Arıtma tesislerinde debi dağıtım kanallarının hesabı /
Yazar: EBUBEKİR YÜKSEL
Danışman: PROF.DR. YILMAZ MUSLU
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü
Derece: Yüksek Lisans, 1995
Konu: Çevre Mühendisliği = Environmental Engineering
Dizin: Arıtma tesisleri = Treatment plants ; Debi = Flow

Özet:
Çevre Mühendisliğinde debi dağıtım problemi ile, ayrık sistemde arıtma tesisi giriş yapılarının hesabında, birleşik sistemde ise dolu savakların boyutlandırılmasında karşılaşılır. Bu çalışmada arıtma tesislerinde kullanılan debi dağıtım kanallarının boyutlandırılması için bir iterasyon yöntemi geliştirilmiş ve nümerik uygulamaları verilmiştir. Beş bölüm olarak sunulan bu çalışmanın birinci bölümünde, birleşik sistem kanallarında dolu savaklarla akım ve kirlenme kontrolü hakkında kısa bir bilgi yer almaktadır. İkinci bölümde, dolu savakların hesabı için literatürde mevcut yöntemler ayrıntılı olarak ele alınmış ve geliştirilen bir nümerik yaklaşımın bunlar arasındaki yeri belirtilmiştir. Üçüncü bölümde, debi dağıtım kanallarının hesabı için geliştirilen analitik yöntemler ele alınmıştır. Dördüncü bölümde, arıtma tesislerinde debi dağıtım kanallarının bilgisayarla hesabı için literatürde mevcut hesap metodları açıklanmıştır. Beşinci bölüm, bu çalışmanın esasını teşkil eden nümerik yöntemin ve geliştirilen bilgisayar programlarının açıklanmasına ayrılmıştır. Bu bölümde savaklı giriş yapılarında debi dağıtımı için nümerik bir çözüm elde edilmiştir. Bu maksatla, ikinci bölümde ayrıntılı olarak incelenen yan savak problemi için en uygun sonuç veren nümerik bir yaklaşım kullanılmıştır. Savaklar arasındaki geçişte su yüzü profili kanal tabanına paralel kabul edilmiştir. Böylece savakları birleştirmek ve tüm savakları tek bir savak olarak idealize etmek mümkün olmuştur. Bu nümerik çözümde su yüzünün enine doğrultudaki alçalması bir katsayısı ile hesaba katılmıştır. Savak kafi derecede küçük parçalara ayrılmış ve her bir savak parçası için Froude sayısının fonksiyonu olan bir C^, debi katsayısı kullanılmıştır. Geliştirilen bilgisayar programlan, deney sonuçlarına uygulanmış ve teori ile pratik arasında tam bir uyum olduğu gözlenmiştir. Daha sonra geliştirilen bilgisayar programlarının çeşitli uygulamaları verilmiş ve elde edilen sonuçlar özetlenmiştir.

Abstract:
In water and wastewater treatment plants, as well as in various applications of environmental engineering such as storm water overflows in combined sewerage systems, open channels with side discharge weirs are often used to distribute incoming flow to parallel treatment units or diversion works. Such channels are referred to as distribution channels. In the first chapter of this thesis flow distribution in combined sewerage system is studied with the consideration of pollution control. A combined sewer carries both wastewater and storm-water runoff. Wastewater-treatment facilities are generally sized to handle dry-weather wastewater flows, but not the high flow rates and volumes associated with storm-water runoff. Where existing combined sewers must be used to deliver to a treatment facility, it may be necessary to provide a diversion or overflow structure. Storm water may be diverted by side weirs, baffled side weirs, transverse weirs, leaping weirs and relief siphons. Flow control in distribution channels of treatment units is normally achieved by rectangular weirs and submerged orifices. In this study, control of flow by means of side discharge weirs has been considered. A trough investigation of various methods regarding the design of side weirs is therefore necessary. A literature survey was made for this purpose in chapter 2. Side weirs can be classified in two different groups: Side weirs with water depths increasing from upstream to downstream directions (subcritical flow) and those with decreasing water depths (supercritical flow). In distribution channels of treatment units, mostly side weirs with increasing water surface profile are encountered. Various approaches developed and proposed by De Marchi (1934); Collinge (1957); Fair, Geyer (1980); Chao and Trussell (1980); Tchobanoglous (1981); Benefield (1984); and Muslu-Tozluk (1994) were reviewed in detail. Numerical examples were solved for the sake of comparison. It was concluded that the approach developed by Muslu-Tozluk (1994) is usable for numerical application and it also agrees well with the experimental results. Analytical approaches to flow distribution in treatment plants were studied in Chapter 3. They are approximate methods because variation in flow over side weirs is neglected, although its variation is controlled