Both the complex geometrical morphology of rough-walled rock fractures and the nonlinearity of fluid flow contribute to resistance in fluid flow through rock fractures.The interactions of the shear-flow process furthe...Both the complex geometrical morphology of rough-walled rock fractures and the nonlinearity of fluid flow contribute to resistance in fluid flow through rock fractures.The interactions of the shear-flow process further complicate the characterisation of flow behaviours in rock fractures.In this study,an improved friction factor model involving both the effects of viscous and inertial forces is presented based on the Forchheimer equation.The model incorporates two key variables,i.e.Reynolds number and relative roughness,which reflect the effects of flow regimes and fracture roughness,respectively.The changes in geometrical parameters induced by shearing are considered,with the peak asperity height predicted through a correlation with post-peak roughness degradation.The hydraulic aperture during shearing is estimated using a suggested equation that accounts for the mobilised contact area ratio and variable aperture distribution.The parametric sensitivity analysis reveals that shear-induced changes in fracture geometry enhance the flow nonlinearity in rock fractures.The model performs well in predicting the friction factor based on two validation criteria.Then,the proposed friction factor model is incorporated into the three-dimensional distinct element code(3DEC)in the form of the Darcy-Weisbach equation.Coupled with the numerically implemented mechanical model and hydraulic aperture prediction model,numerical simulations of coupled shear-flow processes in single rock fractures are conducted.The simulation outcomes are validated through comparison with the experimental results,showing acceptable agreement and demonstrating that the numerical model is capable of accurately evaluating the hydro-mechanical coupling behaviour during the shearing of rock fractures.展开更多
The experimental analysis takes too much time-consuming process and requires considerable effort,while,the Artificial Neural Network(ANN)algorithms are simple,affordable,and fast,and they allow us to make a relevant a...The experimental analysis takes too much time-consuming process and requires considerable effort,while,the Artificial Neural Network(ANN)algorithms are simple,affordable,and fast,and they allow us to make a relevant analysis in establishing an appropriate relationship between the input and output parameters.This paper deals with the use of back-propagation ANN algorithms for the experimental data of heat transfer coefficient,Nusselt number,and friction factor of water-based Fe_(3)O_(4)-TiO_(2) magnetic hybrid nanofluids in a mini heat sink under magnetic fields.The data considered for the ANN network is at different Reynolds numbers(239 to 1874),different volume concentrations(0%to 2.0%),and different magnetic fields(250 to 1000 G),respectively.Three types of ANN back-propagation algorithms Levenberg-Marquardt(LM),Broyden-Fletcher-Goldfarb-Shanno Quasi Newton(BFGS),and Variable Learning Rate Gradient Descent(VLGD)were used to train the heat transfer coefficient,Nusselt number,and friction factor data,respectively.The ANOVA t-test analysis was also performed to determine the relative accuracy of the three ANN algorithms.The Nusselt number of 2.0%vol.of Fe_(3)O_(4)-TiO_(2) hybrid nanofluid is enhanced by 38.16%without a magnetic field,and it is further enhanced by 88.93%with the magnetic field of 1000 Gauss at a Reynolds number of 1874,with respect to the base fluid.A total of 126 datasets of heat transfer coefficient,Nusselt number,and friction factor were used as input and output data.The three ANN algorithms of LM,BFGS,and VLGD,have shown good acceptance with the experimental data with root-mean-square errors of 0.34883,0.25341,and 1.0202 with correlation coefficients(R2)of 0.99954,0.9967,and 0.94501,respectively,for the Nusselt number data.Moreover,the three ANN algorithms predict root-mean-square errors of 0.001488,0.005041,and 0.006924 with correlation coefficients(R2)of 0.99982,0.99976,and 0.99486,respectively,for the friction factor data.Compared to BFGS and VLGD algorithms,the LM algorithm predicts high accuracy for Nusselt number,and friction factor data.The proposed Nusselt number and friction factor correlations are also discussed.展开更多
