Theoretical, simulation and experimental investigation of 1D hybrid pressure distribution for internal gear motors and pumps

Trong Hoa Pham,Dinh Tu Nguyen,Jürgen Weber 대한기계학회 2020 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.34 No.1

Internal gear motor and pump is the typical rotating machine which operates in hybrid regime of lubrication. Calculation of the pressure distribution in the oil-lubrication film is the fundamental issue for determination of the upper and lower speed limit as well as analysis of the stability phenomenon of internal gear motor and pump. However, the simultaneously existence problem of hydrodynamic and hydrostatic pressure in case of hybrid regime is a challenge for calculation. This paper introduces an approach for calculation of 1D hybrid pressure distribution. The Reynolds equation with appropriate boundary condition is solved to obtain 2D hydrodynamic pressure distribution by using the finite difference method (FDM). The resistance network model (RNM) is used to predict the 1D hydrostatic pressure profile. Based on the hydrostatic and hydrodynamic pressure, the 1D total pressure profile can be retrieved. The CFD simulation has been performed to obtain the hydrostatic pressure profile and then compare to the hydrostatic pressure distribution by using RNM. A test rig has been designed to measure the oil-film pressure at five different points over the circumferential direction. Results pointed out that the numerical calculation agree well with the experimental results, particularly at high values of the working pressure.

필 댐에 관한 지진하중-간극수압의 상호작용 평가를 위한 기초연구

정의중,백성철,남열우,이섬범,박인준,김홍택,Jeung. Eu-Jung,Baek. Sung-Chu,Nam. Yel-Woo,Lee. Seom-Beom,Park. Inn-Joon,Kim. Hong-Taek 한국방재학회 2007 한국방재학회 학술발표대회논문집 Vol.2007 No.1

In case of having no consideration for pore pressure, we may underestimate earthquakes in seismic analysis of fill dam. because we can not consider hydrodynamic pressures induced by earthquakes. Nevertheless, there are few actual results on hydrodynamic pressures variation due to the principal variables of seismic analysis of fill dam. So, in this study we study earthquake-pore pressure interaction performing divers variable analysis, as considering Sesimic load-Pore Pressure. 필 댐의 내진해석은 간극수압을 고려하지 않을 경우에는 지진에 의한 동수압을 고려할 수 없기 때문에 지진력을 과소평가할 수 있다 그러나 현재까지도 필 댐의 내진해석에서 주요 변수에 따른 동수압의 변화는 연구 실적이 많지 않다. 따라서 본 연구에서는 지진하중과 간극수압을 모두 고려하는 경우에 대해 다양한 변수분석을 수행하여 지진과 간극수압의 상호작용을 알아보았다.

자유수면을 갖는 흐름의 동수압 모형

장원재(Jang Won Jae),이승오(Lee Seung Oh),이종욱(Lee Jong Wook),조용식(Cho Yong-Sik) 대한토목학회 2007 대한토목학회논문집 B Vol.27 No.4B

동수압을 고려한 자유수면 흐름을 해석하고 수치모형과 적용사례들을 제시하였다. 본 연구에 사용된 지배방정식으로 비정상 상태의 비압축성 유체에 대한 연속방정식과 비점성 Navier-Stokes 방정식을 사용하였다. 난류완결문제를 해결하기 위해서 k-ε 방정식을 사용하여서 난류 와점성계수를 구할 수 있다. 본 연구에서 자유수면과 동수압을 고려하기 위해서 수치모의를 3단계로 나누어서 수행하였다. 제 1단계에서는 운동량방정식을 연직방향에 대해 음해적으로 차분하였다. 제2단계에서는 유속과 동수압 보정항으로 이루어진 식을 연속방정식에 대입하여 타원형 방정식인 동수압-포와송 방정식을 제안하였고, 이 방정식을 통해서 얻어지는 유속은 질량보존법칙을 만족하게 된다. 마지막으로 자유수면과 최종유속을 보정 및 계산하였다. 본 연구에서 제시한 수치모형을 검증하기 위해 해석해가 있는 정사각형 수조에서 수면의 자유 진동과 직선수로에서의 고립파의 전파 문제에 대하여 수치모의를 수행하였고, 수치모의 된 결과는 해석해와 잘 일치하였다. 또한 수중방파제에 의한 비선형파의 전파양상과 타원형 천퇴에 의한 파의 변형에 관한 수치모의를 수행하였다. 전반적으로 수치모의에 의한 결과와 실험 자료가 일치하는 경향을 보였다. Hydrodynamic pressure model and application problems are presented to analyze free surface flow in this study. The governing equations for an unsteady incompressible fluid employ the continuity equation and inviscid Navier-Stokes equation. For the turbulence closed problem, k-ε model is employed and turbulence eddy viscosity is resolved. Numerical simulations are conducted in three steps to calculate the velocity component in each direction, the free surface elevations and the hydrodynamic pressures. At the first step, the momentum equations are discretized by using a semi-implicit method over the vertical direction. At the second step, velocity fractional equations with hydrodynamic pressure correction terms are substituted into the continuity equation, which yields an elliptic equation called as the hydrodynamic pressure-Poisson equation. The local mass can be, therefore, conserved by solving that elliptic equation. Finally, the free surface elevation and the final velocities are computed by substituting into the continuity equation. The numerical accuracy is verified by comparing numerical results with analytical solutions of the sloshing free surface movement at a square basin and solitary wave propagation in a rectangular. The overall agreement between calculated and analytical solutions is excellent. Also, numerical calculation for the propagation phase of non-linear wave in submerged bar and wave deformation in elliptic shoal are conducted and results of numerical model show good agreement with experimental data.

