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During the last century, researchers studied integer partition theory extensively. We are more interested in exploring partition identities among many aspects of integer partitions. In this thesis, we study a constructive method developed by Kur sungoz to nd new identities on Rogers-Ramanujan type integer partitions and overpartitions. For this aim, we give a reproof of two Rogers-Ramanujan identities using the constructive method. Combining two types of partitions, we introduced 2-colored Rogers-Ramanujan partitions. By nding some functional equations and using the constructive method, some identities have been found. Our results coincide with some extreme cases of Rogers-Ramanujan-Gordon's identities. A correspondence between colored partitions and those overpartitions is provided. Our second result is nding the missing cases of parity consideration on Rogers- Ramanujan-Gordon's identities due to Andrews's suggestion in his seminal paper about parity in partition identities. Four cases had proven by Sang, Shi, and Yee, we reproved them using the said constructive method and then found and proved the remaining cases by the same method.

A stream water wheel is a machine for convertingthe energy of moving water into power. It consists of a large metal wheel, witha number blades arranged on the outer rim which allows the wheel to be rotatedby the water striking the blades. Water wheels were used since ancient as aprimary source of power. It was used for irrigation, grain milling andsupplying villages with water. In the present study, a stream water wheelturbine of 5 m in diameter is numerically simulated using ANSYS-CFX packageunder different flow conditions. The wake region behind the turbine ismonitored where it influences on other turbines next to it. The simulationresults have shown that in case of constructing a farm of wheel turbines, thestreamwise span should not be less than 6 m. The stream wheel turbines worksnormally at a tip speed ratio TSR less than unity.

Weirs arebarriers placed across a river and designed to control the flowing water inorder to prevent floods, make waterways operable for inland navigation andmeasure flow discharge. Although there are many types of weirs, mainly usedones are sharp-crested, circular-crested (cylindrical), broad crested and ogeeweirs. In the present study, triangular broad-crested weirs are numericallyinvestigated under different flow conditions. Different interior angles of 90o,100o, 110o and 120o are included for theopening of weirs. The flowing water over weirs is simulated using CFDtechniques and evaluated at different flow regimes with inlet discharges of0.012 m3 s-1, 0.036 m3 s-1and 0.06m3 s-1. The simulation results have shown that the waterlevel upstream the weir is inversely proportional to the opening angle, wherean increment of 10o in the opening angle leads to a drop in waterlevel about 1.5 cm. In addition, applying a discharge of 0.012 m3 s-1,an uncovered region with water is created downstream the triangular broad-crestedweirs, while the bed downstream of the rectangular broad-crested weir iscovered with a thin layer of water at the same flow discharge. Theaforementioned results are compared with a comparative data and show goodagreement. By using triangular broad-crested weirs, it is important to measurethe wake region and the hitting point of falling water downstream the weirswhere this area must be strengthened well in order to resist water power andreduce the risk of drift.

Hidrokinetik türbinler, akan suyun kinetik enerjisini elektriğe dönüştürmek için kullanılan elektromekanik cihazlardır. Bu çalışmada, farklı akış koşulları altında bir helezonik hidrokinetik türbin, tasarlanmış ve simüle edilmiştir. Türbin kanatlarının kesit alanı, hidrofoil, ANSYS FLUENT tarafından sağlanan Adjoint çözücü kullanılarak optimize edilmiştir. Solidite değeri 0.2 ve büküm açısı 120o olan 4 kanatlı ve 3 kanatlı türbinler en iyi performansı gösterdi. Akışkan-katı etkileşimi (FSI) tekniğini kullanarak, her iki türbin için de performans eğrileri geliştirildi ve literatürde bulunan deneysel verilere dayanılarak doğrulandı. The hydrokinetic turbines are electromechanical devices used to convert the kinetic energy of flowing water into electricity. In the present study, a helical hydrokinetic turbine has been designed and simulated under different flow conditions. The cross-sectional area of the turbine blades, the hydrofoil, was optimized using the Adjoint solver, which is provided by ANSYS FLUENT. The 4-bladed and 3-bladed helical turbines of a solidity value of 0.2 and a twist angle of 120o showed the best performance. Using the fluid-solid interaction (FSI) technique, a performance curve was developed for each of the two turbines and validated against an experimental data available in the literature. 167