This paper deals with the experimental investigation on Nusselt number,friction factor and thermal en-hancement factor of a double pipe heat exchanger equipped with twisted tape consisting wire nails(WN-TT) and plain ...This paper deals with the experimental investigation on Nusselt number,friction factor and thermal en-hancement factor of a double pipe heat exchanger equipped with twisted tape consisting wire nails(WN-TT) and plain twisted tapes(P-TT) with three different twist ratios of y 2.0,4.4 and 6.0. Test runs are conducted using the water as the working fluid with Reynolds number range between 2000 and 12000 for WN-TT and P-TT. It is found that Nusselt number,friction factor and thermal enhancement factor in the tube equipped with WN-TT appreciably higher than those in the tube fitted with P-TT and plain tube. Over the range considered Nusselt number,friction factor and thermal enhancement factor in a tube with WN-TT are respectively,1.08 to 1.31,1.1 to 1.75 and 1.05 to 1.13 times of those in tube with P-TT. The better performance of WN-TT is due to combined effects of the follow-ing factors:(1) common swirling flow generated by P-TT,(2) additional turbulence offered by the wire nails. Em-pirical correlations for Nusselt number,friction factor and thermal enhancement factor are also formulated from the experimental results of WN-TT and P-TT.展开更多
Ventilation system analysis for underground mines has remained mostly unchanged since the Atkinson method was made popular by Mc Elroy in 1935. Data available to ventilation technicians and engineers is typically limi...Ventilation system analysis for underground mines has remained mostly unchanged since the Atkinson method was made popular by Mc Elroy in 1935. Data available to ventilation technicians and engineers is typically limited to the quantity of air moving through any given heading. Because computer-aided modelling, simulation, and ventilation system design tools have improved, it is now important to ensure that developed models have the most accurate information possible. This paper presents a new technique for estimating underground drift friction factors that works by processing 3 D point cloud data obtained by using a mobile Li DAR. Presented are field results that compare the proposed approach with previously published algorithms, as well as with manually acquired measurements.展开更多
The Atkinson equation along with its friction factor is commonly used to estimate pressure requirement in mine ventilation.However,friction factor correlation of flow through broken rock,typically found in blasted sto...The Atkinson equation along with its friction factor is commonly used to estimate pressure requirement in mine ventilation.However,friction factor correlation of flow through broken rock,typically found in blasted stope,gob,rock pit or block caving rock deposits,etc.,is currently unavailable.Also,it is impractical to conduct direct measurements of flow resistance in an inaccessible broken rock zone.This paper aims to develop a new friction factor correlation of flow through broken rock that can be used directly in Atkinson equation.The proposed correlation is valid for broken rocks with diameter between 0.04 and 1.2 m and porosity ranging from 0.23 to 0.7.展开更多
Experiments and simulations on flow and heat transfer behavior of Therminol-55 liquid phase heat transfer fluid have been conducted in a ribbed tube with the outer diameter and inner diameter 25.0 and 20.0 mm,pitch an...Experiments and simulations on flow and heat transfer behavior of Therminol-55 liquid phase heat transfer fluid have been conducted in a ribbed tube with the outer diameter and inner diameter 25.0 and 20.0 mm,pitch and rib height of 4.5 and 1.0 mm.respectively.Experimental results show that the heat transfer and thermal performance of Therminol-55 liquid phase heat transfer fluid in the ribbed tube are considerably improved compared to those of the smooth tube.The Nusselt number increase with the increase of Reynolds number.The increase in heat transfer rate of the ribbed tube has a mean value of 2.24 times.Also,the pressure drop results reveal that the average friction factor of the ribbed tube is in a range of 2.4 and 2.8 times over the smooth tube.Numerical simulations of three-dimensional flow behavior of Therminol-55 liquid phase heat transfer fluid are carried out using three different turbulence models in the ribbed tube.The numerical results show that the heat transfer of ribbed tube is improved because vortices are generated behind ribs,which produce some disruptions to fluid flow and enhance heat transfer compared with smooth tube.The numerical results prove that the ribbed tube can improve heat transfer and fluid flow performances of Therminol liquid phase heat transfer fluid.展开更多
Direct calculations of unsteady-state Weymouth equations for gas volumetric flow rate occur more frequently in the design and operation analysis of natural gas systems. Most of the existing gas pipelines design proced...Direct calculations of unsteady-state Weymouth equations for gas volumetric flow rate occur more frequently in the design and operation analysis of natural gas systems. Most of the existing gas pipelines design procedures are based on a particular friction factor and steady-state flow analysis. This paper examined the behavior of different friction factors and the need to develop model analysis capable of calculating unsteady-state gas flow rate in horizontal and inclined pipes. The results show different variation in flow rate with Panhandle A and Panhandle B attaining stability in accurate time with initial unsteadiness at the instance of flow. Chen and Jain friction factors have opposition to flow with high flow rate: The prediction also reveals that Colebrook-White degenerated to Nikuradse friction factor at high Reynolds number. The horizontal and inclined flow equations are considerably enhanced on the usage of different friction factors with the aid of Matlab to handle these calculations.展开更多
