• Journal of the Korean Society of Propulsion Engineers
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• v.20 no.3
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• pp.78-86
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• 2016

In this paper we propose a new frame transfer function model describing the variations of a heat release rate in response to an external flow oscillation in gas turbine systems. A critical difference of our model compared to the so-called $n-{\tau}$ model which has been widely used for a prediction of combustion instability (CI), is that our model is able to describe a nonlinear relation between phase and frequency. In contrast, the phase part of the $n-{\tau}$ model is a pure time delay and thus the phase should be a linear function of frequency, which is inconsistent with many experimental results of real combustion systems. For an illustration, our new model is applied to experimental data and the effect of phase nonlinearity is investigated in the context of combustion instability.

• Journal of the Korean Society of Propulsion Engineers
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• v.22 no.3
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• pp.46-52
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• 2018

A simple Crocco's $n-{\tau}$ time delay model and linear analysis of fluid flow coupled with acoustics are combined to investigate the high frequency combustion instability in the combustion chamber of LOX/hydrocarbon engines. The partial differential equation of the velocity potential is separated into ordinary differential equations, and eigenvalues that correspond to tangential resonance modes in the cylindrical chamber are determined. A general solution is obtained by solving the differential equation in the axial direction, and boundary conditions at the injector face and nozzle entrance are applied in order to calculate the chamber admittance. Frequency analysis of the transfer function is used to evaluate the stability of system. Stability margin is determined from the system gain and phase angle for the desired frequency range of 1T mode. The chamber model with variable baffle length and configurations are also considered in order to enhance the 1T mode stability of the combustion chamber.

• Journal of the Korean Society of Propulsion Engineers
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• v.1 no.2
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• pp.74-83
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• 1997

The definition of burning admittance and conventional n-$\tau$ stability rating technique are combined to investigate the high frequency combustion instabilities inside the cylindrical combustion chamber. Perturbed flow variables are written as the sum of fluctuating and time-averaged mean quantities on the assumption that the terms of the order higher than unity are sufficiently small, hence linearized governing equations could be formulated. Chamber admittances up and downstream of the flame front calculated with appropriate boundary conditions result in the burning admittance and corresponding n-$\tau$ neutral stability curve. Configurational and operational design factors are tested to detect the unstable wave-induced LOX-RP1 combustion instabilities. Operational design factors, e.g. pressure or O/F ratio, appear less influential to drive high frequency instability while the location of the flame front and configurational factors enhance or deteriorate the stabilities strongly. Conclusively, LOX-RP1 combustion inside the cylindrical combustion chamber is apt to be unstable against long residence time and shortened chamber length.

• Nuclear Engineering and Technology
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• v.5 no.1
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• pp.30-37
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• 1973

The Nishitani's equations for impedance of anodic oxide films have been derived based on a p-i-n model under the assumption of $\omega$$\varepsilon$$\rho$$_{ο}$<<4$\pi$<<$\omega$$\varepsilon$$\rho$$_{\omega}$, where $\omega$ is angular frequency, $\varepsilon$ is dielectric constant, and $\rho$$_{ο}$ and $\rho$$_{\omega}$ are the resistivity of the interface region and the intrisic region of the anodic oxide film, respectively. Since it is not possible to evaluate all parameters in the equations, however, any clear physical picture cannot be obtained from the equations. Therefore, the equations are modified under the assumption of $\omega$$\tau$$_{\omega}$>>1 and In(1+$\omega$$^2$$\tau$$_{ο}$$^2$)<<1, where $\tau$$_{\omega}$=$\varepsilon$$\rho$$_{\omega}$(4$\pi$) and $\tau$$_{ο}$=$\varepsilon$$\rho$$_{ο}$/(4$\pi$). The modified equations are then used to explain the change in the frequency characteristics of anodic oxide films when they are heated. The change in impedance of anodic oxide films when they are heated is attributed mainly to the increase in the diffusion layer and to the decrease in the resistivity of anodic oxide films.s.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 1999.11a
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• pp.177-183
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• 1999

In this paper, we analyze transmission characteristics of ultrashort laser pulses using the property of Raised-cosine pulse which are systematically obtained following Class-2 PRS model. The high-order pulses are easily derived front a modified PRS system model as Class-1 PRS model. This may be based on the fact that the spectra and bandwidths of the high-order pulses are beautifully related to their orders. And we make clear they are very useful to cover wider area and more accurate transmission characteristics of ultrashort pulses than Gaussian or Sech pulse approximations used conventionally. First modifying the generalized PRS system model, we propose a new model for deriving any type of high-order pulse. And we offer a novel analysis method of ultrashort pulse transmission which has any shape and FWHM, using the proposed model. In addition, by fixing the pulse range $\tau$=1(ps) and varying the order of the pulse from n=1 to n=100, we obtain spectra of ultrashort pulses with 1(ps)-100(fs) FWHM's, and width of FWHM in the Class-2 PRS model 50~100(fs) smaller than Class-1 PRS model. As a one-step further, we derive PSD's of their pulse trains when they are applied to Unipolar signaling scheme. These PSD's are derided in the range of possible pulse intervals. All of these results are not only coincided with some conventional experimental works but also will to applied to any pioneering ultrashort pulse in the future.

