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2016年 第37卷 第8期    刊出日期：2016-08-01

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论文

Boundary-layer disturbances subjected to free-stream turbulence and simulation on bypass transition

Hong QIN, Ming DONG

2016, 37(8):  967-986.  doi:10.1007/s10483-016-2111-8

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The phenomena associated with the entrainment of free-stream turbulence (FST) into boundary-layer flows are relevant for a number of subjects. It has been believed that the continuous spectra of the Orr-Sommerfeld (O-S)/Squire equations describe the entrainment process, and thus they are used to specify the inlet condition in simulation of bypass transition. However, Dong and Wu (Dong, M. and Wu, X. On continuous spectra of the Orr-Sommerfeld/Squire equations and entrainment of free-stream vortical disturbances. Journal of Fluid Mechanics, 732, 616-659 (2013)) pointed out that continuous spectra exhibit several non-physical features due to neglecting the non-parallelism. They further proposed a large-Reynolds-number asymptotic approach, and showed that the non-parallelism is a leading-order effect even for the short-wavelength disturbance, for which the response concentrates in the edge layer. In this paper, the asymptotic solution is verified numerically by studying its evolution in incompressible boundary layers. It is found that the numerical results can be accurately predicted by the asymptotic solution, implying that the latter is adequate for moderate Reynolds numbers. By introducing a series of such solutions as the inflow perturbations, the bypass transition is investigated via the direct numerical simulation (DNS). The transition processes, including the evolution of streaks, the amplification of secondary-instability modes, and the emergence of turbulent spots, agree with the experimental observations.



Effect of particles on turbulent thermal field of channel flow with different Prandtl numbers

Caixi LIU, Yuhong DONG

2016, 37(8):  987-998.  doi:10.1007/s10483-016-2112-8

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The direct numerical simulation (DNS) of heat transfer in a fully developed non-isothermal particle-laden turbulent channel flow is performed. The focus of this paper is on the modulation of the particles on turbulent thermal statistics in the particle-laden flow with three Prandtl numbers (Pr=0.71, 1.5, and 3.0) and a shear Reynolds number (Re_τ=180). Some typical thermal statistics, including normalized mean temperature and their fluctuations, turbulent heat fluxes, Nusselt number and so on, are analyzed. The results show that the particles have less effects on turbulent thermal fields with the increase of Prandtl number. Two reasons can explain this. First, the correlation between fluid thermal field and velocity field decreases as the Prandtl number increases, and the modulation of turbulent velocity field induced by the particles has less influence on the turbulent thermal field. Second, the heat exchange between turbulence and particles decreases for the particle-laden flow with the larger Prandtl number, and the thermal feedback of the particles to turbulence becomes weak.

Global instability of Stokes layer for whole wave numbers

Wei KONG, Jisheng LUO

2016, 37(8):  999-1012.  doi:10.1007/s10483-016-2113-8

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The study on the global instability of a Stokes layer, which is a typical unsteady flow, is usually a paradigm for understanding the instability and transition of unsteady flows. Previous studies suggest that the neutral curve of the global instability obtained by the Floquet theory is only mapped out in a limited range of wave numbers (0.2≤α≤0.5). In this paper, the global instability is investigated with numerical simulations for all wave numbers. It is revealed that the peak of the disturbances displays irregularity rather than the periodic evolution while the wave number is beyond the above range. A "neutral point" is redefined, and a neutral curve of the global instability is presented for the whole wave numbers with this new definition. This work provides a deeper understanding of the global instability of unsteady flows.

Linear spatial instability analysis in 3D boundary layers using plane-marching 3D-LPSE

Jianxin LIU, Shaolong ZHANG, Song FU

2016, 37(8):  1013-1030.  doi:10.1007/s10483-016-2114-8

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It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional (3D) boundary layers to predict the transition with the e^N method, especially when the boundary layer varies significantly in the spanwise direction. The 3D-linear parabolized stability equation (3DLPSE) approach, a 3D extension of the two-dimensional LPSE (2D-LPSE), is developed with a plane-marching procedure for investigating the instability of a 3D boundary layer with a significant spanwise variation. The method is suitable for a full Mach number region, and is validated by computing the unstable modes in 2D and 3D boundary layers, in both global and local instability problems. The predictions are in better agreement with the ones of the direct numerical simulation (DNS) rather than a 2D-eigenvalue problem (EVP) procedure. These results suggest that the plane-marching 3D-LPSE approach is a robust, efficient, and accurate choice for the local and global instability analysis in 2D and 3D boundary layers for all free-stream Mach numbers.

