• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.24 no.3
• /
• pp.426-434
• /
• 2000

This paper deals with a generalized similarity solution for the one-dimensional solidification of ternary or higher-order multicomponent alloys. The present approach not only retains the existing features of binary systems such as temperature- solute coupling, shrinkage-induced flow, solid-liquid property differences, and finite back diffusion, but also is capable of handling a multicomponent alloy without restrictions on the partition coefficient and microsegregation parameter. For an alloy of N-solute species, governing equations in the mushy region reduce to (N+2) nonlinear ordinary differential equations via similarity transformation, which are to be solved along with the closed-form solutions for the solid and liquid regions. A linearized correction scheme adopted in the solution procedure facilitates to determine the solidus and liquidus positions stably. The result for a sample ternary alloy agrees excellently with the numerical prediction as well as the reported similarity solution. Additional calculations are also presented to show the utility of this study. Finally, it is concluded that the present analysis includes the previous analytical approaches as subsets.

• Journal of applied mathematics & informatics
• /
• v.31 no.5_6
• /
• pp.631-642
• /
• 2013

In this paper we reconsider the problem of steady mixed convection boundary-layer flow over a vertical flat plate studied in [6],[7] and [13]. Under favorable assumptions, we prove existence of multiple similarity solutions, we study also their asymptotic behavior. Numerical solutions are carried out using a shooting integration scheme.

• The KSFM Journal of Fluid Machinery
• /
• v.8 no.3 s.30
• /
• pp.26-32
• /
• 2005

One of noticeable features in the cross flow fan is that a working fluid passes through impeller blade twice without distinction between the inlet and exit angles. Also, it does produce higher circumferential velocity than other types of blade at the same flow rate in accordance with the application of the forward curved shape. However, a design theory for the cross-flow fall has not yet been formed owing to an eccentric vortex, which is the remarkable characteristics, occurred in a cross-flow fan. Furthermore, the eccentric vortex, which is difficult to control the size and position, is the important cause of performance decrease. In this study, experiments we carried out to estimate the similarity of the cross-flow fan with various scales and rotational velocity changes. Pressure coefficients to flow coefficients with various scales of the cross-flow fan are plotted to the application of the general similarity law of the turbomachinery in the cross-flow fan with Archimedes spiral, which is the important factor having an effect on it.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.25 no.5
• /
• pp.731-740
• /
• 2001

A numerical study on the quantitative analogy between the fully developed turbulent flow in a straight square duct rotating about an axis perpendicular to that of the duct and that in a stationary curved duct of square cross-section is carried out. In order to clarify the similarity of the two flows, dimensionless parameters K(sub)TR=Re(sup)1/4/√Ro and Rossby number, Ro, in a rotating straight duct flow were used as a set corresponding to K(sub)TC=Re(sup)1/4/√λ and curvature ratio, λ, in a stationary curved duct flow so that they have the same dynamical meaning as those of the fully developed laminar flows. For the large values of Ro or λ, it is shown that the flow field satisfies the asymptotic invariance property, that is, there are strong quantitative similarities between the two flows such as flow patterns and friction factors for the same values of K(sub)TR and K(sub)TC.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 1999.03b
• /
• pp.71-75
• /
• 1999

An approximate similarity theory has been applied to predict the forming load of non-axisymmetric forging of aluminum alloys through model material tests. The approximate similarity theory is applicable when strain rate sensitivity geometrical size and die velocity of model materials are different from those of real materials. Actually the forming load of yoke which is an automobile part made of aluminum alloys(Al-6061) is predicted by using this approximate similarity theory. Firstly upset forging tests are have been carried out to determine the flow curves of three model materials and aluminum alloy(Al-6061) and a suitable model material is selected for model material test of Al-6061 And then and forging tests of aluminum yokes have been performed to verify the forming load predicted from the model material which has been selected from above upset forging tests, The forming loads of aluminum yoke forging predicted by this approximate similarity theory are in good agreement with the experimental results of Al-6061 and the results of finite element analysis using DEFORM-3D.

