ارائه مدل يك بعدي براي برآورد توزيع سرعت در كانال روباز كم عرض

Introducing One-Dimensional Model to Estimate Velocity Distribution in Narrow Open-Channels

برآورد توزيع سرعت به عنوان يك پارامتر كليدي در تخمين ديگر پارامتر هاي هيدروليكي جريان نظير دبي و تنش برشي از اهميت زيادي برخوردار است؛ و در دهه هاي اخير، برآورد پروفيل توزيع سرعت جريان در كانالهاي كم عرض با نسبت عرض به عمق كمتر از 5، توجه بسياري از محققين را به خود معطوف داشته است. در اين مقاله يك مدل تحليلي براي برآورد توزيع سرعت جريان آشفته و كاملا توسعه يافته، بر مبناي ميانگين گيري رينولدز معادلات ناوير استوكس (RANS) و يك توزيع لزجت گردابي ارائه شده است. مدل پيشنهادي قابليت كاربرد در هر دو دسته كانال هاي عريض و كم عرض را دارد. اين مدل با داده هاي اندازه گيري شده در كانال هاي آزمايشگاهي مستطيلي و نيز داده هاي حاصل از يك سايت واقعي كانال فاضلاب مقايسه و معتبرسازي شده است. به دليل وابستگي معادله توزيع سرعت پيشنهادي به پارامتر كولز، تاثير اين پارامتر بر ميزان دقت در توصيف پروفيل سرعت و پيش بيني محل وقوع سرعت ماكزيمم نيز مورد مطالعه قرار گرفته است. در مطالعه حاضر، پارامتر كولز از طريق برازش به دست آمده و مقاديري كه به ازاي آن، مدل پيشنهادي كمترين ميزان خطا را در برآورد پروفيل سرعت ارائه مي دهد، پيشنهاد گرديده است. نتايج نشان مي دهد كه پروفيل هاي سرعت به دست آمده از مدل پيشنهادي مطابقت بالايي با داده هاي اندازه گيري شده داشته و گراديان منفي سرعت در نزديكي سطح آزاد آب را به خوبي نشان مي دهد. مقدار پارامتر كولز براي كانال فاضلاب كمتر از مقدار اين پارامتر براي كانال هاي آزمايشگاهي به دست آمد.

Determining the velocity distribution -as a key parameter for estimating other hydraulic parameters- has been always of interest. Velocity distribution in the inner region of the flow (y<0.2D) where y is the vertical distance from the bed and D is the flow depth is well described by the logarithmic law. However, this law deviates from the experimental data in the outer region (y>0.2D). The log-Wake law is among the most accepted laws for determining the velocity distribution in wide open channels. The law modifies the logarithmic law by adding a Wake function; but in the case of narrow open channels, it deviates from the measured data near the free surface. Distribution profile derived by the log-Wake law depicts the velocity which increases monotonically with increase of the distance from the bed. Thus, it is not capable to show the negative gradient of velocity near the free surface which happens in narrow open channels. In narrow open channels, the three dimensional structure of the flow and the transport momentum from the side walls to the central zone -due to strong secondary currents- will cause the maximum velocity to occur below the water surface. This is called velocity-dip phenomenon which -for the first time- is reported more than a century ago. Since that time, numerous investigations have been conducted by many researchers in order to propose new models; not only for describing the dip phenomenon and negative gradient of velocity near the free surface, but also to predict the position of the maximum velocity accurately and to converge the experimental data throughout the whole flow depth. This paper introduces an analytical model based on Reynolds Averaged Navier Stokes (RANS) equations and an eddy viscosity distribution, to estimate velocity distribution in turbulent fully-developed flows. The proposed model is suitable for both narrow and wide open channels and is capable of predicting the dip phenomenon. The numerical results are verified with experimental data measured in several rectangular lab channels and data collected from an actual sewer channel. Since the proposed equation for velocity distribution is dependent on Coles Wake parameter (Π), the effect of this parameter has been studied on the level of accuracy and description of velocity profile as well as prediction of dip phenomenon and location of maximum velocity. Many researchers have proposed different values for Coles Wake parameter. Thus, seemingly there is no universal constant value for this parameter. In this study, the value of Coles Wake parameter is proposed using data from different channels, based on the least error calculated in predicting the velocity profiles by the proposed model. The results show that the profiles derived by the model agreeably match with experimental data, and predict the velocity-dip phenomenon. The model also contains few errors in comparison with the data measured in the channels. This shows a high level of accuracy in defining velocity distribution profile of the flow. The value of Coles Wake parameter estimated for channel-sewer is less than that for lab channels.