A two-equation turbulence model has been dereloped for predicting two-phase flow the two equations describe the conserration of turbulence kinetic energy and dissipation rate of that energy for the incompressible carr...A two-equation turbulence model has been dereloped for predicting two-phase flow the two equations describe the conserration of turbulence kinetic energy and dissipation rate of that energy for the incompressible carrier fluid in a two-phase flow The continuity, the momentum, K and εequations are modeled. In this model,the solid-liquid slip veloeites, the particle-particte interactions and the interactions between two phases are considered,The sandy water pipe turbulent flows are sueeessfuly predicted by this turbulince model.展开更多
A parameter estimation algorithm is introduced and used to determine the parameters in the standard k-epsilon two equation turbulence model (SKE). It can be found from the estimation results that although the paramete...A parameter estimation algorithm is introduced and used to determine the parameters in the standard k-epsilon two equation turbulence model (SKE). It can be found from the estimation results that although the parameter estimation method is an effective method to determine model parameters, it is. difficult to obtain a set of parameters for SKE to suit all kinds of separated flow and a modification of the turbulence model structure should be considered. So, a new nonlinear k-e two-equation model (NNKE) is put forward in this paper and the corresponding parameter estimation technique is applied to determine the model parameters. By implementing the NNKE to solve some engineering turbulent flows, it is shown that NNKE is more accurate and versatile than SKE. Thus, the success of NNKE implies that the parameter estimation technique may have a bright prospect in engineering turbulence model research.展开更多
This paper describes a numerical simulation of thermal discharge in the cooling pool of an electrical power station, aiming to develop general-purpose computational programs for grid generation and flow/pollutant tran...This paper describes a numerical simulation of thermal discharge in the cooling pool of an electrical power station, aiming to develop general-purpose computational programs for grid generation and flow/pollutant transport in the complex domains of natural and artificial waterways. Three depth-averaged two-equation closure turbulence models, k-ε, k- w, and k- w, were used to close the quasi three-dimensional hydrodynamic model. The k- w model was recently established by the authors and is still in the testing process. The general-purpose computational programs and turbulence models will be involved in a software that is under development. The SIMPLE （Semi-Implicit Method for Pressure-Linked Equation） algorithm and multi-grid iterative method are used to solve the hydrodynamic fundamental governing equations, which are discretized on non-orthogonal boundary-fitted grids with a variable collocated arrangement. The results calculated with the three turbulence models were compared with one another. In addition to the steady flow and thermal transport simulation, the unsteady process of waste heat inpouring and development in the cooling pool was also investigated.展开更多
The paper mainly focuses on describing the modification made to a new depth-averaged two-equation turbulent closure model based on the revised κ-ω model recently. In the case of side discharged jets with tempera- t...The paper mainly focuses on describing the modification made to a new depth-averaged two-equation turbulent closure model based on the revised κ-ω model recently. In the case of side discharged jets with tempera- ture difference and transverse current, the new model has been investigated numerically in detail. As a practical example of application to use the new model, the side discharge of the cooling water from three outlets into a natu- ral river on one bank has been simulated, and the geomorphic variation under water has been treated suitably. Two depth-averaged models, and have been used, the later was the unique one up to the present. Emphasis is placed on the comparative research with different models under the same computational conditions. It has been verified that if the discharged flow rates are relatively small, when the pollutant plume in the near and transitional zons is predicted, the agreement with experimental and field data simulated by the model is better than by the model or other methods commonly used in engineering.展开更多
Based on the revised turbulent k-w model, a new depth-averaged two-equation closure model is offered in this paper. Through numerical investigation, it is shown that the - model has the same order of accuracy as the -...Based on the revised turbulent k-w model, a new depth-averaged two-equation closure model is offered in this paper. Through numerical investigation, it is shown that the - model has the same order of accuracy as the - model in predicting the eddy regions produced by side temprature jets with transverse currents, but the newly developed model is better than the - model in predicting the jet width,展开更多
Different factors affecting the efficiency of the orifice energy dissipator were investigated based on a series of theoretical analyses and numerical simulations. The main factors investigated by dimension analysis we...Different factors affecting the efficiency of the orifice energy dissipator were investigated based on a series of theoretical analyses and numerical simulations. The main factors investigated by dimension analysis were identified, including the Reynolds number （Re）, the ratio of the orifice diameter to the inner diameter of the pipe （ did ）, and the ratio of distances between orifices to the inner diameter of the pipe （ LID ）. Then, numerical simulations were conducted with a k-ε two-equation turbulence model. The calculation results show the following： Hydraulic characteristics change dramatically as flow passes through the orifice, with abruptly increasing velocity and turbulent energy, and decreasing pressure. The turbulent energy appears to be low in the