• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.8 no.3
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• pp.437-450
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• 1996

A set of stability equations is formulated for natural convection flows adjacent to a vertical isothermal surface melting in cold pure water. It takes account of the nonparallelism of the base flows. The melting rate is regarded as a blowing velocity at the ice surface. The numerical solutions of the linear stability equations which constitute a two-point boundary value problem are accurately obtained for various values of the density extremum parameter $R=(T_m-T_{\infty})/(T_0-T_{\infty})$ in the range $0.3{\leq}R{\leq}0.6$, by using a computer code COLNEW. The blowing effects on the base flow becomes more significant as ambient temperature ($T_{\infty}$) increases to $T_{\infty}=10^{\circ}C$. The maximum decrease of heat transfer rate is about 6.4 percent. The stability results show that the melting at surface causes the critical Grashof number $G^*$ and the maximum frequency of disturbances to decrease. In comparision with the results for the conventional parallel flow model, the nonparallel flow model has a higher critical Grashof number but has lower amplification rates of disturbances than does the parallel flow model. The spatial amplification contours exhibit that the selective frequency $B_0$ of the nonparallel flow model is higher than that of the parallel flow model and that the effects of melting are rather small. The present study also indicates that the selective frequency $B_0$ can be easily predicted by the value of the frequency parameter $B^*$ at $G^*$, which comes from the neutral stability results of the nonparallel flow model.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.155-165
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• 2023

We consider circular Rayleigh problem of hydrodynamic stability which deals with linear stability of axial flows of an incompressible iniviscid homogeneous fluid to axisymmetric disturbances. For this problem, we obtained two parabolic instability regions which intersect with Batchelor and Gill semi-circle under some condition. This has been illustrated with examples. Also, we derived upper bound for the amplification factor.

• Korea-Australia Rheology Journal
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• v.14 no.2
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• pp.57-62
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• 2002

The sensitivity of the final filament to the ongoing sinusoidal disturbances has been Investigated in the viscoelastic spinning using frequency response method. Amplification ratios or gains of the spinline cross-sectional area at the take-up to any disturbances show resonant peaks along the frequency regime, where the frequencies at theme points directly correspond to the imaginary parts of the successive leading eigenvalues from the linear stability analysis. As shown in Jung et al. (1999) and Lee et al (2001), the sensitivity results on the effect of various process conditions such as spinline cooling and fluid viscoelasticity, obtained by dynamic transient simulation have been corroborated in this study. That is, increasing spinline cooling makes the system less sensitive to disturbances, thus stabilizes the spinning. Also, an increasing viscoelasticity for extension-thickening fluids decreases the sensitivity of the spinning. i.e., stabilizing the system, where, as it increases the sensitivity of the spinning of extension-thinning fluids. Furthermore, it has been found in the present study that the inertia force as one of secondary forces causes the system to be more stabile or less sensitive to process disturbances.

• Korea-Australia Rheology Journal
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• v.15 no.2
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• pp.91-96
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• 2003

The sensitivity of the product to the ongoing sinusoidal disturbances of the process has been investigated in the film casting of viscoelastic polymer fluids using frequency response analysis. As demonstrated for fiber spinning process (Jung et al., 2002; Devereux and Denn, 1994), this frequency response analysis is useful for examining the process sensitivity and the stability of extensional deformation processes including film casting. The results of the present study reveal that the amplification ratios or gains of the process/product variables such as the cross-sectional area at the take-up to disturbances exhibit resonant peaks along the frequency regime as expected for the systems having hyperbolic characteristics with spilt boundary conditions (Friedly, 1972). The effects on the sensitivity results of two important parameters of film casting, i.e., the fluid viscoelasticity and the aspect ratio of the casting equipment have been scrutinized. It turns out that depending on the extension thinning or thickening nature of the fluid, increasing viscoelasticity results in enlargement or reduction of the sensitivity, respectively. As regards the aspect ratio, it has been found that an optimum value exists making the system least sensitive. The present study also confirms that the frequency response method produces results that corroborate well those by other methods like linear stability Analysis and transient solutions response. (Iyengar and Co, 1996; Silagy et al., 1996; Lee and Hyun, 2001).

• International Journal of Automotive Technology
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• v.5 no.2
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• pp.89-94
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• 2004

In this paper, a safe control strategy is considered in the situation when a platoon of vehicles need to decelerate rapidly. When the vehicles ate spaced closely, it is known that the reference information should be transmitted to the whole platoon to minimize the undesirable effects of small leader disturbances. However, the vehicle control should also depend on the preceding vehicle position to maintain the desired distance. Tracking the preceding vehicle position can lead to amplification of the control input along the following vehicles, therefore the vehicles in the rearward generally exert larger maximum control input than the vehicles in the front. The theoretical bounds for the $i^{th}$ vehicle control input are calculated using a linear vehicle and controller model. In the simple illustrative example, the designed controller maintains string stability, and the control inputs of the following vehicles stay within bounds.

