Computational Fluids Dynamics Implementation - Lab Report Example

Name: Instructor: Course: Date: Computational Fluids Dynamics (CFD) Implementation Introduction The paper is about simulation of two fluid with different viscosity and density. Through an S bend having a diameter of 20 mm. The two conditions for the experiment are air as a fluid with an initial Reynolds number of 500 and the second fluids with initial Reynolds number of 50000. The geometry of the pipe applicable in the two cases is similar. For both the experiments the fluid had different densities and viscosities. This was meant to be able to study the relationship of Reynolds number as well as the inlet match numbers (Versteeg, p. 60). Reynolds number It is essential in determining the flow patterns of different flow situations. Some of its applications involve the flow of liquids in a pipe as well as establishing the flow of air through pipes and aircraft wings. It also helps in defining the transition point between the laminar and turbulent flows. This is the ratio of the forces of inertia to friction in flowing fluid through a pipe. The internal movement is caused by the presence of varying velocities at various points of the fluid. The number can be used to determine the dynamic similitude that flows for two fluids having different velocities. For laminar flows, the corresponding Reynolds number is low because of the forces involved in the movement of the fluid. In turbulent flows, the number is usually high due to the higher levels of inertial forces. The Reynolds number can be derived as follows by the following equation (Larsson, p. 293). Where ρ = fluid density (SI units: kg/m3) u = fluid velocity in relation to the object (m/s) L = characteristic linear dimension (m) μ =fluid dynamic viscosity (Pa·s or N·s/m2 or kg/m·s) ν = fluid kinematic viscosity (m2/s). Density and the viscosity of a fluid are essential in the definition of a Reynolds number of a given fluid. When studying the flow in a pipe, the Reynolds number can be defined as follows. Where DH = pipe hydraulic diameter of the pipe (the inside diameter if the pipe is circular) (m). Q = volumetric flow rate (m3/s). A = pipe's cross-sectional area (m2). υ =mean velocity of the fluid (m/s). μ = dynamic viscosity of the fluid (Pa·s = N·s/m2 = kg/(m·s)). ν (nu) = kinematic viscosity (ν = μ/ρ) (m2/s). ρ = fluid density (kg/m3). After a fluid has flowed for some time, it loses its laminar characteristic resulting in the formation of a turbulent flow. As long as the Reynolds number is less than 1000, then the flow is a laminar flow. However, when the number exceeds one thousand, the flow converts to turbulent. The transition value for the Reynolds number is known as the critical Reynolds number. Whenever a fluid flows through the pipes, there is friction that occurs at the contact surfaces of the fluid and the pipe. The diagram below shows the transition between laminar and turbulent flow (Larsson, p. 293). Inlet Mach numbers This refers to the ratio of the speed of flow of a fluid to the sound produced by the same fluid. For incompressible fluids, the Match number is mostly less than the value of 0.3. This is attributed to the fact that density changes caused by differences in velocity are less than five percent. For compressible fluids, the figure is relatively high because the differences in densities caused by the velocity changes is greater than five percent. The figure below is a demonstration of the spectrum of the Mach number (Larsson, p. 293). At lowest flowing speeds the speed of sound is found to be higher opposite to what has been assumed before. At high flow speeds, the speed of sound is found to be least contrary to what many think. In a one-dimensional flow, the fluid is an assumed to be flowing in a given enclosed pipe where its properties change with time. In analyzing the flow, the following assumptions were utilized. The ratio of duct length to width (L/D) is ≤ about 5 (this is done to assume effects of friction and heat transfer), Flow is isentropic (flow is a reversible adiabatic process), Ideal gas law (i.e. P=ρRT) (Larsson, p. 293). The relationship in a channel flow is shown by the following equation. where dP = differential pressure changes M = Mach number ρ =gas density V = flow velocity A = duct area of the duct, dA = changes in duct area For one to increase the Mach number, he or she has to increase the convergence by reducing the cross sectional area of the flowing fluid. This requires a decrease in the fluid`s density. methodology The geometry of the pipe was developed in 3D with the aid of AutoCAD that is a subsequent model of the STARCCM+ simulation software. The required region was then created and a polyhedral mesh developed with the help of the cylindrical mesh model that is general in nature. The polyhedral cells were extruded according to the direction of flow helping to obtain the mesh required for pipe flows in this study (Versteeg, p. 72). Fig 1: an illustration of the extruded piece of the pipe for the study. Pre-requisites Before the simulation of the process, the following features had to be familiarized Technique(s) Associated Tutorial The STAR-CCM+ workflow with the help of Introduction to STAR-CCM+ as the tutorial Creating geometry in 3D-CAD with the help of Cyclone Separator as the tutorial Using visualization tools, scenes features as well as plots using Introduction to STAR-CCM+ as the tutorial (Versteeg, p. 75). Development of the S bends geometry A simulation was created in a new file and saved on the hard disk auto card was used to develop the geometric model in three dimension view. The first step was to develop