• Title, Summary, Keyword: Gauge method

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A CLASSIFICATION OF THE SECOND ORDER PROJECTION METHODS TO SOLVE THE NAVIER-STOKES EQUATIONS

  • Pyo, Jae-Hong
    • Korean Journal of Mathematics
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    • v.22 no.4
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    • pp.645-658
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    • 2014
  • Many projection methods have been progressively constructed to find more accurate and efficient solution of the Navier-Stokes equations. In this paper, we consider most recently constructed projection methods: the pressure correction method, the gauge method, the consistent splitting method, the Gauge-Uzawa method, and the stabilized Gauge-Uzawa method. Each method has different background and theoretical proof. We prove equivalentness of the pressure correction method and the stabilized Gauge-Uzawa method. Also we will obtain that the Gauge-Uzawa method is equivalent to the gauge method and the consistent splitting method. We gather theoretical results of them and conclude that the results are also valid on other equivalent methods.

OPTIMAL ERROR ESTIMATE FOR SEMI-DISCRETE GAUGE-UZAWA METHOD FOR THE NAVIER-STOKES EQUATIONS

  • Pyo, Jae-Hong
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.4
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    • pp.627-644
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    • 2009
  • The gauge-Uzawa method which has been constructed in [11] is a projection type method to solve the evolution Navier-Stokes equations. The method overcomes many shortcomings of projection methods and displays superior numerical performance [11, 12, 15, 16]. However, we have obtained only suboptimal accuracy via the energy estimate in [11]. In this paper, we study semi-discrete gauge-Uzawa method to prove optimal accuracy via energy estimate. The main key in this proof is to construct the intermediate equation which is formed to gauge-Uzawa algorithm. We will estimate velocity errors via comparing with the intermediate equation and then evaluate pressure errors via subtracting gauge-Uzawa algorithm from Navier-Stokes equations.

NUMERICAL PROPERTIES OF GAUGE METHOD FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

  • Pyo, Jae-Hong
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.14 no.1
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    • pp.43-56
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    • 2010
  • The representative numerical algorithms to solve the time dependent Navier-Stokes equations are projection type methods. Lots of projection schemes have been developed to find more accurate solutions. But most of projection methods [4, 11] suffer from inconsistency and requesting unknown datum. E and Liu in [5] constructed the gauge method which splits the velocity $u=a+{\nabla}{\phi}$ to make consistent and to replace requesting of the unknown values to known datum of non-physical variables a and ${\phi}$. The errors are evaluated in [9]. But gauge method is not still obvious to find out suitable combination of discrete finite element spaces and to compute boundary derivative of the gauge variable ${\phi}$. In this paper, we define 4 gauge algorithms via combining both 2 decomposition operators and 2 boundary conditions. And we derive variational derivative on boundary and analyze numerical results of 4 gauge algorithms in various discrete spaces combinations to search right discrete space relation.

A Study on the Hydraulic Automatic Gauge Control System of Adaptive Mass Flow Method (Adaptive mass flow method 유압압하식 자동 두께제어 장치에 관한 연구)

  • 윤순현;김문경
    • Journal of Advanced Marine Engineering and Technology
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    • v.20 no.4
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    • pp.101-107
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    • 1996
  • This test was performed on the hydraulic automatic gauge control(AGC) system of adaptive mass flow method. Fundamental purpose of this study are performance evaluation of this AGC system under the actual rolling condition. It was concluded that the response of AGC system depends on the dynamic characteristics of a reel motor or roll position. The test results are as follows : 1) The control method of reel motor current is better than than of the roll position as AGC system. 2) The more steel strip thickness of delivery side is thick, the larger the gauge deviation is large, and the more it is thin, the larger the gauge deviation rate is large. 3) Because the gauge deviation is large at acceleration and deceleration speed than steady speed, so AGC system is better to adopt over 50m/min. By applying this AGC system, not only the accurary in strip thickness were improved but also productivity was improved dramatically.

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Measurement of Heat Flux in Rocket Combustors Using Plug-Type Heat Flux Gauges

  • Kim, Min Seok;Yu, I Sang;Kim, Wan Chan;Shin, Dong Hae;Ko, Young Sung
    • International Journal of Aeronautical and Space Sciences
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    • v.18 no.4
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    • pp.788-796
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    • 2017
  • This paper proposes a new measurement method to improve the shortcomings of an existing integral method for measuring heat flux in plug-type heat flux gauges in the high-temperature and high-pressure environments of liquid-rocket combustors. Using the existing integral measurement method, the calculation of the surface area for the heat flux in the gauge exhibits error in relation to the actual surface area. To solve this problem, transient profiles obtained from ANSYS Fluent were used to calculate unsteady heat flux as it adjusted to the measured temperature. First, a heat flux gauge was designed and manufactured specifically for use in the high-temperature and high-pressure conditions that are similar to those of liquid rocket combustors. A calibration test was performed to prove the reliability of the manufactured gauge. Then, a combustion experiment was conducted, in which the gauge was used to measure unsteady heat flux in a liquid rocket combustor that used kerosene and liquid oxygen as propellants. Reasonable heat flux values were obtained using the gauge. Therefore, the proposed measurement method is considered to offer significant improvement over the existing integral method.

