Eşikler üzerindeki akım özellikleri ve katı tane hareketi

Abstract

IV ÖZET Doğadaki akarsuların yatakları, hemen her zaman, akımın belirli koşullar altında hareket ettirebileceği katı madde tanelerinden oluşurlar. Katı taneler akım içinde sürüntü ve sıçrama hareketleri ve askı hareketleri yaparlar. Suyun içinde bulunan ve yoğunluğu sudan çok daha fazla o- lan katı tanelerin, akım içinde tabandan uzakta askı ha ~ reket i. yapabilmesi akımın türbülansı nedeniyle olmaktadır. Son yıllara kadar yeterince incelenememiş bir konu olan akımın türbülans yapısı, son yıllarda teknolojik gelişme nin deney olanaklarını arttırmasıyla incelenebilmeye baş lanmıştır. Akımın türbülans yapısının, nasıl olup ta sudan çok daha yoğun katı taneleri tabandan kaldırdığının izahı Of fen-Kline' in taban yakınlarındaki akım modeline atıf ya pılarak Sümer ve diğer araştırıcılar tarafından verilmiştir. Tabanında çeşitli çaplarda katı taneler bulunan bir açık kanalda, akım özelliklerine bağlı olarak, tabanda bulunan tanelerin çeşitli taban yapıları oluşturacak şekilde hare ket ettiklerini biliyoruz. Nehir rejimindeki akımlarda ta ban şekilleri küçük üç boyutlu kum dalgacıkları (ripple) veya daha büyük iki boyutlu eşikler (dune) şeklinde olabi lir. Bu çalışmada akım tarafından (Q=ll l/s, h=6.5 cm) D[-q = 0,82 mm lik taban malzemesi üzerinde oluşturulan eşik taban üzerindeki akım ve tane hareketi incelenmiştir. Akım tarafından ortalama olarak 45 cm boy ve 3 cm yüksek liğe sahip, memba yüzleri yatık, mansap yüzleri yaklaşık 45° lik eşikler oluşturulmuştur. Daha sonra bir eşik üze rindeki çeşitli kesitlerde hız ve türbülans şiddetleri öl çülmüştür.v Ölçümlerde laboratuvar'da bulunan sıcak uç anemometresi kul lanılmış tır- Bu aşamada sıcak ucun kalibrasyonu su sıcaklı ğına bağlı olarak çok çabuk değiştiği içins kalibre işlemini kolayca yapabilmek amacıyla bir sistem geliştirilmiştir. Bu sistem ayrıntılı olarak Bolüm 3.4. de- açıklanmıştır. Sıcak uç anemometresini, bu çalışmada geliştirilen sistem le kalibre ettikten sonra anemometreden alman voltaj de ğerleri bilgisayarla değerlendirilmiştir. Çalışmanın son kısmında eşik üzerindeki katı madde hareke ti incelenmiş ve akım Özelliklerine bağlı olarak tabandaki katı tanelerin harekete geçişini karakterize edebilecek bir ifade bulunmaya çalışılmıştır. Tane deneyleri, olaya etki - yen parametre sayısını azaltmak amacıyla küresel tanelerle yapılmıştır. Tabandaki taneye diğer tanelerin etkisini de gözönüne ala bilmek amacıyla bir eşiğin üzerindeki küçük bir bölge sa bit çaptaki boncuklarla (3 ve 5 mm) kaplanmış, eşik üzerin deki akım özellikleri bilinen kesitlerin orta noktalarına rastlayan boncuklar çıkarılarak, buraya tabandaki malzemey le aynı çapta ve çeşitli yoğunluklardaki taneler konularak hareketleri defalarca gözlenmiştir. Bu deneyler sonucunda tabanda bulunan tanenin hareketinin W/XU^ çökelme hızı pa rametresine bağlı olarak ifade edilebileceği görülmüştür. Deney sonuçlarına göre, sözkonusu parametrenin 50 değerin de akım yapısından etkilenmeye başlayıp titreyen tane aynı parametrenin 12-20 değerlerinde sürüntü hareketi ve 5-12 değerlerinde de askı hareketi yapmaktadır. Tane hareketinin Shields parametrelerine bağlı olarak ifa de edilebileceği görülmüştür. Bu çalışmadaki deney koşul larında, 18 < Re < 85 aralığında tabanda bulunan tanenin akımın türbülans yapısından etkilenerek titremeye başla masının Fr^crO.01, sürüntü hareketi yapmaya başlamasının Fr^crO.04 - 0.06 ve askı hareketi yapmaya başlamasının Fr^ ~ 0.10 ~ 0.7 değerlerinde oluştuğu gözlenmiştir.

