نوع مقاله : مقاله پژوهشی

نویسندگان

• سید محمد زارع ¹
• سهراب نظری ²

¹ دانش آموخته کارشناسی ارشد مهندسی عمران- آب و سازه های هیدرولیکی، واحد اقلید، دانشگاه آزاد اسلامی، اقلید، ایران

² گروه مهندسی عمران آب ، واحد اقلید، دانشگاه آزاد اسلامی، اقلید، ایران

چکیده

آبشستگی موضعی در پایین‌دست جام‌های پرتابی یکی از مسائل مهم در طراحی و ایمنی سازه‌های هیدرولیکی است و هندسۀ جام می‌تواند بر ویژگی‌های حفرۀ فرسایشی تأثیرگذار باشد. هدف این پژوهش، بررسی آزمایشگاهی اثر هندسۀ جام‌های پرتابی دایره‌ای و مثلثی بر مشخصات آبشستگی پایین‌دست و توسعۀ روابط پیش‌بینی‌کننده برای پارامترهای اصلی فرسایش است. آزمایش‌ها در شرایط مختلف هیدرولیکی و هندسی اجرا شد و حداکثر عمق فرسایش (d_s)  فاصلۀ محل وقوع حداکثر عمق فرسایش(L_s)  به‌عنوان متغیرهای وابسته اندازه‌گیری شدند. به‌منظور تحلیل داده‌ها، از تحلیل ابعادی و مدل‌های رگرسیونی توانی چندمتغیره استفاده شد و عملکرد مدل‌ها با شاخص‌های آماری شامل ضریب تعیین (R²) ، ضریب نش–ساتکلیف (NSE)، ریشۀ میانگین مربعات خطا (RMSE)، میانگین قدر مطلق خطا (MAE) و درصد میانگین قدر مطلق خطا (MAPE) ارزیابی گردید. برای مقایسۀ عملکرد دو هندسه، آزمون‌های آماری استنباطی و تحلیل باقیمانده‌ها صورت گرفت و نتایج نشان داد که با افزایش دبی جریان، حداکثر عمق فرسایش و فاصلۀ محل وقوع آن در هر دو نوع جام افزایش می‌یابد. مقایسۀ دو هندسه نشان داد که جام مثلثی، در محدودۀ شرایط آزمایشگاهی مورد بررسی، به‌طور متوسط موجب کاهش حدود 11 درصد در حداکثر عمق فرسایش و افزایش حدود 40 درصد در فاصله محل وقوع حداکثر فرسایش نسبت به جام دایره‌ای می­شود. نتایج آزمون‌های آماری نیز معنی‌دار بودن تفاوت مشاهده‌شده بین دو هندسه را تأیید کرد. مدل‌های رگرسیونی پیشنهادی دقت قابل قبولی داشتند و بررسی نمودارهای یک‌به‌یک و باقیمانده‌ها کفایت کلی مدل‌ها و نبود خطای سیستماتیک قابل توجه را نشان داد. در مجموع، نتایج بیانگر تأثیر معنی‌دار هندسه جام پرتابی بر پاسخ فرسایشی پایین‌دست است. با این حال، نتایج در محدودۀ شرایط آزمایشگاهی مطالعۀ حاضر قابل تفسیر است و بررسی مستقیم مشخصات هیدرودینامیکی جت و اجرای آزمایش‌های تکراری می‌تواند موضوع پژوهش‌های آینده باشد.

کلیدواژه‌ها

• آبشستگی موضعی
• جام پرتابی
• هندسه جام
• حداکثر عمق فرسایش
• تحلیل رگرسیون توانی

موضوعات

• هیدرولیک

عنوان مقاله [English]

Experimental Investigation of the Effect of Circular and Triangular Ski-Jump Bucket Geometries on Downstream Scour Characteristics

نویسندگان [English]

• Seyed Mohammad Zare ¹
• Sohrab Nazari ²

¹ M.Sc. Graduate in Civil Engineering – Water and Hydraulic Structures, Eghlid Branch, Islamic Azad University, Eghlid, Iran.

² Department of Civil -Water Engineering, Eghlid Branch, Islamic Azad University, Eghlid, Iran.

چکیده [English]