middle and high near the pipe wall. For the energy dissipation setup with only one orifice, when Re is smaller than 105, the orifice energy dissipation coefficient K increases rapidly with the increase of Re. When Re is larger than l05, K gradually stabilizes. As diD increases, K and the length of the recirculation region L1 show similar variation patterns, which inversely vary with diD. The function curves can be approximated as straight lines. For the energy dissipation model with two orifices, because of different incoming flows at different orifices, the energy dissipation coefficient of the second orifice （K2） is smaller than that of the first. If LID is less than 5, the K value of the LID model, depending on the variation of/（2, increases with the spacing between two orifices L, and an orifice cannot fulfill its energy dissipation function. If LID is greater than 5, K2 tends to be steady; thus, the K value of the LID model gradually stabilizes. Then, the flow fully develops, and L has almost no impact on the value of K.展开更多
Observation of raindrop size distribution( DSD) with a vertically pointing micro rain radar( MRR) has important significance in the precipitation measurement field. The Mie scattering of large particle,vertical wind a...Observation of raindrop size distribution( DSD) with a vertically pointing micro rain radar( MRR) has important significance in the precipitation measurement field. The Mie scattering of large particle,vertical wind and air turbulence have great influences on the retrieval of DSD measured by MRR. This paper simulates the process of how three factors affect the inversion of DSD and the calculation of other precipitation parameters,then makes the errors analysis. Because the wavelength of MRR is 12.5mm,M ie theory is more suitable for the precipitation particle than Rayleigh approximation,w hich may cause the underestimation of number density of small droplets and the overestimation of that in middle field. The vertical wind results in inaccurate estimation of particle terminal velocity,so the diameter is measured with some errors by empirical relationship,w hich affects the calculating accuracy of radar reflectivity and rain rate. Air turbulence can broaden the pow er spectral density,of which the impact on the inversion of DSD are concentrated in small droplets field. Then the measured data from MRR is analyzed and the results prove the impacts of those factors. Finally,according to the analysis and application limits,the prospect of the future research trend of particle size distribution is conducted.展开更多
An application of the meshless Local Radial Basis Function Collocation Method(LRBFCM)[22,30–33]in solution of incompressible turbulent combined forced and natural convection is for the first time explored in the pres...An application of the meshless Local Radial Basis Function Collocation Method(LRBFCM)[22,30–33]in solution of incompressible turbulent combined forced and natural convection is for the first time explored in the present paper.The turbulent flow equations are described by the low-Re number k−εmodel with Launder and Sharma[23]and Abe et al.[1]closure coefficients.The involved temperature,velocity,pressure,turbulent kinetic energy and dissipation fields are represented on overlapping 5-noded sub-domains through the collocation by using multiquadrics Radial Basis Functions(RBF).The involved first and second order partial derivatives of the fields are calculated from the respective derivatives of the RBF’s.The involved equations are solved through the explicit time stepping.The pressure-velocity coupling is based on Chorin’s fractional step method[11].The adaptive upwinding technique,proposed by Lin and Atluri[27],is used because of the convection dominated situation.The solution procedure is represented for a 2D upward channel flow with differentially heated walls.The results have been assessed by achieving a reasonable agreement with the direct numerical simulation of Kasagi and Nishimura[20]for Reynolds number 4494,based on the channel width,and Grashof number 9.6×105.The advantages of the represented mesh-free approach are its simplicity,accuracy,similar coding in 2D and 3D,and straightforward applicability in non-uniform node arrangements.展开更多
Numerical simulations were performed to predict the film cooling effectiveness on the fiat plate with a three- dimensienal discrete-hole film cooling arrangement. The effects of basic geometrical characteristics of th...Numerical simulations were performed to predict the film cooling effectiveness on the fiat plate with a three- dimensienal discrete-hole film cooling arrangement. The effects of basic geometrical characteristics of the holes, i.e diameter D, length L and pitch S/D were studied. Different turbulent heat transfer models based on constant and variable turbulent Prandtl number approaches were considered. The variability of the turbulent Prandtl number Prt in the energy equation was assumed using an algebraic relation proposed by Kays and Crawford, or employing the Abe, Kondoh and Nagano eddy heat diffusivity closure with two differential transport equations for the temperature variance ko and its destruction rate εθ The obtained numerical results were directly compared with the data that came from an experiment based on Transient Liquid Crystal methodology. All implemented models for turbulent heat transfer performed sufficiently well for the considered case. It was confirmed, however, that the two- equation closure can give a detailed look into film cooling problems without using any time-consuming and inherently unsteady models.展开更多
文摘A two-equation turbulence model has been dereloped for predicting two-phase flow the two equations describe the conserration of turbulence kinetic energy and dissipation rate of that energy for the incompressible carrier fluid in a two-phase flow The continuity, the momentum, K and εequations are modeled. In this model,the solid-liquid slip veloeites, the particle-particte interactions and the interactions between two phases are considered,The sandy water pipe turbulent flows are sueeessfuly predicted by this turbulince model.
