• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.32 no.10
• /
• pp.93-101
• /
• 2004

A method to calculate stability limits is investigated to predict the characteristics of high-frequency combustion instability in liquid-propellant rocket engine. It is based on the theory of linear stability analysis proposed in previous works and useful to predict combustion stability at the beginning stage of engine development. The system of equations governing reactive flow in combustor has the simplified and linearized forms. The overall equation expressing stability limits is adopted. The procedures to evaluate quantitatively each term included in the equation are proposed. The thermo-chemical properties and flow variables required in the evaluation can be obtained from calculation of thermodynamic equilibrium, CFD results, and experimental test data. Based on the existent data, stability limits are calculated with actual rocket engine (KSR-III rocket engine). The present calculations show the reasonable stability limits in a quantitative manner and the stability characteristics of the engine are discussed. The prediction from linear stability analysis could be serve as the first approximation to the true prediction.

• Structural Engineering and Mechanics
• /
• v.12 no.5
• /
• pp.507-526
• /
• 2001

In standard finite element algorithms, the local stability conditions are not accounted for in the formulation of the tangent stiffness matrix. As a result, the loss of the local stability is not adequately related to the onset of the global instability. The phenomenon typically arises with material-type localizations, such as shear bands and plastic hinges. This paper addresses the problem in the context of the planar, finite-strain, rate-independent, materially non-linear beam theory, although the proposed technology is in principle not limited to beam structures. A weak formulation of Reissner's finite-strain beam theory is first presented, where the pseudocurvature of the deformed axis is the only unknown function. We further derive the local stability conditions for the large deformation case, and suggest various possible combinations of the interpolation and numerical integration schemes that trigger the simultaneous loss of the local and global instabilities of a statically determined beam. For practical applications, we advice on a procedure that uses a special numerical integration rule, where interpolation nodes and integration points are equal in number, but not in locations, except for the point of the local instability, where the interpolation node and the integration point coalesce. Provided that the point of instability is an end-point of the beam-a condition often met in engineering practice-the procedure simplifies substantially; one of such algorithms uses the combination of the Lagrangian interpolation and Lobatto's integration. The present paper uses the Galerkin finite element discretization, but a conceptually similar technology could be extended to other discretization methods.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2004.05a
• /
• pp.252-257
• /
• 2004

Free vibration of a semi-circular pipe conveying fluid is analyzed when the pipe is clamped at both ends. To consider the geometric non-linearity, this study adopts the Lagrange strain theory and the extensibility of the pipe. By using the extended Hamilton principle, the non-linear partial differential equations are derived, which are coupled to the in-plane and out-of\ulcornerplant: motions. To investigate the vibration characteristics of the system, the discretized equations of motion are derived from the Galerkin method. The natural frequencies are computed from the linearized equations of motion in the neighborhood of the equilibrium position. From the results. the natural frequencies for the in-plane and out-of-plane motions are vary with the flow velocity. However, no instability occurs the semi-circular pipe with both ends clamped, when taking into account the geometric non-linearity explained by the Lagrange strain theory.

• The Bulletin of The Korean Astronomical Society
• /
• v.36 no.2
• /
• pp.92.2-92.2
• /
• 2011

In view of the planned NASA's and ESA's Solar Probe Plus and Solar Orbiter missions, respectively, to probe the inner heliosphere and the Sun's corona, it is timely to investigate outstanding problems associated with the solar wind. Among them is the temperature anisotropy problem. As the solar wind expands into the interplanetary space, the density and magnetic field decreases radially, thus leading to temperature anisotropy ($T_{\parallel}{\gg}T_{\perp}$). However, the measured temperature anisotropy can at times be characterized by $T_{\perp}$ > $T_{\parallel}$, while at other times the measured $T_{\parallel}/T_{\perp}$ is much milder than predicted by adiabatic theory. Physical reasons remain poorly understood. This notwithstanding, it is known from plasma physics that for $T_{\perp}$ > $T_{\parallel}$ electromagnetic ion-cyclotron (EMIC) and mirror instabilities are excited, while for $T_{\parallel}$ > $T_{\perp}$, fire-hose instability is excited. By constructing the threshold conditions for various instabilities, one may construct a closure relation that may be useful for modeling the solar wind. In the present paper we discuss theoretical construction of the anisotropy-beta relation by means of quasi-linear theories of these instabilities. The present work complements previous efforts on the basis of linear theory, hybrid simulations, and empirical fits of observations.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.30 no.1 s.244
• /
• pp.32-40
• /
• 2006

A linear acoustic analysis has been performed to elucidate damping characteristics of acoustic cavities in a liquid rocket combustor. Results have shown that resonant frequencies of acoustic cavity obtained by classical theoretic approach and by the present linear analysis are somewhat different with each other. This difference is attributed to the limitation of the simplified classical theory. To quantify the damping characteristics, acoustic impedance has been introduced and resultant absorption coefficient and conductance have been evaluated. Satisfactory agreement has been achieved with previous experiment. Finally the design procedure for an optimal tuning of acoustic cavity has been established.