a circle that represented the inlet of the pipe. A new sketch was developed on the XY plane later the grid spacing was adjusted to twenty-five millimeters. A plane view was obtained, and a circle of diameter one hundred millimeters was obtained in the process (Versteeg, p. 72). Illustration of the circle obtained in auto card The profile of the length of pipe was then developed by drawing a line of thirty-five millimeters. With the aid of the center arch, a circle of radius 0.02 meters was developed which helped define the end point of the line (Versteeg, p. 73). A second arc was then developed to be able to provide a complete S-shaped figure. The coordinates for the process were as follows the center point: [0.075 m, 0.02 m]. Start points: [0.075 m, 0.04 m] and end points at: [0.055 m, 0.02 m]. The complete S shape is as shown below The final line of the shape was drawn as shown in the figure below as the complete sketch of the profile of the pipe. With the aid of the sweep feature, the solid part of the figure was developed. This was achieved by having the circle being swept with the line acting as a profile through which the sweeping takes place (Versteeg, p. 73). Complete layout of the profile of the pipe. After completion of the 3D sweep, the following figure was obtained. The inlet and outlet faces of the geometry were specified by naming the different faces of the figure. One of the sides was named inlet and the other the outlet of the pipe. This was essential in ensuring the 3D model retained its identity during conversion of the geometry model in the subsequent steps. A new geometry part was then developed. Renaming of the inlet and outlet automatically added the two sides in two different boundaries of the geometry. Parts were assigned to the different regions of the geometry. The region mode assigned one region for every given part. In the boundary surface the each surface was assigned a different boundary of the geometry. At the end of this stage the new region had been completely developed defining the outlets, inlets as well as the volume of the fluid through the pipe (Versteeg, p. 74). A new geometry scene was then developed with the boundary notes being specified correctly. In our first scenario, we set up a case with the fluid with heavier density at a low viscosity. This was air. The initial Reynolds number was taken to be 500. A polyhedral mesh was then developed which was suited to the pipe flow design. As shown in the diagram below. Boundaries specifying the geometric cylinder were obtained to be able to generate the volume mesh. The generalized cylinder type of extrusion was used in this process. The extrusion credentials were maintained in the whole procedure. The final volume mesh was obtained as follows (Versteeg, p. 74). The next step was to select the physics models for the geometric model. The materials selected were air and oil. The material properties were then set as per the requirements. The initial conditions for the experiments were then set. To achive, an initial Reynolds number of 500 for air an average velocity of 0.429 m/s for better convergence the conditions at the inlet were defined. The same value of velocity was set at the inlets with set values appropriate being given by [0.429, 0.0, 0.0] m/s. The scalar scene was later developed to be able to show the properties of the fluid as it flows through the planar section of the S-bend. Scalar 1 was chosen with the fluids vector as [0, 0, and 1]. The illustration of the dialogue box Scalar 1: scene developed A vector simulation plot was then obtained the section is as illustrated in the figure below. For the first simulation, the iterations were limited to 500 equivalents to the Reynolds number. However, for the second simulation, the iterations number was raised to 50000 that were essential in obtaining a convergence. The simulation was ready for running, and after clicking on the run button, the following is a demonstration of what was observed (Versteeg, p. 72). Illustration of the scalar scene Illustration of the vector scene Changing to oil as the fluid under the experiment The numbers of iterations were changed to 1000. This was important in ensuring there was optimal convergence during the simulation. The mean velocity that was required at the inlet is 4.29 m/s. The scale applied was ten percent of the stream velocity that is free. The intensity of the flow used in this case by calculation using the formulae. Where I =intensity of flow Vt =velocity scale of the flow U =free-stream velocity The regions of the flow the physics values, as well as the intensity values, were selected accordingly. The value property of the intensity was chosen to be 0.12. The number of iteration was made to be 1000. The first solution of the simulation was first cleared before running the second simulation. The final scalar scene was as shown below The vector scene is as shown in the figure below Discussion Task one From the results, several conclusions were mad basing of their corresponding explanations. For the fluid which had a lower density and high viscosity, the air there was a higher increase in pressure difference across the pipe this is because lower density increases the velocity of the molecules of the fluid making the laminar flow to quickly transit to turbulence flow. The high kinetic energy of the molecules is attributed to the low cohesive forces between the like molecules of the fluid minimizing the restriction of the fluid`s flow. The latter has a characteristic of very high-pressure differences caused by the rapid kinetic energy of the molecule. For the fluid that was heavier the oil, it had a