• Title/Summary/Keyword: Runge-Kutta method

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농업수리구조물의 적정설계홍수량 유도를 위한 유출수문곡선모형의 개발(I) (Development of Runoff Hydrograph Model for the Derivation of Optimal Design Flood of Agricultural Hydraulic Structures(1))

  • 이순혁;박명근;맹승진
    • 한국농공학회지
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    • 제37권3_4호
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    • pp.34-47
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    • 1995
  • It is experienced fact as a regular annual event that the structure to he designed on unreasonable flood for the agricultural structures including reservoirs have been brought not only loss of lives, but also enormous property damage. For the solution of this problem at issue, this study was conducted to develop an optimal runoff hydrograph model by comparison of the peak flows and time to peak between observed and simulated flows derived by linear time-invariant and linear time-variant models under the condition of having a short duration of heavy rainfall with uniform rainfall intensity at nine small watersheds which are within the range of 55.9 to 140.7 square kilometers in area in Han, Geum, Nagdong and Yeongsan Rivers. The results obtained through this study can be summarized as follows. 1. Storage constants and Gamma function arguments were calculated within the range of 1.2 to 6.42 and of 1.28 to 8.05 respectively by the moment method as the parameters for the analysis of runoff hydrograph based on linear time-invariant model. 2. Parameters for both linear time-invariant and linear time-variant models were calibrated with nine gaged watershed data, using a trial and error method. The resulting parameters including Gamma function argument, N and storage constant, K for linear time-invariant model were related statistically to watershed characteristic variables such as area, slope, length of main stream and the centroid length of the basin. 3. Average relative errors of the simulated peak discharge of calibrated runoff hydrographs by using linear time-variant and linear time-invariant models were shown to be 0.75 and 5.42 percent respectively to the peak of observed runoff hydrographs. Correlation coefficients for the statistical analysis in the same condition were shown to be 0.999 and 0.978 with a high significance respectively. Therefore, it can be concluded that the accuracy of a linear time-variant model is approaching more closely to the observed runoff hydrograph than that of a linear time-invariant model in the applied watersheds. 4. Average relative errors of the time to peak of calibrated runoff hydrographs by using linear time-variant and linear time-invariant models were shown to be 16.44 and 19.89 percent respectively to the time to peak of observed runoff hydrographs. Correlation coefficients in the same condition were also shown to be 0.999 and 0.886 with a high significance respectively. 5. It can be seen that the shape of simulated hydrograph based on a linear time- variant model is getting closer to the observed runoff hydrograph than that of a linear time-invariant model in the applied watersheds. 6. Two different models were verified with different rainfall-runoff events from data for the calibration by relative error and correlation analysis. Consequently, it can be generally concluded that verification results for the peak discharge and time to peak of simulated runoff hydrographs were in good agreement with those of calibrated runoff hydrographs.

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블레이드 손상에 따른 이축식 터보팬 엔진의 동적 안정성 해석 (Rotordynamic Analysis of a Dual-Spool Turbofan Engine with Focus on Blade Defect Events)

  • 김시태;정기현;이준호;박기현;양광진
    • Tribology and Lubricants
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    • 제36권2호
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    • pp.105-115
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    • 2020
  • This paper presents a numerical study on the rotordynamic analysis of a dual-spool turbofan engine in the context of blade defect events. The blades of an axial-type aeroengine are typically well aligned during the compressor and turbine stages. However, they are sometimes exposed to damage, partially or entirely, for several operational reasons, such as cracks due to foreign objects, burns from the combustion gas, and corrosion due to oxygen in the air. Herein, we designed a dual-spool rotor using the commercial 3D modeling software CATIA to simulate blade defects in the turbofan engine. We utilized the rotordynamic parameters to create two finite element Euler-Bernoulli beam models connected by means of an inter-rotor bearing. We then applied the unbalanced forces induced by the mass eccentricities of the blades to the following selected scenarios: 1) fully balanced, 2) crack in the low-pressure compressor (LPC) and high pressure compressor (HPC), 3) burn on the high-pressure turbine (HPT) and low pressure compressor, 4) corrosion of the LPC, and 5) corrosion of the HPC. Additionally, we obtained the transient and steady-state responses of the overall rotor nodes using the Runge-Kutta numerical integration method, and employed model reduction techniques such as component mode synthesis to enhance the computational efficiency of the process. The simulation results indicate that the high-vibration status of the rotor commences beyond 10,000 rpm, which is identified as the first critical speed of the lower speed rotor. Moreover, we monitored the unbalanced stages near the inter-rotor bearing, which prominently influences the overall rotordynamic status, and the corrosion of the HPC to prevent further instability. The high-speed range operation (>13,000 rpm) coupled with HPC/HPT blade defects possibly presents a rotor-case contact problem that can lead to catastrophic failure.