• Journal of the Korean Society of Propulsion Engineers
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• v.15 no.6
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• pp.98-106
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• 2011

This paper reviews the state-of-the-art thermoacoustic(TA) modeling techniques and research trend to predict major parameters determining combustion instabilities in lean premixed gas turbine combustors. Linear TA modeling results give us an information on eigenfrequencies and initial growth rate of the instabilities. For the prediction, linear relation equation between acoustic waves and heat release oscillations should be derived in the determined system. Key information for this analysis is to determine the heat release fluctuations in the combustor, which is typically obtained by using n-${\tau}$ function from flame transfer function measurements and/or predictions. Great advancement in the linear TA modeling has been made over a couple of decades, and some successful prediction results have been reported in actual gas turbine combustors. However nonlinear TA model developments which are required to analyze nonlinear system behaviors such as limit cycle saturation and transition phenomena are still limited in a very simple system. In order to fully understand combustion instabilities in a complicated real system, nonlinear flame dynamics and acoustic wave interaction with nonlinear system boundary conditions should be explained from the nonlinear TA model developments.

• Journal of the Korean Society for Railway
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• v.15 no.6
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• pp.623-630
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• 2012

Formation used as trackbed foundation for providing vertical bearing capacity onto rail foundation are composed of crushed stones usually with certain type of grain size distribution. Permanent deformation in trackbed foundation can be generated by increasing number of load repetition due to train traffic increases, causing track irregularity. In this study, a specially prepared trackbed foundation materials (M-40) used in Korea has been tested using a large repetitive triaxial compression apparatus in order to understand resilient and permanent deformation characteristics of the material. From these test results, resilient and permanent deformation characteristic are analyzed so that a permanent deformation model is developed which can consider number of load repetition N, confining stress (${\sigma}_3$), shear stress ratio(${\tau}/{\tau}_f$) and stiffness of the material.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 1999.05a
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• pp.237-242
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• 1999

In this paper, we analyze transmission characteristics of ultrashort laser pulses using the property of high-order pulses which are systematically obtained following their orders. The high-order pulses are easily derived from a modified PRS system model. But we make clear they are very useful to cover wider area and more accurate transmission characteristics of ultrashort pulses than Gaussian or Sech pulse approximations used conventionally. This may be based on the fact that the spectra and bandwidths of the high-order pulses are beautifully related to their orders. first modifying the generalized PRS system model, we propose a new model for deriving any type of high-order pulse. And we offer a novel analysis method of ultrashort pulse transmission which has any shape and FWHM, using the proposed model. In addition, by fixing the pulse range $\tau$=1(ps) and varying the order of the pulse from n:1 to n=100, we obtain spectra of ultrashort pulses with 1(ps)-150(fs) FWHM's, which are widely used in fiber communications. As a one-step further, we derive PSD's of their pulse trains when they are applied to Unipolar signaling scheme. These PSD's are decided in the range of possible pulse intervals. All of these results are not only coincided with some conventional experimental works but also will be applied to any pioneering ultrashort pulse in the future.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• v.y2005m4
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• pp.281-287
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• 2005

Nonlinear behaviors such as steep-fronted wave motions and a finite amplitude limit cycle often accompanying combustion instabilities have been numerically investigated using a characteristic-based approximate Riemann solver and the well-known ${\eta}-{\tau}$ model. A resonant pipe initially subjected to a harmonic pressure disturbance described the natural steepening process that leads to a shocked N-wave. For a linearly unstable regime, pressure oscillations reach a limit cycle which is independent of the characteristics of the initial disturbances and depends only on combustion parameters and operating conditions. For the 1.5 MW gas generator under development in KARI, the numerical results show good agreement with experimental data from hot-firing tests.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.7
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• pp.1770-1779
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• 1995

A combined convective heat transfer study for non-Newtonian fluids was experimentally performed in uniformly heated horizontal tubes with laminar flow in the thermal entry region. Velocity profiles were fully developed at the entrance of the heated sections in the tubes. Aqueous solutions of sodium carboxymethylcellulose(CMC ) were used; their behavior showed a reasonably good fit into the power-law model, .tau.=K.gamma.$^{n}$ . The test sections were made of copper with inside diameters of 3.23 cm and 5.042 cm and lengths of approximately 300 cm. Most experimental runs displayed noticeable secondary flows caused by buoyancy ; when present, secondary flows caused significant increase in the rate of heat transfer over the purely forced-convection case. A correlation, which relates the rate of heat transfer for flows with temperature-dependent properties, free convection effects, and non-newtonian effects, was suggested.