lower velocity due to corresponding low viscosity. As a result, there is fewer pressure differences between the fluid at different sections of the pipe as it can be seen in the vector and scalar diagrams (Moin, p. 2745). Task two For the fluid that was lighter the initial Mach number was lower, but with time the rate through which is transformed in the pipe sections was so high attributed to the high velocity of the flowing fluid. This number was noted to be beyond 0.3 at 0.4 the explanation for higher Mach number is that the number is directly proportional to the velocity of the fluid as it flows through the pipe. Hence the great increase in velocity leads to a corresponding increase in the value of the Mach number. However, for the heavier fluid the number was initially higher, but due to small pressure and velocity differences across the pipe, this number was less than 0.3 at the outlet of the pipe. The fluid had a lower Mach number value simply because its velocity was low as well as gradually increased leading to a proportional lower much number of 0.178 that increased at a very slow rate between the inlet and outlet (Moin, p. 2745). Task three The magnitude of the velocity of the less dense fluid across the pipe greatly increased this was attributed to the higher kinetic energy of the molecules as well as its low viscosity levels. This is because a lower viscous fluid has the weaker cohesive bond between the like molecules as well as weak adhesive bonds between the fluid molecules and that of the pipe. As a result, there was less resistance to flow by friction resulting to the higher velocity of the fluid. On the other hand, the denser fluid had minimal changes in velocity which was lower as compared to that of the less dense fluid. This is attributed to the presence of stronger cohesive forces between like molecules of the fluid as well as strong adhesive forces between the fluid and the surface of the pipe. This resulted in higher frictional resistance to the flow of the fluid hence the low velocity of the fluid. Task four The outlet temperature of air which was the less dense fluid was found to be higher at twenty-five degrees Celsius. This is attributed to the higher velocity of fluid towards the end of the pipe increasing the friction within the molecules. The increased friction between the molecules of the fluid and that of the pipe surface generated the extra heat in the outlet of the pipe. This can also be seen in the diagrams showing the heat generation along the different section of the pipe. The outlet temperature of oil our dense fluid were comparatively low at fifteen degrees Celsius. This is attributed to the fact that the fluid had high viscosity minimizing the velocity through which it flows through the pipe. As a result, there was comparatively minimum friction generated between the molecules and the surface of the pipe that led to the development of lower temperatures across the pipe (Brown, p. 70). Task five Generally when comparing the outlet conditions for the two types of flows. It was concluded that the less dense fluid had a lower Reynolds number which decreased the flow of the fluid attributed to the increase I kinematic viscosity of the fluid which is inversely proportional to the Reynolds number. The denser fluid oil had a higher Reynolds number due to its lower kinematic viscosity at the inlet of the flow pipe. However, with time it gradually increased. At the outlet, the Reynolds number was found to be greater than the of the less dense fluid (Brown, p. 70). Secondly, the temperatures at the outlet of the less dense fluid air were higher than that of, the denser fluid, oil. This is attributed to the high velocity and pressure changes at the end of the pipe. The air temperatures were at 25 degrees Celsius which that of oil was found to be fifteen degree Celsius. The pressure at the air`s outlets was at 15 Pascal's while that of oil was at 6 Pascal’s. The air had a higher Mach number as compared to the outlet of the oil. At the end of the experiment, the outlet of the air pipe was found to be superior in most of the parameters that were under study in this type of simulation (Brown, p. 70). Conclusion At the end of the simulation, the different properties of the two fluids flowing through the pipes were determined. This included the pressure, velocity, Reynolds number and Mach numbers. The use of the STAR CCM+ software was essential as it provided the required platform for effective simulation of the process. This simulation ensured the concepts of flow of fluids through pipes are understood without necessarily going to the laboratory and practically doing the experiment. This is attributed to the unique smart features that the program comes along with. The Reynolds number was found to be higher in more viscous fluid and low in less viscous fluids. The Mach number was higher in the fluids that are more viscous as well as being low in the less viscous fluid. REFERENCE Versteeg, Henk Kaarle, and Weeratunge Malalasekera. An introduction to computational fluid dynamics: the finite volume method. Pearson Education, (2007):56-98. Moin, Parviz, et al. "A dynamic subgrid‐scale model for compressible turbulence and scalar transport." Physics of Fluids A: Fluid Dynamics 3.11 (1991): 2746-2757. Brown, David L., Ricardo Cortez, and Michael L. Minion. "Accurate projection methods for the incompressible Navier–Stokes equations." Journal of computational physics 168.2 (2001): 464-499. Larsson, Johan, Ivan Bermejo-Moreno, and Sanjiva K. Lele. "Reynolds-and Mach-number effects in canonical shock-turbulence interaction." Journal of Fluid Mechanics 717 (2013): 293. Read More