The implicit Colebrook equation has been the standard for estimating pipe friction factor in a fully developed turbulent regime. Several alternative explicit models to the Colebrook equation have been proposed. To dat...The implicit Colebrook equation has been the standard for estimating pipe friction factor in a fully developed turbulent regime. Several alternative explicit models to the Colebrook equation have been proposed. To date, most of the accurate explicit models have been those with three logarithmic functions, but they require more computational time than the Colebrook equation. In this study, a new explicit non-linear regression model which has only two logarithmic functions is developed. The new model, when compared with the existing extremely accurate models, gives rise to the least average and maximum relative errors of 0.0025% and 0.0664%, respectively. Moreover, it requires far less computational time than the Colebrook equation. It is therefore concluded that the new explicit model provides a good trade-off between accuracy and relative computational efficiency for pipe friction factor estimation in the fully developed turbulent flow regime.展开更多
The ongoing research for model choice and selection has generated a plethora of approaches. With such a wealth of methods, it can be difficult for a researcher to know what model selection approach is the proper w...The ongoing research for model choice and selection has generated a plethora of approaches. With such a wealth of methods, it can be difficult for a researcher to know what model selection approach is the proper way to proceed to select the appropriate model for prediction. The authors present an evaluation of various model selection criteria from decision-theoretic perspective using experimental data to define and recommend a criterion to select the best model. In this analysis, six of the most common selection criteria, nineteen friction factor correlations, and eight sets of experimental data are employed. The results show that while the use of the traditional correlation coefficient, R2 is inappropriate, root mean square error, RMSE can be used to rank models, but does not give much insight on their accuracy. Other criteria such as correlation ratio, mean absolute error, and standard deviation are also evaluated. The AIC （Akaike Information Criterion） has shown its superiority to other selection criteria. The authors propose AIC as an alternative to use when fitting experimental data or evaluating existing correlations. Indeed, the AIC method is an information theory based, theoretically sound and stable. The paper presents a detailed discussion of the model selection criteria, their pros and cons, and how they can be utilized to allow proper comparison of different models for the best model to be inferred based on sound mathematical theory. In conclusion, model selection is an interesting problem and an innovative strategy to help alleviate similar challenges faced by the professionals in the oil and gas industry is introduced.展开更多
Research reports show that the accuracies of many explicit friction factor models, having different levels of accuracies and complexities, have been improved using genetic algorithm (GA), a global optimization approac...Research reports show that the accuracies of many explicit friction factor models, having different levels of accuracies and complexities, have been improved using genetic algorithm (GA), a global optimization approach. However, the computational cost associated with the use of GA has yet to be discussed. In this study, the parameters of sixteen explicit models for the estimation of friction factor in the turbulent flow regime were optimized using two popular global search methods namely genetic algorithm (GA) and simulated annealing (SA). Based on 1000 interval values of Reynolds number (Re) in the range of and 100 interval values of relative roughness () in the range of , corresponding friction factor (f) data were obtained by solving Colebrook-White equation using Microsoft Excel spreadsheet. These data were then used to modify the parameters of the selected explicit models. Although both GA and SA led to either moderate or significant improvements in the accuracies of the existing friction factor models, SA outperforms the GA. Moreover, the SA requires far less computational time than the GA to complete the corresponding optimization process. It can therefore be concluded that SA is a better global optimizer than GA in the process of finding an improved explicit friction factor model as an alternative to the implicit Colebrook-White equation in the turbulent flow regime.展开更多
