• Coupled systems mechanics
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• 제11권2호
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• pp.167-198
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• 2022

In this paper we deal with classical instability problems of heterogeneous Euler beam under conservative loading. It is chosen as the model problem to systematically present several possible solution methods from simplest deterministic to more complex stochastic approach, both of which that can handle more complex engineering problems. We first present classical analytic solution along with rigorous definition of the classical Euler buckling problem starting from homogeneous beam with either simplified linearized theory or the most general geometrically exact beam theory. We then present the numerical solution to this problem by using reduced model constructed by discrete approximation based upon the weak form of the instability problem featuring von Karman (virtual) strain combined with the finite element method. We explain how such numerical approach can easily be adapted to solving instability problems much more complex than classical Euler's beam and in particular for heterogeneous beam, where analytic solution is not readily available. We finally present the stochastic approach making use of the Duffing oscillator, as the corresponding reduced model for heterogeneous Euler's beam within the dynamics framework. We show that such an approach allows computing probability density function quantifying all possible solutions to this instability problem. We conclude that increased computational cost of the stochastic framework is more than compensated by its ability to take into account beam material heterogeneities described in terms of fast oscillating stochastic process, which is typical of time evolution of internal variables describing plasticity and damage.

• 대한기계학회논문집B
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• 제33권6호
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• pp.443-453
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• 2009

The Rayleigh-Taylor instability, the bubble rising in both partially and fully filled containers and the droplet splash are simulated by an in-house solution code(PowerCFD), which are typical benchmark problems among multiphase flows with material interface due to density difference. The present method(code) employs an unstructured cell-centered method based on a conservative pressure-based finite-volume method with interface capturing method(CICSAM) in a volume of fluid(VOF) scheme for phase interface capturing. The present results are compared with other numerical solutions found in the literature. It is found that the present method simulates efficiently and accurately complex free surface flows such as multiphase flows with material interface due to both density difference and instability.

• 한국연소학회:학술대회논문집
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• 한국연소학회 2005년도 제31회 KOSCO SYMPOSIUM 논문집
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• pp.294-301
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• 2005

The instabilities in rocket engines and gas turbine combustors due to the interaction between the fluid flow (acoustics) and the heat transfer (thermal energy) are called thermoacoustic or combustion instabilities. Almost all analysis assumes constant hot section temperature for Modern mathematical analysis of acoustic oscillations in Rijke type devices. However, it is impossible to predict whether a system is stable or not because the flame or heater response model can have a dramatic effect on predicted growth rates. In this study, A standard ${\kappa}-{\varepsilon}$ turbulent model and hybrid combustion model(eddy breakup model and chemical reaction) were used. After steady solution was gotten, unsteady calculation is simulated by perturbating on pressure boundary. As a result, we obtained the relationship of equivalence ratio and frequency by numerical simulation, and they are comparable to the experimental result. In addition, in spite of these results, there are limitations of using turbulent and combustion model in simulation method of thermoacoutic instability

• 대한기계학회논문집B
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• 제20권9호
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• pp.2965-2972
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• 1996

Transitional flow in an obstructed channel is investigated using numerical simulation. Two-dimensional thin obstacles are mounted symmetrically in the vertical direction and periodically in the streamwise direction. Flow separation occurs at the tip of the sharp obstacles. Depending on the Reynolds number, the flow undergoes Hopf bifurcation as the primary instability leading to a two-dimensional unsteady periodic solution. At higher Reynolds numbers, the unsteady solution exhibits a symmetry-breaking bifurcation which results in an unsteady asymmetric solution. The results are compared with experiments currently available, and show a good agreement.

• 한국연소학회:학술대회논문집
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• 한국연소학회 2005년도 제31회 KOSCO SYMPOSIUM 논문집
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• pp.281-286
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• 2005

To understand fundamental characteristics of combustion in a small scale device, the effects of the momentum and heat loss on the stability of laminar premixed flames in a narrow channel are investigated by two-dimensional high-fidelity numerical simulation. A general finding is that momentum loss promotes the Saffman-Taylor (S-T) instability which is additive to the Darrieus-Landau (D-L) instabilities, while the heat loss effects result in an enhancement of the diffusive-thermal (D-T) instability. These effects are also valid in nonlinear behavior of the premixed flame. The simulations of multiple cell interactions are also conducted with heat and momentum loss effects.

