圆管内湍流流动能量耗散率近似算法的可靠性分析

为了检验能量耗散率近似算法的可靠性 ,将按近似算法计算得到的管内湍流体均能量耗散率与按热力学方法导出的解析式并采用公认的摩擦因子公式计算的体均能量耗散率进行了对比。结果表明 ,若选择适当的湍流时均速度梯度模型 ,用近似算法计算的体均能量耗散率与用解析式计算的值接近 ,说明该近似算法的准确性可以满足工程计算的需要。湍流剪切率的计算误差小于能量耗散率的计算误差。对于牛顿流体在圆管内的湍流流动 ,使用三段速度分布模型计算的体均能量耗散率比采用窦国仁式速度梯度分布模型计算的误差小。参照牛顿流体能量耗散率的计算方法 ,提出了幂律流体管内湍流能量耗散率的近似算法。对于幂律流体 ,以管壁处表观粘度代替牛顿流体粘度 ,并采用牛顿流体时均速度梯度模型 ,按近似方法计算得到的体均能量耗散率与按解析式计算的结果吻合

Reliability analysis on an approach to energy dissipation rate of fluid flow in turbulent pipe

In order to testify the reliability of the approximate approach, the calculated value of volumetrically averaged energy dissipation rate based on the approximate approach are compared with the calculated results from an analytical equation derived on the thermodynamic laws and using the universally accepted equations for the friction factor. It is demonstrated that the accuracy of the approximate approach is acceptable in engineering, provided that the time averaged velocity gradient be determined by using the proper models. By following the approach for Newtonian fluids, an approximate approach to turbulent energy dissipation rate for pipe flow of the power law fluids was proposed. By using a time averaged velocity gradient model for Newtonian fluids in which the Newtonian viscosity is replaced by the apparent viscosity on the pipe wall, the volumetrically averaged energy dissipation rate determined by the proposed approach agrees with the result from the analytical equation. The computing error of turbulent flow shear rate is less than that of energy dissipation. The value of volumetrically averaged energy dissipation rate computed using three stage velocity model is more accurate than that using the time averaged velocity gradient model for Newtonian fluids in pipe flow.