• Title/Summary/Keyword: $k-{\epsilon}$ model

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COMPUTER SIMULATION OF INTRAMOLECULAR HYDROGEN TRANSFER TO CARBONYL OXYGEN BY A MONTE CARLO METHOD: PHOTOREACTIONS VIA REMOTE PROTON TRANSFER IN BENZOYLBENZOATES

  • Hasegawa, Tadashi;Yamazaki, Yuko;Yoshioka, Michikazu
    • Journal of Photoscience
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    • v.4 no.2
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    • pp.61-67
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    • 1997
  • The model based on the idea that the p$_y$-orbital of the carbonyl oxygen is responsible to receiving hydrogen was devised for simulation of intramolecular hydrogen transfer. A Monte Carlo method was applied to free rotation of a molecular chain performed by changing the dihedral angles, and a "hit" was defined as the case when the migrating hydrogen comes within the region defined as the p$_y$-orbital and satisfies all the geometrical requirements for abstraction. A set of parameters was employed for defining the region and the requirements; $\tau$ was defined as the angle formed between O...H vector and its projection on the mean plane of the carbonyl group (- 43$\circ$ < $\tau$ < + 43$\circ$), $\Delta$ as the C=O...H angle (90 -15$\circ$ < $\Delta$ < 90 + 15$\circ$), $\theta$ as the O...H - C angle ( 180 - 80$\circ$< 0 < 180 + 80$\circ$), d as the distance from the center of the lobe of the p$_y$-orbital to hydrogen (0 < d < 1.04 ${\AA}$). The minimum value for the distance between carbonyl oxygen (O$_1$) and the migrating hydrogen (H$_i$) and for that between non-bonded atoms except the pair of O$_1$ and H$_i$ were assumed to be 0.52 ${\AA}$ and 1.54 ${\AA}$, respectively. The apphcation of this model to intramolecular $\beta$-, $\gamma$-, $\delta$-, $\epsilon$-, and $\zeta$-hydrogen abstraction in ketones and $\eta$- and $\theta$- proton transfer in oxoesters gave good results reflecting their photochemical behavior. The model was also used for prediction of photoreactivities of 2-(N,N-dibenzylamino)ethyl 2-, 3- and 4-benzoylbenzoate (1a - c). (1a - c).

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A Numerical Analysis of Gravity and Free Surface Effects on a Two-Dimensional Supercavitating Flow (2차원 초공동 유동의 중력과 자유표면 효과에 대한 수치해석)

  • Kim, Hyoung-Tae;Lee, Hyun-Bae
    • Journal of the Society of Naval Architects of Korea
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    • v.51 no.5
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    • pp.435-449
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    • 2014
  • The effects of the gravity field and the free surface on the cavity shape and the drag are investigated through a numerical analysis for the steady supercavitating flow past a simple two-dimensional body underneath the free surface. The continuity and the RANS equations are numerically solved for an incompressible fluid using a $k-{\epsilon}$ turbulence model and a mixture fluid model has been applied for calculating the multiphase flow of air, water and vapor using the method of volume of fluid and the Schnerr-Sauer cavitation model. Numerical solutions have been obtained for the supercavitating flow about a two-dimensional $30^{\circ}$ wedge in wide range of depths of submergence and inflow velocities. The results are presented for the cavity shape, especially the length and the width, and the drag of the wedge in comparison with those of the case for the infinite fluid flow neglecting the gravity and the free surface. The influences of the gravity field and the free surface on the aforementioned quantities are discussed. The length and the width of the supercavity are reduced and the centerline of the cavity rises toward the free surface due to the effects of the gravity field and the free surface. The drag coefficient of the wedge, however, is about the same except for shallow depths of submergence. As the supercavitating wedge is approaching very close to the free surface, it is found the length and the width of a cavity are shorten even though the cavitation number is reduced. Also the present result suggests that, under the influence of the gravity field and the free surface, the length of the supercavity for a certain cavitation number varies and moreover is proportional to the inverse of the submergence depth Froude number.

