• Title/Summary/Keyword: Runge-kutta method

Search Result 503, Processing Time 0.022 seconds

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

  • Kim, Sitae;Jung, Kihyun;Lee, Junho;Park, Kihyun;Yang, Kwangjin
    • Tribology and Lubricants
    • /
    • v.36 no.2
    • /
    • pp.105-115
    • /
    • 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.

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

  • 이순혁;박명근;맹승진
    • Magazine of the Korean Society of Agricultural Engineers
    • /
    • v.38 no.3
    • /
    • pp.112-126
    • /
    • 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.

  • PDF

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

  • Kim, Suk-Jong
    • Journal of the Korean Society of Fisheries and Ocean Technology
    • /
    • v.40 no.1
    • /
    • pp.29-36
    • /
    • 2004
  • This study deals with an analysis on the sinking resistance for the model purse seine, in the case of different netting material and sinkers. The experiment was carried out using rune simplified model seines of knotless nettings. Dimension of model seines 420cm for corkline and 85cm for seine depth, three groups of models rigged 25, 45 and 60g with the same weighted sinkers in water were used. These were named PP-25, PA-25, PES-25, PP-45, PA-45, PES-45, PP-60, PA-60 and PES-60 seine. The densitie($\rho$) of netting materials were 0.91g/cm$cm^3$, 1.14g/cm$cm^3$ and 1.38g/cm$m^3$. Experiments carried out in the observation channel in a flume tank under still water conditions. Sinking motion was recorded by the one set of TV-camera for VTR, and reading coordinate carried out by the video digitization system. Differential equations were derived from the conservation of momenta of the model purse seines and used to determine the sinking speeds of the depths of leadline and the other portions of the seines. An analysis carried out by simultaneous differential equations for numerical method by sub-routine Runge-Kutta-Gill The results obtained were as follows : 1. Average sinking speed of leadline for the model seines rigged 60g with the same weighted sinkers in water was fastest for 12.2cm/sec of PES seine, followed by 11.4cm/sec of PA and 10.7cm/sec of PP seines. 2. The coefficient of resistance for netting of seine was estimated to be $K_D=0.09(\frac{\rho}{\rho_w})^4$ 3. The coefficient of resistance for netting bundle of seine was estimated to be $C_R=0.91(\frac{\rho}{\rho_w})$ 4. In all seines, the calculated depths of leadline closely agreed with the measured ones, each 25g, 45g, 60g of weighted sinkers were put into formulas meas.=1.04cal., meas.=0.99cal. and meas.=0.98 cal.