文摘A parameter estimation algorithm is introduced and used to determine the parameters in the standard k-epsilon two equation turbulence model (SKE). It can be found from the estimation results that although the parameter estimation method is an effective method to determine model parameters, it is. difficult to obtain a set of parameters for SKE to suit all kinds of separated flow and a modification of the turbulence model structure should be considered. So, a new nonlinear k-e two-equation model (NNKE) is put forward in this paper and the corresponding parameter estimation technique is applied to determine the model parameters. By implementing the NNKE to solve some engineering turbulent flows, it is shown that NNKE is more accurate and versatile than SKE. Thus, the success of NNKE implies that the parameter estimation technique may have a bright prospect in engineering turbulence model research.
基金supported by FAPESP (Foundation for Supporting Research in So Paulo State), Brazil, of the PIPE Project (Grant No. 2006/56475-3)
文摘This paper describes a numerical simulation of thermal discharge in the cooling pool of an electrical power station, aiming to develop general-purpose computational programs for grid generation and flow/pollutant transport in the complex domains of natural and artificial waterways. Three depth-averaged two-equation closure turbulence models, k-ε, k- w, and k- w, were used to close the quasi three-dimensional hydrodynamic model. The k- w model was recently established by the authors and is still in the testing process. The general-purpose computational programs and turbulence models will be involved in a software that is under development. The SIMPLE （Semi-Implicit Method for Pressure-Linked Equation） algorithm and multi-grid iterative method are used to solve the hydrodynamic fundamental governing equations, which are discretized on non-orthogonal boundary-fitted grids with a variable collocated arrangement. The results calculated with the three turbulence models were compared with one another. In addition to the steady flow and thermal transport simulation, the unsteady process of waste heat inpouring and development in the cooling pool was also investigated.
文摘The paper mainly focuses on describing the modification made to a new depth-averaged two-equation turbulent closure model based on the revised κ-ω model recently. In the case of side discharged jets with tempera- ture difference and transverse current, the new model has been investigated numerically in detail. As a practical example of application to use the new model, the side discharge of the cooling water from three outlets into a natu- ral river on one bank has been simulated, and the geomorphic variation under water has been treated suitably. Two depth-averaged models, and have been used, the later was the unique one up to the present. Emphasis is placed on the comparative research with different models under the same computational conditions. It has been verified that if the discharged flow rates are relatively small, when the pollutant plume in the near and transitional zons is predicted, the agreement with experimental and field data simulated by the model is better than by the model or other methods commonly used in engineering.
文摘Based on the revised turbulent k-w model, a new depth-averaged two-equation closure model is offered in this paper. Through numerical investigation, it is shown that the - model has the same order of accuracy as the - model in predicting the eddy regions produced by side temprature jets with transverse currents, but the newly developed model is better than the - model in predicting the jet width,
文摘Different factors affecting the efficiency of the orifice energy dissipator were investigated based on a series of theoretical analyses and numerical simulations. The main factors investigated by dimension analysis were identified, including the Reynolds number （Re）, the ratio of the orifice diameter to the inner diameter of the pipe （ did ）, and the ratio of distances between orifices to the inner diameter of the pipe （ LID ）. Then, numerical simulations were conducted with a k-ε two-equation turbulence model. The calculation results show the following： Hydraulic characteristics change dramatically as flow passes through the orifice, with abruptly increasing velocity and turbulent energy, and decreasing pressure. The turbulent energy appears to be low in the middle and high near the pipe wall. For the energy dissipation setup with only one orifice, when Re is smaller than 105, the orifice energy dissipation coefficient K increases rapidly with the increase of Re. When Re is larger than l05, K gradually stabilizes. As diD increases, K and the length of the recirculation region L1 show similar variation patterns, which inversely vary with diD. The function curves can be approximated as straight lines. For the energy dissipation model with two orifices, because of different incoming flows at different orifices, the energy dissipation coefficient of the second orifice （K2） is smaller than that of the first. If LID is less than 5, the K value of the LID model, depending on the variation of/（2, increases with the spacing between two orifices L, and an orifice cannot fulfill its energy dissipation function. If LID is greater than 5, K2 tends to be steady; thus, the K value of the LID model gradually stabilizes. Then, the flow fully develops, and L has almost no impact on the value of K.
