• Title/Summary/Keyword: simultaneous equations

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Extension of the LQR to Accomodate Actuator Saturation Bounds for Flexible Space Structures (제한된 제어입력을 갖는 유연우주구조물에 대한 확장된 LQR)

  • Lee, Sang-Chul
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.30 no.8
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    • pp.71-77
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    • 2002
  • We consider the simultaneous slewing and vibration suppression control problem of an idealized structural model which has a rigid hub with two cantilevered flexible appendages and finite tip masses. The finite clement method(FEM) is used to obtain linear finite dimensional equations of motion for the model. In the linear quadratic regulator(LQR) problem, a simple method is introduced to provide a physically meaningful performance index for space structure models. This method gives us a mathematically minor but physically important modification of the usual energy type performance index. A numerical procedure to solve a time-variant LQR problem with inequality control constraints is presented using the method of particular solutions.

Performance Enhancement of a Low Speed Axial Compressor Utilizing Simultaneous Tip Injection and Casing Treatment of Groove Type

  • Taghavi-Zenouz, Reza;Behbahani, Mohammad Hosein Ababaf
    • International Journal of Aeronautical and Space Sciences
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    • v.18 no.1
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    • pp.91-98
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    • 2017
  • Performance of a low speed axial compressor is enhanced through a proper configuration of blade row tip injection and casing treatment of groove type. Air injectors were mounted evenly spaced upstream of the blade row within the casing groove and were all aligned parallel to the compressor axis. The groove, which covers all the blade tip chord length, extends all-round the casing circumference. Method of investigation is based on solution of the unsteady form of the Navier-Stokes equations utilizing $k-{\omega}$ SST turbulence model. Extensive parametric studies have been carried out to explore effects of injectors' flow momentums and yaw angles on compressor performance, while being run at different throttle valve setting. Emphasis has been focused on situations near to stall condition. Unsteady numerical analyses for untreated casing and no-injection case for near stall condition provided to discover two well-known criteria for spike stall inception, i.e., blade leading edge spillage and trailing edge back-flow. Final results showed that with only 6 injectors mounted axially in the casing groove and at yaw angle of 15 degrees opposite the direction of the blade row rotation, with a total mass flow rate of only 0.5% of the compressor main flow, surprisingly, the stall margin improves by 15.5%.

Beam finite element model of a vibrate wind blade in large elastic deformation

  • Hamdi, Hedi;Farah, Khaled
    • Wind and Structures
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    • v.26 no.1
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    • pp.25-34
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    • 2018
  • This paper presents a beam finite element model of a vibrate wind blade in large elastic deformation subjected to the aerodynamic, centrifugal, gyroscopic and gravity loads. The gyroscopic loads applied to the blade are induced by her simultaneous vibration and rotation. The proposed beam finite element model is based on a simplex interpolation method and it is mainly intended to the numerical analysis of wind blades vibration in large elastic deformation. For this purpose, the theory of the sheared beams and the finite element method are combined to develop the algebraic equations system governing the three-dimensional motion of blade vibration. The applicability of the theoretical approach is elucidated through an original case study. Also, the static deformation of the used wind blade is assessed by appropriate software using a solid finite element model in order to show the effectiveness of the obtained results. To simulate the nonlinear dynamic response of wind blade, the predictor-corrector Newmark scheme is applied and the stability of numerical process is approved during a large time of blade functioning. Finally, the influence of the modified geometrical stiffness on the amplitudes and frequencies of the wind blade vibration induced by the sinusoidal excitation of gravity is analyzed.

Computer Simulation of Automobile Air-Conditioners (자동차 에어컨 컴퓨터 시뮬레이션)

  • Kim, H.J.;Jung, D.S.;Kim, C.B.;Kim, K.H.;Kang, J.K.
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.8 no.2
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    • pp.240-253
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    • 1996
  • The refrigeration cycle of automobile air-conditioners is simulated in an effort to provide a computational tool for optimum thermodynamic design. In the simulation, thermodynamic and heat transfer analysis was performed for the four major components : evaporator, condenser, compressor, and expansion valve. Effectiveness-NTU method was used for modeling both evaporator and condenser. The evaporator was divied into many subgrids and simultaneous cooling and dehumidifying analysis was performed for each grid to predict the performance accurately. Blance equations were used to model the compressor instead of using the compressor map. The performance of each component was checked against the measured data with CFC-12. Then, all the components were combined to yield the total system performance. Predicted cycle points were compared against the measured data with HFC-134a and the deviation was found to be less than 5% for all data. Finally, the system model was used to predict the performance of CFC-12 and HFC-134a for comparison. The results were very reasonable as compared to the trend deduced from the measured data.