VI FLOW CHARACTERISTICS AND SEDIMENT TRANSPORT OVER THE DUNES SUMMARY The beds of rivers in nature are made up of sediment par ~ tides which the flow can move under certain conditions» The motion of sediment particles in flow can be separated, into two groups. a) Bed load and saltation: The particles at low flow velocity move by sliding, rolling and jumping. b) Suspension: At higher flow velocities, some of the par ticles move in flow medium away from the bed* Since discrimination of bed load, saltation and suspension is quite difficult, while studying sediment motion, discri mination of bed load and suspension is sufficient. The motion in the vicinity of the wall is in general func tion of YjU^, v. Here y is the distance from the wall, U is the shear' velocity, V is the kinematic viscosity of the fluid. By making dimensional analysis between these parameters, it can be seen that the dimensionless variable which characterizes the distance from the wall is as follows y U y v The turbulent boundary layer is studied in two regions + a) The wall region: is the region where y < 70. This region is studied in two sub-regionsVII a-1. Viscous sub-layer: is a region of which the thickness is not constant. The zone where y+< 2.5 is named passive and the zone where 2.5 < y < 5 is named active a-2. Generation region: is the region where 5 < y < 70. b) Outer region: is the region which is next to the wall region. Until recent years the structure of flow near the wall was assumed of random character. However the studies made with new techniques in recent years showed that the structure of flow near the wall was not random but quasi- cyclic. Of fen-Kline carrying out studies on this problem have proposed the following model for the quasi-cyclic sequenceo.f events in the vicinity of the wall. The flow at the bottom of an open channel is made up of low speed and high-speed regions» The low speed region is called low speed wall streak. The low-speed wall-streak having a finite length in vertical direction to the flow, is lifted up into the flow by a suddenly formed locals inverse pressure gra dient. The cell lifted up into the flow while being carried by the mean flow enlarges at the same time with respect to the centre of the cell in opposite direction. This opposite flow in the vicinity of the wall can be characterized by a local, inverse pressure gradient in that region. This structure, while passing over another low-speed wall-streak, lifts up this low-speed wall-streak into the flow. That is to say that the second cell has been lifted up into the flow. Then the second cell enlarges and interacts with the first cell, bursts and returns back to the wall. Lifting up into the flow, enlargement and disappearance sequence of the fluid particle which rises up into the flow from the vicinity of the wall, is called the bursting process. Sümer, making use of the model explained above, explains the phenomenon of lifting up of sediment into the flow from the bed as follows. Let us consider a particle which is on the bed. The high speed fluid while approaching the bed with a certain angle when strikes the bed divides into two towards the edges. The fluid moving towards the edges sweeps the particle in the vicinity into the neighboring low-speed wall-streak. In this case the particle will find itself swept into the low-speed wall-streak. In case the particle is sufficiently greater than the viscous sub-layer thickness, it will be inavoidable for it to escape being.S-iS VIII effected by the mechanism lifting the low-speed wall- streak up into the flow» This mechanism is a local s inverse and temporary pressure gradient due to the bursting which passes over the low-speed wall-streak. Therefore particle will feel the effect of the pressure gradient. The partic being lifted up from the bed with this effect moves in the flow till bursting disintegrates Initiation of motion of particles on the bed begins when bed shear stress reaches a certain value. However in prac tice mean flow velocity instead of bed shear stress is used for initiation of movement on the bed. In literature various formulas have been given for U which is the. cr velocity at which some of the particles on bed begin moving, for U^, the velocity at which the bed begins to take a wavy form, for U2»the velocity at which the increase in height of the sand waves end and for U3, the velocity at which the sand waves on the bed completely disappear» Many expressions are present also for dimensions of the sand waves on the bed depending on flow characteristics. However all these expressions are of statistical character. The sand wave which is formed on the bed is not a constant structure. It moves with a very low velocity with respect to flow velocity. This movement is in the same direction as the flow in subcritical flows and in the opposite direc tion to the flow in supercritical flows. There is no doubt that the sand waves being formed on the bed are in forms of heaps in some regions and of scours in other regions of the bed. Until today the problem why the wavy form of the bed is formed has not been solved satis factorily. Once the first heap is formed we can explain the mechanism of the wavy form; but we can not know exactly the reason for the first heap. The reasons