PERFORMANCE ASSESSMENT OF THE RANS TURBULENCE MODELS IN PREDICTION OF AERODYNAMIC NOISE FOR AIR-CONDITIONER INDOOR UNIT (에어컨 실내기의 공력소음 예측을 위한 RANS 난류모델의 성능 평가)

  • Min, Y.H.;Kang, S.;Hur, N.;Lee, C.;Park, J.
    • Journal of computational fluids engineering
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    • v.17 no.4
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    • pp.81-86
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    • 2012
  • The objective of the present study is to investigate the effects of various turbulence models on the aerodynamic noise of an air-conditioner (AC) indoor unit. The results from URANS (unsteady Reynolds-averaged Navier-Stokes) simulations with the standard k-$\varepsilon$, k-$\omega$ shear stress transport (SST) and Spalart-Allmaras (S-A) turbulence models were analyzed and compared with the noise data from the experiments. The frequency spectra of the far-field acoustic pressure were computed using the Farrasat equation derived from the Ffowcs Williams-Hawkings (FW-H) equation based on the acoustic analogy model. Two fixed fan casings and the rotating cross-flow fan were used as the source surfaces of the dipole noise in the Farrasat equation. The result with the standard k-$\epsilon$ model showed a much better agreement with the experimental data compared to the k-w SST and S-A models. The differences in the pressure spectra from the different turbulence models were discussed based on the instantaneous vorticity fields. It was found that the over-estimated power spectra with the k-w SST and S-A models are related to the emphasized small-scale vortices produced with these models.

Performance Estimation of Cross-Flow Fan by Numerical Method (수치해석적 기법을 이용한 횡류홴 성능 평가)

  • Kim, D.-W.;Lee, J.-H.;Park, S.-K.;Kim, Youn-J.
    • 유체기계공업학회:학술대회논문집
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    • 2002.12a
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    • pp.152-157
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    • 2002
  • A cross-flow fan is widely used on many industrial fields: a blower for the general industry, mining industry, automobile and home appliances. The design point of the cross-flow fan is generally chosen by based on the region within low static pressure and high flow rate. It relatively makes high dynamic pressure at low speed because a working fluid passes through an impeller blade twice. However, it has low static pressure efficiency between $30\%$ and $40\%$ because of relative high impact loss. Recently, in the air-conditioning systems, the operating behaviors at the off-design points are highly regarded to broaden the application area for various air-cooling loads. Especially, at the low flow rate, there exists a rapid pressure head reduction, a noise increase and an irregular flow against a rearguider as a scroll of centrifugal fan. Numerical analyses are carried out for cross-flow fan including the impeller, the rearguider and the stabilizer. Numerical domains are discretized by hexahedral cells. Three-dimensional, unsteady governing equations are solved using FVM, SIMPLE algorithm, sliding grid system and standard k-$\epsilon$ turbulence model.

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Secondary flows through an impeller of centrifugal compressor at design and off-design conditions (설계점 및 탈설계점에서의 원심압축기 회전차 내부 2차유동)

  • Choe, Yeong-Seok;Gang, Sin-Hyeong
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.20 no.11
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    • pp.3573-3588
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    • 1996
  • The flow through a centrifugal compressor impeller was calculated using the 3-dimensional Navier-Stokes solution method. A control volume method based on a rotating curvilinear coordinate system was used to solve the time-averaged Navier-Stokes equations, and a standard k-.epsilon. model was used to obtain eddy viscosity. Numerical results and experimental data were compared for the overall performance of the impeller, the pressure distributions along the shroud wall and the detailed flowfields at the design and off-design conditions, which showed good coincidence. The flow through the impeller is complex with the curvature of the streamlines and rotation. The development of secondary flows and the jet-wake flow characteristics, which is the main source of flow loss, was discussed. Calculation results show quite different patterns as the flow rate changes.

