∆r data (using symbols) to the above log-log plot. Repeat the calculation of coefficients p and K as above. In FLUENT, use "first-order upwind" scheme for momentum to solve for the flowfield on the three meshes. Let's see how p changes when using a first-order accurate discretization. You can strip the headers and footers in this file and read this into MATLAB as column data using the load function in MATLAB.Ĥ. Hint: In FLUENT, you can write out the data in any "XY" plot to a file by selecting the "Write to File" option in the Solution XY Plot menu. Add a line corresponding to the least-squares fit to this plot. Using MATLAB, perform a linear least squares fit of Where the coefficient K and power p depend upon the order of accuracy of the discretization. Where u_c is the centerline value from FLUENT and u_exact is the corresponding exact (analytical) value. At the exit of the pipe where the flow is fully-developed, we can define the error in the centerline velocity as For each mesh, calculate the % error relative to the analytical value. Calculate the corresponding value from fully-developed pipe analysis. Calculate the shear stress Tau_xy at the wall in the fully-developed region for the three meshes. Axial velocity u should be on the abscissa and r on the ordinate.Ģ. Use a legend to identify the various curves. In all, you should have four curves in a single plot. Indicate the equation you used to generate this profile. Also, plot the corresponding velocity profile obtained from fully-developed pipe analysis. Plot the axial velocity profiles at the exit obtained from the three meshes. Use FLUENT with the "second-order upwind" scheme for momentum to solve for the flowfield on meshes of 100 × 5, 100 × 10 and 100 × 20 (axial divisions × radial divisions).ġ. The video below shows how to use ANSYS Fluent to set up and solve a problem like this.Ĭonsider developing flow in a pipe of length L = 8 m, diameter D = 0.2 m, ρ = 1 kg/m3, µ =2 × 10^−3 kg/m s, and entrance velocity u_in = 1 m/s (the conditions specified in the Problem Specification section). John Cimbala and Matthew Erdman, The Pennsylvania State University Problem Specification (pdf file) Exercise 2: Laminar Flow within Two Rotating Concentric Cylinders Contributed by Prof. The book employs the English gravitational system as well as the International System (or SI).Author: Rajesh Bhaskaran, Cornell UniversityĮxercises (OLD) Exercises Exercise 1: Vertical Channel Flow #PIPE FLOW M FILE PROFESSIONAL#With its clear explanations, Pipe Flow is recommended as a textbook for engineering students and as a reference for professional engineers who need to design, operate, and troubleshoot piping systems. In addition, references and further reading sections enable the readers to explore all the topics in greater depth. Sample problems and their solution are provided throughout the book, demonstrating how core concepts are applied in practice. The results are also presented in straightforward tables and diagrams. Experimental test data and published formulas are examined, integrated and organized into broadly applicable equations. The book draws together and reviews the growing body of experimental and theoretical research, including important loss coefficient data for a wide selection of piping components. #PIPE FLOW M FILE HOW TO#Throughout the book, the authors demonstrate how to accurately predict and manage pressure loss while working with a variety of piping systems and piping components. Pipe Flow provides the information required to design and analyze the piping systems needed to support a broad range of industrial operations, distribution systems, and power plants.
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