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Authors
Abstract(s)
Um parâmetro fundamental no projeto de sistemas de condutas de fluidos é a perda de energia causada pelo atrito viscoso, a qual é quantificada pelo fator de atrito. Em escoamentos turbulentos a expressão padrão utilizada para quan- tificar essa perda de energia é a correlação empírica introduzida por Colebrook (1939), que deve ser calculada iterativamente. Como alternativa, várias correla- ções explícitas já foram propostas e podem reduzir o tempo computacional em simulações de grandes sistemas de condutas. Neste contexto, este trabalho per- mitiu avaliar a precisão de 43 correlações explícitas e também a complexidade ou eficiência computacional, tanto das correlações explícitas quanto dos méto- dos de cálculo da correlação de Colebrook. Foram calculados os erros relativos e os coeficientes de determinação das correlações explícitas em relação à corre- lação de Colebrook e, através das funções tic e toc no programa de computador GNU Octave, foram medidos seus tempos computacionais. O método mais ve- loz de cálculo da correlação de Colebrook consome aproximadamente o dobro do tempo computacional da correlação explícita mais lenta. As correlações ex- plícitas com o melhor equilíbrio entre precisão e velocidade são: a correlação de Serghides (1984) (Equações (44), (45), (46) e (47)), que apresenta erros máximo de 0.00314% e médio de 0.00055%; a correlação de Shacham (1980) (Equa- ções (34) e (35)), com erro máximo de 0.01740% e erro médio de 0.00206%; a correlação de Brkic ́ e Praks (2019) (Equações (88), (90), (91) e (92)) que possui erro máximo de 0.12447% e erro médio de 0.05500%; e a correlação de Fang, Xu e Zhou (2011) (Equação (69)), que apresenta erros de até 0.49149% e erro médio de 0.16294%.
A fundamental parameter in the design of pipe system is the energy loss due to viscous friction, which is quantified by the friction factor. For turbulent flow, the standard formula is the empirical correlation introduce by Colebrook (1939), which must be computed iteratively. Alternatively, many explicit correlations were proposed and may reduce the computational time in large pipe systems simu- lations. In this context, this work allowed to evaluate the accuracy of 43 explicit correlations and also the computational complexity or efficience of both explicit correlations and iterative computations of Colebrook’s correlation. It was calcula- ted the relative errors and coefficients of determination of the explicit correlations against correlation by Colebrook and, using the tic and toc functions in GNU Oc- tave software, the computational times were measured. It was discovered that the fastest method of calculation of Colebrook’s correlation spend twice the com- putational time of the slowest explicit correlation. The explicit correlations with the best balance between accuracy and computational time are: correlation by Serghides (1984) (Equations (44), (45), (46) and (47)), with causes maximum er- ror of 0.00314% and average error of 0.00055%; correlation by Shacham (1980) (Equations (34) and (35)), which has maximum error of 0.01740% and average er- ror of 0.00206%; correlation by Brkic ́ e Praks (2019) (Equations (88), (90), (91) e (92)), which causes maximum error of 0.12447% and average error of 0.05500%; and correlation by Fang, Xu e Zhou (2011) (Equation (69)), which has errors up to 0.49149% and average error of 0.16294%.
A fundamental parameter in the design of pipe system is the energy loss due to viscous friction, which is quantified by the friction factor. For turbulent flow, the standard formula is the empirical correlation introduce by Colebrook (1939), which must be computed iteratively. Alternatively, many explicit correlations were proposed and may reduce the computational time in large pipe systems simu- lations. In this context, this work allowed to evaluate the accuracy of 43 explicit correlations and also the computational complexity or efficience of both explicit correlations and iterative computations of Colebrook’s correlation. It was calcula- ted the relative errors and coefficients of determination of the explicit correlations against correlation by Colebrook and, using the tic and toc functions in GNU Oc- tave software, the computational times were measured. It was discovered that the fastest method of calculation of Colebrook’s correlation spend twice the com- putational time of the slowest explicit correlation. The explicit correlations with the best balance between accuracy and computational time are: correlation by Serghides (1984) (Equations (44), (45), (46) and (47)), with causes maximum er- ror of 0.00314% and average error of 0.00055%; correlation by Shacham (1980) (Equations (34) and (35)), which has maximum error of 0.01740% and average er- ror of 0.00206%; correlation by Brkic ́ e Praks (2019) (Equations (88), (90), (91) e (92)), which causes maximum error of 0.12447% and average error of 0.05500%; and correlation by Fang, Xu e Zhou (2011) (Equation (69)), which has errors up to 0.49149% and average error of 0.16294%.
Description
Mestrado de dupla diplomação com a UTFPR - Universidade Tecnológica Federal do Paraná
Keywords
Perda de carga Fator de atrito Correlação de Colebrook Correlações explícitas.