• 대한수학회논문집
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• 제15권1호
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• pp.155-172
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• 2000

Mode interactions at Unstable fluid interfaces induced by a shock wave (Richtmyer-Meshkov Instability) are studied both analytically and numerically. The analytical approach is based on a potential flow model with source singularities in incompressible fluids of infinite density ratio. The potential flow model shows that a single bubble has a decaying growth rates at late time and an asymptotic constant radius. Bubble interactions, bubbles of different radii propagates with different velocities and the leading bubbles grow in size at the expense of their neighboring bubbles, are predicted by the potential flow model. This phenomenon is validated by full numerical simulations of the Richtmyer-Meshkov instability in compressible fluids for initial multi-frequency perturbations on the unstable interface.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2002년도 학술대회지
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• pp.683-686
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• 2002

The hydrodynamic instability of the three-dimensional boundary-layer over a rotating disk has been numerically investigated for three cases flows using linear stability theory (i.e. Rossby number, Ro = -1, 0, and 1). Detailed numerical values of the disturbance wave number, wave frequency, azimuth angle, radius (Reynolds number, Re) and other characteristics have been calculated for $K{\acute{a}}rm{\acute{a}}n$, Ekman and $B{\"{o}}ewadt$ boundary-layer flows. Neutral curves for these flows are presented. Presented are the neutral stability results concerning the two instability modes (Type I and Type II) by using a two-point boundary value problem code COLUEW that was based upon the adaptive orthogonal collocation method using B-spline. The prediction from the present results on both instability modes among the three cases agrees with the previously known numerical and experimental data well.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2001년도 제16회 학술발표회 논문초록집
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• pp.17-20
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• 2001

본 연구에서는 KSR-III 액체 로켓엔진의 연소특성을 수치적인 방법으로 성능의 예측과 음향불안정성에 대해 해석하였으며 성능 예측에서는 여러 가지 시험조건에서 시험결과와 계산결과를 비교ㆍ검토하였다. 또한 음향불안정성은 KSR-III 액체 로켓에서 대체로 안정한 결과를 보여 주었으나 일부의 탈설계조건에서 압력섭동에 의해 불안정성이 야기될 수 있는 결과를 보였다. 이러한 결과들은 현재의 시험결과와 공학적인 오차범위 내에서 일치하는 경향을 보이고 있으므로 수치적 계산으로 성능 및 음향불안정을 효과적으로 예측할 수 있을 것으로 판단된다.

• 대한기계학회논문집B
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• 제30권6호
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• pp.578-586
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• 2006

Numerical simulations are carried out to investigate the thermal effects of the gravitational potential on the centrifugal instability of a Taylor-Couette flow, and to further study the detailed flow fields and flow bifurcations to spiral vortices. The effects of centrifugal potential on the centrifugal instability are also investigated in the current study. Spiral vortices have various types of mode depending on Grashof number and Reynolds number. The correlation of Richardson number with the spiral angle of the spiral vortices shows that the structure of the spiral vortices strongly depends on the Richardson number. The heat transfer rate of the inner cylinder increases with increasing Grashof number. It is also confirmed that the torque required to rotate the inner cylinder increases as Grashof number increases.

• 한국연소학회지
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• 제22권3호
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• pp.41-46
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• 2017

This study has numerically investigated the flame-acoustics interactions in the turbulent partially premixed flame field. In the present approach, in order to analyze the combustion instability, the present approach has employed the LES-based combustion model as well as the Helmholtz solver. Computations are made for the validation case of the partially premixed LIMOUSINE burner. In terms of the FFT data, numerical results are compared with experimental data. Moreover, Helmholtz equation in frequency domain is solved by combining CFD field data including the flight time from a nozzle to the flame zone. Based on numerical results, the detailed discussions are made for the essential features of the combustion instability encountered in the partially premixed burner.