Abstract： The most popularly used fin types in compact heat exchangers are the serrated fins, wavy fins, louvered fins and plain fins. Amongst these fin types the serrated fins assume lot of importance due to its enh...Abstract： The most popularly used fin types in compact heat exchangers are the serrated fins, wavy fins, louvered fins and plain fins. Amongst these fin types the serrated fins assume lot of importance due to its enhanced thermo-hydraulic performance. Thermo-hydraulic design of CHEs （Compact heat exchangers） is strongly dependent upon the predicted/measured dimensionless performance （Colburnj factor and Fanning friction vs. Reynolds number） of heat transfer surfaces. This paper describes the numerical analysis to study the heat transfer coefficient and friction factor of Serrated fins in water medium. CFD （Computational fluid dynamics） methodology has been used to develop the single phase water heat transfer coefficient and friction factor correlations for serrated fins using ANSYS Fluent 14.5. The results are compared with previous air-cooled models and experimental results of water. The water cooled CFD analysis results shows that the Prandtl number has a large effect on the Nusselt number of the serrated fin geometry. Finally, the generalized correlations are developed for serrated fins taking all geometrical parameters into account. This numerical estimation can reduce the number of tests/experiments to a minimum for similar applications.展开更多
Experiments of de-ionized water flowing in microchannels made in copper blocks were carried out to obtain pressure drop and friction factor and to investigate any possible discrepancies from conventional theory. Three...Experiments of de-ionized water flowing in microchannels made in copper blocks were carried out to obtain pressure drop and friction factor and to investigate any possible discrepancies from conventional theory. Three channels with widths of 0.5 mm, 1.0 mm, 1.71 mm, a depth of 0.39 mm and a length of 62 mm were tested. For adiabatic tests, the temperature of the working fluid was maintained at 30 ℃, 60 ℃ and 90 ℃ without any heat fluxes supplied to the test section. The experimental conditions covered a range of Reynolds numbers from 234 to 3,430. For non-adiabatic tests, the inlet temperature and heat flux applied were 30 ℃ and 147 kW/m2 and only for the 0.635 mm channel. The friction factors obtained for the widest channel （Dh = 0.635 mm） are reported for both adiabatic and non-adiabatic experiments to assess possible temperature effects. The paper focuses on the effect of hydraulic diameter on pressure drop and friction factor over the experimental conditions. The pressure drop was found to decrease as the inlet temperature was increased, while the friction factors for the three test sections did not show significant differences. The experimental friction factors were in reasonable agreement with conventional developing flow theory. The effect of temperature on friction factor was not considerable as the friction factor with and without heat flux was almost the same.展开更多
The effect of friction factor on the unsteady state mixed convective-radiative heat transfer in an inclined cylindrical annulus is investigated from continuity, momentum and energy equations. The outer cylinder is kep...The effect of friction factor on the unsteady state mixed convective-radiative heat transfer in an inclined cylindrical annulus is investigated from continuity, momentum and energy equations. The outer cylinder is kept at a constant temperature while the inner cylinder is heated with constant heat flux. The governing equations are normalized and solved using the vorticity-stream function and the BFC （body fitted coordinates） methods. The two heat transfer mechanisms of convection and radiation are treated independently and simultaneously. A computer program （Fortran 90） was built to calculate Nusselt number （Nu） and friction factorffor unsteady state condition for fluid Prandtl number fixed at （Pr = 0.7） （for air as working fluid） with radius ratio （/~ = 2.6）, Rayleigh number （0 〈 Ra 〈 103）, Reynolds number （50 〈 Re 〈 2,000）, conduction-radiation parameter （0 〈 N 〈 10）, optical thickness （0 〈 l＂ 〈 10） and different annulus inclination with horizontal plane （0~ _〈 d 〈 90~） for concentric cylindrical annulus. For the range of parameters considered, results show that radiation enhance heat transfer. It is also indicated in the results that as 3 increasefwill be decrease and also when Re increasefwill be decrease for any value of Ra causing increase in heat transfer. The maximum value off can be recognized at ~ = 90~ and the minimum value at 6 = 0~ for low Re. There is an optimum value of annulus inclination that gives maximum value of Nu, this maximum value appears at 90~ of annulus inclination comparison of the result with the previous work shows a good agreement.展开更多
基金supported by the China Scholarship Council(CSC)(Grant No.202006060033).