• Korean Chemical Engineering Research
• /
• v.57 no.5
• /
• pp.723-729
• /
• 2019

A theoretical analysis was conducted of convective instability driven by buoyancy forces under transient temperature fields in an annular porous medium bounded by coaxial vertical cylinders. Darcy's law and Boussinesq approximation are used to explain the characteristics of fluid motion and linear stability theory is employed to predict the onset of buoyancy-driven motion. The linear stability equations are derived in a global domain, and then cast into in a self-similar domain. Using a spectral expansion method, the stability equations are reformed as a system of ordinary differential equations and solved analytically and numerically. The critical Darcy-Rayleigh number is founded as a function of the radius ratio. Also, the onset time and corresponding wavelength are obtained for the various cases. The critical time becomes smaller with increasing the Darcy-Rayleigh number and follows the asymptotic relation derived in the infinite horizontal porous layer.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.32 no.6
• /
• pp.104-109
• /
• 2004

On this paper study is concentrated on the breakup and atomization characteristics of spray formed by impinging jet injectors(like-doublet) used in liquid rocket engine(LRE). On the process of breakup and atomization, injection velocity and ambient gas pressure are the main parameters, so that these are used as variables that specify the experimental condition. Injection velocity varied from 3m/s to 30m/s and ambient gas pressure changed from 0.1MPa to 4.0MPa with nitrogen gas. As results, measured physical quantities decreased with increasing injection velocity and ambient gas pressure. But the decreasing ratios are different from those of the theory.

• Transactions of Materials Processing
• /
• v.14 no.6 s.78
• /
• pp.527-532
• /
• 2005

Among the failure modes which can occur in tube hydroforming such as wrinkling, bursting or buckling, the bursting by local instability under excessive tensile stresses is irrecoverable phenomenon. Thus, the accurate prediction of bursting condition plays an important role in producing the successfully hydroformed part without any defects. As the classical forming limit criteria, strain-based forming limit diagram (FLD) has widely used to predict the failure in sheet metal forming. However, it is known that the FLD is extremely dependant on strain path throughout the forming process. Furthermore, The application of FLD to hydroforming process, where strain path is no longer linear throughout forming process, may lead to misunderstanding for fracture initiation. In this work, stress-based forming limit diagram (FLSD), which is strain path-independent and more general, was applied to prediction of forming limit in tube hydroforming. Combined with the analytical FLSD determined from plastic instability theory, finite element analyses were carried out to find out the state of stresses during hydroforming operation, and then FLSD is utilized as forming limit criterion. In addition, the approach is verified by a series of bulge tests in view of bursting pressure and shows a good agreement. Consequently, it is shown that the approach proposed in this paper will provide a feasible method to satisfy the increasing practical demands for judging the forming severity in hydroforming processes.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 2005.05a
• /
• pp.92-96
• /
• 2005

Among the failure modes which can be occurred in tube hydroforming such as wrinkling, bursting or buckling, the bursting by local instability under excessive tensile stresses is irrecoverable phenomenon. Thus, the accurate prediction of bursting condition plays an important role in producing the successfully hydroformed part without any defects. As the classical forming limit criteria, strain-based forming limit diagram has widely used to predict the failure in sheet metal forming. However, it is known that the FLD is extremely dependant on strain path throughout the forming process. Furthermore, the path-dependent limitation of FLD makes the application to hydroforming process, where strain path is no longer linear throughout forming process, more careful. In this work, stress-based forming limit diagram (FLSD), which is strain path-independent and more general, was applied to prediction of forming limit in tube hydroforming. Combined with the analytical FLSD determined from plastic instability theory, finite element analyses were carried out to find out Ihe state of stresses during hydroforming operation, and then FLSD is utilized as forming limit criterion. In addition, the approach is verified with a series of bulge tests in view of bursting pressure and shows a good agreement. Consequently, it is shown that the approach proposed in this paper will provide a feasible method to satisfy the increasing practical demands for judging the farming severity in hydroforming processes.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
• /
• v.13 no.4
• /
• pp.215-222
• /
• 1984

An analytical study on the thermal instability of fluid in a vertical solt between two permeable walls has been carried out using fast converging power series solution method. For given values of prandtl number Pr and permeability paramter ${\sigma}$, the critical Grashof number $Gr_c$ and the critical wave number ac are found as eigenvalues of the problem formulated by the stability equations and the appropriate boundary conditions which are derived on the basis of linear stability theory. In the case of ${\sigma}\;>\;10^4$, the results approach those of solid boundary case, but in the case of ${\sigma}\;<\;10^3$, the decrease of $Gr_c$ and $a_c$become more prominent. In other words, the permeable walls cause the flow to be more unstable than the solid walls. This is considered to be due to the slip of the fluid on the wail, which decrease the friction force.