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Kararsız akım altında düzgün tabanda basınç dalgalanmaları

Pressure fluctuations under the unsteady flow over the smooth bottom

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  1. Tez No: 961802
  2. Yazar: SAMED BERKUT BÜTÜN
  3. Danışmanlar: PROF. DR. ŞEVKET ÇOKGÖR
  4. Tez Türü: Yüksek Lisans
  5. Konular: İnşaat Mühendisliği, Civil Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 2025
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Lisansüstü Eğitim Enstitüsü
  11. Ana Bilim Dalı: İnşaat Mühendisliği Ana Bilim Dalı
  12. Bilim Dalı: Hidrolik ve Su Kaynakları Mühendisliği Bilim Dalı
  13. Sayfa Sayısı: 115

Özet

Artan su ve enerji ihtiyaçları, iklim düzenleme gereksinimleri veya afetlerden korunma amacıyla dünyada yaygın şekilde inşa edilen yapılar olan barajların temel işlevi, akarsuyun önünde bir set oluşturup suyu bir bölgede biriktirmek ve gerektiğinde suyun güvenli bir şekilde rezervuardan akarsuya geçişini sağlamaktır. Rezervuarda bekleyen suyun ve kararlı akımın baraj gövdesine tesiri hidrostatik koşullar çerçevesinde gerçekleşmektedir ve barajların inşasından önceki hidrolik mühendisliği hesaplarının geneli hidrostatik etkilere dairdir. Ancak rezervuardaki suyun mansaba tahliyesi işlemi esnasında durgun su harekete geçmekte, barajların suyu mansaba aktarma işlevini haiz elemanları olan dolusavakların tabanında kararsız akım oluşmaktadır. Dolusavaklardan kararsız akımın geçmesi, dolusavak tabanında öngörülemez basınç dalgalanmalarının görülmesine yol açmaktadır ki günümüze değin konuyla ilgili yapılan çalışmalarda, basınç dalgalanmalarının baraj tabanındaki beton blokların stabilitesini olumsuz etkilediği gösterilmiş ve olumsuzlukları en aza indirecek çareler aranmıştır. 1954'te Dickinson Barajı'nda, 1974'te Keban Barajı'nda, 1983'te Big Sandy Barajı'nda ve 2017'de Oroville Barajı'nda meydana gelmiş olan dolusavak çökmelerinin sebebi; isabetli ölçümlerle modellenmesi hususunda hâlen yetersiz kalınan, tahmin edilemez durumdaki hidrodinamik kuvvetlerin beton bloklar üzerinde yarattığı hasar ve destabilizasyonlardır. Bu çalışmanın hedefi; dolusavak tabanındaki basınç dalgalanmalarının mekaniğini matematiksel bir çerçevede incelemek, böylece gelecekteki baraj hesaplarında daha stabil ve güvenli taban dizaynlarına yeni bilgi ve çıkarımlar sağlamak olmuştur. Çalışmanın deney aşaması, dolusavakları temsilen bir açık kanal düzeneği kurmakla başlamıştır. Kanalda, ölçüm bölgesinin gerisinde, suyun kararlı ve kararsız akım gerçekleştirmesini sağlamak için açılır kapanır bir kapak mevcuttur. Dolusavak tabanında kararlı ve kararsız akım altında gerçekleşecek basınç dalgalanmalarını incelemek için kanal tabanına ilk kapak yerinden 2 m, ikinci kapak yerinden 0.5 m uzaklıkta, birbirinden birer cm mesafeyle ayrılmış, akım yönünde sıralı art arda üç delik açılmış ve deliklere bağlanan transdüserler vasıtasıyla basınç ölçer Arduino'ya her bir deneyde 25 saniye boyunca, saniyede ortalama 75 adet veri sağlanmıştır. Arduino'dan bilgisayara sağlanan ham veriler kalibre edilip işlendikten sonra, yine Excel yazılımı kullanılarak kararlı ve kararsız akıma ait basınç dalgalanmalarının ortalama eğrileri çizilmiş, türbülans bileşenlerinin RMS değerleri kararlı ve kararsız akım için ayrı ayrı hesaplanmış ve sensörler arası korelasyon incelenmiş, türbülans bileşenlerinin olasılık yoğunluk dağılım histogramları oluşturulmuştur. Ayrıca; türbülansın karakteristik davranışlarıyla, kararsız akımın başlangıçtan zirveye ulaşma hızıyla ilgili olan kararsızlık parametresi arasındaki ilişki de incelenmiştir. Sonuçlar göstermiştir kararsız akım gerçekleştiğinde türbülans bileşenlerinin RMS değerleri önemli miktarda artmış ve en büyük değerler kararsız akımın düşüş fazında görülmüş, ayrı noktalarda ölçüm yapan üç transdüser arasında yüksek bir korelasyon gözlemlenmiş, türbülans bileşenlerinin olasılık yoğunluk dağılımı histogramlarında bazen pozitif, bazen negatif tarafa doğru hafif çarpıklıklar görülmüştür ve belirli bir yönelimde istikrar göstermeyen bu çarpıklıkların arkasında türbülansın karakteristiğine yorulabilecek bir sebep saptanamamıştır. Kararsızlık parametresi ile türbülans bileşenlerine ait RMS değerleri grafik üzerinde incelenmiş, uyum gösterdikleri kısımlar olmakla birlikte aralarında net bir korelasyon saptanamamıştır. Çalışmadan varılan saptamalarda da görülmüştür ki kararsız akım koşulları altında, dolusavak tabanı ön görülemez şiddette ve yönlerdeki basınç dalgalanmalarına maruz kalmaktadır ve kanal tabanının temsil ettiği dolusavak tabanındaki beton bloklar, söz konusu basınçların etkisiyle bazen kırılma, bazen de emme kuvvetiyle yerinden kaldırılma riskleriyle karşı karşıyadır. Çalışmadan çıkarılan sonuçlar, konuyla alakalı yapılmış literatür taramasında gözlemlenenen bilgi ve çıkarımlarla çoğunlukla tutarlılık göstermektedir. Neticede; dolusavak tabanı dizaynı yapılırken, su tahliyesi için kapakların açıldığı veya taşkına maruz kalındığı hâllerde ortaya çıkacak kararsız akımın dolusavak tabanındaki beton blokların stabilitesi için hayati riskler teşkil ettiği ortaya koyulmuştur. Hidrostatik etkilere ek olarak taban stabilitesini olumsuz etkileyen ekstra basınç ve emme kuvvetleri meydana getiren türbülans, kararsız akım geldiği esnada kararlı akımdakine göre ciddi büyüme göstermekte ve en büyük değerler kararsız akımın düşüş evresinde gözlemlenmekte; negatif ve pozitif çalkantı bileşenleri arasında görülme frekansı bakımından istikrarlı bir üstünlüğün olmadığı saptanmaktadır.