基金supported by National Natural Science Foundation of China ( Grant No. 41327003 41475020 and 41505135)
文摘Observation of raindrop size distribution( DSD) with a vertically pointing micro rain radar( MRR) has important significance in the precipitation measurement field. The Mie scattering of large particle,vertical wind and air turbulence have great influences on the retrieval of DSD measured by MRR. This paper simulates the process of how three factors affect the inversion of DSD and the calculation of other precipitation parameters,then makes the errors analysis. Because the wavelength of MRR is 12.5mm,M ie theory is more suitable for the precipitation particle than Rayleigh approximation,w hich may cause the underestimation of number density of small droplets and the overestimation of that in middle field. The vertical wind results in inaccurate estimation of particle terminal velocity,so the diameter is measured with some errors by empirical relationship,w hich affects the calculating accuracy of radar reflectivity and rain rate. Air turbulence can broaden the pow er spectral density,of which the impact on the inversion of DSD are concentrated in small droplets field. Then the measured data from MRR is analyzed and the results prove the impacts of those factors. Finally,according to the analysis and application limits,the prospect of the future research trend of particle size distribution is conducted.
基金The authors would like to express their gratitude to Slovenian Technology Agency for support in the framework of the project Young Researcher from Economy,operation partly financed by the European UnionEuropean Social Fund(RV)Slovenian Research Agency for funding in the framework of the project J2-0099 Multiscale Modeling of Liquid-Solid Systems(BS).
文摘An application of the meshless Local Radial Basis Function Collocation Method(LRBFCM)[22,30–33]in solution of incompressible turbulent combined forced and natural convection is for the first time explored in the present paper.The turbulent flow equations are described by the low-Re number k−εmodel with Launder and Sharma[23]and Abe et al.[1]closure coefficients.The involved temperature,velocity,pressure,turbulent kinetic energy and dissipation fields are represented on overlapping 5-noded sub-domains through the collocation by using multiquadrics Radial Basis Functions(RBF).The involved first and second order partial derivatives of the fields are calculated from the respective derivatives of the RBF’s.The involved equations are solved through the explicit time stepping.The pressure-velocity coupling is based on Chorin’s fractional step method[11].The adaptive upwinding technique,proposed by Lin and Atluri[27],is used because of the convection dominated situation.The solution procedure is represented for a 2D upward channel flow with differentially heated walls.The results have been assessed by achieving a reasonable agreement with the direct numerical simulation of Kasagi and Nishimura[20]for Reynolds number 4494,based on the channel width,and Grashof number 9.6×105.The advantages of the represented mesh-free approach are its simplicity,accuracy,similar coding in 2D and 3D,and straightforward applicability in non-uniform node arrangements.
文摘Numerical simulations were performed to predict the film cooling effectiveness on the fiat plate with a three- dimensienal discrete-hole film cooling arrangement. The effects of basic geometrical characteristics of the holes, i.e diameter D, length L and pitch S/D were studied. Different turbulent heat transfer models based on constant and variable turbulent Prandtl number approaches were considered. The variability of the turbulent Prandtl number Prt in the energy equation was assumed using an algebraic relation proposed by Kays and Crawford, or employing the Abe, Kondoh and Nagano eddy heat diffusivity closure with two differential transport equations for the temperature variance ko and its destruction rate εθ The obtained numerical results were directly compared with the data that came from an experiment based on Transient Liquid Crystal methodology. All implemented models for turbulent heat transfer performed sufficiently well for the considered case. It was confirmed, however, that the two- equation closure can give a detailed look into film cooling problems without using any time-consuming and inherently unsteady models.
