Who Wants to Be a CFD Expert In

Who Wants to Be a CFD Expert? • In the ME 566 course title, CFD for Engineering Design, what does the acronym CFD stand for? A. Car Free Day B. Cash Flow Diagram C. Computational Fluid Dynamics • Lifelines • • Phone a Friend Ask the Audience

ME 566 Project • Mixing in a Model Combustor • You are to determine the effect that the angle of the side inlets has on mixing in the combustor. T. -M. Liou and Y. -Y. Wu, Experimental Thermal and Fluid Science 1992, 5: 401 -409.

• Tasks • You can choose a single angle of 5 , 10 , 15 , or 20 away from the perpendicular side inlets. • 3 cases to study 1 2 3 +

• Physical dimensions of the combustor • The length unit is in mm 15 15 120 15 Y Y 1. 58 30 X Z 2000

• Experimental setup • • Hydrocarbon gas mixture is supplied through the axial inlet Air is supplied through the two side inlets The combustor bulk mean velocity is 23. 9 m/s The combustor Reynolds number is 4. 56 104 Air Gas mixture Air

• Comments • The experimental results can be used as a guideline. • To augment the experimental findings on mixing, you can set the temperatures of the side inlet and axial jets to different values and use temperature as a passive fluid marker (i. e. solve thermal energy equation with no buoyancy force). Tside CFX-Pre: - Buoyancy Option: Non Buoyant - Heat Transfer Option: Thermal Energy Taxial Assume adiabatic at walls

Project Report • You report should include • a comment on the validity of the CFD simulation for the perpendicular angle based on comparison to experimental data • a clear statement of your findings on the effect of the side inlet angle on mixing within the combustor • a clear presentation of the computational model’s geometry, boundary conditions and properties. Wherever possible, quantify the influence that the two most significant model parameters have on your solution

• You report should include • a description of the basis of your geometry and mesh designs 15 15 120 15 Y Y 1. 58 30 X Z 2000 • a comment of the applicability of the k model for this flow • a statement on the degree of convergence obtained by the solver

Frequently Asked Questions (FAQs) • How to create a side inlet with an angle : 1. 2. 3. 4. Draw a line with dimension L (where L = 15 mm) Draw a line with dimension L/cos (where = 5 ~ 20 ) Join two lines together (Constraints Coincident) Specify the angle between two lines (Dimensions Angle) 4 Y* = 2 L Y* = 1 L/cos Y* = 0 X* = 0 2 L 3 1

• What fluid properties should be used for hydrocarbon gas mixture? • You can assume the gas mixture has the same properties as air • What entrance velocity should be used? • One way to find out entrance velocity is to read U/Uref and V/Uref from Tables 1 A and 1 B, where Uref = 23. 9 m/s • What turbulence intensity and length scale values should be used? • One way to find out turbulence intensity is to read u’/Uref and v’/Uref from Tables 1 A and 1 B • For length scale, select the turbulence option: Intensity and Auto Compute Length

• Inlet velocity and turbulence intensity for the side inlet can be found from Table 1 A at Y* = 2 X* = 0. 5 • For example, at Y* = 2: • • V/Uref = 8. 26 E-1 at X* = 0. 25 v’/Uref = 1. 03 E-2 at X* = 0. 25 (V/Uref)avg = 8. 27 E-1 (v’/Uref)avg = 1. 09 E-2 Y* = 2 Y* Y* = 1 Y* = 0 X*

• How to define velocity at the inlet with side angle? • Mass and Momentum Option Cart. Vel. Components u = -Vsin (m/s), v = -Vcos (m/s), w = 0 (m/s) V V Vsin Vcos

Questions?

Order of Accuracy • A certain discretisation scheme is used to estimate the temperature in a rectangular fin. The computations are done with a uniform mesh having a spacing of x. Table 1 shows the variation of the predicted heat flux at the base of the fin, , with the mesh spacing. x [m] 0. 05 0. 025 0. 01 0. 005 0. 0025 0. 00125 0. 000625 [watts] 110. 1 162. 8 193. 8 204. 1 209. 2 211. 9 212. 9 Table 1 • Q 1: Estimate the order of accuracy of the numerical method. The exact heat flux is 214. 3 [watts]. • Q 2: The order appears to decrease for the finer meshes. What numerical errors are affecting the solutions obtained with fine meshes?

• • : error, a: constant, x: mesh spacing, n: order of accuracy x (m) 0. 05 0. 025 0. 010 0. 005 0. 0025 0. 00125 0. 000625 (watts) 110. 1 162. 8 193. 8 204. 1 209. 2 211. 9 212. 9 104. 2 51. 5 20. 5 10. 2 5. 1 2. 4 1. 4 1/ 2 2. 02 2. 51 2. 00 2. 13 1. 71 • The order of accuracy is first order x 1/ x 2 2 2. 5 2 2 Order (n) 1. 02 1. 01 1. 00 1. 09 0. 78

Who Wants to Be a CFD Expert? • The order of accuracy appears to decrease for the finer meshes. What numerical errors are affecting the solutions obtained with fine meshes? A. Discretisation error B. Round-off error C. Truncation error • Lifelines • • Phone a Friend Ask the Audience x (m) 0. 05 0. 025 0. 010 0. 005 0. 0025 0. 00125 0. 000625 104. 2 51. 5 20. 5 10. 2 5. 1 2. 4 1. 4 Order (n) 1. 02 1. 01 1. 00 1. 09 0. 78

Numerical Errors (Sec. 10. 2) • Round-off errors are the result of the computational representation of real numbers by means of a finite number of significant digits, which is termed the machine accuracy. • Discretisation error / Truncation error • The discretisation error is associated with the neglected contributions due to the truncation of high-order terms. Taylor series expansion