Performance of a Cross-Flow Fan with Various Stabilizer Positions and Rearguider Shapes (스태빌라이져 위치 및 리어가이더 형상변화에 따른 횡류홴의 성능특성 연구)

  • Kim, D.W.;Kim, H.S.;Yoon, T.S.;Park, S.K.;Kim, Yon J.
    • The KSFM Journal of Fluid Machinery
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    • v.7 no.4 s.25
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    • pp.7-15
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    • 2004
  • The design point of the cross-flow fan is generally based on the region within low static pressure and high flow rate. It relatively makes high dynamic pressure at low speed because a working fluid passes through an impeller blade twice. However, it has low static pressure efficiency between $30\%$ and $40\%$ because of relative high impact loss. The purpose of this study is to research the reciprocal relation among each parameter. Experiments and numerical analyses are conducted on effects of a stabilizer and a rearguider on performance analysis of a cross-flow fan. Two-dimensional, unsteady governing equations are solved using FVM, PISO algorithm, sliding grid system and standard $k-{\epsilon}$ turbulence model. Experiments are also carried out to estimate the performance of the modeled cross-flow fan. It is clarified that the rearguider of Archimedes type has excellent results for the most part.

Study on the turbulent structure for two-dimensional recirculating flows by curvature dependent 2-equation model (曲率修正2方程式모델을 利용한 2次元 再循環 亂流 流動構造의 硏究)

  • 박상우;정명균
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.11 no.3
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    • pp.444-453
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    • 1987
  • In the present study, a new computational closure model is proposed in order to contain physical models in the k- and .epsilon.- equations. The time scale of the third-order diffusive transport of turbulent kinetic energy in a curved streamline flow field is assumed as a function of a velocity time scale and a curvature time scale, the latter being derived from the analogy between buoyancy and streamline curvature effects on turbulence. The curvature time scale is represented by a combination of Brunt-Vaisala frequency of the curvature instability and the velocity time scale. Besides the modification of diffusive transport time scale, the destruction term in the dissipation rate equation is modeled to incorporate the streamline curvature effect on the dissipation rate of turbulent kinetic energy as a function of the ratio between velocity time scale and curvature time scale. The new curvature dependent 2-equation model is found to yield very good prediction accuracy for the various turbulent recirculating flows. Particurarly, the recovery of the mean velocity profile in the redeveloping region after the reattachment is correctly simulated by the present model.

Optimal Design of a Fine Actuator for Optical Pick-up (광픽업 미세구동부의 최적설계)

  • Lee, Moon-G;Gweon, Dae-Gab
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.5
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    • pp.819-827
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    • 1997
  • In this paper, a new modeling of a fine actuator for an optical pick-up has been proposed and multiobjective optimization of the actuator has been performed. The fine actuator is constituted of the bobbin which is supported by wire suspension, the coils which wind around the bobbin, and the magnets which cause the magnetic flux. If current flows in the coils, magnetic force is so produced as to be balanced with spring force of wire, so the bobbin is pisitioned. In this model the transfer function from input voltage to output displacementof bobbin has been obtained so that we can describe this integrated system with electromagnetic and mechanical parts. Wire suspension is regarded as a continuous Euler beam, damper as distributed viscous damping, and bobbin as a rigid body which can move up- and down- ward motion only. According to the model, the high frequency dynamic characteristics of the fine actuator can be known and the effect of damping can be investigated while the conventional second order model cannot. In multiobjective optimization, two objective functions have been chosen to maximize the fundamental frequency and the sensitivity with respect to the input voltage of the actuator so that Pareto's optimal solutions have been obtained using .epsilon.-constraint method. These objective functions will satisfy the trends which will enhance the access speed and reduce the tracking error in the optical pick-up technology of next generation. In the result of optimization, we obtain the designs of the optical pick-up fine actuator which has high speed, high sensitivity and low resonant peak. Furthermore, we offer the relation between two object functions so that the designer can make easy choice.