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Inelastic vector finite element analysis of RC shells

  • Min, Chang-Shik;Gupta, Ajaya Kumar
    • Structural Engineering and Mechanics
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    • v.4 no.2
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    • pp.139-148
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    • 1996
  • Vector algorithms and the relative importance of the four basic modules (computation of element stiffness matrices, assembly of the global stiffness matrix, solution of the system of linear simultaneous equations, and calculation of stresses and strains) of a finite element computer program for inelastic analysis of reinforced concrete shells are presented. Performance of the vector program is compared with a scalar program. For a cooling tower problem, the speedup factor from the scalar to the vector program is 34 for the element stiffness matrices calculation, 25.3 for the assembly of global stiffness matrix, 27.5 for the equation solver, and 37.8 for stresses, strains and nodal forces computations on a Gray Y-MP. The overall speedup factor is 30.9. When the equation solver alone is vectorized, which is computationally the most intensive part of a finite element program, a speedup factor of only 1.9 is achieved. When the rest of the program is also vectorized, a large additional speedup factor of 15.9 is attained. Therefore, it is very important that all the modules in a nonlinear program are vectorized to gain the full potential of the supercomputers. The vector finite element computer program for inelastic analysis of RC shells with layered elements developed in the present study enabled us to perform mesh convergence studies. The vector program can be used for studying the ultimate behavior of RC shells and used as a design tool.

Modified SIMPLE Algorithm for the Numerical Analysis of Incompressible Flows with Free Surface (개량된 SIMPLE알고리듬을 이용한 비압축성 자유계면유동의 수치해석)

  • Hong Chun Pyo;Lee Jin ho;Mok Jin ho
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.29 no.5 s.236
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    • pp.609-616
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    • 2005
  • While the SIMPLE algorithm is most widely used for the simulations of flow phenomena that take place in the industrial equipments or the manufacturing processes, it is less adopted for the simulations of the free surface flow. Though the SIMPLE algorithm is free from the limitation of time step, the free surface behavior imposes the restriction on the time step. As a result, the explicit schemes are faster than the implicit scheme in terms of computation time when the same time step is applied to, since the implicit scheme includes the numerical method to solve the simultaneous equations in its procedure. If the computation time of SIMPLE algorithm can be reduced when it is applied to the unsteady free surface flow problems, the calculation can be carried out in the more stable way and, in the design process, the process variables can be controlled based on the more accurate data base. In this study, a modified SIMPLE algorithm is presented fur the free surface flow. The broken water column problem is adopted for the validation of the modified algorithm (MoSIMPLE) and for comparison to the conventional SIMPLE algorithm.

Volumetric Interferometry Using Spherical Wave Interference for Three-dimensional Coordinate Metrology

  • Rhee, Hyug-Gyo;Chu, Ji-Young;Kim, Seung-Woo
    • Journal of the Optical Society of Korea
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    • v.5 no.4
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    • pp.140-145
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    • 2001
  • We present a new method of volumetric interferometer, which is intended to measure the three-dimensional coordinates of a moving object in a simultaneous way with a single optical setup. The method is based on the principles of phase-measuring interferometry with phase shifting. Two diffraction point sources, which are made of the polished ends of single-mode optical fibers are embedded on the object. Two spherical wavefronts emanate from the diffraction point sources and interfere with each other within the measurement volume. One wavefront is phase-shifted by elongating the corresponding fiber using a PZT extender. A CCD array sensor fixed at the stationary measurement station detects the resulting interference field. The measured phases are then related to the three-dimensional location of the object with a set of non-liner equations of Euclidean distance, from which the complete set of three-dimensional spatial coordinates of the object is determined through rigorous numerical computation based upon the least square error minimization.

