بررسی تحلیلی نظریه‌های سرعت طولی در راستای عمقی جریان

نوع مقاله: مقاله پژوهشی

چکیده

        محاسبه سرعت طولی در راستای قائم و استخراج نظریه­های کاربردی برای آن در طول سالیان در بین مهندسان هیدرولیک رواج داشته­ است. در بسیاری از تحقیقات پیشین، محققان با تقسیم عمق جریان به چندین قسمت مجزا از کف کانال تا سطح آب اقدام به استخراج روابط کاربردی برای هر قسمت نموده­اند. به جز زیرلایه لزج که همگی بر پروفیل خطی سرعت در آن اتفاق نظر دارند، مابقی عمق جریان معمولاً با قانون لگاریتمی شبیه­سازی می­گردد که دقت تخمین سرعت توسط این قانون با فاصله گرفتن از کف کانال کمتر می­شود. همچنین قانون لگاریتمی قابلیت شبیه­سازی نقطه سرعت بیشینه که در عمقی پائین­تر از سطح آب رخ می­دهد را نیز ندارد. دراین تحقیق با جمع­آوری دوازده سری داده آزمایشگاهی که توسط محققان پیشین و در شرایط آزمایشگاهی مختلف برداشت شده است و همچنین با به کارگیری سه نظریه لگاریتمی، خیزآب و خیزآب اصلاح شده اقدام به شبیه­سازی پروفیل­های سرعت طولی در راستای قائم گردید. در نهایت مشاهده شد که پروفیل سرعت استخراج شده توسط قانون خیزآب اصلاح شده تطابق بهتری با داده­های آزمایشگاهی دارد و قادر به پیش­بینی نقطه سرعت بیشینه در عمقی پائین­تر از سطح آب است. برای حل معادله مربوط به این نظریه پارامتر­های ون کارمن، ضریب قدرت خیزآب و سرعت برشی مجهول فرض گردید و سپس با استفاده از روش بهینه­سازی غیرخطی کمترین مربعات اقدام به استخراج مقادیر مربوطه گردید.

کلیدواژه‌ها


عنوان مقاله [English]

Analytical Investigation of Longitudinal Velocity Theories in Flow Vertical Direction

چکیده [English]

Computation of longitudinal velocity in the vertical direction and extracting the applied theories have been conventional manner from past years among the hydraulic engineers. In many previous investigations, the researchers have tried to extract some applied equations, separately, by dividing the flow depth namely from bed to water surface to various regions. As it is accepted by all of the researchers, the laminar sublayer zone has a linear velocity profile while out of this zone, the velocity simulation follows a logarithmic law which its accuracy in estimation of the velocity decreases by increasing the distance from the bottom of the channel. Also, it is not applicable for dip phenomenon which occurs bellow the free surface. In the current study, 12 experimental data series, operated under different experimental conditions, were collected from previous researches. Also, three common theories of log law, log- wake law, and modified log- wake law have been applied to simulate longitudinal velocity profile in the vertical direction. Finally, it is seen that the modified log- wake law has a better agreement with the experimental data, and also it can be operated for predicting the dip phenomenon bellow the free surface. For solving the equation of the mentioned theory, the factors of von Karman, wake strength, and shear velocity are assumed unknown. Then, the mentioned parameters have been extracted using a non-linear optimization technique of the least square curve fitting.

کلیدواژه‌ها [English]

  • Longitudinal velocity in vertical direction
  • Log law
  • Log- wake law
  • Modified log- wake law
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