نوع مقاله : مقاله پژوهشی

نویسندگان

• مصطفی اکبری خیرآبادی ¹
• مهدی کرمی مقدم ²
• تورج سبزواری ³
• زهرا قدم پور ⁴

¹ دانشجوی دکتری مهندسی عمران، گرایش آب و سازه های هیدرولیکی، دانشگاه آزاد اسلامی واحد استهبان، ایران

² استادیار، گروه کشاورزی، دانشگاه پیام نور، ایران.

³ دانشیار، گروه مهندسی عمران، واحد استهبان، دانشگاه آزاد اسلامی، استهبان، ایران.

⁴ استادیار، گروه مهندسی عمران، واحد استهبان، دانشگاه آزاد اسلامی، استهبان، ایران.

چکیده

یکی از راه­ های افزایش ظرفیت تخلیه در سرریزها، استفاده از سرریزهای غیرخطی است. نوع جدید سرریزهای غیرخطی، سرریز کلیدپیانویی است. اکثر تحقیقات گذشته روی سرریز کلید پیانویی نوع مستطیلی تمرکز داشته و عملکرد سرریز کلیدپیانویی ذوزنقه ­ای کمتر بررسی شده است. در این تحقیق، اثر زاویۀ دیوار جانبی کلید و ارتفاع سرریز کلیدپیانویی ذوزنقه ­ای روی بار آبی کل بالادست و ضریب دبی سرریز به‌صورت آزمایشگاهی بررسی شد. آزمایش ­ها روی سرریز کلیدپیانویی مستطیلی به عنوان شاهد و سرریز کلیدپیانویی ذوزنقه ­ای با زاویۀ دیوار جانبی 4، 8، 12 و 14 درجه اجرا شد. سه نسبت­ ارتفاع سرریز به عرض یک سیکل (P/W_u) برابر 0.75، 0.875 و 1 برای سرریزها انتخاب شد. نتایج بررسی­ ها نشان می­دهد در دبی ­های بالا، در یک دبی مشخص، بار آبی ایجاد شده در بالادست سرریز کلیدپیانویی مستطیلی نسبت به سرریزهای کلید پیانویی ذوزنقه ای بیشتر است. حداکثر ضریب دبی ( برابر 0.611) مربوط است به سرریز کلیدپیانویی ذوزنقه ­ای با زاویۀ دیوار جانبی 12 درجه. حداکثر و متوسط ضریب دبی در بار آبی بالا، به‌ترتیب حدود 14 درصد و 10 درصد بیشتر از ضریب دبی در نوع مستطیلی است. همچنین، با افزایش نسبت ارتفاعی P/W_u، مقدار ضریب دبی در سرریز کلیدپیانویی ذوزنقه ­ای کاهش می­ یابد. نتایج تحقیق نشان می­دهد رابطۀ لمپریر برای سرریز کلیدپیانویی مستطیلی تیپ A و در شرایط خاص هیدرولیکی جواب قابل قبول ارائه می­دهد.

کلیدواژه‌ها

• استغراق محلی
• سرریز زیگزاگی
• سرریز کلیدپیانویی
• ظرفیت تخلیه
• کشش سطحی

عنوان مقاله [English]

Experimental Study of Effect of Sidewall Angle and Weir Height on Total Head and Discharge Coefficient in Trapezoidal Piano Key Weir

نویسندگان [English]

• mostafa akbari ¹
• mehdi karami moghadam ²
• touraj sabzevari ³
• zahra ghadampour ⁴

¹ PhD Candidate in Civil Engineering, (water and hydraulic structure), Islamic Azad University, Estahban branch, Estahban, Iran.

² Assistant Professor, Department of Agriculture, Payame Noor University (PNU), Iran. Email: m_karami_mo@yahoo.com

³ Associate Professor, Department of Civil Engineering, Estahban Branch, Islamic Azad University, Estahban, Iran

⁴ Assistant Professor, Department of Civil Engineering, Estahban Branch, Islamic Azad University, Estahban, Iran.

