenvalues of one-dimensional Dirac operators, Lyapunov exponents and rotation numbers, depend on the coefficients in a very strong way. That is, they are not only continuous in coefficients with respect to the usual L^p topologies, but also with respect to the weak topologies of the Lp spaces. The continuity results of this paper are a basis to study these quantities in a quantitative way.

Periodic Eigenvalues of One-Dimensional p-Laplacian with Indefinite Weights

Rotation numbers are used in this paper to study the periodic and anti-periodic eigenvalues of the one-dimensional p-Laplacian with a periodic weight which changes sign. The analysis proves that for any nonnegative integer n, ρ -1(n/2) is the union of two closed intervals, one of which lies in [FK(W+3mm?3mm][TPP533A,+3mm?2mm] + and the other in [FK(W+3mm?3mm][TPP533A,+3mm?2mm] -, and the endpoints of these intervals yield the corresponding periodic and anti-periodic eigenvalues.