The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Experimental validation of theoretical models in two-phase high-viscosity ratio liquid–liquid flows in horizontal and slightly inclined pipes

Effect of swirling flow on fluidized bed drying of wheat grains

Prediction of acceleration length in turbulent gas–solid flows

An experimental study was conducted on the development length of a two-phase flow produced by the loading of solid particles by means of a particle feeder into air flowing through a horizontal pipe. Development length was defined as the sufficient distance downstream of the particle feeder in which a homogeneous particle distribution in air sensed with the variation of local friction factors was attained. The static pressure gradients dP/dx were measured along the test pipe to determine the local friction factors to estimate the development length for a variety of air-solid particle suspensions. Crushed wheat and semolina particles of different size, shape and apparent density were used to determine the influence of physical particle characteristics on the extent of development region. The measurements were conducted in air flow Reynolds number range of 51500\leqRe\leq109000 at particle loading ratios of Mp/Ma, 5%\leq Mp/Ma\leq 30%. In the covered ranges of the variables, development length was found to be a strong function of Re such that an increase in Re caused a decrease in the development length while loading ratio seemed to be of secondary importance. Although the particle size by itself was found to be of not much importance for the size range covered in the experiments, for the critical values of Re (103000) and Mp/Ma(5%) particle size was found to be effective on the development length.

Effect of Particle Size and Loading on Development Region in Two-Phase Flows

A Calibration Method for 3-Tube Pressure Probes

The common feature of the experimental studies upon 3-D boundary layer development on swept flat plates cited in the available literature is the application of streamwise and/or spanwise pressure gradients. In fact; presence of the pressure gradients was suggested to be vital for having crossflow effective in 3-D boundary layer transition. In the presented paper here, this idea is questioned evaluating the results of an experimental investigation conducted on swept flat plates under the absence of a pressure gradient. In this context the influence of plate sweep angle l; itself on transition is determined simply through the natural transition measurements on the test plates with different l.

https://journals.tubitak.gov.tr/engineering/issues/muh-98-22-1/muh-22-1-4-96046.pdf

Melda Özdinç Çarpinlioğlu

Papers

Effect of Particle Size and Loading on Development Region in Two-Phase Flows

A Calibration Method for 3-Tube Pressure Probes

A Comment Upon Previous Studies on 3-D Boundary Layer Transition