A multitype sensor placement method for the modal estimation of structure

  • Pei, Xue-Yang;Yi, Ting-Hua;Li, Hong-Nan
    • Smart Structures and Systems
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    • v.21 no.4
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    • pp.407-420
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    • 2018
  • In structural health monitoring, it is meaningful to comprehensively utilize accelerometers and strain gauges to obtain the modal information of a structure. In this paper, a modal estimation theory is proposed, in which the displacement modes of the locations without accelerometers can be estimated by the strain modes of selected strain gauge measurements. A two-stage sensor placement method, in which strain gauges are placed together with triaxial accelerometers to obtain more structural displacement mode information, is proposed. In stage one, the initial accelerometer locations are determined through the combined use of the modal assurance criterion and the redundancy information. Due to various practical factors, however, accelerometers cannot be placed at some of the initial accelerometer locations; the displacement mode information of these locations are still in need and the locations without accelerometers are defined as estimated locations. In stage two, the displacement modes of the estimated locations are estimated based on the strain modes of the strain gauge locations, and the quality of the estimation is seen as a criterion to guide the selection of the strain gauge locations. Instead of simply placing a strain gauge at the midpoint of each beam element, the influence of different candidate strain gauge positions on the estimation of displacement modes is also studied. Finally, the modal assurance criterion is utilized to evaluate the performance of the obtained multitype sensor placement. A bridge benchmark structure is used for a numerical investigation to demonstrate the effectiveness of the proposed multitype sensor placement method.

Forklift Weight Measurement System using Anchor Bolt Type Strain Gauge Sensor (Anchor 볼트 형태의 Strain Gauge 센서를 이용한 지게차 적재 중량 측정 시스템)

  • Han, Chi-moon;Yim, Choon-Sik;Lee, Seong-Real
    • Journal of Advanced Navigation Technology
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    • v.23 no.2
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    • pp.200-206
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    • 2019
  • The most frequent type of safety-accident in industry is the overturning of forklift. The leading cause of this accident is overload in forklift. Thus, it is needed to measure the weight on board of forklift. The most common method is based on load cell, and this method has the merit of high accuracy. However, high price is the disadvantage of this method. In this paper, we propose the new measurement system of the weight on board of forklift based on the strain gauge sensor, which has the disadvantage of low accuracy. The differentiation of the proposed system is that the shape of the strain gauge sensor customized for anchor bolt of forklift in order to improve the accuracy and durability. In system four strain gauge sensors are inserted into four anchor bolts. The test result shows that 1% error of measurement is obtained in the proposed anchor bolt type strain gauge sensors.

AN OVERVIEW OF BDF2 GAUGE-UZAWA METHODS FOR INCOMPRESSIBLE FLOWS

  • Pyo, Jae-Hong
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.15 no.3
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    • pp.233-251
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    • 2011
  • The Gauge-Uzawa method [GUM] in [9] which is a projection type algorithm to solve evolution Navier-Stokes equations has many advantages and superior performance. But this method has been studied for backward Euler time discrete scheme which is the first order technique, because the classical second order GUM requests rather strong stability condition. Recently, the second order time discrete GUM was modified to be unconditionally stable and estimated errors in [12]. In this paper, we contemplate several GUMs which can be derived by the same manner within [12], and we dig out properties of them for both stability and accuracy. In addition, we evaluate an stability condition for the classical GUM to construct an adaptive GUM for time to make free from strong stability condition of the classical GUM.

The Design of Filter for Hearth Liquid Level Estimation in Blast Furnace (고로 용융물 레벨 변화 추정을 위한 디지털 필터 설계)

  • Cho, Nae-Soo;Han, Mu-Ho;Kwon, Woo-Hyen;Choi, Youn-Ho
    • Journal of Sensor Science and Technology
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    • v.21 no.1
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    • pp.75-81
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    • 2012
  • Optimizing the tapping time of a blast furnace is important to a stable operation and life extension. To optimize the tapping time of the blast furnace, the location of Hearth Liquid Level should be recognized. There are several ways to measure the hearth liquid level in the blast furnace, such as Electromotive Force(EMF) measurement, pressure measurement by putting in nitrogen probe and manometry with strain gauge. In this paper, it will be discussed using strain gauge among the three methods. Conventional strain gauge must be revised periodically. Since, internal pressure, temperature of internal refractory material and wind pressure have effect on the strain gauge. However, static pressure value is required to compensate. To solve these problems, this paper suggests finding relationship between Hearth Liquid Level and strain gauge output, adding digital filter in strain gauge. Using the proposed method, it was possible to estimate the hearth liquid level and determine the appropriate tapping time. Usefulness of the proposed method through simulations and experimental results are confirmed.