by means of a dimensionless parameter M xu M = - (1) in which qx is the rate of flow for the first and o^ is the rate of flow for the last inlet structure. Design formulas were derived and an approximate hydraulic profile was also given as a result of a literature survey. In chapter 4, computer methods have been outlined for flow distribution in rectangular prismatic channels when flow control is achieved by different means. A numerical method proposed by Chao and Trussel (1980) was explained. This is a step method wherein the flow characteristics of each weir determined by proceeding step by step from the downstream end of the distribution channel to the upstream end where the flow enters the channel. Weir coefficient Cw was estimated from Subramanya and Awasthy (1972) formula assuming an average weir head whereas it changes along the channel. This is the most important weakness of the method which was corrected by the approach of Muslu and Tozluk (1995). This point was taken into account at the present study. Another drawback for the numerical approach of Chao and Trussell (1980) is that there are various iteration procedure inside the program due to the step by step application of hydraulic formulas. Depth of flow at the upstream end of each weir is determined at the end of an iteration procedure which results in too long computer times. In chapter 5 a new approach was developed based upon computer programming for the flow distribution in treatment units. In the numerical method outlined in Chapter 4, hydraulic head on the weir is assumed constant whereas it increases or decreases in flow direction. There is a numerical error due to the step by step calculation because flow is a continuous phenomenon. Therefore in Chapter 5, a procedure was developed in which weirs were divided into small portions to represent flow conditions continuously. Each weir portion was considered as an individual unit having a discharge coefficient Cw. Dimensionless coordinates were used and C^ was expressed as a function of Froude number Fr. <=? - (0-614-(f^TI (2) as suggested by Subramanya and Awasthy (1972) in which Fr is a function of the diverted jet from the side weir. On the other hand, water depth decreases towards the weir crest in directions perpendicular to the channel axis. Change in water depth was expressed by a dimensionless parameter v|/=^ (3) in which h' is depth of water at the weir plane whereas h is the water depth of water at channel axis, as shown in the following figure: 4_" Figure 1. Lateral water surface profile in a distribution channel with side weirs In this thesis, a function of i|/=l- 0.036 Fr (4) empirically derived by Muslu (1995) was used to determine the hydraulic profile along the channel. In the present approach inclination of the diverted flow from the weir is thus taken account by means of a Froude number whereas transversal slope is considered using a dimensionless parameter \j/. These dimensionless parameters were introduced into the energy equation. In order to generalize the results, flow depths were normalized using the following dimensionless parameters. Dimensionless depth = z = - (5) Dimensionless length = x = - b (6) Specific energy height E was assumed to be constant. A definite integral was obtained for the length of a side weir portion in which dimensionless depth of water increased from zx to Z2. Calculation procedure starts with the first weir portion under consideration. Here, the dimensionless flow depth z, should be known in order to perform the program. An iteration procedure is therefore necessary. With the known value of zx, dimensionless flow depth Z2 for the first weir portion was obtained from the definite integral (Eq. 2.20) in which L / b is chosen in such a way that results become independent of the L / b value used in the calculation. Output data obtained from the first weir portion were used as an input data to the next weir portion. This procedure is repeatedly performed for each weir portion until the value of t^ of the last weir portion is obtained. If this value corresponds to the downstream conditions at the end of the distribution channel, the value of zx used in the first iteration is correct, i.e. there is no need to repeat the calculations. Computer programs are given in Appendixes A to E. See table below for the computer output as an example in which 6 denotes the total dimensionless weir length in the distribution channel i.e. L (6XL2192) EAL/b = - = - - - - =6 b 1.2192 Table 1. Computer output obtained from Zi = 0.9638542 ; p/E = 0.80083534 AL/b= 0.04 ; Q = 0.65723 m3/ s ; b= 1.219200 m ;