Extended Abstract
Introduction
       Local scour downstream of hydraulic structures is an important concern in the design and long-term safety of spillways and energy dissipation systems. High-velocity flow issuing from ski-jump buckets interacts with the downstream water and movable bed, resulting in the formation of scour holes. The characteristics of these scour holes depend on hydraulic conditions, sediment properties, tailwater depth, and bucket geometry. Among these factors, bucket geometry can influence the measured scour response downstream. Although numerous studies have investigated scour downstream of ski-jump buckets, comparative experimental studies focusing on different bucket geometries remain limited. Therefore, the present study investigated the influence of circular and triangular ski-jump bucket geometries on downstream scour characteristics. The main hypothesis of this study was that changing the bucket geometry under similar hydraulic and sediment conditions could significantly modify the downstream scour response. Accordingly, the objective was to experimentally compare the effects of circular and triangular ski-jump buckets on the maximum scour depth (ds) and the distance from the bucket to the location of maximum scour (Ls). In addition, power-law regression models were developed to predict these scour characteristics.
Materials and Methods
       A series of physical model experiments was conducted using circular and triangular ski-jump buckets under controlled laboratory conditions. The experimental program included different hydraulic and geometric conditions and consisted of 108 experimental runs. A movable sediment bed was used to evaluate the downstream scour response. The maximum scour depth (ds) and the distance to the location of maximum scour (Ls) were considered as the principal dependent variables. The effects of discharge, tailwater conditions, and characteristic geometric parameters of the buckets were investigated. Dimensional analysis was used to identify the governing dimensionless parameters. Based on the experimental data, separate multivariable power-law regression models were developed for each bucket geometry and scour parameter. The performance of the proposed models was evaluated using the coefficient of determination (R²), Nash–Sutcliffe efficiency (NSE), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). One-to-one plots and residual analyses were also used to assess the agreement between measured and predicted values and to identify possible systematic errors. Furthermore, statistical tests were performed to evaluate the significance of differences between the scour characteristics produced by the two bucket geometries at a 5% significance level. Each experimental condition was conducted once, and independent repeated tests were not performed for all conditions. Consequently, between-run variability could not be directly quantified. However, the sediment bed was prepared and leveled before each experiment, and the hydraulic and geometric conditions were controlled according to the experimental design.
Results and Discussion
       The results showed that discharge was one of the principal parameters affecting downstream scour development. Increasing discharge generally increased both the maximum scour depth and the distance to the location of maximum scour for both circular and triangular buckets. Comparison of the two geometries revealed clear differences in their measured scour responses. Within the investigated range of experimental conditions, the triangular ski-jump bucket produced a lower average maximum scour depth than the circular bucket. The average reduction in maximum scour depth was approximately 11%. The distance to the location of maximum scour also differed between the two configurations. The triangular bucket increased this distance by approximately 40% compared with the circular bucket. Therefore, under the investigated laboratory conditions, the maximum scour occurred farther downstream when the triangular configuration was used. Statistical comparisons confirmed that the differences between the circular and triangular buckets were significant at the 5% significance level for both maximum scour depth and the location of maximum scour. These results indicate that bucket geometry has a significant effect on the measured scour response. The proposed power-law regression models provided satisfactory predictions within the range of the experimental data. The statistical performance indices showed good overall agreement between measured and predicted values. In addition, the one-to-one plots demonstrated that the predicted values were reasonably distributed around the line of equality. Residual analyses also supported the overall adequacy of the proposed models. The residuals were generally distributed around zero, with no pronounced systematic pattern. However, the normality assumption was not equally supported for all models. Therefore, model performance was assessed using a combination of statistical indices and graphical analyses. The results provide direct experimental evidence that bucket geometry affects downstream scour characteristics. However, hydraulic variables such as velocity distribution, residual jet energy, pressure distribution, and bed shear stress were not directly measured. Therefore, the detailed hydrodynamic mechanisms responsible for the observed differences cannot be confirmed directly and require further investigation.
Conclusions
       This study experimentally investigated the influence of circular and triangular ski-jump bucket geometries on downstream local scour characteristics. The results demonstrated that discharge and bucket geometry significantly affected the maximum scour depth and the location of maximum scour. Increasing discharge generally increased both scour depth and the downstream distance to the location of maximum scour. Within the investigated experimental range, the triangular bucket reduced the average maximum scour depth by approximately 11% compared with the circular bucket. In contrast, the distance to the location of maximum scour increased by approximately 40% for the triangular configuration. Statistical analyses confirmed that the differences between the two geometries were significant for both investigated scour parameters. Furthermore, the proposed multivariable power-law regression models showed satisfactory predictive capability within the range of the experimental data. The combined use of statistical performance indices, one-to-one plots, and residual analyses supported the overall applicability of the developed models. Overall, the findings confirm that ski-jump bucket geometry is an important factor influencing downstream scour characteristics. Under the laboratory conditions investigated, the triangular bucket showed more favorable performance in terms of reducing maximum scour depth while shifting the location of maximum scour farther downstream. The absence of repeated tests and the lack of direct measurements of jet hydrodynamic characteristics are limitations of the present study. Future investigations should include repeated experiments under representative conditions and direct measurements of flow characteristics to provide a better understanding of the mechanisms governing downstream scour.
 Conflict of Interest
       The authors declare that they have no conflict of interest regarding the preparation and publication of the materials and findings presented in this study.
Funding
       The authors received no financial support for the research, authorship, or publication of this article.

Data Availability Statements
       The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.
 Author Contribution
Seyed Mohammad Zare: Data Collection, Working in Laboratory and Sohrab Nazari: Writing, Methodology, Investigation and Data Curation, Analysis, Guidance and Supervision, Text Editing, Completion and Data Collection.
 Acknowledgement
       The authors wish to express their sincere gratitude to the Editor, two anonymous reviewers and the copy editor for their insightful comments and constructive feedback, which significantly improved the quality of this manuscript.

کلیدواژه‌ها [English]

• Local scour
• Ski-jump bucket geometry
• Maximum scour depth
• Dimensional analysis
• Power regression modeling