2010 Vol. 31, No. 8

Display Method:
Formation of Radially Expanding Liquid Sheet by Impinging Two Round Jets
WANG Zhi-liang, S. P. Lin, ZHOU Zhe-wei
2010, 31(8): 891-900. doi: 10.3879/j.issn.1000-0887.2010.08.001
Abstract(1283) PDF(864)
A thin circular liquid sheet can be formed by impinging two identicalround jets against each other. The liquid sheet expands to a certain critical radial distance and breaks. The unsteady process of the formation and breakup of the liquid sheet in the ambient gas was smiulated num erically. Both liquid and gas were treated as incompressible Newtonian fluids. The flow considered was axi-symm etric. The liquid-gas interface was modeled with a level set function. A finite difference scheme was used to solve the governing Navier-Stokes equations with physical boundary conditions. The numerical results show how a thin circular sheet can be formed and broken at its circular edge, in slow motion. The sheet continues to thin as it expands radially. Hence the Weber number decreases rad ially. The Weber number is defined asu2h/, where and are respectively the liquid density and the surface tension, and u and h are, respectively, the average velocity and the half sheet thickness at a local radial location in the liquid sheet. The num erical results show that the sheet indeed terminates at a radial location where the Weber num ber reaches one as observed in experiments. The spatio-tem poral linear theory predicts that the breakup is initiated by the sinuousm ode at the critical Weber number Wec=1 be low which absolute instability occurs. The other independentmode called varicose mode grow smore slowly than the sinuousmode according to the linear theory. However our numerical results show that the varicose mode actually overtakes the sinuous mode during the non linear evolution, and is respon sible for the final breakup. The linear theory predicts the nature of disturbance waves correctly only at the onset of instability, but cannotpredict the exact consequence of the instability.
Hydraulic Calculation of Steady Uniform Flows in Trapezoidal Compound Open Channels
ZENG Yu-hong, WANG Yue-hua, HUAI Wen-xin
2010, 31(8): 901-908. doi: 10.3879/j.issn.1000-0887.2010.08.002
Abstract(1193) PDF(794)
Hydraulic calculation of steady uniform flow in trapezoidal compound open channels was studied. Based on the force balance of water in each sub-section, the average velocities of the main channel, side slope and floodplain were deduced, and the lateralmomentum exchanges between the sub-sections were expressed by using the apparent shear stress. Toverify the model,seven groups of UK-FCF measured data with a relative water depth between the flood-plain and the main channel varying from 0.057 to 0.4 were adopted for comparison. The result shows that the calculated velocity is larger than them easured data when relative water depth is small, while it is smaller than or close to the measured value for cases with a larger relative water depth. The influence of the apparent shear stress on the calculation of velocity on the flood-plain is not obvious, while it is much greater on the main channel. The three-stage model is compared with Liu's two-stage model, and the conclusion is that the former can give a better prediction for a three-stage trapezoidal compound channel. Finally, the apparent shear stress is calculated and compared with the measured data, and the result shows that the values of momentum transfer coefficient adopted are appropriate.
Visco-Elastic Fluid Flow Past an Infinite Vertical Porous Plate in the Presence of First Order Chemical Reaction
Rebhi A. Damseh, Ben Bella A. Shannak
2010, 31(8): 909-916. doi: 10.3879/j.issn.1000-0887.2010.08.003
Abstract(1320) PDF(791)
An analys is was developed in order to study the unsteady free convection flow of an incompressible, visco-elastic fluid on a continuously moving vertical porous plate in the presence of a firs-torder chemical reaction. The governing equations were solvednumerically using an implicit finite difference technique. The selected numerical method was validated by comparing the results with the analytical solutions. Numerical results for the details of the velocity profiles which were shown on graphs were presented. A parametric study was performed to illustrate the in fluence of the visco-elastic parameter, dmiension less chemical reaction parameter and plate moving velocity on the steady state velocity profiles, the tmie dependent friction coefficient, Nusselt number and Sherwood number.