文摘Both the complex geometrical morphology of rough-walled rock fractures and the nonlinearity of fluid flow contribute to resistance in fluid flow through rock fractures.The interactions of the shear-flow process further complicate the characterisation of flow behaviours in rock fractures.In this study,an improved friction factor model involving both the effects of viscous and inertial forces is presented based on the Forchheimer equation.The model incorporates two key variables,i.e.Reynolds number and relative roughness,which reflect the effects of flow regimes and fracture roughness,respectively.The changes in geometrical parameters induced by shearing are considered,with the peak asperity height predicted through a correlation with post-peak roughness degradation.The hydraulic aperture during shearing is estimated using a suggested equation that accounts for the mobilised contact area ratio and variable aperture distribution.The parametric sensitivity analysis reveals that shear-induced changes in fracture geometry enhance the flow nonlinearity in rock fractures.The model performs well in predicting the friction factor based on two validation criteria.Then,the proposed friction factor model is incorporated into the three-dimensional distinct element code(3DEC)in the form of the Darcy-Weisbach equation.Coupled with the numerically implemented mechanical model and hydraulic aperture prediction model,numerical simulations of coupled shear-flow processes in single rock fractures are conducted.The simulation outcomes are validated through comparison with the experimental results,showing acceptable agreement and demonstrating that the numerical model is capable of accurately evaluating the hydro-mechanical coupling behaviour during the shearing of rock fractures.
基金supported by the Recovery and Resilience Plan(PRR)and by European Funds Next Generation EU under the Project“AET—Alliance for Energy Transition,”no.C644914747-00000023,investment project no.56 of the Incentive System“Agendas for Business Innovation”.
文摘The experimental analysis takes too much time-consuming process and requires considerable effort,while,the Artificial Neural Network(ANN)algorithms are simple,affordable,and fast,and they allow us to make a relevant analysis in establishing an appropriate relationship between the input and output parameters.This paper deals with the use of back-propagation ANN algorithms for the experimental data of heat transfer coefficient,Nusselt number,and friction factor of water-based Fe_(3)O_(4)-TiO_(2) magnetic hybrid nanofluids in a mini heat sink under magnetic fields.The data considered for the ANN network is at different Reynolds numbers(239 to 1874),different volume concentrations(0%to 2.0%),and different magnetic fields(250 to 1000 G),respectively.Three types of ANN back-propagation algorithms Levenberg-Marquardt(LM),Broyden-Fletcher-Goldfarb-Shanno Quasi Newton(BFGS),and Variable Learning Rate Gradient Descent(VLGD)were used to train the heat transfer coefficient,Nusselt number,and friction factor data,respectively.The ANOVA t-test analysis was also performed to determine the relative accuracy of the three ANN algorithms.The Nusselt number of 2.0%vol.of Fe_(3)O_(4)-TiO_(2) hybrid nanofluid is enhanced by 38.16%without a magnetic field,and it is further enhanced by 88.93%with the magnetic field of 1000 Gauss at a Reynolds number of 1874,with respect to the base fluid.A total of 126 datasets of heat transfer coefficient,Nusselt number,and friction factor were used as input and output data.The three ANN algorithms of LM,BFGS,and VLGD,have shown good acceptance with the experimental data with root-mean-square errors of 0.34883,0.25341,and 1.0202 with correlation coefficients(R2)of 0.99954,0.9967,and 0.94501,respectively,for the Nusselt number data.Moreover,the three ANN algorithms predict root-mean-square errors of 0.001488,0.005041,and 0.006924 with correlation coefficients(R2)of 0.99982,0.99976,and 0.99486,respectively,for the friction factor data.Compared to BFGS and VLGD algorithms,the LM algorithm predicts high accuracy for Nusselt number,and friction factor data.The proposed Nusselt number and friction factor correlations are also discussed.