Quantitative Analysis of the Twenty Marker Components in Gwakhyangjeonggi-san using Ultra-Performance Liquid Chromatography with Mass Spectrometer (LC-MS/MS를 이용한 곽향정기산(藿香正氣散) 추출물 중 20종 성분의 함량분석)

  • Seo, Chang-Seob;Shin, Hyeun-Kyoo
    • Korean Journal of Pharmacognosy
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    • v.45 no.2
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    • pp.113-120
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    • 2014
  • Generally, Gwakhyangjeonggi-san has been used for treatment of diarrhea-predominant irritable bowel syndrome. In this study, an ultra-performance liquid chromatography-electrospray ionization-mass spectrometer method was established for the simultaneous quantification of marker compounds 1-20 in Gwakhyangjeonggi-san water extract. All analytes were separated by gradient elution using two mobile phases on a UPLC BEH $C_{18}$ ($100{\times}2.1mm$, $1.7{\mu}m$) column and maintained at $45^{\circ}C$. The injection volume was $2.0{\mu}L$ and the flow rate was 0.3 mL/min with detection at mass spectrometer. Regression equations of the compounds 1-20 were acquired with $r^2$ values ${\geq}0.9950$. The values of limit of detection and quantification of all analytes were 0.01-2.79 ng/mL and 0.03-8.37 ng/mL, respectively. The amounts of the compounds 1-20 in Gwakhyangjeonggi-san water extract were not detected $-3,236.67{\mu}g/g$. The established LC-MS/MS methods will be valuable to improve quality control of traditional herbal formula, Gwakhyangjeonggi-san.

A Study on the Development of Low Reynolds Number Second Moment Turbulence Model (저레이놀즈수 2차 모멘트 난류모형 개발에 관한 연구)

  • 김명호;최영돈;신종근
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.17 no.6
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    • pp.1596-1608
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    • 1993
  • Low Reynolds number second moment turbulence model which be applicable to the fine gird near the wall region was developed. In this model, turbulence model coefficients in the pressure strain model of the Reynolds stress equation was expressed as functions of turbulence Reynolds number $R_{t}\equivk^{2}/(\nu\varepsilon)).$ In the derivation procedure of the present low Reynolds number algebraic stress model, Laufer's near wall experimental data on Reynolds stresses were curve fitted as functions of R$_{t}$ and the resulting simultaneous equations of the model coefficients were solved by using the boundary conditions at wall and high Reynolds number limiting conditions. Predicted Reynolds stresses and dissipation rate of turbulent kinetic energy etc. in the 2 dimensional parallel, plane channel flow and pipe flow were compared with the preditions obtained by employing the Launder-Shima model, standard algebraic stress model and several experimental data. Results show that all the Reynolds stresses and dissipation rate of turbulent kinetic energy predicted by the present low Reynolds number algebraic stress model agree better with the experimental data than those predicted by other algebraic stress models.

Design and Sensitivity Analysis of Input Shaping Filter in the Z-domain (Z-영역에서 입력성형기의 설계와 민감도 해석)

  • Park, Un-Hwan;Lee, Jae-Won;Im, Byeong-Deok
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.7 s.178
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    • pp.1854-1862
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    • 2000
  • Input shaping method is to convolute input shaper, which is sequence of impulses, with reference input command not to excite the natural frequency of system. To reduce residual vibration for the ch ange of frequency, the number of impulses should be increased. Until now, amplitudes and time interval of those has been searched from the derivative of residual vibration. However, if time interval of impulses is fixed as the half of vibration period of system, input shaper H(z) in z-domain becomes (I-pz-1)n/K in which increasing n is the mean that robustness for change of parameter is improved. Also, design of many types of input shapers in z-domain is very easy because sensitivity curve is displayed with $\mid$H(z)zn$\mid$$\times$100. In the z-domain, EI(Extra-Insensitive) input shaper could be designed without solving nonlinear simultaneous equations as design in continuous time domain. In addition to, the design possibility of input shaper for a damped system was shown.