Numerical analysis of unsteady hydrodynamic performance of pump-jet propulsor in oblique flow

Qiu, Chengcheng,Pan, Guang,Huang, Qiaogao,Shi, Yao The Society of Naval Architects of Korea 2020 International Journal of Naval Architecture and Oc Vol.12 No.-

In this study, the SST k - ω turbulence model and the sliding mesh technology based on RANS method have been adopted to simulate the exciting force and hydrodynamic of a pump-jet propulsor in different oblique inflow angle (0°, 10°, 20°, 30°) and different advance ratio (J = 0.95, J = 1.18, J = 1.58).The fully structured grid and full channel model have been adopted to improved computational accuracy. The classical skewed marine propeller E779A with different advance ratio was carried out to verify the accuracy of the numerical simulation method. The grid independence was verified. The time-domain data of pump-jet propulsor exciting force including bearing force and fluctuating pressure in different working conditions was monitored, and then which was converted to frequency domain data by fast Fourier transform (FFT). The variation laws of bearing force and fluctuating pressure in different advance ratio and different oblique flow angle has been presented. The influence of the peak of pulsation pressure in different oblique flow angle and different advance ratio has been presented. The results show that the exciting force increases with the increase of the advance ratio, the closer which is to the rotor domain and the closer to the blades tip, the greater the variation of the pulsating pressure. At the same time, the exciting force decrease with the oblique flow angle increases. And the vertical and transverse forces will change more obviously, which is the main cause of the exciting force. In addition, the pressure distribution and the velocity distribution of rotor blades tip in different oblique flow angles has been investigated.

Numerical analysis of unsteady hydrodynamic performance of pump-jet propulsor in oblique flow

Qiu, Chengcheng,Pan, Guang,Huang, Qiaogao,Shi, Yao The Society of Naval Architects of Korea 2020 International Journal of Naval Architecture and Oc Vol.12 No.1

In this study, the SST k - ω turbulence model and the sliding mesh technology based on RANS method have been adopted to simulate the exciting force and hydrodynamic of a pump-jet propulsor in different oblique inflow angle (0°, 10°, 20°, 30°) and different advance ratio (J = 0.95, J = 1.18, J = 1.58).The fully structured grid and full channel model have been adopted to improved computational accuracy. The classical skewed marine propeller E779A with different advance ratio was carried out to verify the accuracy of the numerical simulation method. The grid independence was verified. The time-domain data of pump-jet propulsor exciting force including bearing force and fluctuating pressure in different working conditions was monitored, and then which was converted to frequency domain data by fast Fourier transform (FFT). The variation laws of bearing force and fluctuating pressure in different advance ratio and different oblique flow angle has been presented. The influence of the peak of pulsation pressure in different oblique flow angle and different advance ratio has been presented. The results show that the exciting force increases with the increase of the advance ratio, the closer which is to the rotor domain and the closer to the blades tip, the greater the variation of the pulsating pressure. At the same time, the exciting force decrease with the oblique flow angle increases. And the vertical and transverse forces will change more obviously, which is the main cause of the exciting force. In addition, the pressure distribution and the velocity distribution of rotor blades tip in different oblique flow angles has been investigated.

Study of modified Westergaard formula based on dynamic model test on shaking table

Mingming Wang,Yi Yang,Weirong Xiao 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.64 No.5

The dynamic model test of dam-reservoir coupling system for a 203m high gravity dam is performed to investigate effects of reservoir water on dynamic responses of dam during earthquake. The hydrodynamic pressure under condition of full reservoir, natural frequencies and acceleration amplification factors along the dam height under conditions of full and empty reservoir are obtained from the test. The results indicate that the reservoir water have a stronger influence on the dynamic responses of dam. The measured natural frequency of the dam model under full reservoir is 21.7% lower than that of empty reservoir, and the acceleration amplification factor at dam crest under full reservoir is 18% larger than that under empty reservoir. Seismic dynamic analysis of the gravity dams with five different heights is performed with the Fluid-Structure Coupling Model (FSCM). The hydrodynamic pressures from Westergaard formula are overestimated in the lower part of the dam body and underestimated in its upper part to compare with those from the FSCM. The underestimation and overestimation are more significance with the increase of the dam height. The position of the maximum hydrodynamic pressure from the FSCM is raised with the increase of dam height. In view of the above, the Westergaard formula is modified with consideration in the influence of the height of dam, the elasticity of dam on the hydrodynamic pressure. The solutions of modified Westergaard formula are quite coincident with the hydrodynamic pressures in the model test and the previous report.