Özet (Çeviri)

Increasing water and energy demands, climatic and geographical regulations or disaster prevention requirements lead to the construction of dams worldwide. The primary function of a dam is collecting the water in a reservoir area by creating a barrier in front of a river and transferring the water from reservoir to river again safely. The effect of the stored stationary water in reservoir and the steady flow on dam body occurs at a hydrostatic level, and the hydraulic engineering calculations before the dam construction are generally about these hydrostatic effects. However, during a flood discharge or release of the stored water to downstream, the previously stationary water transitions into motion and the steady flow transitions into unsteady flow. Unsteady flow through spillway causes unpredictable pressure fluctuations on spillway floor, and the negative effects of the pressure fluctuations on stability of concrete blocks have been indicated and the solutions to minimize these effects have been analyzed in previous studies in the literature. The spillway collapses that occurred in Dickinson Dam in 1954, Keban Dam in 1974, Big Sandy Dam in 1983 and Oroville Dam in 2017 are due to the destabilization and damages caused by the unpredictable hydrodynamic forces that are still inadequate to model with accurate measurements. The aim of this study is to examine the mechanics of the pressure fluctuations on spillway floor in a mathematical framework and providing new information and inferences for more stable and safe base designs in future calculations. In the context of instrumentation, a 50 cm x 50 cm plexiglass barrier that was able to close the channel completely was cut off and two nests were created to get the plexiglass gate inside, 3 and 4.5 meters after the beginning of the open channel. Another gate was placed at the end of the channel as well. A pump was attached to the system between the water pool and the channel. Three transducers perceiving the water pressure and converting them to the electronical signals were placed at the floor of the open channel. An Arduino was produced by an electronical engineer, which was able to take the electronical signals by transducers from the channel floor and record them in an Excel file in a computer with a timestamp 75 times on average per second as numeric values in 25 seconds of time series. The experimental stage of the study began with preparing the open channel representing the spillway and filling the pool that stores the water under the channel in order to be used for experiments by getting raised by a pump. Behind the measurement location in the open channel, an adjustable gate was placed in order to provide the steady and unsteady flow conditions separately. To investigate the pressure fluctuations under steady and unsteady flow on the smooth floor, three holes with 1 cm of interval and consecutively in flow direction were drilled and one transducer was connected to each hole; thus, on average 75 signals per second were sent to the Arduino for 25 seconds. Two types of pressure measurements were done: Pressure measurement during flow and the calibration measurement. The actual pressure measurement began with starting the pump to rise the stored water from pool under the channel to inside the V-notch weir behind the channel. After a while, the water was spilled to the open channel and the end gate was completely opened and the first gate was closed with 4.5 cm of opening with channel floor. Thus, it was provided that a 4.5 cm of steady flow was permitted to progress through the channel and also the water remained was accumulating behind the gate until 35 cm of water height, due to the difference between the incoming discharge and the permitted to pass through the opening under the gate. After the accumulating was completed, pressure measurement operation started in the computer and then, the plexiglass barrier was opened with various speeds for each experiment, and after various times of waiting sections in different experiments, closed again until 4.5 cm of gap. Therefore, unsteady flow was created and both steady and unsteady flows were measured and recorded in the Excel file in the computer. In the calibration context, the upstream and the downstream gates were closed and an amount of water was stored inside in stationary situation. Then, pressure measurement was completed and after saving the Excel file, small amount of water was spilled by slightly opening the end gate and the gate was closed again. So, with the less amount of stationary water, the pressure measurement was repeated. These operations were repeated 6 times until the water height got almost zero. By using the calibration data in Excel, a calibration curve is almost a straight line was obtained, and a second order equation was extracted with curve-fitting method. The result of the equation was equal to the measurement results converted to the numeric value from electronical signals by Arduino, and the unknown in the equation was the real pressure value in terms of centimetre. The calibration process was realized for all of the experiment results in Excel and the water pressures were calculated. After calibration