Carbon nanotubes on unsteady MHD non-Darcy flow over porous wedge in presence of thermal radiation energy

R. KANDASAMY, R. MOHAMMAD, I. MUHAIMIN

2016, 37(8):  1031-1040.  doi:10.1007/s10483-016-2115-8

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The thermal radiation energy is the clean energy with a much lower environmental impact than the conventional energy. The objective of the present work is to investigate theoretically the effect of copper nanoparticles and carbon nanotubes (CNTs) in the presence of base fluid (water) with the variable stream condition due to the thermal radiation energy. Single-walled carbon nanotubes (SWCNTs) in the presence of base fluid flow over a porous wedge play a significant role compared to those of copper nanoparticles on absorbing the incident solar radiation and transiting it to the working fluid by convection.

New way to construct high order Hamiltonian variational integrators

Minghui FU, Kelang LU, Weihua LI, S. V. SHESHENIN

2016, 37(8):  1041-1052.  doi:10.1007/s10483-016-2116-8

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This paper develops a new approach to construct variational integrators. A simplified unconventional Hamilton's variational principle corresponding to initial value problems is proposed, which is convenient for applications. The displacement and momentum are approximated with the same Lagrange interpolation. After the numerical integration and variational operation, the original problems are expressed as algebraic equations with the displacement and momentum at the interpolation points as unknown variables. Some particular variational integrators are derived. An optimal scheme of choosing initial values for the Newton-Raphson method is presented for the nonlinear dynamic system. In addition, specific examples show that the proposed integrators are symplectic when the interpolation point coincides with the numerical integration point, and both are Gaussian quadrature points. Meanwhile, compared with the same order symplectic Runge-Kutta methods, although the accuracy of the two methods is almost the same, the proposed integrators are much simpler and less computationally expensive.

Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting

M. HAJHOSSEINI, M. RAFEEYAN

2016, 37(8):  1053-1066.  doi:10.1007/s10483-016-2117-8

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A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule (GDQR) method. The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation. Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS, and good agreement is found. The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam. It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam, i.e., generating more voltage outputs over a wide frequency range, absorbing vibration, and being less weight.

Electromechanical responses and instability of electro-active polymer cylindrical shells

Jiusheng REN, Chengmin WANG

2016, 37(8):  1067-1076.  doi:10.1007/s10483-016-2118-9

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Based on the theories of finite deformation elasticity, electromechanical responses and instability of an incompressible electro-active polymer (EAP) cylindrical shell, which is subjected to an internal pressure and a static electric field, are studied. Deformation curves and distribution of stresses are obtained. It is found that an internal pressure together with an electric field may cause the unstable non-monotonic deformation of the shell. It is also shown that a critical thickness for the shell exists, and the shell may undergo the unstable deformation if its thickness is less than this critical value. In addition, the effects of the electric field, axial stretch, thickness, and internal pressure on the instability of the shell are discussed.

Projected Runge-Kutta methods for constrained Hamiltonian systems

Yi WEI, Zichen DENG, Qingjun LI, Bo WANG

2016, 37(8):  1077-1094.  doi:10.1007/s10483-016-2119-8

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Projected Runge-Kutta (R-K) methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations (DAEs) in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.

Low order nonconforming mixed finite element method for nonstationary incompressible Navier-Stokes equations

Chao XU, Dongyang SHI, Xin LIAO

2016, 37(8):  1095-1112.  doi:10.1007/s10483-016-2120-8

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This paper studies a low order mixed finite element method (FEM) for nonstationary incompressible Navier-Stokes equations. The velocity and pressure are approximated by the nonconforming constrained Q₁^rot element and the piecewise constant, respectively. The superconvergent error estimates of the velocity in the broken H¹-norm and the pressure in the L²-norm are obtained respectively when the exact solutions are reasonably smooth. A numerical experiment is carried out to confirm the theoretical results.