• Journal of the Korean Society for Precision Engineering
• /
• v.19 no.12
• /
• pp.142-149
• /
• 2002

In this paper, the metal forming process is caused of rise of the unit cost of production in increase of the lead-time and cost because of manufacturing final product through a few the number of processes. Flow control complex forming is proposed to put into formulation in order to apply cold forging from conventional approximate similarity theory, and the forming loads of the real material(AISI 1008) can be calculated by put at the new similarity formula the load by plasticine model material experiment through hub clutch. In order to reduce lead-time and cost the technology is used to manufacture with lower die of this product. By the application synthetic resin as the raw material, it is have the merit such short lead-time, low cost, good surface finish etc., as compared with the machine work.

• 한국전산유체공학회:학술대회논문집
• /
• 2007.10a
• /
• pp.39-44
• /
• 2007

A similarity solution of the Navier-Stokes equation for the axisymmetric stagnation flow near a plane wall coated with a magnetic fluid of uniform thickness is constructed. The shape functions representing the flow in two (magnetic and normal) fluid layer are determined from a third order boundary value problem, which is solved by the Runge-Kutta method with two shooting parameters. Features of the flow including streamline pattern and interface velocity are investigated for the varying values of density ratio, viscosity ratio, and Reynolds number. The results for the interface and wall shear stress, boundary layer and displacement thickness are also presented.

• Journal of the Korean Society for Precision Engineering
• /
• v.8 no.4
• /
• pp.95-106
• /
• 1991

A numerical computation of turbulent wirling flow in a stationary pipe is presented in this work. Major concerns of this study are: 1) To approve similarity laws which were verified experimentally. 2) To investigate the effects of curvature modification for the K- .epsilon. model. To account for effects of swirl, Rodi's curvature correction and Kim & Chung's are applied. The governing differential equations for eliptic flow are discretized by control volume formulation method, and the discretized equations are calculated ay line by line TDMA and SIMPLE algorithm. The computational results also satisfy similarity laws which are based on swirl angle as in experiments. And the curvature modification of Rodi improves compuational accuacy than the standard K- .epsilon. model. But such lower order closure models are not adequate for the prediction of this complex flow.

• Journal of the Korean Society of Industry Convergence
• /
• v.4 no.4
• /
• pp.387-393
• /
• 2001

The flow characteristics on the centerline in case of free jet, sudden expansion jet and impinging jet have been investigated. Centerline flow behaviors and similaritis with mean velocities, turbulent intensities, shear stresses, isotropic structures and turbulent kinetic energies on the streamwise direction were looked into and compared with three jets, The results show that mean velocities have represented potential core and decayed with similar gradients. The turbulent intensities and shear stresses were presented peak values in the self-preserving region, and then they were in decay. Aeolotropy in the initial region were possible returned to isotropy patterns with asymptotic approach in the downstream region. It has been found that the turbulent kinetic energies for the three cases of jet existed in the similarity and they coincided with Gaussian profile.

• Proceedings of the KSME Conference
• /
• 2001.06e
• /
• pp.825-830
• /
• 2001

A numerical study on a quantitative analogy of the fully developed flow between in a straight square duct rotating about an axis perpendicular to that of the duct and a stationary curved duct of square cross-section is carried out. In order to clarify the similarity of two turbulent flows, the dimensionless parameters $K_{TR} = Re^{1/4}/\sqrt{Ro}$ and the Rossby number, Ro, in a rotating straight duct flow were used as a set corresponding to $K_{TC} = Re^{1/4}/\sqrt{{\lambda}}$ and curvature ratio, ${\lambda}$, in a stationary curved duct flow so that they have the same dynamical meaning as $K_{LR} = Re/\sqrt{Ro}$ and $K_{LC} = Re/\sqrt{{\lambda}}$ of the fully developed laminar flows. For the large values of Ro or A, it is shown that the flow field satisfies the asymptotic invariance property: there are strong quantitative similarities between the two flows such as flow patterns and friction factors for the same values of $K_L$ and $K_T$.