Structural Model on Hypertensive Patient's Lifestyle and Quality of Life (고혈압 환자의 생활양식과 삶의 질에 관한 구조 Model)

  • Lee Jong Ryol;Park Chun Man
    • Health Policy and Management
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    • v.14 no.3
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    • pp.66-96
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    • 2004
  • This study was intended to describe the hypertensive patient's lifestyle and quality of life by creating a hypothetic model on the lifestyle and quality of life and by examining a causeand effect relationship, and to contribute to countermeasures for practicing their lifestyle and improving the quality of life through creating a predictable model. Exogenous variable($\xi$) of hypothetic model in this study composed of a family support, hypertension knowledge, perceived benefit and toughness. Endogenous variable($\eta$) composed of self-esteem, perceived health state, depression, lifestyle and quality of life. There were 6 measured variables for exogenous variable(x). There were 9 measured variables(y) for endogenous variable. Also, there was error variable ($\delta,\;\epsilon$) of an individual. The survey was conducted for 207 hypertensive parents who received an out-patient service for 3 weeks from September 15, 2003 to October 3, 2003 after diagnosing as hypertension from 2 general hospitals in Daegu. As the conformance of hypothetic model in this study, there were $x^2$= 155.81, standard $x^2$ ($x^2$/df)=2.32, GFI=0.003, NFI=0.971, CFI=0.982, and RMSEA=0.080. Generally, the hypothetic model and actual data were well coincided. The higher the hypertension knowledge was(t=6.030), the higher the perceived benefit was(t=9.429), the higher the toughness was(t=2.783), and the higher the perceived health state was(t=2.282), the higher the lifestyle was. However, the degree of depression (t=-0.038), family support(t=1.161), and self-esteem(t=0.518) was not affected. The higher the family support was(t=10.476), the higher the self-esteem was(t=7.244), the higher the perceived health state was(t=6.996), the lower the degree of depression was(t=-2.044), and the higher the practice degree of lifestyle was(t=3.315), the higher the quality of life was. However, the toughness(t=1.672) didn't have a significant influence on the quality of life. It was modified to increase the model conformance and gain a conscious model As the result of model revision, for the model conformance, there were $x^2$= 118.43, standard $x^2$=1.69, GFI=0.923, NFI=0.976, CFI=0.982, and RMSEA=0.078. As the revised model showed the better conformance than hypothetic model, it seemed to be more suitable model. In the revised model, the perceived benefit(t=9.440) affected the lifestyle in the revised model. Then, the lifestyle was influenced by hypertension knowledge(t=6.139), toughness (t=2.757), family support(t=2.078), perceived health state(t=1.962) in the order. As a factor which affected the quality of life, there were the family support(t=l0.46l), self-esteem(t=7.368), perceived health state(t=6.989), lifestyle(t=3.316), toughness(t=2.584), and depression(t=-1.968) in the order. It showed the significant effect.

A Numerical Study on the Effect of PCB Structure Variation on the Electronic Equipment Cooling (PCB 구조변화가 전자장비 냉각에 미치는 영향에 관한 수치적 연구)

  • ;;Park, Kyoung-Woo
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.12
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    • pp.3329-3343
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    • 1995
  • The interaction of mixed convection and surface radiation in a printed circuit board(PCB) is investigated numerically. The electronic equipment is modeled by a two-dimensional channel with three hot blocks. In order to calculate the turbulent flow characteristics, the low Reynolds number k-.epsilon. model which is proposed by Launder and Sharma is applied. The S-4 approximation is used to solve the radiative transfer equation. The effects of the Reynolds number and geometric configuration variation of PCB on the flow and heat transfer characteristics are analyzed. As the results of this study, it is found that the thermal boundary layer occured at adiabatic wall in case with thermal radiation included, and the effect of radiation is also found to be insignificant for high Reynolds numbers. It is found, as well, that the heat transfer increases as the Reynolds number and block space increase and the channel height decreases and the heat transfer of vertical channel is greater than that of horizontal channel.