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Advanced Thermal and Fluid Engineering - Deriving the FDM Formula - Engineering Assessment Answer
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The electricity generator can modelled by a damper that extract energy from the motion of the cylinder with a constant damping constant of c. The structural damping is considered to be negligibly small. The energy extracted from the motion by the electricity generator (damper) can be calculated by
Part two: One-dimensional convection-diffusion problem
Assignment (please read the problem description before doing the assignment)
? Develop a finite difference method (FDM) formula for solving the equation. The procedure of deriving the FDM formula must be included in the report.
? Develop a MATLAB program and use this program to do the simulation and answer the following questions. Divide the soil depth into 200 cells when solving the problem numerically. You must attach the MATLAB program in your report.
? If ?=0.0002 m^2/s, find out when the temperature at the depth of 1.5 m reaches 25°C.
? If the temperature at the depth of 1.5 m reaches 25°C is defined as T1.5, do the simulations for
? in the range of 0.0002 m^2 to 0.001 m^2 with an interval of 0.0001 m2 and discuss how ? on T1.5 and why.
Question 2
The water on the ground flows into the soil through the pore space of the soil (the space between soil particles). The flow velocity is very small of 0.002×(1+j) m/s and it does not change along the vertical direction. Initially, the temperature is (10+j) °C in the whole soil volume (including soil and the water in the soil). The temperature of the water on top of the ground level is 30°C and remains constant. The warm water moves into the soil and increases the temperature in the soil.
Engineering Assessment Answer
TASK: Part one: Simple initial value problem Assignment (1) Find out the equation of motion of the cylinder. The derivation procedure of the equation must be included in the report. (2) Develop a numerical method for predicting the vibration of the cylinder. The procedure of deriving the FDM formula must be included in the report. (3) Develop a MATLAB program for solving the problem. The MATLAB program code must be included in the report. (4) Keeping the damping coefficient of c = 100 N·m/s, conduct numerical simulations for KC=2 to 20 with an interval of 2 and find out the variation of the power with the KC number. (5) Keeping the KC number to be constant of KC=10, conduct numerical simulations for c=0 to 2000 N·m/s with an interval of 50 and find the variation of the power with c. (6) In the report, show the time histories of the vibration for all the calculated cases. (7) Discuss how KC and c affect power generation. Question 1 An energy extraction device includes a cylinder elastically mounted on a spring and the electricity generator. The cylinder vibrates only in a direction parallel to the flow and drives an electricity generator. The electricity generator extracts the energy from the cylinder in the same way as a damper. It is modelled as a damper with a damping constant c when the vibration is studied. The flow velocity is a combined steady and oscillatory flow.
The electricity generator can modelled by a damper that extract energy from the motion of the cylinder with a constant damping constant of c. The structural damping is considered to be negligibly small. The energy extracted from the motion by the electricity generator (damper) can be calculated by
Part two: One-dimensional convection-diffusion problem
Assignment (please read the problem description before doing the assignment)
? Develop a finite difference method (FDM) formula for solving the equation. The procedure of deriving the FDM formula must be included in the report.
? Develop a MATLAB program and use this program to do the simulation and answer the following questions. Divide the soil depth into 200 cells when solving the problem numerically. You must attach the MATLAB program in your report.
? If ?=0.0002 m^2/s, find out when the temperature at the depth of 1.5 m reaches 25°C.
? If the temperature at the depth of 1.5 m reaches 25°C is defined as T1.5, do the simulations for
? in the range of 0.0002 m^2 to 0.001 m^2 with an interval of 0.0001 m2 and discuss how ? on T1.5 and why.
Question 2
The water on the ground flows into the soil through the pore space of the soil (the space between soil particles). The flow velocity is very small of 0.002×(1+j) m/s and it does not change along the vertical direction. Initially, the temperature is (10+j) °C in the whole soil volume (including soil and the water in the soil). The temperature of the water on top of the ground level is 30°C and remains constant. The warm water moves into the soil and increases the temperature in the soil.
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