농업수리구조물의 적정설계홍수량 유도를 위한 유출수문곡선 모형의 개발(II) (Development of Runoff Hydrograph Model for the Derivation of Optimal Design Flood of Agricultural Hydraulic Structures(II))

  • 이순혁;박명근;맹승진
    • 한국농공학회지
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    • 제38권3호
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    • pp.112-126
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    • 1996
  • This study was conducted to develop an optimal runoff bydrograph model by comparison of the peak discharge and time to peak between observed and simulated flows derived by four different models, that is, linear time-invariant, linear time-variant, nonlinear time-invariant and nonlinear time-variant models under the conditions of heavy rainfalls with regionally uniform rainfall intensity in short durations at nine small watersheds. The results obtained through this study can be summarized as follows. 1. Parameters for four models including linear time-invariant, linear time-variant, nonlinear time-invariant and nonlinear time-variant models were calibrated using a trial and error method with rainfall and runoff data for the applied watersheds. Regression analysis among parameters, rainfall and watershed characteristics were established for both linear time-invariant and nonlinear time-invariant models. 2. Correlation coefficients of the simulated peak discharge of calibrated runoff hydrographs by using four models were shown to be a high significant to the peak of observed runoff graphs. Especially, it can be concluded that the simulated peak discharge of a linear time-variant model is approaching more closely to the observed runoff hydrograph in comparison with those of three models in the applied watersheds. 3. Correlation coefficients of the simulated time to peak of calibrated runoff hydrographs by using a linear time-variant model were shown to be a high significant to the time to peak of observed runoff hydrographs than those of the other models. 4. The peak discharge and time to peak of simulated runoff hydrogaphs by using linear time-variant model are verified to be approached more closely to those of observed runoff hydrographs than those of three models in the applied watersheds. 5. It can be generally concluded that the shape of simulated hydrograph based on a linear time-variant model is getting closer to the observed runoff hydrograph than those of three models in the applied watersheds. 6. Simulated hydrographs using the nonlinear time-variant model which is based on more closely to the theoritical background of the natural runoff process are not closer to the observed runoff hydrographs in comparison with those of three models in the applied watersheds. Consequently, it is to be desired that futher study for the nonlinear time-variant model should be continued with verification using rainfall-runoff data of the other watersheds in addition to the review of analyical techniques.

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旋網의 沈降 抵抗 解析 - 2. 網地材料와 沈子量 다른 模型網의 경우 - (An Analysis on the Sinking Resistance of Purse Seine - 2. In the Case of the Model Purse Seine with Different Netting Material and Sinkers -)

  • 김석종
    • 수산해양기술연구
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    • 제40권1호
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    • pp.29-36
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    • 2004
  • 선망의 침강 저항 특성을 해명하기 위한 기초 연구로서, 망지의 재료가 다르고 침자량이 동일한 선망 모형의 침강특성을 해석하였다. 실험에 사용한 선망은, 그물실의 직경 및 발의 길이가 같은 폴리프로피렌系 (밀도 0.91g/cm$cm^3$), 폴리아미드系 (밀도 1.14g/cm$cm^3$) 및 폴리에스터系 (밀도 1.38g/cm$cm^3$)의 매듭 없는 망지를 사용하여, 뜸줄의 길이 420cm, 그물의 폭 86cm가 되도록 제작하였다. 이 그물들의 발줄에 침자를 25g, 45g, 60g 의 3 단계로 바꾸어 9종류의 모형그물을 만들고, 각각 PP-25, PA-25, PES-25, PP-45, PA-45, PES-45, PP-60, PA-60 및 PES-60그물이라고 이름을 붙였다. 회류수조의 수로 위에 투망장치를 설치해서 정지 상태의 수중에 투망하고, 관측부 전면에 설치한 비디오 카메라를 이용하여 촬영 녹화하였다. 그리고, 그물에 표시한 측정점의 좌표를 화상해석장치로 읽고 실험치를 구하였다. 여기서, 선망의 수직방향의 침강운동을 나타낸 이론식을 이용하여 수치해석을 행하였는데, 그 결과는 다음과 같다. 1. 침자량이 60g일 때, 아랫자락의 평균 침강속도는 PES그물 12.2 cm/sec로 가장 빠르고, PA그물 11.4 cm/sec, PP 그물 10.7cm/sec 순으로 늦게 나타났다. 2. 망지의 저항계수 $K_D$는, 계산결과 $K_D=0.09(\frac{\rho}{\rho_w})^4$의 관계식으로 나타낼 수 있었다. 3. 그물다발의 저항계수 $C_R$은, 계산결과 $C_R=0.91(\frac{\rho}{\rho_w})$의 관계식으로 나타낼 수 있었다. 4. 선망 투망후 경과시간에 따른 그물 아랫자락의 도달수심에 대한 실험치와 계산치의 관계는 상관성이 매우 높아, 침자량이 25g일 때 meas.=1.04 cal., 45g일 때 meas.=0.99cal.였으며, 60g일 때 meas.=0.98cal.의 관계를 나타냈다.