Effect of Thermal Conductivity on Heat Transfer for a Power-Law Non-Newtonian Fluid Over a Continuous Stretched Surface With Various Injection Parameter
Faiza A. Salama
2010, 31(8): 917-923. doi: 10.3879/j.issn.1000-0887.2010.08.004
Abstract(1192) PDF(871)
An analysis of the steady two-dimen sional non-Newtonian flow on a power-lawstretched surface with suction or injection was considered. The thermal conductivity was assumed to vary as a linear function of temperature. The transformed governing equations in the present study were solved numerically by using the Runge-Kutta method. Some of the results obtained for a special case of the problem were compared to the results published in a previous work and were found to be in excellent agreement. Two cases were considered, one corre-sponding to a cooled surface temperature and the other, to a uniform surface temperature. The numerical results show that variable thermal conductivity parameter B, injection parameterd and the power-law indexn have sign ificant in fluences on the temperature profiles and the Nus-seltnumber in the above two cases.
Effects of Induced Magnetic Field on the Peristaltic Flow of Johnson-Segalman Fluid in a Vertical Symmetric Channel
Sohail Nadeem, Noreen Sher Akbar
2010, 31(8): 924-933. doi: 10.3879/j.issn.1000-0887.2010.08.005
Abstract(1418) PDF(738)
The influence of heat transfer and induced magnetic field on peristaltic flow of a Johnson-Segalman fluid was studied. The purpose of the present investigation was to study the effects of induced magnetic field on the peristaltic flow of non-Newtonian fluid. The two-dimensional equations of Johnson-Segamlan fluid were smiplified by assuming a long wave length and low Reynolds number. The obtained equations were solved for the stream function, magnetic force function, and axial pressure gradient by using a regular perturbation method. The expressions for the pressure rise, temperature, induced magnetic field, pressure gradient, and stream function were sketched for variousem bedded param eters and were interpreted.
Effects of Variable Specific Heat on the Stability of Hypersonic Boundary Layer on a Flat Plate
JIA Wen-li, CAO Wei
2010, 31(8): 934-940. doi: 10.3879/j.issn.1000-0887.2010.08.006
Abstract(1536) PDF(932)
The gas temperature within hypersonic boundary layer flow is so high that the specific heat of gas is nolonger a constant but relates with temperature. How variable specific heat to influence on boundary layer flow stability is worth researching. The effect of the variable specific heat on the stability of hypersonic boundary layer flows was studied and compared with the case of the specific heat to be supposed constant, based on the liner stability theory. It is found that the variable specific heat indeed has some effects on the neutral curves of both first-mode and second-mode waves, and on the maximum rate of growth either. Therefore, the relation ship between specific heat and temperature should be considered in the study of the stability of the boundary layer.
First-Order Gradient Damage Theory
ZHAO Bing, ZHENG Ying-ren, ZENG Ming-hua, TANG Xue-song, LI Xiao-gang
2010, 31(8): 941-948. doi: 10.3879/j.issn.1000-0887.2010.08.007
Abstract(1256) PDF(761)
Taking the strain tensor, scalar damage variable and damage gradient as the state variables of Helmholtz free energy, the general expressions of first-order gradient damage constitutive equations were derived directly from the basic law of irreversible thermodynamics by constitutive functional expansion method at natural state. When damage variable was equal to zero, the expressions could be simplified to linear elastic constitutive equations; when the damage gradient vanished, the expressions could be smiplified to the classical damage constitutive equations based on the strain equivalence hypothesis. One-dimensional problem is presented to indicate that the damage field changes from non-periodic solutions to the spatial periodic-like solutions with stress in crement. The peak value region developes to a localization band. The onsetm echanism of strain localization is advised. Damage localization emerges after damage occurs for a short tmie. The width of localization band is proportional to the internal characteristic length.
