• 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 Astronomical Society
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• v.17 no.1
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• pp.1-14
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• 1984

Analyses of an integrated form $N(\tau)={\int}_{\tau}^{\infty}n(\tau)d{\tau}$ of the distribution of cluster ages, rather than its differential form $n(\tau)$, demonstrate that the observed distribution has clusters older than about 500 million years in a significant excess over theoretical model distributions. Considerations on cluster disruption processes show that a single disruption time-scale, frequently employed by current theoretical models, is no longer an adequate parameter for describing survival probability of clusters over wide age range, because different initial conditions of these clusters produce corresponding spreads in their lifetimes. To take into account for the spread in initial conditions, we have introduced an age-dependent disruption time, and deduced its age-dependence from the present-day age distribution of clusters. Results show a distinct two-stage variation: The newly introduced disruption time stays constant at about 50 million years for clusters younger than about 100 million years, while for clusters older than that it increases monotonically with the cluster age. This leads us to conclude that clusters experience different types of disrupting causes as they get old.

• Journal of the Korean Statistical Society
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• v.7 no.1
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• pp.17-26
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• 1978

For testing $\beta_i=\beta, i=1,...,k$, in the regression model $Y_{ij} = \alpha_i + \beta_ix_{ij} + e_{ij}, j=1,...,n_i$, a simple and robust test based on Kendall's tau is proposed. Its asymptotic distribution is proved to be chi-square under the null hypthesis and noncentral chi-square under an appropriate sequence of alternatives. For the optimal designs, the asymptotic relative efficiency of the proposed procedure with respect to the least squares procedure is the same as that of the Wilcoxon test with respect to the t-test.

• 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.

• Structural Engineering and Mechanics
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• v.2 no.1
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• pp.35-48
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• 1994

A plasticity-based concrete model is proposed. The failure surface is elliptic in the ${\sigma}-{\tau}$ stress space. Independent hardening as well as softening is assumed in tension, compression, and shear. The nonlinear inelastic action initiates from the origin in the ${\sigma}-{\varepsilon}$(${\tau}-{\gamma}$) diagram. Several parameters are incorporated to control hardening/softening regions. The model is incorporated into a nonlinear finite element program along with other classical models. Several examples are solved and the results are compared with experimental data and other failure criteria. "Reasonable results" and stable solutions are obtained for different types of reinforced concrete oriented structures.

• Korean Journal of Agricultural Science
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• v.13 no.2
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• pp.255-264
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• 1986

The objectives of this study were to examine the viscoelastic behaviour of stem samples of rice in force-relaxation and rheological model to represent its relaxation behaviour, and to study the effects of rate of deformation and initial deformation on the relaxation time. The results were as follows; 1. In the process of loading and unloading, there is any plastic deformation so called elasto-plastic hysterisis. 2. Loading and unloading of stem of rice for several cycles has also shown the reduction of plastic or residual deformation and work hardening. 3. The relaxation behaviour of stem of rice in compression may be described by a generalized Maxwell model consisting of three Maxwell units in parallel. The rheological equation of such a model is given as $$F(t)=C_1e^{{-t/{\tau}}_1}+C_2e^{{-t/{\tau}}_2}+C_3e^{{-t/{\tau}}_3}$$ 4. Force relaxation always increased with increasing rates of deformation and initial deformation.

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.545-556
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• 2005

Hjort(1990) obtained the nonparametric Bayes estimator $\^{F}_{c,a}$ of $F_0$ with respect to beta processes in the random censorship model. Let $X_1,{\cdots},X_n$ be i.i.d. $F_0$ and let $C_1,{\cdot},\;C_n$ be i.i.d. G. Assume that $F_0$ and G are continuous. This paper shows that {$\^{F}_{c,a}$(u){\|}0 < u < T} converges weakly to a Gaussian process whenever T < $\infty$ and $\~{F}_0({\tau})\;<\;1$.

• 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.

• Journal of Astronomy and Space Sciences
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• v.26 no.4
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• pp.425-438
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• 2009

We reevaluate the Burton equation (Burton et al. 1975) of predicting Dst index using high quality hourly solar wind data supplied by the ACE satellite for the period from 1998 to 2006. Sixty magnetic storms with monotonously decreasing main phase are selected. In order to determine the injection term (Q) and the decay time ($\tau$) of the equation, we examine the relationships between $Dst^*$ and $VS_s$, ${\Delta}Dst^*$ and $VS_s$, and ${\Delta}Dst^*$ and $Dst^*$ during the magnetic storms. For this analysis, we take into account one hour of the propagation time from the ACE satellite to the magnetopause, and a half hour of the response time of the magnetosphere/ring current to he solar wind forcing. The injection term is found to be $Q(nT/h)\;=\;-3.56VS_s$ for $VS_s$ > 0.5mV/m and Q(nT=h) = 0 for $VB_s\;{\leq}\;0.5mV/m$. The $\tau$ (hour) is estimated as $0.060Dst^*\;+\;16.65$ for $Dst^*$ > -175nT and 6.15 hours for $Dst^*\;{\leq}\;-175nT$. Based on these empirical relationships, we predict the 60 magnetic storms and find that the correlation coefficient between the observed and predicted $Dst^*$ is 0.88. To evaluate the performance of our prediction scheme, the 60 magnetic storms are predicted again using the models by Burton et al. (1975) and O'Brien & McPherron (2000a). The correlation coefficients thus obtained are 0.85, the same value for both of the two models. In this respect, our model is slightly improved over the other two models as far as the correlation coefficients is concerned. Particularly our model does a better job than the other two models in predicting intense magnetic storms ($Dst^*\;{< \atop \sim}\;-200nT$).