文摘This paper deals with the experimental investigation on Nusselt number,friction factor and thermal en-hancement factor of a double pipe heat exchanger equipped with twisted tape consisting wire nails(WN-TT) and plain twisted tapes(P-TT) with three different twist ratios of y 2.0,4.4 and 6.0. Test runs are conducted using the water as the working fluid with Reynolds number range between 2000 and 12000 for WN-TT and P-TT. It is found that Nusselt number,friction factor and thermal enhancement factor in the tube equipped with WN-TT appreciably higher than those in the tube fitted with P-TT and plain tube. Over the range considered Nusselt number,friction factor and thermal enhancement factor in a tube with WN-TT are respectively,1.08 to 1.31,1.1 to 1.75 and 1.05 to 1.13 times of those in tube with P-TT. The better performance of WN-TT is due to combined effects of the follow-ing factors:(1) common swirling flow generated by P-TT,(2) additional turbulence offered by the wire nails. Em-pirical correlations for Nusselt number,friction factor and thermal enhancement factor are also formulated from the experimental results of WN-TT and P-TT.
基金supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant CRDPJ 44580412Barrick Gold Corporation and Peck Tech Consulting Ltd
文摘Ventilation system analysis for underground mines has remained mostly unchanged since the Atkinson method was made popular by Mc Elroy in 1935. Data available to ventilation technicians and engineers is typically limited to the quantity of air moving through any given heading. Because computer-aided modelling, simulation, and ventilation system design tools have improved, it is now important to ensure that developed models have the most accurate information possible. This paper presents a new technique for estimating underground drift friction factors that works by processing 3 D point cloud data obtained by using a mobile Li DAR. Presented are field results that compare the proposed approach with previously published algorithms, as well as with manually acquired measurements.
文摘The Atkinson equation along with its friction factor is commonly used to estimate pressure requirement in mine ventilation.However,friction factor correlation of flow through broken rock,typically found in blasted stope,gob,rock pit or block caving rock deposits,etc.,is currently unavailable.Also,it is impractical to conduct direct measurements of flow resistance in an inaccessible broken rock zone.This paper aims to develop a new friction factor correlation of flow through broken rock that can be used directly in Atkinson equation.The proposed correlation is valid for broken rocks with diameter between 0.04 and 1.2 m and porosity ranging from 0.23 to 0.7.
基金Supported by the National Natural Science Foundation of China(11472093 and21276056)
文摘Experiments and simulations on flow and heat transfer behavior of Therminol-55 liquid phase heat transfer fluid have been conducted in a ribbed tube with the outer diameter and inner diameter 25.0 and 20.0 mm,pitch and rib height of 4.5 and 1.0 mm.respectively.Experimental results show that the heat transfer and thermal performance of Therminol-55 liquid phase heat transfer fluid in the ribbed tube are considerably improved compared to those of the smooth tube.The Nusselt number increase with the increase of Reynolds number.The increase in heat transfer rate of the ribbed tube has a mean value of 2.24 times.Also,the pressure drop results reveal that the average friction factor of the ribbed tube is in a range of 2.4 and 2.8 times over the smooth tube.Numerical simulations of three-dimensional flow behavior of Therminol-55 liquid phase heat transfer fluid are carried out using three different turbulence models in the ribbed tube.The numerical results show that the heat transfer of ribbed tube is improved because vortices are generated behind ribs,which produce some disruptions to fluid flow and enhance heat transfer compared with smooth tube.The numerical results prove that the ribbed tube can improve heat transfer and fluid flow performances of Therminol liquid phase heat transfer fluid.