Dynamic and Quasi-Static Bending of Saturated Poroelastic Timoshenko Cantilever Beam
YANG Xiao, WEN Qun
2010, 31(8): 949-960. doi: 10.3879/j.issn.1000-0887.2010.08.008
Abstract(1499) PDF(741)
Based on the three-dmiensional Gurtin-type variational principle of the incompressible saturated porousmedia, first, a one-dimensionalm athematical model for dynamics of the saturated poroelastic Timoshenko Cantilever beam was established with a ssumptions of deformatin of the classical single phase Tmioshenko beam and the movement of pore fluid only in the axial direction of the saturated poroelasic beam. This mathematical model can be degene rated into the Euler-Bernoullim odel, Rayleigh model and Shear model of the saturated poroelastic beam, respe ctively, under some specialcases. Secondly, dynamic and quasi-static behavior of a saturated poroelastic Tmioshenko cant ilever beam with mipermeable and permeable at its fixed and free end, respectively, subjected to a step load at its free end, was analyzed by the Laplace transform. The variations of the deflections at the beam free end against the tmie were shown in figures, and the influences of the in teraction coefficient between the porefluid and solid skele to naswellas the slenderness ratio of the beam on the dynamic/quasi-static performances of the beam were examined. It is shown that the quasi-static deflections of the saturated poroela stic beam possess the creep behavior smiilar to that of viscoelastic beam. In dynamic responses, with the slenderness ratio increasing, the vibration periods and amplitudes of the deflections at the free end increase, and the tmie needed for deflections to approachits stationary values also increases. Whereas, with the interaction coefficient increasing, the vibrations of the beam deflections decay more strongly, and, eventually, the deflections of the saturated poroelastic beam converge to the static deflections of the classic single phase Tmioshenko beam.
Singularity Analysis of Duffing-van der Pol System With Two Bifurcation Parameters Under Multi-Frequency Excitations
QIN Zhao-hong, CHEN Yu-shu
2010, 31(8): 971-978. doi: 10.3879/j.issn.1000-0887.2010.08.009
Abstract(1476) PDF(800)
Bifurcation properties of Duffing-van der Pol System with two parameters under multi-frequency excitations were studied. It was discussed for three cases 1 λ1 was considered as bifurcation parameter, 2 λ2 was considered as bifurcation parameter, 3 λ1 and λ2 were both considered as bifurcation parameters. According to the definition of transition sets, the whole parametric space was divided into several different persistent regions by the transition sets for different cases. The bifurcation diagrams in different persistent regions were obtained, which could provide a theoretical basis for optmial design of the system.
A Class of Boundary Value Problems for Third-Order Differential Equation With a Turning Point
MO Jia-qi, WEN Zhao-hui
2010, 31(8): 979-985. doi: 10.3879/j.issn.1000-0887.2010.08.010
Abstract(1170) PDF(759)
A class of boundary value problem for differential equation with a turning point was considered. Using the method of multiple scales and others, the uniformly valid asymptotic expansion of solution for the boundary value problem was constructed.
Almost Sure Stability Condition of Weakly Coupled Two-DOF Linear Nonautonomous Random Systems
MA Tian-wei
2010, 31(8): 986-991. doi: 10.3879/j.issn.1000-0887.2010.08.011
Abstract(1167) PDF(707)
Sufficient condition of almost sure stability of two-dimensional oscillating systems under parametric excitations was investigated. The systems considered were assumed to becom posed of two weakly coupled subsystems. The driving actions were considered to be stationary stochastic processes satisfying ergodic properties. The properties of quadratic forms were used in conjunction with the bounds for eigenvalues to obtain, in close form, the sufficient condition for amlost sure stability of the system.
Eigenfunction Expansion Method and Its Application to Two-Dimensional Elasticity Problems Based on Stress Formulation
HUANG Jun-jie, Alatancang, WANG Hua
2010, 31(8): 992-1000. doi: 10.3879/j.issn.1000-0887.2010.08.012
Abstract(1485) PDF(684)
Eigen function expansion method of solving two-dmiensional elasticity problems was proposed based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above two-dmien sional problems was rewritten as an upper triangular differential system. For the associated operatorm atrix, the existence and comple teness of two normed or thogonal eigen function systems in some space are obtained, which belong to the two block operators arising in the operator. Moreover, the general solution of the proceeding two-dimensional problem is given by the eigenfunction expansion.