Investigation on the Drag Coefficient of the Steady and Unsteady Flow Conditions in Coarse Porous Media

The study of the steady and unsteady flow through porous media and the interactions between fluids and particles is of utmost importance. In the present study, binomial and trinomial equations to calculate the changes in hydraulic gradient (i) in terms of flow velocity (V) were studied in the steady and unsteady flow conditions, respectively. According to previous studies, the calculation of drag coefficient (Cd) and consequently, drag force (Fd) is a function of coefficient of friction (f). Using Darcy-Weisbach equations in pipes, the hydraulic gradient equations in terms of flow velocity in the steady and unsteady flow conditions, and the analytical equations proposed by Ahmed and Sunada in calculation of the coefficients a and b of the binomial equation and the friction coefficient (f) equation in terms of the Reynolds number (Re) in the porous media, equations were presented for calculation of the friction coefficient in terms of the Reynolds number in the steady and unsteady flow conditions in 1D (one-dimensional) confined porous media. Comparison of experimental results with the results of the proposed equation in estimation of the drag coefficient in the present study confirmed the high accuracy and efficiency of the equations. The mean relative error (MRE) between the computational (using the proposed equations in the present study) and observational (direct use of experimental data) friction coefficient for small, medium and large grading in the steady flow conditions was equal to 1.913, 3.614 and 3.322%, respectively. In the unsteady flow condition, the corresponding values of 7.806, 14.106 and 10.506 % were obtained, respectively.

Investigation on the Drag Coefficient of the Steady and Unsteady Flow Conditions in Coarse Porous Media

The study of the steady and unsteady flow through porous media and the interactions between fluids and particles is of utmost importance. In the present study, binomial and trinomial equations to calculate the changes in hydraulic gradient (i) in terms of flow velocity (V) were studied in the steady and unsteady flow conditions, respectively. According to previous studies, the calculation of drag coefficient (Cd) and consequently, drag force (Fd) is a function of coefficient of friction (f). Using Darcy-Weisbach equations in pipes, the hydraulic gradient equations in terms of flow velocity in the steady and unsteady flow conditions, and the analytical equations proposed by Ahmed and Sunada in calculation of the coefficients a and b of the binomial equation and the friction coefficient (f) equation in terms of the Reynolds number (Re) in the porous media, equations were presented for calculation of the friction coefficient in terms of the Reynolds number in the steady and unsteady flow conditions in 1D (one-dimensional) confined porous media. Comparison of experimental results with the results of the proposed equation in estimation of the drag coefficient in the present study confirmed the high accuracy and efficiency of the equations. The mean relative error (MRE) between the computational (using the proposed equations in the present study) and observational (direct use of experimental data) friction coefficient for small, medium and large grading in the steady flow conditions was equal to 1.913, 3.614 and 3.322%, respectively. In the unsteady flow condition, the corresponding values of 7.806, 14.106 and 10.506 % were obtained, respectively.

Hydrogeological and Hydro Chemical Evaluation of Groundwater in Karbala Region Using Geographic Information System (GIS)

The study area is located in the holy governorate of Karbala, Iraq; the research studied a predictive mathematical model of groundwater within Dibdiba Formation and by fifty (50) wells distributed randomly within the boundaries of the study area, all of them fall within the unconfined aquifer. Likewise, there is no component to direct the activity of these wells, where a mathematical model for the study area has been developed using the groundwater system modeling program (GMS v.10). The area was divided into a grid where the dimensions of a single cell ranged from 250m×250m. The model of the steady flow state was adjusted utilizing pressure driven conductivity extending from 9 to 15 m/day with a 0.15 storage coefficient to match the groundwater levels measured with the calculated groundwater table. The model was run for unsteady flow condition in the first scenario with fifty (50) wells and five (5) years. The drawdown in the groundwater tables ranged between (0.05-1.05) m. In the second scenario, the model was run after adding thirty-six (36) wells for five (5) years, groundwater limits 0.15-1.15 meters. The drawdown values are concentrated near wells sites, and the drawdown decline as we move away from the sites of these wells and this reflects the nature of the water reservoir located in the study area, which is characterized by high production where compensation resulting from the operation of the wells decline rapidly by the reservoir. Therefore, the values of the drawdown in elevations appeared very low. The study also showed the possibility of drilling additional wells in this area, depending on this model to benefit from them in the future for different uses.

Investigation of Aerodynamics and Heat Transfer of a Highly Loaded Turbine Blade Using the Universal Intermittency Function

Efficiency and performance of gas turbine engines are affected by the flow field around the blades. The flow field inside a gas turbine engine is very complex. One of the characteristics of the flow inside an engine is existence of periodic unsteady wakes, originating from the upstream stator blades. The unsteady wakes, with their highly vortical core, impinge on the downstream blade surfaces and cause an intermittent transition of the flow regime from laminar to turbulent. This study aims at investigating and modeling the behavior and development of the boundary layer along the suction surface of a highly loaded low-pressure turbine blade under steady and unsteady inlet flow condition. The current paper includes results of a computational work substantiated by the experimental verifications. For the experimental investigations, the linear cascade facility in Turbomachinery Performance and Flow research Lab (TPFL) at Texas A&M University was used to simulate the periodic unsteady flow condition inside gas turbine engine. Moving wakes, originating from upstream blades, were simulated in this facility by moving rods attached to two parallel timing belts. Measurements and calculations were conducted at Reynolds number of 110,000. This Reynolds number pertains to cruise condition of a low-pressure turbine. At this Reynolds number, the flow around the blades is transitional and highly susceptible to flow separation. Aerodynamics experiments include measuring the boundary layer, locating its transition, separation and finally re-attachment using miniature hot wire probes. Heat transfer measurements along the suction and pressure surfaces were conducted utilizing a specially designed heat transfer blade that was instrumented with liquid crystal coating. To numerically simulate the transitional behavior of the boundary layer under periodic unsteady flow condition, a new intermittency function is developed which is based on the universal intermittency function developed by Chakka and Schobeiri [1]. Accurate prediction of the boundary layer behavior under the above conditions requires minimum and the maximum intermittency functions. These functions were developed inductively using the experimental results that were obtained in the absence of flow separation. In the current investigation the impact of the separation on the minimum and maximum intermittency are accounted for. The enhanced minimum and maximum intermittency functions along with the universal intermittency are implemented in a RANS based solver for computational simulation. The computational results are compared with (a) experimental ones and (b) with the computational results from RANS that involves Langtry-Menter [2, 3] method.