文摘Direct calculations of unsteady-state Weymouth equations for gas volumetric flow rate occur more frequently in the design and operation analysis of natural gas systems. Most of the existing gas pipelines design procedures are based on a particular friction factor and steady-state flow analysis. This paper examined the behavior of different friction factors and the need to develop model analysis capable of calculating unsteady-state gas flow rate in horizontal and inclined pipes. The results show different variation in flow rate with Panhandle A and Panhandle B attaining stability in accurate time with initial unsteadiness at the instance of flow. Chen and Jain friction factors have opposition to flow with high flow rate: The prediction also reveals that Colebrook-White degenerated to Nikuradse friction factor at high Reynolds number. The horizontal and inclined flow equations are considerably enhanced on the usage of different friction factors with the aid of Matlab to handle these calculations.
文摘The implicit Colebrook equation has been the standard for estimating pipe friction factor in a fully developed turbulent regime. Several alternative explicit models to the Colebrook equation have been proposed. To date, most of the accurate explicit models have been those with three logarithmic functions, but they require more computational time than the Colebrook equation. In this study, a new explicit non-linear regression model which has only two logarithmic functions is developed. The new model, when compared with the existing extremely accurate models, gives rise to the least average and maximum relative errors of 0.0025% and 0.0664%, respectively. Moreover, it requires far less computational time than the Colebrook equation. It is therefore concluded that the new explicit model provides a good trade-off between accuracy and relative computational efficiency for pipe friction factor estimation in the fully developed turbulent flow regime.
文摘The ongoing research for model choice and selection has generated a plethora of approaches. With such a wealth of methods, it can be difficult for a researcher to know what model selection approach is the proper way to proceed to select the appropriate model for prediction. The authors present an evaluation of various model selection criteria from decision-theoretic perspective using experimental data to define and recommend a criterion to select the best model. In this analysis, six of the most common selection criteria, nineteen friction factor correlations, and eight sets of experimental data are employed. The results show that while the use of the traditional correlation coefficient, R2 is inappropriate, root mean square error, RMSE can be used to rank models, but does not give much insight on their accuracy. Other criteria such as correlation ratio, mean absolute error, and standard deviation are also evaluated. The AIC （Akaike Information Criterion） has shown its superiority to other selection criteria. The authors propose AIC as an alternative to use when fitting experimental data or evaluating existing correlations. Indeed, the AIC method is an information theory based, theoretically sound and stable. The paper presents a detailed discussion of the model selection criteria, their pros and cons, and how they can be utilized to allow proper comparison of different models for the best model to be inferred based on sound mathematical theory. In conclusion, model selection is an interesting problem and an innovative strategy to help alleviate similar challenges faced by the professionals in the oil and gas industry is introduced.
文摘Research reports show that the accuracies of many explicit friction factor models, having different levels of accuracies and complexities, have been improved using genetic algorithm (GA), a global optimization approach. However, the computational cost associated with the use of GA has yet to be discussed. In this study, the parameters of sixteen explicit models for the estimation of friction factor in the turbulent flow regime were optimized using two popular global search methods namely genetic algorithm (GA) and simulated annealing (SA). Based on 1000 interval values of Reynolds number (Re) in the range of and 100 interval values of relative roughness () in the range of , corresponding friction factor (f) data were obtained by solving Colebrook-White equation using Microsoft Excel spreadsheet. These data were then used to modify the parameters of the selected explicit models. Although both GA and SA led to either moderate or significant improvements in the accuracies of the existing friction factor models, SA outperforms the GA. Moreover, the SA requires far less computational time than the GA to complete the corresponding optimization process. It can therefore be concluded that SA is a better global optimizer than GA in the process of finding an improved explicit friction factor model as an alternative to the implicit Colebrook-White equation in the turbulent flow regime.
