Begell House Inc. International Journal of Fluid Mechanics Research FMR 2152-5102 39 5 2012
Analytical Solution of Natural Convection Flow in Vertical Concentric Annuli with Internal Heat Generation/Absorption 373-380 Basant K. Jha Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria Abiodun O. Ajibade Department of Mathematics, Ahmadu Bello University Zaria, Nigeria Equations governing the steady, laminar fully developed natural convection flow in vertical concentric annuli in presence of temperature dependent heat sources/sinks are developed. These equations are solved analytically in terms of modified Bessel's functions subject to the appropriate conditions. In the present analysis, convection current is setup due to the temperature difference between the outer surface of the inner cylinder and inner surface of the outer cylinder as well as the presence of heat sources or sinks in the system. Expressions for velocity field, temperature field, mass flow rate and skin-friction (at the outer surface of inner cylinder and inner surface of the outer cylinder) are obtained in terms of modified Bessel's function.
An Analytical Model for Velocity Distribution and Dip-Phenomenon in Uniform Open Channel Flows 381-395 Snehasis Kundu Department of Mathematics, Indian Institute of Technology Kharagpur, West Bengal,India Koeli Ghoshal Department of Mathematics, Indian Institute of Technology Kharagpur, West Bengal, India An analytical equation for velocity distribution in uniform open-channel flows is proposed based on an eddy viscosity with a modified wake correction and on an analysis of shear stress distribution. The proposed equation for the velocity distribution in vertical direction is able to predict the velocity-dip-phenomenon. The new log-wake modified eddy viscosity model is compared with the previous models. The proposed equation i. e., total-dip-modified-log-wake law for velocity distribution is compared with the experimental data obtained by Coleman, Wang and Qian, Lyn and Kironoto and Graf. The total-dip-modified-log-wake law agrees well with the experimental data and predicts the velocity dip position accurately. It has been found that the Coles' wake strength has significant effect on the location of the dip position and the value increases with the increase of dip-correction parameter.
Explanation of Scatter Phenomenon in Wind-Tunnel Experiments for Airfoils at High Incidences by the Multi-Equilibrium States of Separated Flow 396-415 Zhengyin Ye National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, P.R. China Naizhen Zhou National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, P.R. China Xiaopeng Wang National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, P.R. China Coupled with k-ω SST turbulent model, the unsteady Reynolds-averaged Navier−Stokes equations are solved in the time-domain to obtain the steady and/or unsteady separated flow for airfoils at high incidences. Different kinds of vibrations are designed for the airfoils to simulate different disturbances. The effects of different disturbances on the separated flow are studied, especially at high incidences when the multi-equilibrium states phenomenon for the separated flow exists. It is found that, for the given Reynolds number and airfoils with thickness larger than 20 %, multi-equilibrium states exist for the separated flows around the airfoils, and the equilibrium state of the separated flow may transit under certain disturbances at some range of incidences. Generally, the plunging disturbance and pitching disturbance are more effective than the forward-backward disturbance in leading to the equilibrium state of the separated flow transiting from one state to another. The average aerodynamic force will change when the equilibrium state of the separated flow-field transit. These phenomena can be an explanation for the poor repeatability and scatter phenomenon of aerodynamic characteristics for configurations at high incidences in wind-tunnel experiments.
Frictional Pressure Drop for Gas − Non-Newtonian Liquid Flow through 90° and 135° Circular Bend: Prediction Using Empirical Correlation and ANN 416-437 Nirjhar Bar Chemical Engineering Department, University of Calcutta Kolkata - 700 009, India Sudip Kumar Das University of Calcutta Experiments have been carried out to determine the two-phase frictional pressure drop across 90° and 135° bend for gas-non-Newtonian liquid flow on the horizontal plane. Empirical correlation has been developed to predict the two-phase friction factor using the physical and dynamic variables of the system. The applicability of Artificial Neural Networks (ANN) methodology have also been reported. The ANN prediction have been reported using Multilayer Perceptrons (MLP) trained with five different algorithms, namely: Backpropagation (BP), Scaled Conjugate gradient (SCG), Delta-Bar-Delta (DBD), Levenberg−Marquardt (LM), Quick-Prop (QP). Four different transfer functions were used in a single hidden layer for all algorithms. The χ-square test confirms that the best network for prediction of frictional pressure drop is when it is trained with Backpropagation algorithm in the hidden and output layer with the transfer function 4 in hidden layer having 13 processing elements for 90° bend. The χ-square test also confirms that the best network for prediction of frictional pressure drop is when it is trained with Levenberg − Marquardt algorithm in the hidden and output layer with the transfer function 1 in hidden layer having 7 processing elements for 135° bend. Both the methods are equally predictive in nature but the empirical correlation is based on the physical and dynamic variables of the system, whereas the ANN prediction is not dependent on the individual relationship between the input variables.
Slip Effect on Boundary Layer Flow on a Moving Flat Plate in a Parallel Free Stream 438-447 Krishnendu Bhattacharyya Institute of Science, Banaras Hindu University Gorachand C. Layek Department of Mathematics, University of Burdwan Burdwan, West Bengal, India Rama Subba Reddy Gorla Department of Mechanical Engineering, Cleveland State University, Cleveland, OH, 44115 USA; Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA; Department of Mechanical & Civil Engineering, Purdue University Northwest, Westville, IN 46391, USA This investigation deals with the effect of slip condition at the boundary on boundary layer flow on a moving flat plate in a parallel free stream. Using similarity transformations, the governing PDEs are transformed into a self-similar ODE which is then solved numerically using shooting method. Akin to the no-slip case, in the case of slip dual solutions of velocity distribution are obtained. Most importantly, for increasing slip at the boundary the range of velocity ratio parameter where solution exists increases. Also, due to increase in slip parameter the boundary layer thickness decreases for first solution and increases for second solution.
Edge Effect in Cone and Plate Rheometer 448-465 Khaled M. Bataineh Department of Mechanical Engineering, Jordan University of Science and Technology Irbid, Jordan This paper investigates theoretically and numerically the influence of the edge effect on rheological measurements in cone-plate rheometer. Theoretical discussion for the flow generated by the slow steady rotation of a cone in Newtonian fluid confined by stationary plate is presented. Due to the complicated shape of the boundary, analytical methods cannot be utilized, hence we propose a numerical procedure to solve the problem. The complex flow behavior between finite rotating cone and stationary plate is modeled using the computational Fluid Dynamic software package Fluent 6.3. Equations of motion for steady, axisymmetric, isothermal flow of incompressible Newtonian fluid coupled with continuity equation are solved numerically. The influence of edge effect on flow charac-teristics as a function of cone radius, gap angle, and angular speed is numerically studied. It is shown that the infinite cone and plate assumption is valid for a gap angle of less than 5°. It is also shown that the error in torque measurement due to edge effect is less that 5 % for a gap angle equals or less than 5° up to Reynolds number Re = &#937;R2/v less than 860. Also, when Re is less than 86 for all gap angles studied, the maximum error in torque due to edge effect is less than 5 %. Also, it is shown that reducing the radius of the cone successfully allows the device to be used for high shear rates while maintain acceptable errors. A new definition of Reynolds number that includes gap angle is proposed. The values of the modified Reynolds number successfully characterize the flow regime. Finally, the presented numerical models have been verified against experimental results.