of the raw data provided by the Arduino in an Excel file in the computer, the pressure fluctuation graphs were divided to three parts as steady flow, rising stage of unsteady flow and falling stage of unsteady flow. Then, the mean pressure was calculated for steady flow and it was drawn for each measurement moment as a straight line, so this line was accepted as the average steady flow pressure graph. Concerning the unsteady flow pressures, for both two phase of unsteady flow, the average pressure curves were drawn on Excel software by using the curve fitting function respectively and the third order of equations were extracted for average curves. Attention was paid for the R2 values of equations not to be under 0.85, in order to make the consistency in a rational framework. Thus, by putting the time in unit of ms, the equations yielded results as momentary pressure in unit of centimetre. By subtracting the momentary mean pressure from the actual pressure, the turbulence components were obtained. In order to figure out the magnitude of the turbulence components through the time series, the Root Mean Square (RMS) values of the turbulence components were calculated for both flow conditions and all three sensors respectively. Moreover, the correlation between the time series of the turbulence component for each sensor were calculated and the probability density distribution histograms of turbulence components were created, separately for each of the three phases. To obtain the incoming discharge, the height difference between the empty and filled case of the V-notch weir was read, then it was put in the V-notch discharge equation, and the discharge efficiency factor Cd for 90⁰ of V-notch was used. Thus, the incoming discharge was calculated. Froude numbers were computed for each base and peak flows. Furthermore, the unsteadiness parameter (α) which is about the velocity of the unsteady flow from the finishing of the base flow to the peak point of the unsteady stage was also calculated by considering the suggestions and formulas in the paper, about the relationship between the characteristics of turbulence and the peak velocity, written by Nezu and Nakagawa in 1995. And the unsteadiness parameter was compared with the average RMS values of three sensors for each experiment, on graphs. The results consistently indicated that the RMS values significantly increase during the unsteady flow and they maximize in the falling stage, which means turbulence got greater in unsteady flow and was its greatest period in falling. Very high correlation was observed between all three transducers, so at the consecutively different points of the floor, the pressure fluctuations drew almost the same subtrends in the same timeline. Both negative and positive slight skewnesses were observed on frequency histograms of positive and negative turbulence components and any reason which can be interpreted as sourced by the characteristics of turbulence could not be determined behind these skewnesses that do not show a consistency toward any side. In addition, some common behaviors were investigated between unsteadiness parameter and RMS values, but no clear correlation could be detected. Under the unsteady flow conditions, which have two phases as rising and falling, the spillway base is exposed to pressure fluctuations of unpredictable magnitude and direction, and the concrete blocks represented by open channel floor are at risk of being lifted by suction force and breaking under the influence of these pressures. The results obtained from the study are mostly consistent with the information and inferences observed in the literature review on the subject. In conclusion; during the spillway base design, it has been determined that the vital risks that are caused by unsteady flow occur when the gates are opened to release the stored water or a flood discharge occurs. Turbulence, which is the source of the breaking and lifting forces that negatively affect the floor stability, significantly indicates clear increase under the unsteady flow and the highest values are observed in its falling phase. When the pressure fluctuations are investigated under the unsteady flow conditions, it is seen that there are positive and negative peaks consecutively throughout the graph, which means there will be an extra fatigue on the floor due to extra opposing hydrodynamic tensions other than the hydrostatic tension, and this situation requires additional precautions like anchors for floor safety. Froude numbers got greater in peak flow and both base and peak flows had Froude numbers bigger than 1, which means both flows were supercritical. Additionally, it is determined that there is no consistent dominance in terms of frequency of occurrence between the negative and positive turbulence components, a bright prepotency between the magnitude of total pressure and total lifting forces could not be found out. In addition, the unsteadiness parameter does not indicate a clear correlation with the magnitude of the turbulence components in an unsteady flow, which means peak velocity is not clearly related to the characteristics of turbulence.

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