文摘Abstract： The most popularly used fin types in compact heat exchangers are the serrated fins, wavy fins, louvered fins and plain fins. Amongst these fin types the serrated fins assume lot of importance due to its enhanced thermo-hydraulic performance. Thermo-hydraulic design of CHEs （Compact heat exchangers） is strongly dependent upon the predicted/measured dimensionless performance （Colburnj factor and Fanning friction vs. Reynolds number） of heat transfer surfaces. This paper describes the numerical analysis to study the heat transfer coefficient and friction factor of Serrated fins in water medium. CFD （Computational fluid dynamics） methodology has been used to develop the single phase water heat transfer coefficient and friction factor correlations for serrated fins using ANSYS Fluent 14.5. The results are compared with previous air-cooled models and experimental results of water. The water cooled CFD analysis results shows that the Prandtl number has a large effect on the Nusselt number of the serrated fin geometry. Finally, the generalized correlations are developed for serrated fins taking all geometrical parameters into account. This numerical estimation can reduce the number of tests/experiments to a minimum for similar applications.
文摘Experiments of de-ionized water flowing in microchannels made in copper blocks were carried out to obtain pressure drop and friction factor and to investigate any possible discrepancies from conventional theory. Three channels with widths of 0.5 mm, 1.0 mm, 1.71 mm, a depth of 0.39 mm and a length of 62 mm were tested. For adiabatic tests, the temperature of the working fluid was maintained at 30 ℃, 60 ℃ and 90 ℃ without any heat fluxes supplied to the test section. The experimental conditions covered a range of Reynolds numbers from 234 to 3,430. For non-adiabatic tests, the inlet temperature and heat flux applied were 30 ℃ and 147 kW/m2 and only for the 0.635 mm channel. The friction factors obtained for the widest channel （Dh = 0.635 mm） are reported for both adiabatic and non-adiabatic experiments to assess possible temperature effects. The paper focuses on the effect of hydraulic diameter on pressure drop and friction factor over the experimental conditions. The pressure drop was found to decrease as the inlet temperature was increased, while the friction factors for the three test sections did not show significant differences. The experimental friction factors were in reasonable agreement with conventional developing flow theory. The effect of temperature on friction factor was not considerable as the friction factor with and without heat flux was almost the same.
文摘The effect of friction factor on the unsteady state mixed convective-radiative heat transfer in an inclined cylindrical annulus is investigated from continuity, momentum and energy equations. The outer cylinder is kept at a constant temperature while the inner cylinder is heated with constant heat flux. The governing equations are normalized and solved using the vorticity-stream function and the BFC （body fitted coordinates） methods. The two heat transfer mechanisms of convection and radiation are treated independently and simultaneously. A computer program （Fortran 90） was built to calculate Nusselt number （Nu） and friction factorffor unsteady state condition for fluid Prandtl number fixed at （Pr = 0.7） （for air as working fluid） with radius ratio （/~ = 2.6）, Rayleigh number （0 〈 Ra 〈 103）, Reynolds number （50 〈 Re 〈 2,000）, conduction-radiation parameter （0 〈 N 〈 10）, optical thickness （0 〈 l＂ 〈 10） and different annulus inclination with horizontal plane （0~ _〈 d 〈 90~） for concentric cylindrical annulus. For the range of parameters considered, results show that radiation enhance heat transfer. It is also indicated in the results that as 3 increasefwill be decrease and also when Re increasefwill be decrease for any value of Ra causing increase in heat transfer. The maximum value off can be recognized at ~ = 90~ and the minimum value at 6 = 0~ for low Re. There is an optimum value of annulus inclination that gives maximum value of Nu, this maximum value appears at 90~ of annulus inclination comparison of the result with the previous work shows a good agreement.
