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Lab sheet for Computational Fluid Dynamics College of Engineering Pune

Lab # 1: Finite Difference solutions Class: M-Tech (Thermal)

Date: Time: Diffusion Equation

Consider the problem of transient flow between infinite parallel plates. Recall that the governing equation for the unknown u(y, t) in this case is given by

,where we used

,s being a constant.

The boundary conditions of the problem are u(0, t) = 0 and u(h, t) = U, while the initial condition is u(y, 0) = 0.Additionally, the following data has been incorporated in the codes: = 0.000217 m2/s, = 800 kg/m3, U = 40 m/s, h = 4 cm.1. Develop the code using FTCS (Explicit) scheme for tmax=3 s to compute the velocity within the domain for (i) dp/dx = 0, (ii) dp/dx = 20000 N/m2/m, and (iii) dp/dx = -30000 N/m2/m. Select the option of computing the time step using the stability criterion. (Refer the code: Lab1_1_1D Unsteady Diffusion_FTCS Solver.sci)2. Develop the code using BTCS (Implicit) scheme for tmax=3 s to compute the velocity within the domain fora. t = 0.01 s, dp/dx = 0,b. t = 0.01 s, dp/dx = 20000 N/m2/m,c. t = 0.002 s, dp/dx = 20000 N/m2/m.

Obtain the plots for the velocity variation and paste these plots in the appropriate boxes given in the answer sheets given below. (Refer the code: Lab1_2_1D Unsteady Diffusion_Implicit Solver.sci). Write down the discussions in the space provided.

(a)(b)(c)Fig. 1.1: Numerically calculated velocity profiles using fully explicit scheme for (a) dp/dx = 0, (b) dp/dx = 20000 and (c) dp/dx = -30000 N/m2/m

Discuss Fig. 1.1

(a)(b)(c)Fig. 1.2: Numerically calculated velocity profiles using fully implicit scheme for (a) t = 0.01 s, dp/dx = 0, (b) t = 0.01 s, dp/dx = 20000 N/m2/m, (c) t = 0.002 s, dp/dx = 20000 N/m2/m.

Discuss Fig. 1.2 here, limited inside this text box only

Lab sheet for Computational Fluid Dynamics College of Engineering Pune

Lab # 2: Finite Difference solutions Class: M-Tech (Thermal)

Date: Time:

Laplace Equation

Consider the problem of steady-state conduction in a rectangular domain. Recall that the governing equation for the unknown T(x, y) in this case is given by

The boundary conditions of the problem are T (0, y) = 0, T (a, y) = 0, T(x, 0) = 0 and T(x, b) = T1. Use the following data: a = 1, b= 3, T1 = 50, x-grid points = 20, y-grid points = 50. Develop the code using FDM to obtain the temperature distribution.

Obtain the plot for temperature distribution (temperature contour plots) for this case. (Refer the code Lab1_3_ 2DLaplacian.sci)

(a)Fig. 2.1: Temperature contours: Numerical solution