Investigation of water flow in porous textile under centrifugal forces

Dewatering of cotton textile with variable porosity under centrifugal forces has been examined theoretically and experimentally within the scope of the doctoral study. In this way, experimental studies have been carried out to determine the porosity under compression. Then, dehydration rate of textile was measured according to input parameters. Afterwards, conservation equations were written and they were simplified by considering the physics of phenomenon. At the end of study, mathematical models were developed in order to calculate the amount of remaining water on the textile and dewatering rate time dependently. When previous studies in the literature were examined, it was seen that there were some researches which aim to minimize the amount of water remaining on the textile under centrifugal forces. Experimental results mentioned in the studies were generally considered parameters such as spinning speed, amount of load and surface tension. However, there was no time dependent solution method by creating necessary dimensionless number. Even though, there are different parametric studies in order to decrease water level after spinning, there is not any valid comprehensive mathematical model. The semi-empirical statements are valid only in the space where experimental work has been done. Additionally, the patent applications under D06F35 patent class were investigated to reduce the amount of water on the textile after spinning process. It is observed that the main topics are related with water heating, steam applications, algorithms and perforated drum forms. In the thesis study, it is aimed to develop porous media flow model under centrifugal force including capillary pressure and variable porosity effects unlike the literature. Experimental setups were prepared in order to obtain the effects of mentioned parameters and determine the flow regime during dewatering. Experimental studies were basically carried out in two steps. In the experimental studies, test materials were preferred to demonstrate deformable porosity under centrifugal loading and define saturation effected by capillary number. Because of above mentioned properties, the bed sheets defined in EN60456:2011 washing standard for household appliances were used for tests. The thickness of single layer and diameter of fibers were measured by optical device. Same parameters were calculated by utilizing Pierce model. It was observed that the measured and calculated values were parallel to each other. Afterwards, porous media was formed by stacking the sheets on top of each other. Then, the porosity of textile specimen was calculated by using predetermined calculations. However, textile porosity shows variable property due to centrifugal forces. Therefore, different number of textile samples were exposed to compression tests. Force balance was written down for the analysis of the measurement variables and dimensionless expressions in convenient form were determined. The porosities were correlated with input parameters such as thickness, pressure and number of layers as a result of regression analysis performed in Minitab. In the second phase of experimental studies, a test setup based on washing machine was prepared. Test sets (loads) which were formed by cutting the sheets in different numbers and sizes, could be mounted on to the periphery of the washing machine's drum. A homogeneous porous media was simulated by using these loads during dewatering tests. In the test setup, washing machine was settled onto platform and the motorized valve is connected under tub. When the control system commanded the water evacuation before spinning, the valve was motorized and it ensured to pass water onto scale. There was also data acquisition system which was also connected to experimental setup to measure drum speed, temperature, inlet water, outlet water and power consumption. In the experimental studies, the effects of parameters such as the amount of load, spin speed and temperature on water removing rate and amount of water remaining on the textile were aimed to examine. The acceleration rate of drum was the main influential parameter on centrifugal pressure and porosity of textile so that wide range between "600-1400 rpm" were planned to investigate during tests. The number of sheet layers was also another powerful input defined in the summary of literature. Therefore, the mass of test load was changed to simulate number of sheet layers. The third factor was the temperature to acquire impression of water viscosity and surface tension on desaturation. As a result, full factorial experimental design was created and 18 tests were performed. Raw data obtained from the experiments was analyzed by converting to spinning index and saturation number which were defined in the literature. When our experimental study was compared with results obtained by Denton (1974a), it was noticed that the of spinning index values of both studies were close to each other. Thus, performed experimental study was verified by comparing with the literature. When spinning index obtained from the experiment was examined, it was seen that spinning index was decreasing while target spin speed increases. In addition, spinning index increased when the amount of load decreased. In fact, the change of spinning index versus time was analyzed, it was seen that most of the water moved away from the porous medium during acceleration and major decrease occured in the spinning index. As the drum reached the target spin speed, reduction rate of the spinning index decreased and approached the asymptote at the end of the experiment. Same experimental data was analyzed again by transforming into the saturation number. In order to obtain the saturation number, equation for calculating the porosity after press experiment was utilized. It was determined that irreducible saturation obtained from the experiment reduces similarly, as the spin speed of the drum was increased. In the initial phase of spinning, saturation number increases due to the reduction of porosity. During acceleration phase, it was seen that saturation number suddenly decreases. At the target spin speed of drum, saturation number approached the asymptote value towards the end of spin process. After the experimental study, conservation of momentum and continuity equations were written down separately for solid and liquid phases on the rotating axis. When the continuity equation for the solid phase was solved, it appeared that there was no solid output from the system. Afterwards, the momentum equation for the solid phase was solved and the relationship between strain rate and pressure difference was obtained. When the continuity equation for the liquid phase was solved, the equation that showed the speed of water removing from the drum was obtained. As the experimental data is analyzed by using this equation, it is seen that speed of the water removed from the drum is at maximum level during acceleration. It was determined that the maximum dewatering speed value increased, as the amount of test load increased. When Reynolds number for the liquid phase was calculated, flow regime was determined as Darcy since the obtained value was at low level. Then, the momentum equation was written in the integral form and mathematical operations were performed. Finally, an equation that contained acceleration, capillary pressure, centrifugal pressure and Darcy terms were obtained. After the reduction of momentum equation, capillary pressure and permeability of textile were aimed to be determined from experimental data. At the end of the spin process, capillary pressure became equal to centrifugal pressure since water output from the porous media approaches zero. In this case, necessary dimensionless numbers were created by utilizing momentum equation. Afterwards, regression analysis in Minitab was done and the equality that explains the capillary pressure is obtained. It was seen that capillary pressure is increasing while remaining moisture content of porous media increased. By utilizing the experimental data since the beginning of spin extraction, the permeability of textile was correlated. The permeability and capillary pressure expressions were achieved by examining equations in dimensionless forms. After experimental studies and reduction of conservation equations, a simulation program was developed by using Matlab. The inputs of the simulation were drum diameter, drum width, spinning algorithm, temperature and amount of load. In every step, porosity was calculated iteratively and it was written down in continuity and momentum equations. Then, permeability and capillary pressure parameters were calculated by utilizing equations obtained in data reduction section. Finally, the dewatering rate per time step could be achieved. When the numerical and experimental studies were compared, It was shown that results are parallel and the difference between the experimental and the calculated values was at most ±5%. As, the graphs of time dependent water flow and spinning index were drawn, it was seen that obtained curves were compatible with the experimental studies. In conclusion, developed software was compared with experimental results conducted at washing systems with different drum sizes. At this point, 3 product group with different capacities were chosen. Although experiments were not conducted with larger diameter than 480 mm diameter and higher that 1400 rpm drum speed, since nondimensionalizations were applied during modeling, it was expected that simulation converges at these points and parallel results with experiments are obtained. When measurement and simulation results were compared, it was obtained that the results were different in the range of ±4 %. When the data from experimental results were nondimensionalized conveniently, it was determined that correct results were obtained with the prepared simulation. The methods are investigated to increase the spinning efficiency, by using the software. It was calculated that the drum investigation with 520 mm drum diameter and 275 mm drum deepness decreased the remaining moisture content thoroughly. On the other hand, the reduction of surface tension could be evaluated. For the further studies, the effects of chemicals in order to decrease the surface tension could be investigated experimentally.