# حل عددی توزیع دوبعدی سرعت جریان در مقاطع مرکب مستقیم

نویسندگان

1 کارشناس ارشد سازه های آبی، دانشگاه علوم کشاورزی و منابع طبیعی گرگان

2 دانشیار دانشگاه علوم کشاورزی و منابع طبیعی گرگان

3 دانشیار گروه مهندسی آب دانشگاه علوم کشاورزی و منابع طبیعی گرگان

چکیده

پارامتر سرعت در رودخانه از مهم‌ترین متغیرهای هیدرولیک جریان بوده و در بسیاری از مباحث مهندسی رودخانه مانند استخراج رابطه دبی- اشل و انتقال رسوبات کاربرد مؤثری دارد. در برخی طرح‌های مهندسی رودخانه، محاسبه سرعت متوسط جریان کفایت می‌کند. در بعضی دیگر از پروژه‌ها از قبیل طراحی سازه‌های هیدرولیکی در رودخانه، طراحی کانال‌های پایدار، محاسبات سیل در رودخانه‌ها و دشت‌های سیلابی باید توزیع عرضی و عمقی سرعت جریان در رودخانه محاسبه گردد. برای محاسبه توزیع دوبعدی سرعت جریان در جهت‌های عرضی و عمقی، مدل‌های ریاضی زیادی ارائه‌شده‌اند که ازنظر کاربردی دارای پیچیدگی‌های زیادی می‌باشند. در این تحقیق از مدل ریاضی ساده و کاربردی کین و همکاران و تلفیق آن با معادلات لزجت گردابه‌ای و سرعت دیواره اینشتین برای تعیین توزیع دوبعدی سرعت جریان در کانال‌های با مقطع مرکب صاف و زبر استفاده شد. با حل عددی این مدل ریاضی به روش تفاضل‌های محدود، داده های منحنی‌های هم سرعت جریان در کانال‌های مرکب به ازاء عمق‌های مختلف جریان و ضرایب زبری دشت‌های سیلابی محاسبه و با داده‌های آزمایشگاهی مقایسه گردید. همچنین توزیع‌های عرضی سرعت جریان در این کانال‌ها محاسبه شد و با پروفیل­های اندازه‌گیری شده مقایسه شد. این مقایسه­ها نشان‌ داد که مدل ریاضی پیشنهادی با ضریب تبیین 92/0=2R، جذر میانگین مربعات خطای 036/0= RMSE و میانگین مطلق خطا 8/2 %= MAPE درصد دارای دقت قابل‌قبولی است. این مدل با فرض شرایط جریان به‌صورت ماندگار و یکنواخت و با صرف‌نظر کردن از اثر جریان­های ثانویه توسعه داده شد.

کلیدواژه‌ها

عنوان مقاله [English]

### Numerical Solution of Two-Dimensional Velocity Distribution in Straight Compound Channels

نویسندگان [English]

• Abdolreza Zahiri 2
• Mahdi Meftah 3
1 MSc Graduated in Water Strictures, Gorgan University of Agricultural Sciences and Natural REsources
2 Water and Soil Engineering, Water Engineering, Gorgan University of Agricultural Sciences and Natural Resources
3 Water and Soil Engineering Faculty, Water Engineering department, Gorgan University of Agricultural Sciences and Natural Resources
چکیده [English]

In the river, velocity parameter is one of the most important hydraulic variables and is effectively used in many river engineering fields like development of stage-discharge curve and sediment transport. In some river engineering schemes, the calculation of average flow velocity is sufficient. However, for some other projects, such as designing hydraulic structures in the river, stable channel design, flood calculations in rivers and floodplains, the lateral and vertical distributions of flow velocity should be calculated. To calculate the two-dimensional distribution of the velocity of flow (in transverse and vertical directions) many mathematical models have been presented with many complexities from practical point of view. In this research, a simple and practical mathematical model of Kean et al in combination with eddy viscosity equation as well as Einstein's law of the wall velocity was used to determine the two-dimensional flow velocity distribution in the smooth and rough compound channels. By numerical solution of this mathematical model, using finite differences method, isovel curves data were calculated for some experimental compound channels with different flow depths and floodplain's roughness coefficients and then they were compared with the experimental data. Also, transverse distributions of the flow velocity were calculated in these channels and compared with the measured profiles. These comparisons showed that the proposed mathematical model with coefficient of determination (R2)=0.92, root-mean-square error (RMSE)=0.036 and mean absolute percentage error (MAPE)= 2.8% had an acceptable accuracy. The proposed mathematical model was developed with steady and uniform flow assumption, neglecting the secondary flow effect.

کلیدواژه‌ها [English]

• Compound channel
• Flood plain
• Main channel
• Two-dimensional velocity
• Wall velocity

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