Free Surface Flow in a Trench Channel Using 3-D Finite Volume Method

이길성,박기두,오진호 한국수자원학회 2011 한국수자원학회논문집 Vol.44 No.6

In order to simulate a free surface flow in a trench channel, a three-dimensional incompressible unsteady Reynolds-averaged Navier-Stokes(RANS) equations are closed with the model. The artificial compressibility(AC) method is used. Because the pressure fields can be coupled directly with the velocity fields, the incompressible Navier-Stokes(INS) equations can be solved for the unknown variables such as velocity components and pressure. The governing equations are discretized in a conservation form using a second order accurate finite volume method on non-staggered grids. In order to prevent the oscillatory behavior of computed solutions known as odd-even decoupling, an artificial dissipation using the flux- difference splitting upwind scheme is applied. To enhance the efficiency and robustness of the numerical algorithm, the implicit method of the Beam and Warming method is employed. The treatment of the free surface, so-called interface-tracking method, is proposed using the free surface evolution equation and the kinematic free surface boundary conditions at the free surface instead of the dynamic free surface boundary condition. AC method in this paper can be applied only to the hydrodynamic pressure using the decomposition into hydrostatic pressure and hydrodynamic pressure components. In this study, the boundary-fitted grids are used and advanced each time the free surface moved. The accuracy of our RANS solver is compared with the laboratory experimental and numerical data for a fully turbulent shallow-water trench flow. The algorithm yields practically identical velocity profiles that are in good overall agreement with the laboratory experimental measurement for the turbulent flow.

A finite element based approach to observe hydrodynamic pressure in reservoir adjacent to concrete gravity dam

Santosh Kumar, Das,Kalyan Kumar, Mandal,Arup Guha, Niyogi Techno-Press 2022 Ocean systems engineering Vol.12 No.4

This paper deals with the study of hydrodynamic pressure in reservoir adjacent to the concrete gravity dam subjected to dynamic excitation. Widely famous finite element method is used to discretize the reservoir domain for modelling purpose. Pressure is considered as nodal variable following Eulerian approach. A suitable nonreflecting boundary condition is applied at truncated face of reservoir to make the infinite reservoir to finite one for saving the computational cost. Thorough studies have been done on generation of hydrodynamic pressure in reservoir with variation of different geometrical properties. Velocity profile and hydrodynamic pressure are observed due to harmonic excitation for variation of inclination angle of dam reservoir interface. Effect of bottom slope angle and inclined length of reservoir bottom on hydrodynamic pressure coefficient of reservoir are also observed. There is significant increase in hydrodynamic pressure and distinct changes in velocity profile of reservoir are noticeable for change in inclination angle of dam reservoir interface. Change of bottom slope and inclined length of reservoir bottom are also governing factor for variation of hydrodynamic pressure in reservoir subjected to dynamic excitation.

Minimization of Hydrodynamic Pressure Effect on the Ultraprecision Mirror Grinding

Sun-Kyu Lee,Yuji Miyamoto,Tsunemoto Kuriyagawa,Katsuo Syoji 한국정밀공학회 2005 International Journal of Precision Engineering and Vol.6 No.1

This paper describes an investigation about the fluid delivering method that minimizes the generation of hydrodynamic pressure and improves the grinding accuracy. Traditionally, grinding fluid is delivered for the purpose of cooling, chip flushing and lubrication. Hence, a number of conventional investigations are focused on the delivering method to maximize fluid flux into the contact arc between the grinding wheel and the work piece. It is already known that hydrodynamic pressure generates due to this fluid flux, and that it affects the overall grinding resistance and machining accuracy. Especially in the ultra-precision mirror grinding process that requires extremely small amount of cut per pass, its influence on the machining accuracy becomes more significant. Therefore, in this paper, a new delivering method of grinding fluid is proposed with focus on minimizing the hydrodynamic pressure effect. Experimental data indicates that the proposed method is effective not only to minimize the hydrodynamic pressure but also to improve the machining accuracy.

Minimization of Hydrodynamic Pressure Effect on the Ultraprecision Mirror Grinding

Lee, Sun-Kyu,Miyamoto, Yuji,Kuriyahawa, Tsunemoto,Syoji, Katsuo Korean Society for Precision Engineering 2005 International Journal of Precision Engineering and Vol.6 No.1

This paper describes an investigation about the fluid delivering method that minimizes the generation of hydrodynamic pressure and improves the grinding accuracy. Traditionally, grinding fluid is delivered for the purpose of cooling, chip flushing and lubrication. Hence, a number of conventional investigations are focused on the delivering method to maximize fluid flux into the contact arc between the grinding wheel and the work piece. It is already known that hydrodynamic pressure generates due to this fluid flux, and that it affects the overall grinding resistance and machining accuracy. Especially in the ultra-precision mirror grinding process that requires extremely small amount of cut per pass, its influence on the machining accuracy becomes more significant. Therefore, in this paper, a new delivering method of grinding fluid is proposed with focus on minimizing the hydrodynamic pressure effect. Experimental data indicates that the proposed method is effective not only to minimize the hydrodynamic pressure but also to improve the machining accuracy.