چکیده [English]

Extended Abstract
 
Introduction
The simplest form of non-linear weirs, the labyrinth weirs enjoy a high foot width as a disadvantage. A recently welcome type of the weirs, the piano key weir (PKW) possesses smaller foot width thanks to having ramps, overhangs, and parallel sidewalls (Crookstoon et al., 2018). Several investigations were carried out on the performance of a PKW. Surveying on PKW with W_i/W_o=1.2, Anderson and Tullis (2013) got the fact that applying total head (H_t) in the equation of Lamperier (2009) estimates the discharge higher by 10.1% on average and by 10.9% at most. In addition to the study of physical models, the 3D numerical simulation was done on PKW by Lefebvre et al. (2014) and Pralong et al. (2011b) yielding the results conforming with the experimental data. Most of the hitherto conducted researches were focused on RPKWs with few attention paid on the hydraulic of TPKWs. In this research, the impact of increase in the key angle and the weir's height in TPKWs on the total upstream head and on C_d were investigated. Also, the results obtained with reference to this type of weir were compared to the rectangular type as well as the recent works in the literature.
 
Materials and Methods
Laboratory Model
The experiments were conducted in the flume of hydraulic laboratory of Water and Power Organization of Khuzestan. The flume was of 7m length, 0.6m width, and 0.5m height. Five models were employed for the experiments in the free-flow condition. These include RPKW and TPKW with sidewalls making angles 4º, 8º, 12º, and 14º with the flow direction.
Experiment Process
Following the installment of one of the models in the flume, the flow was regulated with a certain discharge by means of a pump and a triangular weir. After the flow was stabilized, the water level at the upstream together with the water head on the weir (H) was taken. Then, the total head (H_t) and discharge coefficient were computed through the following:
 
 
Where, H_t (m) designates the total upstream head at the upstream, H (m) stands for the piezometric head relative to the weir elevation, and V_u (m/s) is the flow velocity at the upstream.
 
Results and Discussion
The relation between the ratio H_t/p < /em> and C_d is illustrated in Figure (1) for all the models used in this research.
The maximum amount of the coefficient C_d for RPKWs and TPKWs with key angles 4º, 8º, 12º, and 14º were attained, respectively as 0.54, 0.58, 0.56, 0.611, and 0.59. This guarantees that the maximum discharge coefficient belongs to TPKW with sidewall angle 12º. The figure also substantiates that C_d takes less values in RPKWs respective to TPKWs, a fact agreeing with the findings of Safarzadeh and Noroozi (2014). Figure (2) draws the curve of H_t/p < /em> against C_d for three height ratios P/W_u.
As observed, for all the ratios, first the C_d value grows and reaches its maximum, and then decreases. The decrease in C_d values occurs also along with an increase in the ratio P/W_u. The differences among the values of C_d in various ratios of P/W_u broaden as the ratio H_t/p < /em> increases. So, there is a reverse relationship between C_d and P/W_u.
 
Conclusion
In this research, the discharge coefficient and the total heads of trapezoidal and rectangular piano key weirs were studied and compared. Three cycles, total crest length of 1.65 m, the ratio W_i/W_o=1, and three height ratios 0.75, 0.875, and 1 were adopted for the key piano weirs. The sidewall angles of the key for the trapezoidal piano key weirs were selected as 4º, 8º, 12º, and 14º. The most important results obtained were as follows:
- In a certain discharge, the total upstream head of TPKW is less than that of the rectangular counterpart.
- The discharge coefficient value in TPKW is greater than in RPKW.
- The highest discharge coefficient 0.611 corresponded to the 12 º piano key weir.
- The Lampiere's equation (2009) provides an acceptable solution for type A and in particular situations.
- An increase in P/W_u leads to a decrease in discharge coefficient value.
- The maximum discharge capacity of the 12 º TPKW is 2.35 times that of ogee weir, and it is 2.8 times that of the linear sharp-crested weir.
 
Acknowledgement
This article was excerpted from a Ph.D. thesis in Water and Hydraulic Structures, Islamic Azad University, Estahban Branch.

کلیدواژه‌ها [English]

• Discharge Coefficient
• Labyrinth Weir
• Local Submergence
• Surface Tension