• 한국전산유체공학회:학술대회논문집
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• 2006.10a
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• pp.110-119
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• 2006

An accurate and cost efficient method PSE is used for the stability analysis of 2D or 3D compressible boundary layers. A highly accurate finite difference PSE code has been developed at a general curvilinear coordinate system using an implicit marching procedure to deal with a broad range of transition predictions problems. Evolution of disturbances in compressible flat plate boundary layers are studied for free-stream Mach numbers ranging from 0 to 1.5. The effect of mean-flow nonparallelism is found to be weak on two dimensional waves and strong on three dimensional waves. The maximum amplification rate increases monotonically with Mach number. The present PSE solutions are compared with previous numerical investigations and experimental results and are found to be in good agreement.

• International Journal of Air-Conditioning and Refrigeration
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• v.10 no.1
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• pp.50-63
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• 2002

The Karman boundary-layer has been numerically investigated for the disturbance wave number, wave velocity, azimuth angle and radius (Reynolds number, Re). The disturbed flow over rotating disk can lead to transition at a much lower Re than that of the well-known Type I instability. This early transition is due to the excitation of the Type II. Presented are the neutral stability results concerning these instabilities by solving newly formulated stability equations with consideration of whole convective terms. When the present numerical results are compared with the previously known results, the value of critical Re corresponding to Type I is moved from ${Re}_{c.1}$=285.3 to 270.2 and the value corresponding to Type II from ${Re}_{c.2}$=69.4 to 36.9, respectively. Also, the corresponding wave number is moved fro)m $k_1$=0.378 to 0.386 for Type I; from $k_2$=0.279 to 0.385 for Type II. For Type II, the upped limit of wave number and azimuth angle is $k_u$=0.5872, $\varepsilon_u$=$-17.5^{\circ}$, while its lower limit is near $k_u$=0, $\varepsilon_u$=$-28.4^{\circ}$. This implies that the disturbances will be relatively fast amplified at small Re and within narrow bands of wave number compared with the previous results.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.12 no.8
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• pp.771-781
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• 2000

The Karman boundary-layer, has been numerically investigated for the disturbance wave number, wave velocity, azimuth angle and radius (Reynolds number, Re). The disturbed flow over rotating disk can lead to transition at a much lower Re than that of the well-known Type 1 mode of instability. This early transition is due to the excitation of the Type II mode. Presented are the neutral stability results concerning these modes by solving new formulated vorticity equations with consideration of whole convective terms. When the present numerical results are compared with the previously known results, the value of critical Re corresponding to Type I is moved from Rec,! =285.3 to 270.2 and the value corresponding to Type II is from $Re_{c,2}$=69.4 to 36.9, respectively. Also, the corresponding wave number is moved from $k_1$ =0.378 to $k_1$ =0.389 for Type I; from $k_2$ =0.279 to $k_2$=0.385 for Type II. For Type II, the upper limit of wave number and azimuth angle is $k_U$=0.5872,$varepsilon_U=-18^{\circ}$ , while its lower limit is$k_L$ =0.05, $varepsilon_L=-27^{\circ}$ This implies that the disturbances will be relatively fast amplified at small Re and within narrow bands of wave number compared with the previous results.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.9
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• pp.817-824
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• 2012

Transmission of unwanted vibration to sensitive systems can cause various problems including performance degradation and system malfunction. The most common approach to limit the transmission of harmful vibration disturbances to the sensitive system is adapting passive vibration isolator. The classical passive vibration isolator comprising a viscous damper and spring element in parallel, however, exhibits conflicting performance characteristics in that low amplification at the resonance, which is desirable, can only be achieved at the sacrifice of vibration isolation performance in high frequency region, which is undesirable. In this paper, vibration isolation characteristics of various passive isolator schemes in literature to circumvent this conflict are introduced and compared.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2012.04a
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• pp.232-237
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• 2012

Transmission of unwanted vibration to sensitive systems can cause various problems including performance degradation and system malfunction. The most common approach to limit the transmission of harmful vibration disturbances to the sensitive system is adapting passive vibration isolator. The classical passive vibration isolator comprising a viscous damper and spring element in parallel, however, exhibits conflicting performance characteristics in that low amplification at the resonance, which is desirable, can only be achieved at the sacrifice of vibration isolation performance in high frequency region, which is undesirable. In this paper, vibration isolation characteristics of various passive isolator schemes in literature to circumvent this conflict are introduced and compared.