timer Asked: Apr 18th, 2020

Question Description

Simulate the steady laminar and turbulent pipe flow using Ansys Fluent as shown in the figure. Choose
proper fluid properties and inlet velocity to simulate flows of Reynolds number (based on the diameter
of the pipe) equaling 655 for laminar flow and 111,569 for turbulent pipe flow, respectively. (see the files attached)

The theoretical document for verification. (see the files attached)

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EML 6930 Computational Fluid Dynamics, Spring, 2020 Homework 5 Please submit answers, all figures and tables in a single pdf or docx format. Submit the required Excel file as well. For the simulation files, only submit .cas.gz and .dat.gz for each simulation (total 8 simulations). Problem 1 (50 pts) Simulate the steady laminar and turbulent pipe flow using Ansys Fluent as shown in the figure. Choose proper fluid properties and inlet velocity to simulate flows of Reynolds number (based on the diameter of the pipe) equaling 655 for laminar flow and 111,569 for turbulent pipe flow, respectively. Table 1 - Main Dimensions Parameter Radius of Pipe, R Diameter of Pipe, D Length of the Pipe, L Unit m m m Value 0.02619 0.05238 7.62 Uniform Grid Non-uniform Grid Axis Inlet Outlet Velocity Profile Pipe Wall Uniform velocity profile is specified at inlet, and the flow will reach the fully developed regions after a certain distance downstream. No-slip boundary condition will be used on the wall, and zero gauge pressure for the outlet. You may consider creating a quarter of the pipe to take the advantage of symmetry of the geometry. This could greatly decrease the number of cells in your mesh. a) List the material properties and inlet velocities used for your simulations, both laminar and turbulent flows. b) Create three different 3D meshes: coarse, medium, and fine (Note the maximum allowed number of cells is 512k for the student version). List parameters you changed when creating the meshes, total number of cells, and minimum Orthogonal Quality. Also use the 2D mesh provided to perform simulations (When launching Fluent, choose 2D mode and change to Axisymmetric in Physics>General… tab). Conducting simulations for all meshes (total number of simulations is 8). Plotting residuals and check the mass balance. c) Create lines shown in the table below. Here, we assume the x axis is in the axial direction. You may need to change the coordinates according to the orientation of your geometry. Line Name Inlet-line x=10D x=20D x=40D x=60D x=100D Outlet-line x0 0 0.5238 1.0476 2.0952 3.1428 5.2380 7.62 y0 0 0 0 0 0 0 0 x1 0 0.5238 1.0476 2.0952 3.1428 5.2380 7.62 y1 0.02619 0.02619 0.02619 0.02619 0.02619 0.02619 0.02619 Use XY Plot to plot velocity profiles at these lines in a single figure for laminar and turbulent simulations, respectively. Similarly, plot static pressure and velocity magnitude along the centerline. For all these figures, only show results from the fine 3D mesh and 2D mesh. d) Extract the Wall Shear Stress values (𝜏 ) along the axial direction on the pipe wall. You can save it as a .xy file from Fluent and open it with a text editor, and copy the value at xβ‰ˆ7 to the Excel file. Similarly, extract the pressure value along the centerline to calculate pressure drop from the inlet to the outlet. Extract the velocity values along the β€œoutlet-line” and copy them to the Excel. It will be used for plotting the fully-developed velocity profile with analytical or empirical data (AFD used later is the abbreviation of it). List the y+ value at the end of pipe for all turbulent simulations. e) Fill the blanks in the Excel table below for verification and validation. Show proper procedures for obtaining AFD data. Discuss which mesh solution is closest to the AFD data, and explain why this is the case? Plot the fully-developed velocity profiles from all meshes with AFD data in a single figure for laminar and turbulent flows, respectively (You can do it in Excel). Discuss the developing length for laminar and turbulent pipe flows and compare them with that using the formulas in the theoretical document. To know more about analytical or empirical solutions of laminar and turbulent pipe flows, refer to the theoretical document attached. In the Excel file, create a table like this and fill the blanks accordingly. U m is the maximum/centerline velocity at the outlet. sims Coarse grid: laminar Medium grid: laminar CFD, Pressure drop AFD, pressure drop CFD, 𝜏 at xβ‰ˆ7 AFD, 𝜏 CFD, Um at xβ‰ˆ7 AFD, Um Fine grid: laminar 2D grid: laminar Coarse grid: turbulent Medium grid: turbulent Fine grid: turbulent 2D grid: turbulent Theoretical Fluid Mechanics for Laminar and Turbulent Pipe Flow For a uniform flow inlet, the flow can be divided into two regimes: developing profile region and fully-developed flow region. The corresponding velocity profiles and pressure drops are showing in the figure. For a laminar flow, the entrance length can be estimated by 𝐿𝑒 ⁄𝐷 β‰… .06𝑅𝑒, where D is the diameter of the pipe and characteristic length used in the Re number. For a turbulent flow, the entrance length is 𝐿𝑒 ⁄𝐷 ~4.4𝑅𝑒 1/6. The skin friction coefficient is a dimensionless skin shear stress which is nondimensionalized by πœπ‘€ the dynamic pressure of a free stream, 𝐢𝑓 = 0.5πœŒπ‘‰ 2 , where πœπ‘€ is the local wall shear stress and V is mean velocity at the inlet. For a laminar flow, the skin friction coefficient is related to 16 Reynolds number as 𝐢𝑓 = 𝑅𝑒. For a turbulent pipe flow, the empirical solution is 𝐢𝑓 = 0.079𝑅𝑒 βˆ’0.25. The Darcy friction factor f is also widely used in the literature, which is related to the skin friction coefficient as 𝑓 = 4𝐢𝑓 . It is well-known that the fully-developed velocity profile shows a parabolic shape in a laminar π‘Ÿ 2 𝑒 pipe flow from Hagen–Poiseuille equation as, π‘ˆ = 1 βˆ’ (𝑅) , where R is the radius of the pipe, π‘š π‘ˆπ‘š = 2𝑉 is the maximum velocity and V is the mean velocity. π‘’βˆ— 𝑒 𝑅 For a turbulent flow in a circular pipe, π‘ˆ = 1 βˆ’ 2.5 π‘ˆ 𝑙𝑛 π‘…βˆ’π‘Ÿ, where the maximum velocity π‘š π‘š βˆ— π‘ˆπ‘š = (1 + 1.326βˆšπ‘“)𝑉, and the friction velocity 𝑒 = βˆšπœπ‘€ β„πœŒ. ...
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