for the formation of the first heap on the bed may be as follows: a) The particles moving faster prevent the particles moving slower and cause them to move even slower. b) Heaping up of part of the particles which once begin moving but which can not be carried along with the mean flow velocity.IX c) The coarse particles not being able to begin movement in case the particles on the bed are not uniform» The sand waves which are formed on the bed depending on the flow, fluid and bed material characteristics may be of different sizes. These are named differently according to their various characteristics. We name the smaller and three-dimensional ones as ripples whereas the greater ones which cover the complete flow section and which are two- dimensional are called dunes. In this study the structure of flow and particle motion on dune type of beds is investigated. The experiments have been carried out in the Hydraulics Laboratory of the Technical University of Istanbul» Firstly,, lengths and shapes of dunes have been determined by sprea ding material of D_` = 0.82 mm on the bed of a channel similar to the channel used in the experiments and passing a discharge of 11 1/s at 6.5 cm depth through this channel* Under the conditions mentioned above dunes which were in average 45 cm in length and 3 cm in height have been formed whose upstream surfaces were almost flat and downstream surfaces were inclined with 45°. These dunes have been constructed of sand and made firm by using cement on the bed of the channel which was to be used in the experiments. We can list the flow measurements made in the channel as follows: a) Discharge of flow: measurements of discharge have been made by means of a triangular weir of right angle; later on these measurements have been checked by the integration of velocity profiles. b) Water surface profile: Piezometers have been placed at different places on the bottom of the dune and connected to a vertical plate equipped with gages. The level of water in the piezometers give the elevation of water sur face above the dune. We can derive the conclusion that the flow is lowered while passing over the peak point of the dune from the water surface profile obtained in the manner explained above. c) Measurements of velocity and turbulence intensity: a hot film anemometer and a MINC DECLAB 23 Computer have been used for these measurements. As a result of theX measurements made on the dune and on the flat bed we see that: Velocity shows a logarithmic trend with distance from the bed. The turbulence intensities show greater values near the bottom and smaller values with distance from the bottom. The turbulence intensities are always of greater values at sections on dunes with respect to flat bottom. The turbulence intensity reaches its maximum value at the end of the eddy region beyond the dune peak, decreases along the dune and takes its minimum value at the dune peak. < The Ujjj value at dune peak is almost the same value with the flat bot-tom value. We can expect a motion related to the characteristics of the particle on the bed, in case of constant flow. Here four cases can be distinguished: a) The particle on the bottom does not move at all b) The particle on the bottom vibrates with the effects of the flow but does not move c) The particle makes bed load and saltation motions d) The particle makes suspension motion. In the last part of this study a parameter which would characterize the motions of the particle has been investi gated. With this objective spherical particles of different densities (therefore possessing different settling velo cities) have been prepared. The motions of these particles both on flat bottom and at different sections on the dune have been observed. Particles have been produced at two different diameters. The settling velocities and densities of 3 mm particles vary between 1,5 - 37,15 cm/ s and 1, 008- 2,618 g/cm3 respectively. The same characteristics of the 5 mm particles vary between 4,67 - 46,1 cm/ s and 1,022 - 2,294 g/cm3. As a result of the experiments it was seenXI that the particle motion can be expressed in terms of the W/XU^ settling velocity parameter. Here W is the settling velocity of the particle in still water, U^ is the shear stress velocity and X. is the Karman constant (0.40). Accor ding to this the particles on the bottom do not move at all for values of W/XU^ greater than 50 approximately. The particles begin vibrating with the effects of flow but can not move for values of settling velocity parameter of 40^50. For values of 12-20 of the same parameter the particles on bed makes bed load motion and for values of 5-12 of the parameter the particle makes suspension motion. The case when W/X U^ is smaller than 1 is accepted in literature as the limit for the particle to make always suspension motion. The experimental results have also been analyzed with respect to Shields' parameter. This analysis is made for values of Re ^ between 18-85. The following results can be attained as conclusion of this analysis. a) The initiation of bed load motion falls almost on the Shields curve (Fr2 cr 0.04-0.06) b) The initiation of vibration is at Fr2~ 0,01 c) A curve above the Shields' curve exist for initiation of suspension motion (Fr2 ~ 0.10 `- 0.20)